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Actuators
Volume 14
Issue 2
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Actuators, Volume 14, Issue 2 (February 2025) – 61 articles

Cover Story (view full-size image): The high prevalence of foot drop highlights the need for devices that restore gait functionality. A portable, lightweight, low-cost, and efficient active ankle–foot orthosis is in demand. This work presents an active ankle–foot orthosis prototype that aims to fulfill these goals. The device is based on a design previously simulated by our group, evaluated on a test bench for low-level control. A cam-based actuator assists with dorsiflexion without affecting plantar flexion. The system’s dynamical behavior was assessed on a test bench using a PID controller. Performance metrics showed low errors for step inputs and periodic perturbations, with root-mean-squared tracking errors ranging from 0.1 to 6.5 degrees, depending on speed. View this paper
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17 pages, 15169 KiB  
Article
Research on the Five-Axis Support-Free Additive Manufacturing Method for Overhanging Parts
by Xingguo Han, Gaofei Wu, Xuan Liu, Wenquan Li, Xiaohui Song and Lixiu Cui
Actuators 2025, 14(2), 99; https://doi.org/10.3390/act14020099 - 19 Feb 2025
Viewed by 146
Abstract
When printing overhanging parts with traditional additive manufacturing (AM) equipment, it is necessary to add support structures under the overhanging structure. The process of printing support structures not only wastes materials, but also increases the manufacturing time. Therefore, in order to reduce or [...] Read more.
When printing overhanging parts with traditional additive manufacturing (AM) equipment, it is necessary to add support structures under the overhanging structure. The process of printing support structures not only wastes materials, but also increases the manufacturing time. Therefore, in order to reduce or eliminate the need for support structures when printing parts with overhanging structures, such as propellers, a five-axis support-free printing method for overhanging parts is proposed for one of the most commonly used processes involving AM technology: fused deposition modeling (FDM). By offsetting the surface of the basic part, the offset surface is intersected with the model to be printed to obtain the spatial surface-layered curve. The contour offset method for the spatial curve is used to obtain the printing path, and continuous path planning is performed on it. While the presented method is targeted specifically at this ideal overhanging part, physical experiments on five-axis FDM equipment are performed. Compared with the traditional three-axis AM method, the time taken to print parts using this support-free five-axis AM method is shortened by 13.76–26.93%, and the printing material required is reduced by 17.24–29.29%. The experimental results show that this method realizes support-free printing of overhanging parts with the five-axis AM equipment, which not only saves materials and time consumed during part of the printing, but also improves the surface quality of the parts. Full article
(This article belongs to the Section Actuators for Manufacturing Systems)
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<p>Model of five-axis AM device.</p> Full article ">Figure 2
<p>Forward kinematics analysis of five-axis AM device.</p> Full article ">Figure 3
<p>Inverse kinematics analysis of a five-axis AM device.</p> Full article ">Figure 4
<p>Basic steps in the five-axis AM method.</p> Full article ">Figure 5
<p>Basic steps in curved layer slicing: (<b>a</b>) the propeller model; (<b>b</b>) the surface to be offset; (<b>c</b>) one of the overhanging parts of the model; (<b>d</b>) the layered curves.</p> Full article ">Figure 5 Cont.
<p>Basic steps in curved layer slicing: (<b>a</b>) the propeller model; (<b>b</b>) the surface to be offset; (<b>c</b>) one of the overhanging parts of the model; (<b>d</b>) the layered curves.</p> Full article ">Figure 6
<p>Path planning for a continuous curve: (<b>a</b>) the initial layering curve marked in red; (<b>b</b>) the initial outer contour marked in green; (<b>c</b>) the initial inner filling curve marked in blue.</p> Full article ">Figure 7
<p>Path planning for a continuous curve: (<b>a</b>) the start and end points of the offset curve; (<b>b</b>) the continuous curve.</p> Full article ">Figure 8
<p>Flowchart of the five-axis AM system.</p> Full article ">Figure 9
<p>The printing experiment: (<b>a</b>) a model of the part; (<b>b</b>) the five-axis AM platform; (<b>c</b>) the manufacturing process.</p> Full article ">Figure 10
<p>Comparison of the parts manufactured using different methods: (<b>a</b>) the part manufactured using the three-axis AM method; (<b>b</b>) the part manufactured using the five-axis AM method.</p> Full article ">Figure 11
<p>Comparison of the top surface of the parts manufactured using different methods: (<b>a</b>) one of overhanging parts of the model manufactured by three-axis AM method (red box); (<b>b</b>) one of overhanging parts manufactured by five-axis AM method (green box).</p> Full article ">Figure 12
<p>The bottom surface of the overhanging parts that printed by three-axis AM method (red dotted box) and the five-axis AM method (green dotted box).</p> Full article ">Figure 13
<p>The manufacturing process for the propeller part: (<b>a</b>) the first paddle; (<b>b</b>) the second paddle; (<b>c</b>) the last paddle.</p> Full article ">
15 pages, 3935 KiB  
Article
Study on the Vibration Characteristics of Separated Armature Assembly in an Electro-Hydraulic Servo Valve Under Interference Fit
by Tong Li, Jinghui Peng, Songjing Li, Juan Zhang and Aiying Zhang
Actuators 2025, 14(2), 98; https://doi.org/10.3390/act14020098 - 19 Feb 2025
Viewed by 118
Abstract
The electro-hydraulic servo valve is a critical component that transforms electrical signals into hydraulic signals, thereby controlling the hydraulic system. It finds extensive application in precision control systems. The stability of the electro-hydraulic servo valve is primarily influenced by the armature assembly. Unlike [...] Read more.
The electro-hydraulic servo valve is a critical component that transforms electrical signals into hydraulic signals, thereby controlling the hydraulic system. It finds extensive application in precision control systems. The stability of the electro-hydraulic servo valve is primarily influenced by the armature assembly. Unlike integral armature assembly, the separated armature assembly, comprising the armature, spring tube, flapper, and feedback spring, is joined through an interference fit, which introduces prestress within the assembly. The existence of prestress may affect the operational mode of the armature assembly. Consequently, this paper investigates the vibration characteristics of the separated armature assembly under interference fit conditions. Comparative analysis reveals that interference fit indeed generates prestress, which cannot be overlooked. To further validate the reliability of the simulation results, the natural frequency of the separated armature assembly is determined by applying a sweeping frequency signal to the torque motor using an electric drive, thereby verifying the feasibility of the simulation analysis. Additionally, the impact of interference on the vibration characteristics of the separated armature assembly is examined, confirming the accuracy of the simulation analysis method based on the interference fit. The research on vibration characteristics of a separated armature assembly provides technical support for the structural optimization design of the electro-hydraulic servo valve, thereby enhancing its performance. Full article
(This article belongs to the Special Issue Recent Developments in Precision Actuation Technologies)
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<p>Separated armature assembly.</p> Full article ">Figure 2
<p>Meshing. (<b>a</b>) Node coupling is not considered in meshing; (<b>b</b>) node coupling is considered in meshing.</p> Full article ">Figure 3
<p>Contact setting.</p> Full article ">Figure 4
<p>Calculation results.</p> Full article ">Figure 5
<p>Deformation nephogram.</p> Full article ">Figure 6
<p>Stress nephogram.</p> Full article ">Figure 7
<p>Modal analysis results under interference fit. (<b>a</b>) First-order vibration mode. (<b>b</b>) Second-order vibration mode. (<b>c</b>) Third-order vibration mode. (<b>d</b>) Fourth-order vibration mode. (<b>e</b>) Fifth-order vibration mode. (<b>f</b>) Sixth-order vibration mode.</p> Full article ">Figure 8
<p>Modal test of armature assembly. (<b>a</b>) Schematic diagram of the experimental system. (<b>b</b>) Data acquisition system.</p> Full article ">Figure 9
<p>Frequency domain analysis of armature end displacement under sweep signal.</p> Full article ">Figure 10
<p>The influence of interference on the modes of armature assembly. (<b>a</b>) The influence of interference between the armature and the spring tube on the modes. (<b>b</b>) The influence of interference between the spring tube and the flapper on the modes. (<b>c</b>) The influence of interference between the flapper and the feedback spring on the modes.</p> Full article ">Figure 10 Cont.
<p>The influence of interference on the modes of armature assembly. (<b>a</b>) The influence of interference between the armature and the spring tube on the modes. (<b>b</b>) The influence of interference between the spring tube and the flapper on the modes. (<b>c</b>) The influence of interference between the flapper and the feedback spring on the modes.</p> Full article ">
17 pages, 1151 KiB  
Article
Numerical Analysis of a Hypersonic Body Under Thermochemical Non-Equilibrium and Different Catalytic Surface Conditions
by Odelma Teixeira and José Páscoa
Actuators 2025, 14(2), 102; https://doi.org/10.3390/act14020102 - 19 Feb 2025
Viewed by 135
Abstract
This work results from a numerical investigation of the thermochemical non-equilibrium effects on the surface properties of a hypersonic body. Non-equilibrium within an air mixture composed of 11 chemical species was considered when solving the Navier–Stokes–Fourier equations using a density-based algorithm in OpenFOAM. [...] Read more.
This work results from a numerical investigation of the thermochemical non-equilibrium effects on the surface properties of a hypersonic body. Non-equilibrium within an air mixture composed of 11 chemical species was considered when solving the Navier–Stokes–Fourier equations using a density-based algorithm in OpenFOAM. The influence of thermal and chemical non-equilibrium on the surface properties of a hypersonic double-cone test body was studied by considering two types of surfaces. It was found that the heat flux and pressure distribution along the surface are higher under non-equilibrium free-stream conditions. Unlike what was observed at the impingement point, where the vibrational non-equilibrium effects on the surface properties are almost independent of the surface type, at the stagnation point, these effects are highly dependent on the catalytic activity of the surface. At the stagnation point, the vibrational non-equilibrium effects are more pronounced on a fully catalytic surface than on a non-catalytic surface. Under the studied conditions, the vibrational non-equilibrium reduces the heat flux by 18% for a non-catalytic surface, while for a fully catalytic surface, it reduces the heat flux by 38%. Additionally, the presence of vibrational non-equilibrium in the free-stream reduces the pressure by 24% for a non-catalytic surface, while for a fully catalytic surface, it is reduced by 42%. Full article
(This article belongs to the Special Issue Flow Control and Beyond Enhancing Performance and Energy Efficiency in Complex Fluid System)
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Figure 1
<p>Simulation model diagram.</p> Full article ">Figure 2
<p>Double-cone model: (<b>a</b>) geometric parameters (dimensions in cm); (<b>b</b>) solution domain and boundary conditions.</p> Full article ">Figure 3
<p>Code validation: (<b>a</b>) heat flux; (<b>b</b>) pressure. Distribution along the double-cone surface.</p> Full article ">Figure 4
<p>Grid convergence analysis: (<b>a</b>) maximum heat flux location; (<b>b</b>) size of the separation zone.</p> Full article ">Figure 5
<p>Pressure contours considering five-species (top) and eleven-species air mixtures (bottom).</p> Full article ">Figure 6
<p>Vibro-electronic temperature contours at equilibrium and non-equilibrium free-stream conditions for: (<b>a</b>) five-species air mixture; (<b>b</b>) eleven-species air mixture.</p> Full article ">Figure 7
<p>Surface heat flux distribution along the double-cone surface for five-species and eleven-species air mixtures for different free-stream conditions: (<b>a</b>) equilibrium; (<b>b</b>) non-equilibrium.</p> Full article ">Figure 8
<p>Surface pressure distribution along the double-cone surface for five-species and eleven-species air mixture for different free-stream conditions: (<b>a</b>) equilibrium; (<b>b</b>) non-equilibrium.</p> Full article ">Figure 9
<p>Distribution of surface properties for equilibrium and non-equilibrium conditions: (<b>a</b>) heat flux; (<b>b</b>) pressure. Comparison between non-catalytic surface (NCS) and fully catalytic surface (FCS).</p> Full article ">Figure 10
<p>Distribution of flow properties along the impingement point line (Y = 0.052 m) for equilibrium and non-equilibrium conditions: (<b>a</b>) pressure; (<b>b</b>) trans-rotational temperature (<math display="inline"><semantics> <msub> <mi mathvariant="normal">T</mi> <mrow> <mi>t</mi> <mi>r</mi> </mrow> </msub> </semantics></math>); (<b>c</b>) vibro-electronic temperature (<math display="inline"><semantics> <msub> <mi mathvariant="normal">T</mi> <mrow> <mi>v</mi> <mi>e</mi> </mrow> </msub> </semantics></math>). Comparison between non-catalytic surface (NCS) and fully catalytic surface (FCS).</p> Full article ">Figure 11
<p>Temperature distributions along the stagnation line (Y = 0 m) for equilibrium and non-equilibrium conditions: (<b>a</b>) trans-rotational (<math display="inline"><semantics> <msub> <mi mathvariant="normal">T</mi> <mrow> <mi>t</mi> <mi>r</mi> </mrow> </msub> </semantics></math>); (<b>b</b>) vibro-electronic temperature (<math display="inline"><semantics> <msub> <mi mathvariant="normal">T</mi> <mrow> <mi>v</mi> <mi>e</mi> </mrow> </msub> </semantics></math>). Comparison between non-catalytic surface (NCS) and fully catalytic surface (FCS).</p> Full article ">
23 pages, 8016 KiB  
Article
Flow Characteristics of a Dual Sweeping Jet Impinging on a Flat Surface
by Muhammad Zubair and Xin Wen
Actuators 2025, 14(2), 101; https://doi.org/10.3390/act14020101 - 19 Feb 2025
Viewed by 150
Abstract
The dual sweeping jet (DSJ)-producing fluidic oscillator is a novel device developed by sharing a feedback channel between two standard fluidic oscillators. This device produces a pair of sweeping jets in the outer domain and has the potential to be used for the [...] Read more.
The dual sweeping jet (DSJ)-producing fluidic oscillator is a novel device developed by sharing a feedback channel between two standard fluidic oscillators. This device produces a pair of sweeping jets in the outer domain and has the potential to be used for the better and uniform treatment of impinged surfaces. Therefore, it is important to investigate the extent of the synchronicity of these jets at different Re numbers and various aspect ratios in outer domains, and to comprehend their internal switching mechanism simultaneously. The time-averaged flow fields demonstrated that, at lower Re numbers, both sweeping jets were symmetric about their centerlines and the cores were strong. The strength of the cores deteriorated at higher Re numbers, and the flare regions became wider and stronger. Moreover, the transverse velocities pulled the sweeping jets away from the origin and a high upwash flow formed in-between the jets. The phase-averaged flow fields vividly illustrated the sharing mechanism between the two power nozzles through the formation of left- and right-loops consecutively in the shared feedback channel. These primary loops generated an auxiliary mechanism on both sides of a fluidic oscillator, which actually controlled the synchronicity of the two sweeping jets in the outer domain. Additionally, they also showed that both jets are properly synchronized and have strong cores at lower Re numbers. However, at higher Re numbers, greater velocities were found in the switching and sweeping mechanisms which caused asynchrony between the sweeping jets but nonetheless impinged a larger area and covered the region in-between the jets properly. The power nozzles were also found to self-feed themselves due to the hindrance at the ‘outer shoulders’ of this fluidic oscillator and hence caused the premature formation of a recirculation bubble of vorticity between the power nozzle and its respective outer island. Lastly, the aspect ratio analysis revealed that the asynchrony of DSJ at higher Re numbers can be mitigated by reducing the aspect ratio. Full article
(This article belongs to the Special Issue Active Flow Control: Recent Advances in Fundamentals and Applications—3rd Edition)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Schematic of DSJ fluidic oscillator (<b>a</b>) and its computational domain (<b>b</b>).</p> Full article ">Figure 2
<p>Numerical model validation at H = 7 hd: (<b>a</b>) Strouhal numbers for Re 1800 to 9200, (<b>b</b>) Ratio of Peak Velocities for Re 9200. Wen et. al. 2018 [<a href="#B4-actuators-14-00101" class="html-bibr">4</a>].</p> Full article ">Figure 3
<p>Time-averaged contours at Re 1800, AR 2.34: (<b>a</b>) velocity magnitude (streamwise), (<b>b</b>) velocity magnitude (sweeping direction), (<b>c</b>) turbulent fluctuations (streamwise), (<b>d</b>) turbulent fluctuations (sweeping direction).</p> Full article ">Figure 4
<p>Phase-averaged contours at Re 1800, AR 2.34.</p> Full article ">Figure 5
<p>Time-averaged contours at Re 5500, AR 2.34: (<b>a</b>) velocity magnitude (streamwise), (<b>b</b>) velocity magnitude (sweeping direction), (<b>c</b>) turbulent fluctuations (streamwise), (<b>d</b>) turbulent fluctuations (sweeping direction).</p> Full article ">Figure 6
<p>Phase-averaged contours at Re 5500, AR 2.34.</p> Full article ">Figure 7
<p>Time-averaged contours at Re 9200, AR 2.34: (<b>a</b>) velocity magnitude (streamwise), (<b>b</b>) velocity magnitude (sweeping direction), (<b>c</b>) turbulent fluctuations (streamwise), (<b>d</b>) turbulent fluctuations (sweeping direction).</p> Full article ">Figure 8
<p>Phase-averaged contours at Re 9200, AR 2.34.</p> Full article ">Figure 9
<p>Time-averaged contours of (<b>a</b>) velocity magnitude (streamwise), (<b>b</b>) velocity magnitude (sweeping direction), (<b>c</b>) turbulent fluctuations (streamwise), (<b>d</b>) turbulent fluctuations (sweeping direction) for the external flow field only at Re 9200: (<b>A</b>) AR 1.5, (<b>B</b>) AR 1.0.</p> Full article ">Figure 10
<p>Phase-averaged oscillation for one cycle: contours of time-averaged velocity for both the internal and external flow fields at Re 9200: (<b>A</b>) AR 1.5, (<b>B</b>) AR 1.0.</p> Full article ">
22 pages, 6734 KiB  
Article
Envelope Morphology of an Elephant Trunk-like Robot Based on Differential Cable–SMA Spring Actuation
by Longfei Sun and Huiying Gu
Actuators 2025, 14(2), 100; https://doi.org/10.3390/act14020100 - 19 Feb 2025
Viewed by 104
Abstract
Most trunk-like robots are designed with distributed actuators to mimic the envelope-grasping behavior of elephant trunks in nature, leading to a complex actuation system. In this paper, a modular underactuated elephant trunk-imitating robot based on the combined drive of the cable and shape [...] Read more.
Most trunk-like robots are designed with distributed actuators to mimic the envelope-grasping behavior of elephant trunks in nature, leading to a complex actuation system. In this paper, a modular underactuated elephant trunk-imitating robot based on the combined drive of the cable and shape memory alloy (SMA) springs is designed. Unlike the traditional underactuated structure that can only passively adapt to the envelope of the object contour, the proposed elephant trunk robot can control the cable tension and the equivalent stiffness of the SMA springs to achieve active control of the envelope morphology for different target objects. The overall structure of the elephant trunk robot is designed and the principle of deformation envelope is elucidated. Based on the static model of the robot under load, the mapping relationship between the tension force and the tension angle between modules is derived. The positive kinematic model of the elephant trunk robot is established based on the Debavit–Hartenberg (D–H) method, the spatial position of the elephant trunk robot is obtained, and the Monte Carlo method is used to derive the robot’s working space. The active bending envelope grasping performance is further verified by building the prototype to perform grasping experiments on objects of various shapes. Full article
(This article belongs to the Section Actuators for Robotics)
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Figure 1

Figure 1
<p>Elephant trunk function: (<b>a</b>) Elephant trunk muscle composition; (<b>b</b>) Elephant trunk curled objects.</p> Full article ">Figure 2
<p>Elephant trunk structure: (<b>a</b>) Elephant trunk [<a href="#B19-actuators-14-00100" class="html-bibr">19</a>]; (<b>b</b>) 3D model of elephant trunk-like robot; (<b>c</b>) Modular structure.</p> Full article ">Figure 3
<p>3D model of the unit module: (<b>a</b>) Front view; (<b>b</b>) Back view.</p> Full article ">Figure 4
<p>Force analysis: (<b>a</b>) Simplified model; (<b>b</b>) Mechanical model.</p> Full article ">Figure 5
<p>Robot envelope morphology: (<b>a</b>) Envelope spherical body; (<b>b</b>) Envelope trapezoid; (<b>c</b>) Envelope polygon.</p> Full article ">Figure 6
<p>D–H Coordinate system of elephant trunk robot.</p> Full article ">Figure 7
<p>Workspace: (<b>a</b>) Three-dimensional view of the workspace; (<b>b</b>) Workspace projection in x–y plane.</p> Full article ">Figure 8
<p>Adams model of elephant trunk robot: (<b>a</b>) Adams model (<b>b</b>) Tension spring damper setting (<b>c</b>) Back view.</p> Full article ">Figure 9
<p>Angle curve for elephant trunk robot: (<b>a</b>) Group 1; (<b>b</b>) Group 2; (<b>c</b>) Group 3; (<b>d</b>) Group 4.</p> Full article ">Figure 10
<p>Simulation results of robot envelope morphology: (<b>a</b>) Group 1 (<span class="html-italic">F</span> = 18.8 N, <span class="html-italic">R</span><sub>1</sub> ≈ 18 mm); (<b>b</b>) Group 2 (<span class="html-italic">F</span> = 11.7 N, <span class="html-italic">R</span><sub>2</sub> ≈ 28 mm) (<b>c</b>) Group 3 (<span class="html-italic">F</span> = 7.8 N, <span class="html-italic">R</span><sub>3</sub> ≈ 50 mm); (<b>d</b>) Group 4 (<span class="html-italic">F</span> = 11.3 N, <span class="html-italic">R</span><sub>4</sub> ≈ 80 mm).</p> Full article ">Figure 11
<p>Elephant trunk robot prototype.</p> Full article ">Figure 12
<p>Experimental system components.</p> Full article ">Figure 13
<p>The control system of the elephant trunk robot.</p> Full article ">Figure 14
<p>Mechanical property test experiment of SMA spring.</p> Full article ">Figure 15
<p>SMA spring tension response.</p> Full article ">Figure 16
<p>Variation of contraction force and elongation of SMA spring.</p> Full article ">Figure 17
<p>Elephant trunk envelope morphology: (<b>a</b>) <span class="html-italic">F</span><sub>1</sub> = 8 N; (<b>b</b>) <span class="html-italic">F</span><sub>2</sub> = 10 N; (<b>c</b>) <span class="html-italic">F</span><sub>3</sub> = 12 N.</p> Full article ">Figure 18
<p>Elephant trunk robot grasps objects: (<b>a</b>) Envelope egg (without active SMA springs); (<b>b</b>) Envelope tennis; (<b>c</b>) Envelope cube; (<b>d</b>) Envelope cup; (<b>e</b>) Envelope apple; (<b>f</b>) Envelope cylinder.</p> Full article ">
23 pages, 1136 KiB  
Article
A Reasoned Attempt to Mitigate Vibrations in Nonlinear Flexible Systems Influenced by Tractive–Elastic Rolling Contact Friction Through Input Shaping: A Case Study on a Trolley–Pipe Benchmark Transport System
by Gerardo Peláez, Pablo Izquierdo, Gustavo Peláez and Higinio Rubio
Actuators 2025, 14(2), 97; https://doi.org/10.3390/act14020097 - 17 Feb 2025
Viewed by 204
Abstract
The well-regarded feedforward control strategy known as Input Shaping is aimed at improving the dynamic response of flexible mechanical systems by reducing overshoot and residual vibration amplitude. Its validity has been confirmed by numerous studies dealing with linear system dynamics. However, its application [...] Read more.
The well-regarded feedforward control strategy known as Input Shaping is aimed at improving the dynamic response of flexible mechanical systems by reducing overshoot and residual vibration amplitude. Its validity has been confirmed by numerous studies dealing with linear system dynamics. However, its application in nonlinear systems, particularly those influenced by tractive–elastic rolling contact friction, remains a challenging and less explored open research area. This paper investigates whether Input Shaping, without tractive rolling friction compensation, can effectively mitigate vibrations in a trolley–pipe benchmark transport system. In this system, the pipe is modeled as a rolling disc attached to the trolley by a spring at its center of mass, while the trolley itself is connected to a guiding body frame by an additional spring acting as a proportional control. The natural frequencies of the system are analytically estimated and numerically verified from a corresponding well-suited multibody model. Thus, tailored two-mode shapers are designed based on simultaneous constraints and the convolution sum, respectively. Through multibody simulations, this study evaluates the performance of Input Shaping under tractive–elastic rolling contact friction conditions. The findings highlight both the potential and limitations of this control method in addressing nonlinear mechanical systems influenced by tractive–elastic rolling contact friction. Full article
(This article belongs to the Special Issue Nonlinear Active Vibration Control)
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Figure 1
<p>Application Unshaped and ZV-filtered responses to a step input: The unshaped input and its corresponding response are shown on the left, while the shaped input and the resulting vibration-suppressed response appear on the right.</p> Full article ">Figure 2
<p>(<b>a</b>) Physical representation of the mass-spring-damper system under gross-sliding friction force. (<b>b</b>) Block diagram representation of the system dynamics by the Laplace model.</p> Full article ">Figure 3
<p>Response of the mass-spring system under gross-slip friction, without the derivative damper action, to a nonzero initial position. Conditions: <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> [N/m], <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.20</mn> </mrow> </semantics></math> [Kg], <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.15</mn> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>Elastic rolling contact of a cylinder rolling freely on a plane under normal load P.</p> Full article ">Figure 5
<p>(<b>a</b>) Reference model of a two-mass and spring system undergoing rolling friction. (<b>b</b>) Impulse response of the rolling disc, showing the nearly undamped x-position of the mass center.</p> Full article ">Figure 6
<p>Steel coil transport system in manufacturing plants.</p> Full article ">Figure 7
<p>The Multibody System is broken up into the spring element ① and the super-element ②.</p> Full article ">Figure 8
<p>Simscape Mechanical Explorer Sketch of the system showing the body frames.</p> Full article ">Figure 9
<p>Simscape (Matlab) multibody model of the system showing bodies interconnected by kinematics joints plus a large number of important multibody formalisms by rigid frame transforms plus body and joint customizations.</p> Full article ">Figure 10
<p>FFT of the signal corresponding to the abscissa position of the center of mass of the pipe. Low-frequency component value 0.079998 [Hz]. High-frequency component 0.159997 [Hz].</p> Full article ">Figure 11
<p>Convolved two-mode ZVD-ZVD shaper for <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>: 0.07998 and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>: 0.159997 Hz undamped frequencies.</p> Full article ">Figure 12
<p>Two-mode input shaper by simultaneous constraints for <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>: 0.07998 and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>: 0.159997 [Hz] and <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math>: 0.0.</p> Full article ">Figure 13
<p>Trapezoidal input motion. Conditions: the ramp-up lasts for <math display="inline"><semantics> <mrow> <mi>t</mi> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> </semantics></math>: 17 [s]. Unshaped input motion. Direct–ZVD-ZVD shaped input motion. Conditions: ramp-up lasts for <math display="inline"><semantics> <mrow> <mi>t</mi> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>5</mn> </msub> </mrow> </semantics></math>: 33 [s].</p> Full article ">Figure 14
<p>Multibody model pipe mass center X-position responses to trapezoidal input motion profile with 12 s ramp-up. Pipe mass center X-position unshaped response. Pipe mass center X-position shaped response for direct–ZVD-ZVD shaped input motion.</p> Full article ">Figure 15
<p>Trapezoidal input motion. Conditions: the ramp-up lasts for <math display="inline"><semantics> <mrow> <mi>t</mi> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> </semantics></math>: 20 [s]. Unshaped input motion. Convolved–ZVD-ZVD shaped input motion.</p> Full article ">Figure 16
<p>Experimental trapezoidal input motion profile responses. Pipe mass center X-position unshaped response. Pipe mass center X-position for convolved–ZVD-ZVD shaped response.</p> Full article ">
20 pages, 7919 KiB  
Article
Design and Performance Analysis of an All-Metal Phase-Change-Material Actuator for Enhanced Sealing and Displacement Output Characteristics
by Shuaiqi Guo, Xianwei Yang and Qingwen Wu
Actuators 2025, 14(2), 96; https://doi.org/10.3390/act14020096 - 16 Feb 2025
Viewed by 244
Abstract
The phase-change-material (PCM) actuator, a non-pyrotechnic technology in aerospace, offers enhanced safety and convenience. This paper presents a novel PCM actuator featuring an all-metal construction to improve reliability and sealing. Characterized by high energy density and temperature-dependent actuation, the actuator’s displacement output characteristics [...] Read more.
The phase-change-material (PCM) actuator, a non-pyrotechnic technology in aerospace, offers enhanced safety and convenience. This paper presents a novel PCM actuator featuring an all-metal construction to improve reliability and sealing. Characterized by high energy density and temperature-dependent actuation, the actuator’s displacement output characteristics (DOCs) are examined through visualization experiments. The results show the formation of a concave gap within the PCM upon cooling, which can be controlled by adjusting the cooling load and temperature to minimize its impact on displacement output. A two-dimensional physical model is developed to investigate how varying thermophysical parameters and boundary conditions affect the phase change process and DOC. The study finds that increasing the thermal conductivity of the PCM and surface heat flow enhances displacement velocity, although the effect diminishes at higher values. Additionally, reducing latent heat significantly boosts output velocity. For a fixed surface heat flow, changes in wall thickness have a minor impact, with velocity variation under 2%. Full article
(This article belongs to the Section Actuator Materials)
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<p>Energy density of different actuator materials (adapted by the author) [<a href="#B2-actuators-14-00096" class="html-bibr">2</a>].</p> Full article ">Figure 2
<p>Design of the PCM actuator in a cross-sectional view.</p> Full article ">Figure 3
<p>PCM is enclosed within the actuator by CMH and a knife-edge flange.</p> Full article ">Figure 4
<p>Experimental system.</p> Full article ">Figure 5
<p>Thermal expansion coefficient vs. temperature relationship of paraffin wax upon heating at a very slow velocity [<a href="#B24-actuators-14-00096" class="html-bibr">24</a>] with fitted curve.</p> Full article ">Figure 6
<p>The comparison of the simulation results between the numerical result (Num) and experimental result (Kong, Q.) [<a href="#B19-actuators-14-00096" class="html-bibr">19</a>].</p> Full article ">Figure 7
<p>Computational domains and boundary conditions.</p> Full article ">Figure 8
<p>The performed analyses for the grid number (<b>a</b>) and time-step size (<b>b</b>) independence tests.</p> Full article ">Figure 9
<p>Sealing results displayed after 50 repetitions.</p> Full article ">Figure 10
<p>The out displacement of actuator comparing different cases.</p> Full article ">Figure 11
<p>Concave PCM state after solidification.</p> Full article ">Figure 12
<p>Schema of central gap in different cases.</p> Full article ">Figure 13
<p>The temperature (<b>left</b>) and thermal strain (<b>right</b>) for the simulation result.</p> Full article ">Figure 14
<p>The results of experimental (Exp) and numerical calculation (Num).</p> Full article ">Figure 15
<p>Displacement output results after 10% parameter change. (<b>a</b>) k, (<b>b</b>) L, (<b>c</b>) δ<sub>w</sub>, and (<b>d</b>) heat flux.</p> Full article ">Figure 16
<p>Results of the t<sub>ps</sub> and u<sub>ps</sub> for the 0.5× to 2.0× parameters. (<b>a</b>) k, (<b>b</b>) L, (<b>c</b>) δ<sub>w</sub>, and (<b>d</b>) heat flux.</p> Full article ">Figure 17
<p>Results of the average velocity and velocity variation for the 0.5× to 2.0× parameters. (<b>a</b>) k, (<b>b</b>) L, (<b>c</b>) δ<sub>w</sub>, and (<b>d</b>) heat flux.</p> Full article ">
16 pages, 30872 KiB  
Article
Design, Simulation, and Testing of Active Cooperative Control Strategies for a Light Sensation Transfer Nursing Robot
by Yuansheng Ning, Lingfeng Sang, Zhengcai Wang, Bianca Ghinoiu, Fuqiu Lu, Hongbo Wang and Luige Vlădăreanu
Actuators 2025, 14(2), 95; https://doi.org/10.3390/act14020095 - 15 Feb 2025
Viewed by 226
Abstract
The transfer of patients, especially elderly or long-term bedridden individuals, has emerged as an important problem due to the growing aging population. The advancement of transfer nursing robots provides an intelligent solution to this problem. This paper presents a Parallel Master–Slave Cross-Coupled (PMSCC) [...] Read more.
The transfer of patients, especially elderly or long-term bedridden individuals, has emerged as an important problem due to the growing aging population. The advancement of transfer nursing robots provides an intelligent solution to this problem. This paper presents a Parallel Master–Slave Cross-Coupled (PMSCC) cooperative control strategy based on adaptive fuzzy controllers to address the motion control challenges of a self-developed light Sensation Transfer Nursing Robot (LSTNR). First, the working principle of the LSTNR is introduced, followed by the establishment of its motion model. Next, the robot’s velocity is designed based on PMSCC cooperative control strategies, with an adaptive fuzzy controller performing motion control. Finally, the proposed cooperative control strategy is simulated and analyzed, and the robot is tested for patient transfer. The results show that the proposed control strategy reduces the velocity cooperation error between the robot’s motors. The average velocity error of the robot is reduced by 92.69%, 92.08%, 47.35%, and 87.78%, respectively, compared to the non-cooperatively controlled robot. This significantly addresses issues such as belt slack, tightness, and patient position deformation during operation, improving the transfer efficiency and effectiveness of the LSTNR. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Working principle and transportation process of the LSTNR. (<b>a</b>) Simplified model of working principle; (<b>b</b>) Working Principle of the LSTNR; (<b>c</b>) Transportation process of the LSTNR.</p> Full article ">Figure 2
<p>The support backplane module. (<b>a</b>) Support backplane module diagram; (<b>b</b>) Support backplane module motion principle.</p> Full article ">Figure 3
<p>The LSTNR system model.</p> Full article ">Figure 4
<p>The mechanical model of a human–robot coupled transfer system.</p> Full article ">Figure 5
<p>The workflow of the LSTNR during a left-side patient transfer.</p> Full article ">Figure 6
<p>The PMSCC cooperative control strategy based on the fuzzy controller of the LSTNR.</p> Full article ">Figure 7
<p>The selection controller for the LSTNR.</p> Full article ">Figure 8
<p>The adaptive fuzzy controller-based PMSCC cooperative control strategy for the LSTNR.</p> Full article ">Figure 9
<p>The LSTNR dynamic performance under no load. (<b>a</b>) Velocity curve; (<b>b</b>) Velocity error curve.</p> Full article ">Figure 10
<p>The LSTNR dynamic performance under load. (<b>a</b>) Load curve; (<b>b</b>) Velocity curve; (<b>c</b>) Velocity error curve; (<b>d</b>) Torque curve.</p> Full article ">Figure 11
<p>The LSTNR prototype and control system.</p> Full article ">Figure 12
<p>The non-cooperatively controlled robot. (<b>a</b>) LSTNR motion status; (<b>b</b>) Velocity curve; (<b>c</b>) Velocity error curve.</p> Full article ">Figure 13
<p>The cooperatively controlled robot. (<b>a</b>) LSTNR motion status; (<b>b</b>) Velocity curve; (<b>c</b>) Velocity error curve.</p> Full article ">Figure 14
<p>Transfer test. (<b>a</b>) Plate extension; (<b>b</b>) Carry; (<b>c</b>) Plate retraction; (<b>d</b>) Plate extension; (<b>e</b>) Remove; (<b>f</b>) Plate retraction.</p> Full article ">Figure 15
<p>Motor velocity curve.</p> Full article ">Figure 16
<p>Velocity error curve.</p> Full article ">Figure 17
<p>Torque curve.</p> Full article ">
16 pages, 28202 KiB  
Article
An Extendable and Deflectable Modular Robot Inspired by Worm for Narrow Space Exploration
by Shufeng Tang, Jianan Yao, Yue Yu and Guoqing Zhao
Actuators 2025, 14(2), 94; https://doi.org/10.3390/act14020094 - 15 Feb 2025
Viewed by 275
Abstract
Inspired by earthworm peristalsis, a novel modular robot suitable for narrow spaces is proposed, capable of elongation, contraction, deflection and crawling. Unlike motor-driven robots, the earthworm-inspired robot achieves extension and deflection in each module through “on–off” control of the SMA springs, utilizing the [...] Read more.
Inspired by earthworm peristalsis, a novel modular robot suitable for narrow spaces is proposed, capable of elongation, contraction, deflection and crawling. Unlike motor-driven robots, the earthworm-inspired robot achieves extension and deflection in each module through “on–off” control of the SMA springs, utilizing the cooperation of mechanical skeletons and gears to avoid posture redundancy. The return to the initial posture and the maintenance of the posture are achieved through tension and torsion springs. To study the extension and deflection characteristics, we established a model through kinematic and force analysis to estimate the relationship between the length change and tensile characteristics of the SMA on both sides and the robot’s extension length and deflection angle. Through model verification and experiments, the robot’s extension, deflection and movement characteristics in narrow spaces and varying curvature narrow spaces were comprehensively studied. The results show that the earthworm-inspired robot, as predicted by the model, possesses accurate extension and deflection performance, and can perform inspection tasks in complex and narrow space environments. Additionally, compared to motor-driven robots, the robot designed in this study does not require insulation in low-temperature environments, and the cold conditions can improve its movement efficiency. This new configuration design and the extension and deflection characteristics provide valuable insights for the development of new modular robots and robot drive designs for extremely cold environments. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Structure diagram of robot. (<b>a</b>) The modular robot with scalability. (<b>b</b>) Explosion diagram of single module robot. (<b>c</b>) Schematic diagram of earthworm-like motion in narrow space. (<b>d</b>) The slithering motion of snakes. (<b>e</b>) The flexible spine of crawling animals. (<b>f</b>) The sequential assembling of modules at 90-degree angles.</p> Full article ">Figure 2
<p>Experimental test platform. (<b>a</b>) Experimental test platform. (<b>b</b>) Experimental mode 1. (<b>c</b>) Experimental mode 2.</p> Full article ">Figure 3
<p>Experimental curves of electrical-thermal-mechanical characteristics. (<b>a</b>) Curves under different initial lengths. (<b>b</b>) Curves under fixed length and different currents. (<b>c</b>) Curves of force under different currents; (<b>d</b>) Curves of length under different currents.</p> Full article ">Figure 4
<p>Kinematics characteristic analysis. (<b>a</b>) Plane geometric frame model. (<b>b</b>) Plane mechanics model. (<b>c</b>) Comparison curve of expansion and contraction motion data between theoretical and simulation. (<b>d</b>) Comparison curve of deflection motion data between theoretical and simulation.</p> Full article ">Figure 5
<p>Robot motion experimental test platform.</p> Full article ">Figure 6
<p>Experiments of expansion and contraction, and deflection. Robot motion experimental test platform. (<b>a</b>) Expansion and contraction displacement–time curve. (<b>b</b>) Deflection angle–time curve.</p> Full article ">Figure 7
<p>An experiment of climbing motion in a pipe. (<b>a</b>) The experiment of the climbing motion. (<b>b</b>) Comparison diagram between experimental data and theoretical data. (<b>c</b>) Theoretical and experimental error curve.</p> Full article ">Figure 8
<p>Narrow pipeline detection–winding pipeline motion experiment.</p> Full article ">Figure 9
<p>Low-temperature testing of the robot module. (<b>a</b>) Test setup for the robot module in low temperatures. (<b>b</b>) Recovery time curves of the robot module after compression under various conditions.</p> Full article ">
20 pages, 10631 KiB  
Article
Improving Low-Frequency Vibration Energy Harvesting of a Piezoelectric Cantilever with Quasi-Zero Stiffness Structure: Theory and Experiment
by Chunli Hua, Donglin Zou and Guohua Cao
Actuators 2025, 14(2), 93; https://doi.org/10.3390/act14020093 - 14 Feb 2025
Viewed by 288
Abstract
In this study, a novel cantilever piezoelectric energy harvester is constructed by using a quasi-zero stiffness (QZS) structure. The QZS structure consists of a classic piezoelectric cantilever beam combined with some accessories that include two pre-compression springs, rolling bearings, slideways and a cylindrical [...] Read more.
In this study, a novel cantilever piezoelectric energy harvester is constructed by using a quasi-zero stiffness (QZS) structure. The QZS structure consists of a classic piezoelectric cantilever beam combined with some accessories that include two pre-compression springs, rolling bearings, slideways and a cylindrical cam. The purpose of the QZS structure is to reduce the natural frequencies of the harvester, so that it can more efficiently collect low-frequency vibration energy. In this study, firstly, the extended Hamilton variational principle is used to establish the dynamic equations of the continuous system. Secondly, the Galerkin method is used to discretize the partial differential equation, and then the analytical solutions of the output voltage, current, power and vibration response of the harvester are obtained. Finally, the influence of the QZS structure on energy harvesting characteristics is studied. Theoretical research shows that the QZS structure can effectively reduce the fundamental natural frequency of the cantilever beam and improve its energy harvesting efficiency. When the spring stiffness is about half of the bending stiffness of the cantilever beam, the uncoupled fundamental natural frequency of the harvester is quasi-zero. For the experimental device considered here, experiments show that the QZS structure can reduce the fundamental natural frequency from 76.4 Hz to 54.1 Hz, decreasing by 22.3 Hz. The maximum output power is increased from 1.43 mW/g2 to 1.95 mW/g2, an increase of 36.4%. The experimental results validate the theoretical model. In short, this paper provides a new idea for the design of energy harvesters suitable for low-frequency vibration. Full article
(This article belongs to the Section Actuator Materials)
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<p>A cantilevered piezoelectric energy harvester with QZS (bimorph configuration, series or parallel connection): (<b>a</b>) isometric view; (<b>b</b>) side view.</p> Full article ">Figure 2
<p>Schematic diagram of installation deviation of the rolling bearing.</p> Full article ">Figure 3
<p>Comparisons of (<b>a</b>) mode shapes and (<b>b</b>) natural frequencies.</p> Full article ">Figure 4
<p>Comparisons of fundamental natural frequency with different (<b>a</b>) stiffness ratio and (<b>b</b>) mass ratio.</p> Full article ">Figure 5
<p>Results comparisons between present calculation and study by Erturk [<a href="#B38-actuators-14-00093" class="html-bibr">38</a>]: (<b>a</b>) voltage FRF; (<b>b</b>) current FRF; (<b>c</b>) power FRF; (<b>d</b>) tip velocity FRF.</p> Full article ">Figure 6
<p>The (<b>a</b>) first natural frequencies, (<b>b</b>) second natural frequencies and (<b>c</b>) third natural frequencies under different compression ratios.</p> Full article ">Figure 7
<p>The (<b>a</b>) first natural frequencies, (<b>b</b>) second natural frequencies and (<b>c</b>) third natural frequencies under different stiffness ratios.</p> Full article ">Figure 8
<p>Electromechanical FRFs for different stiffnesses of horizontal spring: (<b>a</b>) voltage FRF; (<b>b</b>) power FRF; (<b>c</b>) tip acceleration FRF.</p> Full article ">Figure 9
<p>The sensitivity analysis of <span class="html-italic">x</span><sub>0</sub>/<span class="html-italic">d</span>: (<b>a</b>) voltage FRF; (<b>b</b>) power FRF; (<b>c</b>) tip acceleration FRF.</p> Full article ">Figure 10
<p>The designed energy harvester: (<b>a</b>) design model; (<b>b</b>) physical model; (<b>c</b>) partial enlargement of the physical model.</p> Full article ">Figure 11
<p>Experimental setup used for validation of the analytical model.</p> Full article ">Figure 12
<p>(<b>a</b>) Input time−domain acceleration; (<b>b</b>) power spectrum of input acceleration; (<b>c</b>) voltage output FRF; (<b>d</b>) coherence functions.</p> Full article ">Figure 13
<p>Comparison of theoretical and experimental FRFs: (<b>a</b>) tip displacement FRF; (<b>b</b>) voltage FRF; (<b>c</b>) power FRF.</p> Full article ">
17 pages, 1905 KiB  
Article
A Dual-Motor Actuator for Ceiling Lift with High-Force and High-Speed Capabilities
by Ian Lalonde, Jeff Denis, Mathieu Lamy and Alexandre Girard
Actuators 2025, 14(2), 92; https://doi.org/10.3390/act14020092 - 14 Feb 2025
Viewed by 227
Abstract
Patient transfer devices allow for passive movement of patients in hospitals and care centers. Instead of hoisting the patient, it would be beneficial in some cases to assist their movement, enabling them to move by themselves and reducing hospitalization time. However, patient assistance [...] Read more.
Patient transfer devices allow for passive movement of patients in hospitals and care centers. Instead of hoisting the patient, it would be beneficial in some cases to assist their movement, enabling them to move by themselves and reducing hospitalization time. However, patient assistance requires devices capable of precisely controlling output forces at significantly higher speeds than those used for patient transfers alone, and a single-motor solution would be over-sized and would show poor efficiency for accomplishing both functions. This paper presents a ceiling robot, using a dual-motor actuator and adapted control schemes, that can be used to transfer patients, assist patients in their movement, and help prevent falls. The prototype is shown to be able to lift patients weighing up to 318 kg and to assist a patient with a desired force of up to 100 kg with a precision of 7.8%. Also, a smart control scheme to manage falls is shown to be able to stop a patient who is falling by applying a desired deceleration. Full article
(This article belongs to the Special Issue Modeling, Perception and Control of Robotic Systems with Real-World Applications)
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<p>Lifting module overview of the prototype in a real situation with illustrations of its three operating conditions: (<b>A</b>) patient transfer, (<b>B</b>) patient assistance, and (<b>C</b>) fall prevention. HF is for the highly geared mode (high force) and HS is for the lightly geared mode (high speed).</p> Full article ">Figure 2
<p>Operation points mapping (continuous force) with high force for patient transfer, high speed for patient assistance, and brake for fall prevention.</p> Full article ">Figure 3
<p>Generic concepts for design comparison, more specifically, the ratios of each gear stage based on the requirements and the selected components.</p> Full article ">Figure 4
<p>Simplified model of the multifunctional lift using a lumped-parameter approach.</p> Full article ">Figure 5
<p>Multifunctional lift experimental prototype and scheme of the actual gearing topology.</p> Full article ">Figure 6
<p>Mode state machine with transfer mode for high-force capabilities, assistance mode for high-speed capabilities, fall prevention to brake the patient, and fall recovery to lift the patient.</p> Full article ">Figure 7
<p>Measure of the friction in EM2 without and with speed offset from EM1 while a 150 N load is applied.</p> Full article ">Figure 8
<p>Control architecture and force controllers, where (<b>a</b>) is an open-loop current control, (<b>b</b>) a friction compensation algorithm, (<b>c</b>) a friction compensation algorithm with an offset on the speed, (<b>d</b>) a PID current controller, and (<b>e</b>) a DOB.</p> Full article ">Figure 9
<p>Complete trial that encompasses patient assistance, fall prevention, and patient transfer, showing the force measured and the speed contribution of EM2 and EM1.</p> Full article ">Figure 10
<p>Force and speed during a fixed course with friction compensation algorithm [<a href="#actuators-14-00092-f008" class="html-fig">Figure 8</a>b].</p> Full article ">Figure 11
<p>Complete fall sequence with the output speed, the speed contribution of EM2 and of EM1 (see Equation (<a href="#FD1-actuators-14-00092" class="html-disp-formula">1</a>)), the output force, the servo angle, and the output position. The different events are: (a) start of the fall, (b) start of the braking sequence, (c) EM2 stops, (d) EM1 stops, and (e) end of patient recovery.</p> Full article ">
23 pages, 8148 KiB  
Article
Energy-Coupling-Based Control for Unmanned Quadrotor Transportation Systems: Exploiting Beneficial State-Coupling Effects
by Lincong Han, Zengcheng Zhou, Ming Li, Haokun Geng, Gang Li and Menghua Zhang
Actuators 2025, 14(2), 91; https://doi.org/10.3390/act14020091 - 13 Feb 2025
Viewed by 265
Abstract
Cable suspension transport is a crucial method for quadrotors to transport goods and materials. During transportation, the quadrotor transport system (QTS) faces external disturbances and system uncertainties. Particularly, the underactuated nature of the system poses significant challenges to its stable operation. To solve [...] Read more.
Cable suspension transport is a crucial method for quadrotors to transport goods and materials. During transportation, the quadrotor transport system (QTS) faces external disturbances and system uncertainties. Particularly, the underactuated nature of the system poses significant challenges to its stable operation. To solve these problems, this paper proposes a hierarchical control scheme that enhances coupling and leverages advantageous state-coupling to achieve precise positioning and eliminate payload swings for QTS. By leveraging the cascading characteristics of QTS, the design process is greatly simplified through the separate design of the torque input for the inner loop and the force input for the outer loop. Simulation results demonstrate the effective control performance of this method. Full article
(This article belongs to the Special Issue Modeling and Nonlinear Control for Complex MIMO Mechatronic Systems)
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<p>Quadrotor transportation system.</p> Full article ">Figure 2
<p>Structure of the overall control system.</p> Full article ">Figure 3
<p>And <math display="inline"><semantics> <mrow> <mi mathvariant="bold">Θ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for QTS.</p> Full article ">Figure 4
<p>Control inputs <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">τ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Quadrotor attitude.</p> Full article ">Figure 6
<p>Group 1: Robustness test for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="bold">Θ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Group 1: Robustness test for control inputs <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">τ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Group 1: Robustness test for attitude.</p> Full article ">Figure 9
<p>Group 2: Robustness test for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="bold">Θ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>Group 2: Robustness test for control inputs <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">τ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>Group 2: Robustness test for attitude.</p> Full article ">Figure 12
<p>Quadrotor position and payload swing angles for wind gust effect.</p> Full article ">Figure 13
<p>Control inputs for wind gust effect.</p> Full article ">Figure 14
<p>Quadrotor attitude for wind gust effect.</p> Full article ">Figure 15
<p>Quadrotor position and payload swing angles for ground reflection effect.</p> Full article ">Figure 16
<p>Control inputs for ground reflection effect.</p> Full article ">Figure 17
<p>Attitude for ground reflection effect.</p> Full article ">
23 pages, 30439 KiB  
Article
Couple Anti-Swing Obstacle Avoidance Control Strategy for Underactuated Overhead Cranes
by Shuo Meng, Weikai He, Na Liu, Rui Zhang and Cungen Liu
Actuators 2025, 14(2), 90; https://doi.org/10.3390/act14020090 - 13 Feb 2025
Viewed by 330
Abstract
Overhead cranes are widely used for transportation in factories. They move slowly by manual operation to prevent the payload from swinging sharply or colliding with sudden obstacles. To address these issues and enhance work efficiency, this paper proposes a couple anti-swing obstacle avoidance [...] Read more.
Overhead cranes are widely used for transportation in factories. They move slowly by manual operation to prevent the payload from swinging sharply or colliding with sudden obstacles. To address these issues and enhance work efficiency, this paper proposes a couple anti-swing obstacle avoidance control method for 5-DOF overhead cranes. Time polynomial fitting is employed for trajectory planning to achieve obstacle avoidance. To achieve anti-swing of the payloads, a coupled variable incorporating both actuated and underactuated states is defined, alongside a boundary for dynamic performance. Finally, MATLAB simulation and hardware experiments are carried out to verify the reliability and compared with some existing control methods. Full article
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<p>The dynamics model of overhead cranes.</p> Full article ">Figure 2
<p>Obstacle-avoiding strategy.</p> Full article ">Figure 3
<p>Transformation of coordinates.</p> Full article ">Figure 4
<p>Transport trajectories of overhead crane.</p> Full article ">Figure 5
<p>The velocities of movement.</p> Full article ">Figure 6
<p>Linear transportation trajectories in space.</p> Full article ">Figure 7
<p>The swings of payload.</p> Full article ">Figure 8
<p>The control signals.</p> Full article ">Figure 9
<p>The laboratory platform of overhead crane.</p> Full article ">Figure 10
<p>Transport trajectories in hardware experiment.</p> Full article ">Figure 11
<p>The control signals in hardware experiment.</p> Full article ">Figure 12
<p>Obstacle avoidance trajectories.</p> Full article ">
27 pages, 10913 KiB  
Article
Observer-Based Sliding Mode Control for Vehicle Way-Point Tracking with Unknown Disturbances and Obstacles
by Jiacheng Song, Mingjie Shen and Yanan Zhang
Actuators 2025, 14(2), 89; https://doi.org/10.3390/act14020089 - 13 Feb 2025
Viewed by 319
Abstract
In this paper, an advanced vehicle way-point tracking control method, including kinematic control, dynamic control and an obstacle avoidance strategy, is introduced. In the kinematic part, a vehicle kinematic model is established, along with the coordinate transformation between the vehicle and its target. [...] Read more.
In this paper, an advanced vehicle way-point tracking control method, including kinematic control, dynamic control and an obstacle avoidance strategy, is introduced. In the kinematic part, a vehicle kinematic model is established, along with the coordinate transformation between the vehicle and its target. A way-point tracking control law is developed to optimize the vehicle’s movement along predefined way-points. In the dynamic part, a dynamic model considering the actual disturbances and losses is established. An observer compensation technique is utilized to monitor and mitigate disturbances, while sliding mode control, enhanced by a HyperSpiral algorithm, ensures accurate and stable tracking performance. Furthermore, to tackle real-world path planning challenges, an improved way-point tracking obstacle-avoidance algorithm is developed to generate effective way-points for navigating around obstacles. Finally, simulation results validate that the vehicle consistently tracks target way-points in complex scenarios, highlighting the robustness and effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Integrated Intelligent Vehicle Dynamics and Control)
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<p>Control architecture for tracking multiple target points.</p> Full article ">Figure 2
<p>Kinematic model of vehicle in two-dimensional plane.</p> Full article ">Figure 3
<p>Pseudo-code structure logic diagram.</p> Full article ">Figure 4
<p>Single-point tracking simulation image.</p> Full article ">Figure 5
<p>Comparison image of velocity and angular velocity tracking under single-point tracking.</p> Full article ">Figure 6
<p>Single-point tracking system control input.</p> Full article ">Figure 7
<p>Multi-point tracking simulation path.</p> Full article ">Figure 8
<p>Comparison of velocity and angular velocity tracking under multi-point point tracking.</p> Full article ">Figure 9
<p>System control input imitation under multi-point.</p> Full article ">Figure 10
<p>Forward motor observer simulation.</p> Full article ">Figure 11
<p>Rotating motor observer simulation.</p> Full article ">Figure 12
<p>Obstacle-avoidance algorithm generates target path.</p> Full article ">Figure 13
<p>The actual path of the vehicle tracking.</p> Full article ">Figure 14
<p>Control input of vehicle tracking under obstacle-avoidance algorithm.</p> Full article ">
26 pages, 1267 KiB  
Article
An Improved Nonlinear Health Index CRRMS for the Remaining Useful Life Prediction of Rolling Bearings
by Yongze Jin, Xubo Yang, Junqi Liu, Yanxi Yang, Xinhong Hei and Anqi Shangguan
Actuators 2025, 14(2), 88; https://doi.org/10.3390/act14020088 - 11 Feb 2025
Viewed by 362
Abstract
In this article, a novel prediction index is constructed, a hybrid filtering is proposed, and a remaining useful life (RUL) prediction framework is developed. In the proposed framework, different models are built for different operation states of rolling bearings. In the normal state, [...] Read more.
In this article, a novel prediction index is constructed, a hybrid filtering is proposed, and a remaining useful life (RUL) prediction framework is developed. In the proposed framework, different models are built for different operation states of rolling bearings. In the normal state, a linear model is built, and a Kalman filter (KF) is implemented to determine the failure start time (FST). In the degradation state, a dimensionless prediction index CRRMS is constructed, based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet threshold. Then, a double exponential model is established, and the hybrid filtering is proposed to estimate the future trend of CRRMS, which is combined by a particle filter (PF) and an unscented Kalman filter (UKF). At the same time, dynamic failure threshold technology is adaptively used to determine the failure thresholds of different bearings. Furthermore, the RUL is extrapolated at the moment the prediction index exceeds the failure threshold. Finally, the effectiveness and practicability of the proposed method is verified on the bearing dataset given by the PRONOSTIA platform. Full article
(This article belongs to the Special Issue AI, Designing, Sensing, Instrumentation, Diagnosis, Controlling, and Integration of Actuators in Digital Manufacturing—2nd Edition)
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<p>Bearing degradation process.</p> Full article ">Figure 2
<p>Flowchart of the proposed method framework.</p> Full article ">Figure 3
<p>Kurtosis of rolling bearing 1_3.</p> Full article ">Figure 4
<p>Kurtosis of rolling bearing 2_2.</p> Full article ">Figure 5
<p>RMS of rolling bearing 1_3.</p> Full article ">Figure 6
<p>RMS of rolling bearing 2_2.</p> Full article ">Figure 7
<p>PRONOSTIA acceleration test platform.</p> Full article ">Figure 8
<p>Bearing 1_5 temperature signal.</p> Full article ">Figure 9
<p>Bearing 1_5 vibration signal.</p> Full article ">Figure 10
<p>Horizontal vibration signal of the bearing.</p> Full article ">Figure 11
<p>Filtering result of FST point selection based on kurtosis.</p> Full article ">Figure 12
<p>Relative error of FST point selection based on kurtosis.</p> Full article ">Figure 13
<p>Filtering result of FST point selection based on RMS.</p> Full article ">Figure 14
<p>Relative error of FST point selection based on RMS.</p> Full article ">Figure 15
<p>Envelope spectrum of bearing 2_2. (<b>a</b>) Bearing 2_2 FST pre-envelope spectrum. (<b>b</b>) Bearing 2_2 FST post-envelope spectrum.</p> Full article ">Figure 16
<p>The first 15 IMF components of bearings 1_5 based on CEEMDAN.</p> Full article ">Figure 17
<p>CRRMS of all experimental bearings.</p> Full article ">Figure 18
<p>RMS of all experimental bearings.</p> Full article ">Figure 19
<p>Predicted RUL for bearing 1_5.</p> Full article ">Figure 20
<p>Predicted RUL for bearing 2_1.</p> Full article ">Figure 21
<p>Predicted RUL for bearing 2_2.</p> Full article ">Figure 22
<p>Predicted RUL for bearing 3_2.</p> Full article ">
13 pages, 2708 KiB  
Article
Passivity-Based Twisting Sliding Mode Control for Series Elastic Actuators
by Hui Zhang, Jilong Wang, Lei Zhang, Shijie Zhang, Jing Zhang and Zirong Zhang
Actuators 2025, 14(2), 87; https://doi.org/10.3390/act14020087 - 11 Feb 2025
Viewed by 367
Abstract
This paper presents a passivity-based twisting sliding mode control (PBSMC) approach for series elastic actuators (SEAs). To address the time-varying position trajectory tracking control problem in SEAs, a fourth-order dynamic model is developed to accurately characterize the system. The control framework comprises an [...] Read more.
This paper presents a passivity-based twisting sliding mode control (PBSMC) approach for series elastic actuators (SEAs). To address the time-varying position trajectory tracking control problem in SEAs, a fourth-order dynamic model is developed to accurately characterize the system. The control framework comprises an internal loop and an external loop controller, each designed to ensure precise trajectory tracking. The internal loop controller manages the second derivative of the joint trajectory position error, while the external loop focuses on the error itself. Both controllers are based on the PBSMC methodology to reduce complex nonlinear disturbances and minimize tracking errors. The finite-time convergence of the proposed method is rigorously analyzed. The performance and advantages of the method are evaluated and compared through various simulations. Full article
(This article belongs to the Section Control Systems)
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<p>The equivalent schematic diagram of the SEA.</p> Full article ">Figure 2
<p>Comparison of simulation results between PID, backstepping method, and the proposed method without external interference.</p> Full article ">Figure 3
<p>Comparison of simulation results between PID, backstepping method, and the proposed method with external interference.</p> Full article ">Figure 4
<p>Simulation results for SEA (Case 2).</p> Full article ">
22 pages, 9746 KiB  
Article
Stiffness Optimization of a Robotic Drilling System for Enhanced Accuracy in Aerospace Assembly
by Haiyang Xu, Jixiao Xue, Gaojie Guo, Yankai Liu, Mingqi Liu and Deyuan Zhang
Actuators 2025, 14(2), 86; https://doi.org/10.3390/act14020086 - 11 Feb 2025
Viewed by 338
Abstract
The low stiffness of robots significantly limits their applicability within the aerospace assembly and manufacturing sectors. The majority of existing research focuses on optimizing robot posture; however, the efficacy of these approaches is constrained in situations with minimal posture variation. To address this [...] Read more.
The low stiffness of robots significantly limits their applicability within the aerospace assembly and manufacturing sectors. The majority of existing research focuses on optimizing robot posture; however, the efficacy of these approaches is constrained in situations with minimal posture variation. To address this challenge, this study examines a robotic drilling system designed for use in confined spaces. An in-depth analysis of its stiffness model is conducted, and the system’s stiffness limitations are identified using the stiffness ellipsoid evaluation method. Based on the mechanical analysis of the drilling state, a stiffness enhancement method grounded in the local force closure of the end effector is proposed. This method involves locking the end effector’s expansion module with the substrate during the drilling process, thereby enabling the axial drilling forces to be jointly borne by the expansion module and the robot’s base joints. Consequently, the system’s stiffness, particularly in the axial direction, is substantially improved. A series of experiments rigorously validate the effectiveness of the proposed stiffness enhancement method. The experimental results demonstrate that the stiffness-optimized robot reduces axial deformation during drilling by a factor of ten and significantly improves hole quality and exit burr height. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Structure and application of the robotic drilling system: (<b>a</b>) application scenario in a confined space; (<b>b</b>) robotic drilling system; (<b>c</b>) chassis system; (<b>d</b>) four-degree-of-freedom (4-DOF) posture adjustment platform; (<b>e</b>) drilling end effector.</p> Full article ">Figure 2
<p>Schematic diagram and stiffness chain of the robotic drilling system: (<b>a</b>) schematic diagram; (<b>b</b>) stiffness chain.</p> Full article ">Figure 3
<p>Displacement stiffness ellipsoid of the robotic drilling system.</p> Full article ">Figure 4
<p>Structural diagram and degrees of freedom analysis of the expanding positioning system: (<b>a</b>) schematic diagram; (<b>b</b>) degrees of freedom analysis.</p> Full article ">Figure 5
<p>Deformation behavior of the end effector during the drilling process.</p> Full article ">Figure 6
<p>Mechanical analysis of drilling forces in the robot’s optimized stiffness state and end effector structure.</p> Full article ">Figure 7
<p>Mechanical analysis of drilling forces in the robot’s unoptimized stiffness state.</p> Full article ">Figure 8
<p>Experimental validation of stiffness optimization for robot drilling.</p> Full article ">Figure 9
<p>Variation in A-axis joint torque during the robot drilling process.</p> Full article ">Figure 10
<p>Z-Axis deformation of the end effector during the robot drilling process.</p> Full article ">Figure 11
<p>Workpiece and measurement: (<b>a</b>) drilled workpiece; (<b>b</b>) diameter measurement of hole; (<b>c</b>) exit burr observation of holes.</p> Full article ">Figure 12
<p>Hole diameter of robot drilled holes with different stiffness conditions.</p> Full article ">Figure 13
<p>Robot drilling exit burrs under different stiffness conditions.</p> Full article ">
18 pages, 877 KiB  
Review
Collision/Obstacle Avoidance Coordination of Multi-Robot Systems: A Survey
by Guanghong Yang, Liwei An and Can Zhao
Actuators 2025, 14(2), 85; https://doi.org/10.3390/act14020085 - 11 Feb 2025
Viewed by 426
Abstract
Multi-robot systems (MRSs) are widely applied in the fields of joint search and rescue, exploration, and carrying. To achieve cooperative tasks and guarantee physical safety, the robots should avoid inter-robot collisions as well as robot–obstacle collisions. However, the collision/obstacle avoidance task usually conflicts [...] Read more.
Multi-robot systems (MRSs) are widely applied in the fields of joint search and rescue, exploration, and carrying. To achieve cooperative tasks and guarantee physical safety, the robots should avoid inter-robot collisions as well as robot–obstacle collisions. However, the collision/obstacle avoidance task usually conflicts with the given cooperative task, which poses a significant challenge for the achievement of multi-robot cooperative tasks. This paper provides a review of the state-of-the-art results in the collision/obstacle avoidance cooperative control of MRSs. Specifically, the latest developments of collision/obstacle avoidance cooperative control are summarized according to different planning strategies and classified into three categories: (1) offline planning; (2) receding horizon planning; and (3) reactive control. Furthermore, specific design solutions for existing reference/command governors are highlighted to demonstrate the latest research advances. Finally, several challenging issues are discussed to guide future research. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Case of multi-robot collision/obstacle avoidance coordination.</p> Full article ">Figure 2
<p>The framework of reference governor scheme [<a href="#B74-actuators-14-00085" class="html-bibr">74</a>].</p> Full article ">
17 pages, 3174 KiB  
Article
Real-Time Motor Control Using a Raspberry Pi, ROS, and CANopen over EtherCAT, with Application to a Semi-Active Prosthetic Ankle
by Kieran M. Nichols, Rebecca A. Roembke and Peter G. Adamczyk
Actuators 2025, 14(2), 84; https://doi.org/10.3390/act14020084 - 10 Feb 2025
Viewed by 479
Abstract
This paper focused on the implementation method and results of modifying a Raspberry Pi 4 for real-time control of brushless direct-current motors, with application in a semi-active two-axis ankle prosthesis. CANopen over EtherCAT was implemented directly on the Raspberry Pi to synchronize real-time [...] Read more.
This paper focused on the implementation method and results of modifying a Raspberry Pi 4 for real-time control of brushless direct-current motors, with application in a semi-active two-axis ankle prosthesis. CANopen over EtherCAT was implemented directly on the Raspberry Pi to synchronize real-time communication between it and the motor controllers. Kinematic algorithms for setting ankle angles of zero to ten degrees in any combination of sagittal and frontal angles were implemented. To achieve reliable motor communication, where the motors continuously move, the distributed clock synchronization of Linux and Motor driver systems needs to have a finely tuned Proportional-Integral compensation and a consistent sampling period. Data collection involved moving the ankle through 33 unique pre-selected ankle configurations nine times. The system allowed for quick movement (mean settling time 0.192 s), reliable synchronization (standard deviation of 4.51 microseconds for sampling period), and precise movement (mean movement error less than 0.2 deg) for ankle angle changes and also a high update rate (250 microseconds sampling period) with modest CPU load (12.48%). This system aims to allow for the prosthesis to move within a single swing phase, enabling it to efficiently adapt to various speeds and terrains, such as walking on slopes, stairs, or around corners. Full article
(This article belongs to the Special Issue Intelligent Systems, Robots and Devices for Healthcare and Rehabilitation)
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<p>Exploded views of the new TADA design comprising an outside U-joint and inside CAM wedges actuated by brushless DC motors. The bottom half is identical to the exploded top half shown. The motors directly rotate the wedges, which move the ankle to various sagittal and/or frontal angles.</p> Full article ">Figure 2
<p>Conceptual diagram showing the controller software architecture among the Linux and Windows computers. The primary Linux computer (Raspberry PI) contains the Brain and Motor nodes that control the TADA and collects data for the experiments. A secondary Windows computer communicates with the primary computer using a private mobile hotspot using ROS WI-FI communication. The secondary computer collects the data and allows for GUI interaction. The red and blue arrows describe inter- and intra-node communication.</p> Full article ">Figure 3
<p>Example diagrams showing the relationship of the wedge rotation, the TADA control angles, and the anatomical ankle angles for frontal plane variations in EV to IV ankle angles. A similar relationship controls the sagittal variation in PF to DF ankle angles. Intermediate angles can also be used for combined frontal and sagittal motions.</p> Full article ">Figure 4
<p>Plot of the actual SP across the experiment time. Each color represents a different condition. These scatter plots show stable matching of the intended SP with some variability. There are three commanded SPs of 250, 500, and 1000 μs.</p> Full article ">Figure 5
<p>One-sided violin plots of the various conditions of clock synchronization settings with a commanded SP of 250 μs. These violin plots show a kernel-density estimation of the data distribution, where the peak of the plot represents the data that are most dense. A vertical black line represents the controlled SP of 250 μs. Conditions 1–5 (<a href="#actuators-14-00084-t002" class="html-table">Table 2</a>) are shown. The conditions are ordered in this table to group the changes in I first, followed by the base condition (Condition 3) and then the changes in P.</p> Full article ">Figure 6
<p>Example data from one movement, plotting ankle angle commands (intended angle) and actual ankle angle based on the motors’ position sensors. The blue lines represent the IV angles, and the red lines represent the PF angles. The black dots are the 95% rise times, and the black Xs are for the settling times.</p> Full article ">Figure 7
<p>Violin plots of movement times for 95% rise and settling (left side and axis) and PF, IV errors (right side and axis) for the TADA angle changes. Each violin plot gives a kernel-density estimation of the data distribution, and it also contains the box and whisker diagrams to indicate first and third quartiles (Q1 and Q3 as black solid lines), the medians (black solid lines), and the means (black dashed lines).</p> Full article ">Figure 8
<p>Plot of PF and IV angles with the intended orientation (command with red marker) and actual position (based on the motors’ position sensors). The actual orientation is represented by blue dots with blue error bars (T shaped from the blue dot) for PF and IV errors. The full set of actual positions (blue dots) represents 291 TADA orientations, where each blue dot has 8–9 samples.</p> Full article ">
18 pages, 5087 KiB  
Article
Load-Current-Compensation-Based Robust DC-Link Voltage Control for Flywheel Energy Storage Systems
by Hongjin Hu, Wentao Liang, Guang-Zhong Cao, Jingbo Wei and Kun Liu
Actuators 2025, 14(2), 83; https://doi.org/10.3390/act14020083 - 9 Feb 2025
Viewed by 502
Abstract
DC-link voltage control needs to be achieved for flywheel energy storage systems (FESSs) during discharge. However, load disturbances and model nonlinearity affect the voltage control performance. Therefore, this paper proposes a load-current-compensation-based robust DC-link voltage control method for FESSs. In the proposed method, [...] Read more.
DC-link voltage control needs to be achieved for flywheel energy storage systems (FESSs) during discharge. However, load disturbances and model nonlinearity affect the voltage control performance. Therefore, this paper proposes a load-current-compensation-based robust DC-link voltage control method for FESSs. In the proposed method, the model is linearized via load current feedforward compensation and dq-axis current-to-DC-current conversion. The uncertainty of the linear model is analyzed and an H∞ robust control method is applied to overcome the uncertainty. Furthermore, experiments involving the proposed method are conducted on a 1.2 kWh magnetic suspended FESS prototype. Compared with the general proportional integral control method, the proposed method can increase the voltage response speed by 37.1% and reduce the voltage fluctuations by 29.5%. The effectiveness of the proposed method is verified experimentally. Full article
(This article belongs to the Special Issue Actuators in Magnetic Levitation Technology and Vibration Control)
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<p>System description during discharge of the FESS. (<b>a</b>) The overall topology of the FESS during discharge; (<b>b</b>) Block diagram of DC-link voltage control in the FESS.</p> Full article ">Figure 2
<p>Relationships among the DC-link voltage, DC-link current, and load current.</p> Full article ">Figure 3
<p>Block diagram of the control strategy based on load current compensation.</p> Full article ">Figure 4
<p>Input disturbance model of the system.</p> Full article ">Figure 5
<p>H<sub>∞</sub> robust control system block diagram.</p> Full article ">Figure 6
<p>H<sub>∞</sub> robust controller design flowchart based on the LMI.</p> Full article ">Figure 7
<p>Block diagram of the load-current-compensation-based robust DC-link voltage control.</p> Full article ">Figure 8
<p>FESS experimental platform.</p> Full article ">Figure 9
<p>Impact of different weight coefficients on the control performance: (<b>a</b>) experimental results for different <span class="html-italic">C</span><sub>11</sub> coefficients; (<b>b</b>) experimental results for different <span class="html-italic">C</span><sub>12</sub> coefficients; (<b>c</b>) experimental results for different <span class="html-italic">D</span><sub>1</sub> coefficients; (<b>d</b>) experimental results for different <span class="html-italic">D</span><sub>2</sub> coefficients.</p> Full article ">Figure 10
<p>DC-link voltage step response curves under a constant resistance load.</p> Full article ">Figure 11
<p>DC-link voltage curves during load step changes.</p> Full article ">Figure 12
<p>DC-link voltage curves under a motor load.</p> Full article ">Figure 13
<p>Voltage curves in energy feedback mode.</p> Full article ">
21 pages, 9153 KiB  
Article
Theoretical Analysis and Experimental Verification of 2-DOF Linkage Piezoelectric Energy Harvesting
by Yuanyuan Song, Huawen Nan, Ran Zhou, Fangchao Xu and Feng Sun
Actuators 2025, 14(2), 82; https://doi.org/10.3390/act14020082 - 9 Feb 2025
Viewed by 379
Abstract
In the process of energy harvesting, vibration energy harvesting still has several disadvantages, including a high-threshold excitation and a narrow working bandwidth. Therefore, a 2-degrees-of-freedom piezoelectric energy harvester is proposed. By introducing a nonlinear magnetic force to the system, the working bandwidth and [...] Read more.
In the process of energy harvesting, vibration energy harvesting still has several disadvantages, including a high-threshold excitation and a narrow working bandwidth. Therefore, a 2-degrees-of-freedom piezoelectric energy harvester is proposed. By introducing a nonlinear magnetic force to the system, the working bandwidth and the energy-harvesting efficiency of three magnetically coupled piezoelectric cantilever beams can be effectively improved. In this paper, a mathematical model consisting of three electrically coupled magnetically coupled piezoelectric cantilever beam systems is established, and the governing equations of electric coupling are solved numerically and verified experimentally. The dynamic characteristics under different excitations and frequencies are studied. The experiment shows that the working bandwidth can be increased by controlling the distance between three pairs of circular magnets and changing the excitation and frequency to induce resonance. Thus, the self-power requirement of micro-power devices can be realized. Overall, this study provides a promising solution for improving the performance of piezoelectric energy harvesters and offers theoretical insights for designing vibrating piezoelectric energy harvesters. Full article
(This article belongs to the Section Actuator Materials)
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<p>Structure diagram of 2-DOF linkage energy harvester.</p> Full article ">Figure 2
<p>Model diagram of 2-DOF piezoelectric energy harvester system.</p> Full article ">Figure 3
<p>Displacement amplitude frequency of 2-DOF piezoelectric cantilever beam A.</p> Full article ">Figure 4
<p>Displacement amplitude frequency of 2-DOF piezoelectric cantilever beam B.</p> Full article ">Figure 5
<p>Displacement amplitude frequency of 2-DOF piezoelectric cantilever beam C.</p> Full article ">Figure 6
<p>Phase diagram of 2-DOF piezoelectric cantilever beam A.</p> Full article ">Figure 7
<p>Phase diagram of 2-DOF piezoelectric cantilever beam B.</p> Full article ">Figure 8
<p>Phase diagram of 2-DOF piezoelectric cantilever beam C.</p> Full article ">Figure 9
<p>Voltage amplitude frequency of 2- DOF piezoelectric cantilever beam A.</p> Full article ">Figure 10
<p>Voltage amplitude frequency of 2-DOF piezoelectric cantilever beam B.</p> Full article ">Figure 11
<p>Voltage amplitude frequency of 2-DOF piezoelectric cantilever beam C.</p> Full article ">Figure 12
<p>An experimental testing platform for 2-DOF energy harvesters.</p> Full article ">Figure 13
<p>Spectrum analysis curve of piezoelectric cantilever beam A. (<b>a</b>) Displacement curve; (<b>b</b>) voltage curve; (<b>c</b>) phase diagram curve; (<b>d</b>) spectral curve.</p> Full article ">Figure 14
<p>Spectrum analysis curve of piezoelectric cantilever beam B. (<b>a</b>) displacement curve; (<b>b</b>) voltage curve; (<b>c</b>) phase diagram curve; (<b>d</b>) spectral curve.</p> Full article ">Figure 15
<p>Spectrum analysis curve of piezoelectric cantilever beam C. (<b>a</b>) displacement curve; (<b>b</b>) voltage curve; (<b>c</b>) phase diagram curve; (<b>d</b>) spectral curve.</p> Full article ">Figure 16
<p>Mean square voltage curve of piezoelectric cantilever beam A at different excitation levels.</p> Full article ">Figure 17
<p>Mean square voltage curve of piezoelectric cantilever beam B at different excitation levels.</p> Full article ">Figure 18
<p>Mean square voltage curve of piezoelectric cantilever beam C at different excitation levels.</p> Full article ">Figure 19
<p>Mean square voltage curve of piezoelectric cantilever beam A at different longitudinal distances.</p> Full article ">Figure 20
<p>Mean square voltage curve of piezoelectric cantilever beam B at different longitudinal distances.</p> Full article ">Figure 21
<p>Mean square voltage curve of piezoelectric cantilever beam C at different longitudinal distances.</p> Full article ">Figure 22
<p>Curve of external load resistance–mean square voltage.</p> Full article ">Figure 23
<p>Curve of external load resistance–output power.</p> Full article ">
21 pages, 12918 KiB  
Article
Analysis and Optimization Design of Moving Magnet Linear Oscillating Motors
by Minghu Yu, Yuqiu Zhang, Jiekun Lin and Peng Zhang
Actuators 2025, 14(2), 81; https://doi.org/10.3390/act14020081 - 8 Feb 2025
Viewed by 291
Abstract
Permanent Magnet Linear Oscillating Motors (PMLOMs) are popular in micro-positioning systems, biomedical devices, and refrigeration compressors due to their simple structure, high efficiency, rapid response, and quiet operation. This paper proposes a method for the analysis and optimization of electromechanical systems that employs [...] Read more.
Permanent Magnet Linear Oscillating Motors (PMLOMs) are popular in micro-positioning systems, biomedical devices, and refrigeration compressors due to their simple structure, high efficiency, rapid response, and quiet operation. This paper proposes a method for the analysis and optimization of electromechanical systems that employs a moving magnet linear oscillating motor. A simplified magnetic circuit method model was built to derive an electromagnetic thrust formula, and the initial design parameters of the motor and the thrust at the equilibrium position were calculated. Subsequently, a finite element model was developed, and a multi-objective optimization method was applied to refine the key dimensions of the motor to enhance its thrust characteristics. Furthermore, an analysis of the resonant characteristics of the electromechanical coupled system was conducted to identify the optimal operating frequency for the optimization scheme. Finally, the experimental validation of the optimized design was performed on a prototype, with the measured data showing a general correlation with the trends observed in the simulation analysis results. The effectiveness of this system analysis method was validated through experimental data. The results demonstrate that the thrust at the initial position is linearly correlated with both the outer arc radius of the permanent magnet and its mechanical pole arc coefficient. Additionally, the axial length of the outer stator, the axial spacing between the two outer stators, and the axial length of the magnets serve as key influencing parameters for the thrust characteristics within the effective stroke range. Furthermore, when the motor operates at its mechanical resonance frequency, it can attain the maximum efficiency. Full article
(This article belongs to the Section High Torque/Power Density Actuators)
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<p>Structure diagram of PMLOMs.</p> Full article ">Figure 2
<p>Schematic diagram of key parameters. (<b>a</b>) axial section. (<b>b</b>) radial section.</p> Full article ">Figure 3
<p>A model of the excitation magnetic circuit of the left and right stators.</p> Full article ">Figure 4
<p>A model of the armature magnetic circuit of the left and right stators.</p> Full article ">Figure 5
<p>Magnetic field distribution diagram of PMLOMs.</p> Full article ">Figure 6
<p>The thrust characteristics of the initial design.</p> Full article ">Figure 7
<p>Sensitivity analysis between input and output parameters of optimization process.</p> Full article ">Figure 8
<p>Response surface plot of <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>Response surface plot of <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>p</mi> <mn>2</mn> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>Response surface plot of <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>Two-dimensional Pareto front.</p> Full article ">Figure 12
<p>Comparison chart of magnetic reluctance thrust before and after optimization.</p> Full article ">Figure 13
<p>Comparison chart of electromagnetic thrust before and after optimization.</p> Full article ">Figure 14
<p>Comparison chart of total thrust before and after optimization.</p> Full article ">Figure 15
<p>Bode plot of current displacement transfer function.</p> Full article ">Figure 16
<p>Diagram of motor components and overall structure.</p> Full article ">Figure 17
<p>Diagram showing relationship between stroke–current ratio and driving frequency under no-load conditions.</p> Full article ">Figure 18
<p>Diagram showing relationship between stroke–current phase angle difference and driving frequency under no-load conditions.</p> Full article ">
33 pages, 16932 KiB  
Article
Real-Time Simulation-Based Control of an Electro-Hydraulic Flexible Manipulator
by Daniel Hagen, Katrine Als Hansen, Jonas Holmen and Michael Rygaard Hansen
Actuators 2025, 14(2), 80; https://doi.org/10.3390/act14020080 - 8 Feb 2025
Viewed by 333
Abstract
This paper presents the modeling and control of a flexible single-boom crane manipulator using a high-fidelity real-time simulation model. The model incorporates both electro-hydraulic actuation and flexible-body dynamics, with the flexible boom represented via the lumped parameter method. A systematic tuning and validation [...] Read more.
This paper presents the modeling and control of a flexible single-boom crane manipulator using a high-fidelity real-time simulation model. The model incorporates both electro-hydraulic actuation and flexible-body dynamics, with the flexible boom represented via the lumped parameter method. A systematic tuning and validation procedure ensures that the model accurately replicates the physical system’s dynamics, achieving an eigenfrequency accuracy of approximately 97% and a piston-position deviation within 1.2% of the overall stroke length in final tests. The real-time simulation model is utilized in both open-loop and closed-loop control schemes to investigate whether simulated data can reduce dependency on sensor feedback compared to a benchmark controller. While the simulation-based controller alone does not match the fully sensor-based closed-loop accuracy, the simulation-based feedforward improves performance by 83% compared to the standard model-based velocity feedforward. Additionally, integrating the real-time simulation with sensor feedback enhances the benchmark controller’s performance by approximately 16%. These findings highlight the potential of combining real-time, nonlinear simulation with conventional sensor feedback to enhance the control of electro-hydraulic flexible manipulators. Full article
(This article belongs to the Special Issue Control of Hydraulic Robotic Manipulators)
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<p>Overview of the electro-hydraulically actuated flexible crane. The mechanical system (a single boom with a fixed payload), the self-contained electro-hydraulic actuator, and the Beckhoff real-time control system are highlighted.</p> Full article ">Figure 2
<p>Kinematic representation of the single-boom crane. Key dimensions and coordinates are indicated.</p> Full article ">Figure 3
<p>Simplified electro-hydraulic circuit of the SCC, incorporating five pressure sensors (P) and a piston position sensor (S). The numbered components correspond to those listed in <a href="#actuators-14-00080-t002" class="html-table">Table 2</a> while the red dotted lines represent the pilot lines.</p> Full article ">Figure 4
<p>Control system architecture for real-time operation.</p> Full article ">Figure 5
<p>Benchmark controller architecture.</p> Full article ">Figure 6
<p>Hydraulic schematic showing pressure nodes and flow definitions.</p> Full article ">Figure 7
<p>Flow through an orifice.</p> Full article ">Figure 8
<p>Effective hydraulic oil bulk modulus as a function of pressure.</p> Full article ">Figure 9
<p>The simplified lumped parameter model with three segments.</p> Full article ">Figure 10
<p>The multibody system derived using the lumped parameter method.</p> Full article ">Figure 11
<p>Free body diagram and kinetic diagram for the three lumped segments.</p> Full article ">Figure 12
<p>Illustration of the moment arm of the cylinder force, <math display="inline"><semantics> <msub> <mi mathvariant="bold">r</mi> <mrow> <mn>1</mn> <mi>c</mi> <mi>y</mi> <mi>l</mi> </mrow> </msub> </semantics></math>, and the relative position vector, <math display="inline"><semantics> <msub> <mi mathvariant="bold">r</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>y</mi> <mi>l</mi> </mrow> </msub> </semantics></math>. The fixed attachment point (A), the base attachment point (B), and the cylinder mount (C) are highlighted.</p> Full article ">Figure 13
<p>Open-loop simulation-based feedforward control.</p> Full article ">Figure 14
<p>Benchmark control system implemented on the simulated model.</p> Full article ">Figure 15
<p>Closed-loop control strategy with simulation-based feedforward.</p> Full article ">Figure 16
<p>Comparison between the model in Simulink and the model deployed on TwinCAT 3.</p> Full article ">Figure 17
<p>Estimating the eigenfrequency of the boom and cylinder: (<b>a</b>) Measured data. (<b>b</b>) Simulation results.</p> Full article ">Figure 18
<p>Simulated piston position vs. experimental data: (<b>a</b>) Trapezoidal motion reference with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>y</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>120</mn> <mo> </mo> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>. (<b>b</b>) Error between signals.</p> Full article ">Figure 19
<p>Simulated vs. experimental piston pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mi>A</mi> </msub> </semantics></math>: (<b>a</b>) Pressure signals. (<b>b</b>) Error between signals.</p> Full article ">Figure 20
<p>Simulated vs. experimental pump-side pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mi>P</mi> <mi>A</mi> </mrow> </msub> </semantics></math>: (<b>a</b>) Pressure signals. (<b>b</b>) Error.</p> Full article ">Figure 21
<p>Simulated vs. experimental pump-side pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mi>P</mi> <mi>B</mi> </mrow> </msub> </semantics></math>: (<b>a</b>) Pressure signals. (<b>b</b>) Error.</p> Full article ">Figure 22
<p>Simulated vs. experimental rod pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mi>B</mi> </msub> </semantics></math>: (<b>a</b>) Pressure signals. (<b>b</b>) Error.</p> Full article ">Figure 23
<p>Simulated vs. experimental accumulator pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mi>a</mi> <mi>c</mi> <mi>c</mi> </mrow> </msub> </semantics></math>: (<b>a</b>) Pressure signals. (<b>b</b>) Error.</p> Full article ">Figure 24
<p>Trapezoidal motion reference with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>y</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>120</mn> <mo> </mo> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 25
<p>Open-loop position tracking at <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>y</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>120</mn> <mo> </mo> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>: (<b>a</b>) Reference vs. measured piston position. (<b>b</b>) Tracking error.</p> Full article ">Figure 26
<p>Open-loop simulation-based feedforward vs. closed-loop benchmark at <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>y</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>120</mn> <mo> </mo> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>: (<b>a</b>) Piston positions. (<b>b</b>) Tracking error.</p> Full article ">Figure 27
<p>Closed-loop control at <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>y</mi> <mi>l</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>120</mn> <mo> </mo> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>: (<b>a</b>) Reference vs. measured piston position. (<b>b</b>) Tracking error.</p> Full article ">Figure A1
<p>Bladder Accumulator.</p> Full article ">Figure A2
<p>Free body diagram (left) and kinetic diagram (right) for body 3.</p> Full article ">Figure A3
<p>Free body diagram and kinetic diagram of two lumped segments.</p> Full article ">
15 pages, 2160 KiB  
Article
Integrating Strain Gauge Feedback with Adaptive Sliding Mode Motion Control for Piezoelectric Nanopositioning Stage
by Xianfeng Zeng, Feng Nan, Tengfei Li, Changchao Mo, Jiaqiu Su, Kaihong Wei and Xiaozhi Zhang
Actuators 2025, 14(2), 79; https://doi.org/10.3390/act14020079 - 7 Feb 2025
Viewed by 393
Abstract
This paper presents an adaptive sliding mode control (ASMC) scheme based on strain gauge position feedback for compensating for motion errors in a piezoelectric nanopositioning stages and ensures precise and reliable motion tracking control. The innovation of this scheme lies in calibrating the [...] Read more.
This paper presents an adaptive sliding mode control (ASMC) scheme based on strain gauge position feedback for compensating for motion errors in a piezoelectric nanopositioning stages and ensures precise and reliable motion tracking control. The innovation of this scheme lies in calibrating the relationship between the feedback voltage of the strain gauge and the actual stage displacement. Thus, the calibrated feedback displacement is directly used as the position feedback signal for the ASMC scheme. Adaptive rules are employed to adjust the control gains, thereby eliminating the requirement to determine the upper bound of the disturbance. The stability of the ASMC strategy is theoretically proven within the Lyapunov framework. Comparative experiments under external disturbances have confirmed the superiority of the proposed control scheme. Results demonstrate that the proposed control scheme exhibits superior robust tracking performance compared to the traditional sliding mode control (SMC) scheme. Full article
(This article belongs to the Section Precision Actuators)
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<p>The 3D model of the piezoelectric nanoposition stage.</p> Full article ">Figure 2
<p>Experimental setup of the piezoelectric nanopositioning stage.</p> Full article ">Figure 3
<p>Block diagram of the proposed ASMC scheme.</p> Full article ">Figure 4
<p>Calibration results of strain gauge feedback voltage and measured displacement.</p> Full article ">Figure 5
<p>Resolution ratio test results.</p> Full article ">Figure 6
<p>The results of sinusoidal curve tracking with a frequency of 0.005 Hz.</p> Full article ">Figure 7
<p>The results of sinusoidal curve tracking with a frequency of 0.010 Hz.</p> Full article ">Figure 8
<p>Error between feedback displacement and actual displacement at 0.005 Hz.</p> Full article ">Figure 9
<p>Error between feedback displacement and actual displacement at 0.010 Hz.</p> Full article ">
13 pages, 2302 KiB  
Article
Passive Frequency Tuning of Kinetic Energy Harvesters Using Distributed Liquid-Filled Mass
by Rahul Adhikari and Nathan Jackson
Actuators 2025, 14(2), 78; https://doi.org/10.3390/act14020078 - 7 Feb 2025
Viewed by 514
Abstract
Micro-scale kinetic energy harvesters are in large demand to function as sustainable power sources for wireless sensor networks and the Internet of Things. However, one of the challenges associated with them is their inability to easily tune the frequency during the manufacturing process, [...] Read more.
Micro-scale kinetic energy harvesters are in large demand to function as sustainable power sources for wireless sensor networks and the Internet of Things. However, one of the challenges associated with them is their inability to easily tune the frequency during the manufacturing process, requiring devices to be custom-made for each application. Previous attempts have either used active tuning, which consumes power, or passive devices that increase their energy footprint, thus decreasing power density. This study involved developing a novel passive method that does not alter the device footprint or power density. It involved creating a proof mass with an array of chambers or cavities that can be individually filled with liquid to alter the overall proof mass as well as center of gravity. The resonant frequency of a rectangular cantilever can then be altered by changing the location, density, and volume of the liquid-filled mass. The resolution can be enhanced by increasing the number of chambers, whereas the frequency tuning range can be increased by increasing the amount of liquid or density of the liquids used to fill the cavities. A piezoelectric cantilever with a 340 Hz initial resonant frequency was used as the testing device. Liquids with varying density (silicone oil, liquid sodium polytungstate, and Galinstan) were investigated. The resonant frequencies were measured experimentally by filling various cavities with these liquids to determine the tuning frequency range and resolution. The tuning ranges of the first resonant frequency mode for the device were 142–217 Hz, 108–217 Hz, and 78.4–217 Hz for silicone oil, liquid sodium polytungstate, and Galinstan, respectively, with a sub Hz resolution. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>(<b>a</b>) Schematic of 5 × 7 proof mass on cantilever with cavities C<sub>54</sub> and C<sub>52</sub> filled with liquid; (<b>b</b>) top-view schematic of proof mass on cantilever with nomenclature of its rows and columns; and (<b>c</b>) experimental piezoelectric cantilever with 3D printed proof mass on vibration shaker.</p> Full article ">Figure 2
<p>(<b>a</b>) Experimental results illustrating V<sub>pp</sub> as a function of frequency with various liquids with all 100% cavities filled and an empty control mass; (<b>b</b>) V<sub>pp</sub> as a function of frequency with all cavities filled to 25%, 50%, and 100% volume using sodium polytungstate.</p> Full article ">Figure 3
<p>(<b>a</b>) Voltage as a function of frequency for all cavities filled with varying volumes of liquids; (<b>b</b>) results illustrating the 1st resonant frequency mode as a function of filling an individual cavity along a middle column with 25%, 50%, 75%, and 100% liquid sodium polytungstate (change in frequency illustrated in parenthesis); and (<b>c</b>) schematic illustrating the individual cavities filled.</p> Full article ">Figure 4
<p>(<b>a</b>) First resonant frequency mode as a function of filling an individual cavity along the middle column with various liquids; (<b>b</b>) first resonant frequency mode as a function of filling an individual cavity along the middle row with various liquids (each cavity was filled 100%).</p> Full article ">Figure 5
<p>First resonant frequency mode as a function of filling individual rows and columns with varying liquids (<b>a</b>) along individual rows and (<b>b</b>) along individual columns.</p> Full article ">Figure 6
<p>First resonant frequency mode as a function of filling consecutive cavities with varying liquids (<b>a</b>) along consecutive rows and (<b>b</b>) along consecutive columns.</p> Full article ">
19 pages, 7224 KiB  
Article
Designing a Composite Hydraulic Cylinder Using Genetic Algorithms
by Michał Stosiak, Marek Lubecki and Mykola Karpenko
Actuators 2025, 14(2), 77; https://doi.org/10.3390/act14020077 - 7 Feb 2025
Viewed by 526
Abstract
The paper points out the growing interest in the use of composite materials for load-bearing parts, including hydraulic components. The non-negligible benefits of using composite materials in mechanical engineering are pointed out. However, applications of new materials sometimes give rise to new challenges. [...] Read more.
The paper points out the growing interest in the use of composite materials for load-bearing parts, including hydraulic components. The non-negligible benefits of using composite materials in mechanical engineering are pointed out. However, applications of new materials sometimes give rise to new challenges. The strength parameters of a new structure, such as a composite cylinder for a hydraulic actuator, depend on its structure, including the number of layers and the fibre angle. This paper presents the application of a genetic algorithm to optimise the process of selecting the structure of a composite cylinder for a hydraulic actuator. The operation of the algorithm and the process of selecting global parameters (hyperparameters) are described. A block diagram of the algorithm for optimising the structure selection process is presented, and the designed structure is verified. Full article
(This article belongs to the Special Issue Recent Advances in the Design Solutions of Electro-Hydraulic Actuators for Mechatronic Systems)
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<p>Diagram showing Young’s moduli and strengths of different types of Torayca carbon fibres offered by TORAY (Tokyo, Japan) (authors’ elaboration based on [<a href="#B3-actuators-14-00077" class="html-bibr">3</a>]).</p> Full article ">Figure 2
<p>Diagram showing Young’s moduli and strengths of different types of TENAX carbon fibre offered by Taijin (Tokyo, Japan) (authors’ elaboration based on [<a href="#B4-actuators-14-00077" class="html-bibr">4</a>]).</p> Full article ">Figure 3
<p>Block diagram of genetic algorithm.</p> Full article ">Figure 4
<p>An example of an individual representing the layering of a winding element.</p> Full article ">Figure 5
<p>Number of generations to convergence for (<b>a</b>) <span class="html-italic">α<sub>max</sub></span> = 5°; (<b>b</b>) <span class="html-italic">α<sub>max</sub></span> = 15°; (<b>c</b>) <span class="html-italic">α<sub>max</sub></span> = 30°.</p> Full article ">Figure 6
<p>Average design cost for different values of <span class="html-italic">P</span>, <span class="html-italic">N<sub>n</sub></span> and <span class="html-italic">p<sub>mut</sub></span> at (<b>a</b>) <span class="html-italic">α<sub>max</sub></span> = 5°; (<b>b</b>) <span class="html-italic">α<sub>max</sub></span> = 15°; (<b>c</b>) <span class="html-italic">α<sub>max</sub></span> = 30°.</p> Full article ">Figure 7
<p>Value of fitness function reached at end of each iteration for (<b>a</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.1 and <span class="html-italic">α<sub>max</sub></span> = 5°; (<b>b</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.2 and <span class="html-italic">α<sub>max</sub></span> = 5°; (<b>c</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.5 and <span class="html-italic">α<sub>max</sub></span> = 5°.</p> Full article ">Figure 8
<p>Value of fitness function reached at end of each iteration for (<b>a</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.1 and <span class="html-italic">α<sub>max</sub></span> = 15°; (<b>b</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.2 and <span class="html-italic">α<sub>max</sub></span> = 15°; (<b>c</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.5 and <span class="html-italic">α<sub>max</sub></span> = 15°.</p> Full article ">Figure 9
<p>Value of fitness function reached at end of each iteration for (<b>a</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.1 and <span class="html-italic">α<sub>max</sub></span> = 30°; (<b>b</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.2 and <span class="html-italic">α<sub>max</sub></span> = 30°; (<b>c</b>) <span class="html-italic">p<sub>mut</sub></span> = 0.5 and <span class="html-italic">α<sub>max</sub></span> = 30°.</p> Full article ">Figure 10
<p>Hydraulic diagram of actuator test stand: 1—pump; 2—safety valve; 3—pressure gauge; 4—4/3 directional control valve; 5—2-way flow regulator; 6—3-way flow regulator; 7—check valve; 8 and 9—flow meters; 10 and 11—pressure sensors; 12—tested actuator; 13—position sensor; 14—force sensor; 15—load actuator; 16—4/3 directional control valve; 17—pressure sensor; 18—relief valve; 19—safety valve; 20—adjustable throttle valve; 21—pump; 22 and 23—tanks.</p> Full article ">Figure 11
<p>Actuator with [±83/±84/±85/±83] composite cylinder mounted on test stand.</p> Full article ">Figure 12
<p>Deformation of composite [±83/±84/±85/±83] cylinder during internal pressure loading.</p> Full article ">Figure 13
<p>Stress in individual cylinder layers of [±83/±84/±85/±83] cylinder in layer coordinate systems under internal pressure loading.</p> Full article ">Figure 14
<p>Value of strength factor <span class="html-italic">R</span> in individual layers under internal pressure loading.</p> Full article ">Figure 15
<p>Deformation of composite [90/90/±20/]<sub>2</sub> cylinder during pressure loading.</p> Full article ">Figure 16
<p>Stress in individual layers of [90/90/±20/]<sub>2</sub> cylinder in layer coordinate systems under internal pressure loading.</p> Full article ">Figure 17
<p>Value of strength factor <span class="html-italic">R</span> in individual layers under internal pressure loading.</p> Full article ">Figure 18
<p>Block diagram of proposed composite cylinder design method.</p> Full article ">
20 pages, 12818 KiB  
Article
Modal Vibration Suppression for Magnetically Levitated Rotor Considering Significant Gyroscopic Effects and Interface Contact
by Kun Zeng, Yang Zhou, Yuanping Xu and Jin Zhou
Actuators 2025, 14(2), 76; https://doi.org/10.3390/act14020076 - 6 Feb 2025
Viewed by 349
Abstract
Featured with optimal power consumption, active magnetic bearings (AMBs) have been extensively integrated into turbomachinery applications. For turbomachinery components, including the rotor and impeller, their connection is generally based on bolted joints, which would easily induce excessive interface contact. As a result, the [...] Read more.
Featured with optimal power consumption, active magnetic bearings (AMBs) have been extensively integrated into turbomachinery applications. For turbomachinery components, including the rotor and impeller, their connection is generally based on bolted joints, which would easily induce excessive interface contact. As a result, the pre-tightening torque can induce modal vibrations in the rotor upon levitation. Although a notch filter can be adopted to suppress the vibrations, it should be noted that the current reported notch filters are based on fixed center frequency, making it challenging to enable high effectiveness over a broad range of rotor speeds, particularly in cases where the gyroscopic effect is significant. Herein, a modal vibration suppression based on a varying-frequency notch filter is proposed, considering gyroscopic effect and interface contact. First, the rotor–AMB system was developed, taking into consideration the bolted-joint interface contact. This modeled the effect of the interface contact as a time-varying force in the positive feedback. Secondly, the relationship between vibration frequency and rotational speed was obtained, based on simulations. Lastly, a test rig was configured to validate the performance of the frequency-varying notch filter. The experimental data confirm that the filter is capable of attenuating the modal vibrations resulting from interface contact across all operational speeds. Full article
(This article belongs to the Special Issue Advanced Theory and Application of Magnetic Actuators—2nd Edition)
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<p>Overall experimental setup of the rotor AMB test rig.</p> Full article ">Figure 2
<p>A brief illustration of the structure and principle of the radial AMB.</p> Full article ">Figure 3
<p>The schematic view of the modal test.</p> Full article ">Figure 4
<p>The experimental response of the rotor in a run-up procedure with the fixed center frequency notch filter.</p> Full article ">Figure 5
<p>The schematic diagram of the rotor–AMB mechatronic system.</p> Full article ">Figure 6
<p>The first mode shape of the rotor with the cylinder.</p> Full article ">Figure 7
<p>Schematic diagram of the interface contact and the equivalent spring units.</p> Full article ">Figure 8
<p>Schematic representation of the actual contact conditions and separation line between the rotor and cylinder. (<b>a</b>) Diagram of the separation line. (<b>b</b>) Diagram of the actual contact conditions.</p> Full article ">Figure 9
<p>Schematic diagram of closed-loop system model, taking interface contact into consideration.</p> Full article ">Figure 10
<p>Comparison between experimental and theoretical frequency response.</p> Full article ">Figure 11
<p>Campbell chart of the rotor with the cylinder.</p> Full article ">Figure 12
<p>Suspension response of the magnetically suspended rotor (simulation). (<b>a</b>) Time–domain response. (<b>b</b>) Frequency–domain response.</p> Full article ">Figure 13
<p>Suspension response of the magnetically suspended rotor (experiment). (<b>a</b>) Time–domain response. (<b>b</b>) Frequency–domain response.</p> Full article ">Figure 14
<p>The steady response at different rotation speeds in frequency domain. (<b>a</b>) Rotation speed: 100 Hz. (<b>b</b>) Rotation speed: 200 Hz. (<b>c</b>) Rotation speed: 300 Hz.</p> Full article ">Figure 15
<p>Run-up simulation of the magnetically suspended rotor. (<b>a</b>) Simulation response of the rotor in a run-up procedure. (<b>b</b>) Relationship between rotation speed and vibration frequency.</p> Full article ">Figure 16
<p>Bode diagram of different bandwidth notches.</p> Full article ">Figure 17
<p>Schematic diagram of the rotor–AMB system with notch filter.</p> Full article ">Figure 18
<p>Schematic diagram of band-pass filter <span class="html-italic">N<sub>f</sub></span> (<span class="html-italic">s</span>).</p> Full article ">Figure 19
<p>Schematic diagram of the rotor–AMB system, taking the rigid mode into consideration.</p> Full article ">Figure 20
<p>Root locus of the closed-loop system.</p> Full article ">Figure 21
<p>Run-up simulation of the magnetically suspended rotor with notch filter.</p> Full article ">Figure 22
<p>Run-up experiment of the magnetically suspended rotor with notch filter. (<b>a</b>) Response of the rotor in a run-up procedure from 0 to 250 Hz. (<b>b</b>) The response in frequency domain when the rotation is 250 Hz.</p> Full article ">
16 pages, 6005 KiB  
Article
Nonlinear Optimal Control for Spacecraft Rendezvous and Docking Using Symplectic Numerical Method
by Zhengtao Wei, Jie Yang, Hao Wen, Dongping Jin and Ti Chen
Actuators 2025, 14(2), 75; https://doi.org/10.3390/act14020075 - 6 Feb 2025
Viewed by 376
Abstract
This paper addresses the autonomous rendezvous and docking between a chaser spacecraft and a target spacecraft. An optimal control method is employed to plan the rendezvous and docking maneuver, considering various constraints, including force, velocity, field of view, and collision avoidance with a [...] Read more.
This paper addresses the autonomous rendezvous and docking between a chaser spacecraft and a target spacecraft. An optimal control method is employed to plan the rendezvous and docking maneuver, considering various constraints, including force, velocity, field of view, and collision avoidance with a diamond-shaped obstacle. The optimal trajectories are derived using a symplectic algorithm, which ensures high accuracy and enhances computational efficiency. These trajectories serve as the reference for the maneuver. A PD-based tracking control method is proposed to enable real-time feedback control. An air-bearing experimental system, encompassing state measurement, data transmission, and processing, is established to conduct ground-based tracking experiments. Furthermore, specialized simulators for the chaser and target spacecraft, equipped with a docking mechanism, are designed. Experimental results validate both the feasibility of the reference trajectories and the effectiveness of the PD tracking control approach. Full article
(This article belongs to the Special Issue Dynamics and Control of Aerospace Systems—2nd Edition)
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<p>Schematic of the ARVD mission.</p> Full article ">Figure 2
<p>Schematic of the final system configuration in the docking phase.</p> Full article ">Figure 3
<p>A group of superquadratic curves of a = 5, b = 3.</p> Full article ">Figure 4
<p>The pose trajectory of the chaser spacecraft obtained by the symplectic algorithm.</p> Full article ">Figure 5
<p>Time history of the translational and rotational velocities obtained by the symplectic algorithm.</p> Full article ">Figure 6
<p>Time histories of the thrust force and torque generated by the symplectic algorithm.</p> Full article ">Figure 7
<p>Schematic of the ground-based experimental system.</p> Full article ">Figure 8
<p>Schematic of the workflow of the experimental system.</p> Full article ">Figure 9
<p>The pose tracking trajectory of the chaser spacecraft in the experiment.</p> Full article ">Figure 10
<p>Time history of the translational and rotational tracking velocities in the experiment.</p> Full article ">
24 pages, 6972 KiB  
Article
Efficient and High-Precision Method of Calculating Maximum Singularity-Free Space in Stewart Platform Based on K-Means Clustering and CNN-LSTM-Attention Model
by Jie Tao, Huicheng Zhou and Wei Fan
Actuators 2025, 14(2), 74; https://doi.org/10.3390/act14020074 - 6 Feb 2025
Viewed by 299
Abstract
The determination of maximum singularity-free space is critical to structural design and motion control strategy in the Stewart platform. Nevertheless, in practical applications, there exist several limitations such as computational efficiency, calculation precision, and the reliability of computational results. To overcome those shortcomings, [...] Read more.
The determination of maximum singularity-free space is critical to structural design and motion control strategy in the Stewart platform. Nevertheless, in practical applications, there exist several limitations such as computational efficiency, calculation precision, and the reliability of computational results. To overcome those shortcomings, this work proposes an efficient and high-precision method for computing the maximum singularity-free space within the Stewart platform. Firstly, apply K-Means clustering to group the variables, including the range, mean, and standard deviation of driving rod lengths, and the clustering centroids and extreme rod lengths collectively form a set of scenarios to avoid large-scale searching. An additional sorting methodology with a specific parameter is proposed for sorting the aforementioned scenarios in descending order and detecting singular-prone cases. Secondly, compute the initial solution for maximum singularity-free length without gimbal lock through an analytical solution formula, enabling reduction in the search scope. Thirdly, introduce a novel scaling factor to resolve the problem of dimensional inconsistency between rotation and translation within the Jacobian matrix using dual quaternions, and determine the singularity based on the determinant of the newly proposed Jacobian matrix. Finally, employ a CNN-LSTM-Attention model for a secondary verification procedure, specifically targeting the challenge of singularities encountered when solving the forward kinematics of the Stewart platform using zero-position values. The experiments demonstrate that the accelerated discretization method for maximum singularity-free joint space and workspace is applicable to devices with diverse geometric configurations. For two practical Stewart platforms, compared with two conventional methods, this method improves computational efficiency and precision significantly. The computation time of the first platform is reduced by 97.54% and 98.07% respectively, while that of the second platform is cut by 80.84% and 81.80% respectively. In terms of precision, the first platform demonstrates 95.83% and 78% improvement respectively, and the second platform attains 99.99% improvement over two conventional methods. Full article
(This article belongs to the Section Precision Actuators)
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<p>The overview of the proposed method.</p> Full article ">Figure 2
<p>The spatial position relationship of joint points in the Stewart platform.</p> Full article ">Figure 3
<p>The centroids of K-Means clustering.</p> Full article ">Figure 4
<p>The flowchart of K-Means clustering followed by sorting.</p> Full article ">Figure 5
<p>The determinant of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="bold-italic">J</mi> </mrow> <mrow> <mi>x</mi> </mrow> <mrow> <mi>k</mi> </mrow> </msubsup> </mrow> </semantics></math>. (<b>a</b>) Occurrence without singularity; (<b>b</b>) occurrence with singularity.</p> Full article ">Figure 6
<p>The schematic diagram of CNN-LSTM-Attention model.</p> Full article ">Figure 7
<p>Procedure of calculating the maximum singularity-free space on the Stewart platform.</p> Full article ">Figure 8
<p>The experimental Stewart platform YBT6-250.</p> Full article ">Figure 9
<p>The experimental Stewart platform YBT6-2000.</p> Full article ">Figure 10
<p>The results of K-Means clustering based on <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>The descending sorting results of the 128 scenarios.</p> Full article ">Figure 12
<p>Initial search of maximum singularity-free length.</p> Full article ">Figure 13
<p>The search results of drive rod lengths. (<b>a</b>) YBT6-250; (<b>b</b>) YBT6-2000.</p> Full article ">Figure 14
<p>The search procedure for maximum singularity-free joint space.</p> Full article ">Figure 15
<p>The workspace of YBT6-250. (<b>a</b>) Position boundary; (<b>b</b>) orientation boundary.</p> Full article ">Figure 16
<p>The workspace of YBT6-2000. (<b>a</b>) Position boundary; (<b>b</b>) orientation boundary.</p> Full article ">Figure 17
<p>The actual workspace and maximum singularity space of YBT6-250.</p> Full article ">Figure 18
<p>The actual workspace and maximum singularity space of YBT6-2000.</p> Full article ">
19 pages, 21955 KiB  
Article
Research on Dynamic Modeling and Control of Magnetorheological Hydro-Pneumatic Suspension
by Yuansi Chen, Min Jiang, Fufeng Yang, Ruijing Qian, Rongjie Zhai, Hongliang Wang and Shaoqing Xv
Actuators 2025, 14(2), 73; https://doi.org/10.3390/act14020073 - 5 Feb 2025
Viewed by 388
Abstract
A novel magnetorheological semi-active hydro-pneumatic suspension system was proposed to overcome the shortcoming of the traditional hydro-pneumatic suspension without adaptive vibration damping function. It is based on the magnetorheological semi-active vibration reduction technology to effectively improve the ride performance of the vehicle. Firstly, [...] Read more.
A novel magnetorheological semi-active hydro-pneumatic suspension system was proposed to overcome the shortcoming of the traditional hydro-pneumatic suspension without adaptive vibration damping function. It is based on the magnetorheological semi-active vibration reduction technology to effectively improve the ride performance of the vehicle. Firstly, a nonlinear model was established with the Bouc–Wen model based on the mechanical property test results of magnetorheological hydro-pneumatic spring. Secondly, the dynamic model of the single-wheel magnetorheological hydro-pneumatic suspension system was established. Subsequently, the ON-OFF and PID-Fuzzy semi-active control strategies of the single-wheel magnetorheological hydro-pneumatic suspension were proposed based on the ON-OFF and PID-Fuzzy control methods. The simulation results demonstrate that the magnetorheological hydro-pneumatic suspension under PID-Fuzzy control has the best vibration reduction effect in comparison with the passive hydro-pneumatic suspension. The sprung mass acceleration, suspension working space, and dynamic tire deformation are reduced by 24.50%, 21.62%, and 21.01%, respectively. The bench test results verify that magnetorheological hydro-pneumatic suspension and its control methods can effectively improve the ride performance of the system. Full article
(This article belongs to the Section Actuators for Surface Vehicles)
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Figure 1

Figure 1
<p>The schematic diagram of the magnetorheological hydro-pneumatic spring.</p> Full article ">Figure 2
<p>The object picture of magnetorheological hydro-pneumatic spring.</p> Full article ">Figure 3
<p>Magnetorheological hydro-pneumatic spring mechanical properties test system.</p> Full article ">Figure 4
<p>The experimental results (solid line) and the simulation results (dotted line) of the Bouc–Wen model: (<b>a</b>) The force−displacement curve; (<b>b</b>) the force−velocity curve.</p> Full article ">Figure 5
<p>Bouc–Wen model.</p> Full article ">Figure 6
<p>Bouc–Wen model parameters and current fitting curve: (<b>a</b>) the <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>b</b>) the <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>c</b>) the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">A</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>d</b>) the <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>e</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>f</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>g</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve.</p> Full article ">Figure 6 Cont.
<p>Bouc–Wen model parameters and current fitting curve: (<b>a</b>) the <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>b</b>) the <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>c</b>) the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">A</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>d</b>) the <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>e</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>f</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve; (<b>g</b>) the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> </mrow> </semantics></math> curve.</p> Full article ">Figure 7
<p>The three-dimensional image of the magnetorheological hydro-pneumatic system.</p> Full article ">Figure 8
<p>The dynamic model of single-wheel magnetorheological hydro-pneumatic system.</p> Full article ">Figure 9
<p>Magnetorheological hydro-pneumatic suspension ON-OFF semi-active control system.</p> Full article ">Figure 10
<p>Output damping force range of magnetorheological hydro-pneumatic spring.</p> Full article ">Figure 11
<p>Input variable membership curve.</p> Full article ">Figure 12
<p>Output variable membership curve.</p> Full article ">Figure 13
<p>Magnetorheological hydro-pneumatic suspension PID-Fuzzy semi-active control system.</p> Full article ">Figure 14
<p>The comparison diagrams of SMA in random road surface.</p> Full article ">Figure 15
<p>The comparison diagrams of DTD in random road surface.</p> Full article ">Figure 16
<p>The comparison diagrams of DDS in random road surface.</p> Full article ">Figure 17
<p>The comparison diagrams of SMA in the pulse road surface.</p> Full article ">Figure 18
<p>The comparison diagrams of DTD in the pulse road surface.</p> Full article ">Figure 19
<p>The comparison diagrams of DDS in the pulse road surface.</p> Full article ">Figure 20
<p>The site map of magnetorheological hydro-pneumatic suspension system bench.</p> Full article ">Figure 21
<p>Time–domain comparison of upper surface acceleration.</p> Full article ">Figure 22
<p>Frequency–domain comparison of upper surface acceleration.</p> Full article ">
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