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26 pages, 16654 KiB  
Article
Adaptive Fast Smooth Second-Order Sliding Mode Fault-Tolerant Control for Hypersonic Vehicles
by Lijia Cao, Lei Liu, Pengfei Ji and Chuandong Guo
Aerospace 2024, 11(11), 951; https://doi.org/10.3390/aerospace11110951 - 18 Nov 2024
Viewed by 279
Abstract
In response to control issues in hypersonic vehicles under external disturbances, model uncertainties, and actuator failures, this paper proposes an adaptive fast smooth second-order sliding mode fault-tolerant control scheme. First, a system separation approach is adopted, dividing the hypersonic vehicle model into fast [...] Read more.
In response to control issues in hypersonic vehicles under external disturbances, model uncertainties, and actuator failures, this paper proposes an adaptive fast smooth second-order sliding mode fault-tolerant control scheme. First, a system separation approach is adopted, dividing the hypersonic vehicle model into fast and slow loops for independent design. This ensures that the airflow angle tracking error and sliding mode variables converge to the vicinity of the origin within a finite time. A fixed-time disturbance observer is then designed to estimate and compensate for the effects of model uncertainties, external disturbances, and actuator failures. The controller parameters are dynamically adjusted through an adaptive term to enhance robustness. Furthermore, first-order differentiation is used to estimate differential terms, effectively avoiding the issue of complexity explosion. Finally, the convergence of the controller within a finite time is rigorously proven using the Lyapunov method, and the perturbation of aerodynamic parameters is tested using the Monte Carlo method. Simulation results under various scenarios show that compared with the terminal sliding mode method, the proposed method outperforms control accuracy and convergence speed. The root mean square errors for the angle of attack, sideslip angle, and roll angle are reduced by 65.11%, 86.71%, and 45.51%, respectively, while the standard deviation is reduced by 81.78%, 86.80%, and 45.51%, demonstrating that the proposed controller has faster convergence, higher control accuracy, and smoother output than the terminal sliding mode controller. Full article
(This article belongs to the Section Aeronautics)
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Figure 1

Figure 1
<p>Geometric parameters of the HSV model.</p>
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<p>The structure diagram of the control system.</p>
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<p>Angle of bank.</p>
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<p>Angle of attack.</p>
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<p>Sideslip angle and error.</p>
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<p>Error of bank angle.</p>
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<p>Error of attack.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>a</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>e</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Angle of bank.</p>
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<p>Angle of attack.</p>
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<p>Sideslip angle and error.</p>
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<p>Error of bank angle.</p>
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<p>Error of attack.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>a</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>e</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Aerodynamic uncertainty scatter plot.</p>
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<p>Bank angle of TSMFTC.</p>
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<p>Attack angle of TSMFTC.</p>
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<p>Sideslip angle of TSMFTC.</p>
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<p>Bank angle of AFSSOSMFTC.</p>
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<p>Attack angle of AFSSOSMFTC.</p>
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<p>Sideslip angle of AFSSOSMFTC.</p>
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<p>Angle of bank.</p>
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<p>Angle of attack.</p>
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<p>Sideslip angle and error.</p>
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<p>Error of bank angle.</p>
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<p>Error of attack.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>a</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>e</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p>
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22 pages, 8038 KiB  
Article
Fault-Tolerant Control for Quadcopters Under Actuator and Sensor Faults
by Kenji Fabiano Ávila Okada, Aniel Silva Morais, Laura Ribeiro, Caio Meira Amaral da Luz, Fernando Lessa Tofoli, Gabriela Vieira Lima and Luís Cláudio Oliveira Lopes
Sensors 2024, 24(22), 7299; https://doi.org/10.3390/s24227299 - 15 Nov 2024
Viewed by 491
Abstract
Fault detection and diagnosis (FDD) methods and fault-tolerant control (FTC) have been the focus of intensive research across various fields to ensure safe operation, reduce costs, and optimize maintenance tasks. Unmanned aerial vehicles (UAVs), particularly quadcopters or quadrotors, are often prone to faults [...] Read more.
Fault detection and diagnosis (FDD) methods and fault-tolerant control (FTC) have been the focus of intensive research across various fields to ensure safe operation, reduce costs, and optimize maintenance tasks. Unmanned aerial vehicles (UAVs), particularly quadcopters or quadrotors, are often prone to faults in sensors and actuators due to their complex dynamics and exposure to various external uncertainties. In this context, this work implements different FDD approaches based on the Kalman filter (KF) for fault estimation to achieve FTC of the quadcopter, considering different faults with nonlinear behaviors and the possibility of simultaneous occurrences in actuators and sensors. Three KF approaches are considered in the analysis: linear KF, extended KF (EKF), and unscented KF (UKF), along with three-stage and adaptive variations of the KF. FDD methods, especially the adaptive filter, could enhance fault estimation performance in the scenarios considered. This led to a significant improvement in the safety and reliability of the quadcopter through the FTC architecture, as the system, which previously became unstable in the presence of faults, could maintain stable operation when subjected to uncertainties. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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Figure 1

Figure 1
<p>Quadcopter structure and variables.</p>
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<p>Initial configuration of the quadcopter’s control system.</p>
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<p>FDD and FTC systems implemented for the quadcopter.</p>
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<p>Innovation of the fault sub-filter using ATsUKF.</p>
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<p>Estimation of sensor faults using ATsUKF.</p>
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<p>Estimation of actuator faults using ATsUKF.</p>
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<p>Displacement of the quadcopter subjected to actuator and sensor faults.</p>
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<p>Control signals generated in systems with (<b>a</b>) and without (<b>b</b>) FTC.</p>
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<p>Quadcopter displacement in the <span class="html-italic">xy</span> plane.</p>
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<p>Behavior of systems in the presence of lock-up sensor faults.</p>
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<p>Estimation of sensor lock-up faults.</p>
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<p>Behavior of systems in the presence of wind-generated disturbances.</p>
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<p>Fault estimations in (<b>a</b>) sensors and (<b>b</b>) actuators.</p>
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22 pages, 7935 KiB  
Article
Cycle Time-Based Fault Detection and Localization in Pneumatic Drive Systems
by Vladimir Boyko and Jürgen Weber
Actuators 2024, 13(11), 447; https://doi.org/10.3390/act13110447 - 7 Nov 2024
Viewed by 517
Abstract
Compressed air ranks among the most expensive forms of energy. In recent decades, increased efforts have been made to enhance the overall energy efficiency of pneumatic actuator systems and develop reliable fault detection methods for preventing energy losses. However, most of the methods [...] Read more.
Compressed air ranks among the most expensive forms of energy. In recent decades, increased efforts have been made to enhance the overall energy efficiency of pneumatic actuator systems and develop reliable fault detection methods for preventing energy losses. However, most of the methods developed so far require additional sensors, resulting in extra costs, and/or are not applicable during machine operation, which leads to their limited use in the industry. This article introduces a cycle time-based method for detecting faults in pneumatic actuators through the use of proximity switches, enabling cost-effective monitoring in real time without the necessity of further sensors. A systematic analysis is conducted, expanding the current state of knowledge by detailing the influence of all potential leakage points on the movement times of a pneumatic drive and taking into account the different velocity control strategies (meter-out and meter-in) and operating points expressed via the pneumatic frequency ratio. Previously unassessed specifics of internal leakage, including the impact of pressure profiles and differences between differential cylinders and cylinder with equal piston areas, are also presented. The applicability of the proposed method and its detection limits in an industrial environment are examined using pneumatic assembly machines. Full article
(This article belongs to the Section High Torque/Power Density Actuators)
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Figure 1

Figure 1
<p>Potential fault locations within a pneumatic drive (symbolic depiction): (1) external leakage in piston-side chamber A; (2) internal (interchamber) leakage; (3) external leakage in rod-side chamber B; (4 and 5) external leakages between the directional valve and the throttle valves; (6) increased friction.</p>
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<p>Test bench for investigating cycle time-based fault detection with corresponding fault locations.</p>
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<p>Influence of external leakage <span class="html-italic">Q<sub>ext</sub></span> = 20 L/min between cylinder and throttle check valve with meter-out throttling on cylinder pressure and position: (<b>a</b>) piston side A (fault location 1); (<b>b</b>) rod side B (fault location 3).</p>
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<p>Influence of external leakage <span class="html-italic">Q<sub>ext</sub></span> = 20 L/min between directional control valve and throttle check valve with meter-out throttling on cylinder pressure and position: (<b>a</b>) piston side A (fault location 4); (<b>b</b>) rod side B (fault location 5).</p>
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<p>Influence of internal leakage <span class="html-italic">Q<sub>int</sub></span> = 40 L/min in the cylinder (fault location 3) on the meter-out throttled cylinder’s pressure and position.</p>
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<p>Influence of increased piston friction <span class="html-italic">F<sub>add,fr</sub></span> = 20 N (fault location 6) on the meter-out throttled cylinder’s pressure and position.</p>
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<p>Equal delay in the extension and retraction time in case of internal leakage <span class="html-italic">Q<sub>int</sub></span> = 40 L/min in the rodless cylinder Festo DGC-18-200-G-PPV-A with meter-out throttling.</p>
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<p>Influence of external leakage <span class="html-italic">Q<sub>ext</sub></span> = 20 L/min between cylinder and throttle check valve with meter-in throttling on cylinder pressure and position: (<b>a</b>) piston side A (fault location 1); (<b>b</b>) rod side B (fault location 3).</p>
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<p>Influence of external leakage between directional control valve and throttle check valve with meter-in throttling on cylinder pressure and position: (<b>a</b>) piston side A (fault location 4); (<b>b</b>) rod side B (fault location 5).</p>
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<p>Influence of (<b>a</b>) internal leakage <span class="html-italic">Q<sub>int</sub></span> = 30 L/min in the cylinder (fault location 3) and (<b>b</b>) increased piston friction <span class="html-italic">F<sub>add,fr</sub></span> = 20 N (fault location 6) on the meter-in throttled cylinder’s pressure and position.</p>
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<p>Influence of the pneumatic frequency ratio <span class="html-italic">Ω</span> on changes in the movement time of the Ø25 × 50 Hoerbiger R6025/50 differential pneumatic cylinder for different fault locations and at constant fault values. Meter-out throttling: (<b>a</b>) fault location 1; (<b>b</b>) fault location 3; (<b>c</b>) fault location 4; (<b>d</b>) fault location 5; (<b>e</b>) fault location 2; (<b>f</b>) fault location 6. Meter-in throttling: (<b>g</b>) fault location 1; (<b>h</b>) fault location 3; (<b>i</b>) fault location 4; (<b>j</b>) fault location 5; (<b>k</b>) fault location 2; (<b>l</b>) fault location 6.</p>
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<p>(<b>a</b>) Influence of internal leakage on the extension time change of different pneumatic differential cylinders with meter-out throttling as a function of the pneumatic frequency ratio <span class="html-italic">Ω</span>, changes in pressure and position profiles, and interchamber flow direction in (<b>b</b>) well-sized cylinder with <span class="html-italic">Ω</span> &lt; 1.5; (<b>c</b>) well-sized cylinder with <span class="html-italic">Ω</span> = 1.5; (<b>d</b>) oversized cylinder with <span class="html-italic">Ω</span> &gt; 1.5.</p>
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<p>Influence of internal leakage on the extension time change of different pneumatic differential cylinders with meter-out throttling as a function of the mean piston velocity <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>x</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math>.</p>
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<p>Change in the movement time of the Ø25 × 50 Hoerbiger R6025/50 differential pneumatic cylinder at <span class="html-italic">Ω</span> = 1.3 as a function of leakage rate. Meter-out throttling: (<b>a</b>) fault location 1; (<b>b</b>) fault location 3; (<b>c</b>) fault location 4; (<b>d</b>) fault location 5; (<b>e</b>) fault location 2. Meter-in throttling: (<b>f</b>) fault location 1; (<b>g</b>) fault location 3; (<b>h</b>) fault location 4; (<b>i</b>) fault location 5; (<b>j</b>) fault location 2.</p>
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<p>Algorithm for time-based fault detection and localization in pneumatic drives with well-sized, double-acting differential cylinders (PFR <span class="html-italic">Ω</span> ≤ 1.5) and meter-out throttling.</p>
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<p>Algorithm for time-based fault detection and localization in pneumatic drives with oversized, double-acting differential cylinders (PFR <span class="html-italic">Ω</span> &gt; 1.5) and meter-out throttling.</p>
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<p>Algorithm for time-based fault detection and localization in pneumatic drives with double-acting differential cylinders (all PFR values) and meter-in throttling.</p>
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<p>Handling system (<b>a</b>) and its motion sequence (<b>b</b>).</p>
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<p>Changes in cycle time of pneumatic actuators and supply pressure of the handling system as well as room temperature during fault-free operation.</p>
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<p>(<b>a</b>) Pneumatic system for fully automated assembly of a fuel cell stack by XENON Automatisierungstechnik GmbH [<a href="#B39-actuators-13-00447" class="html-bibr">39</a>]; (<b>b</b>) external leakage generation at cylinder 1 (flap actuator).</p>
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<p>Above: Changes in cycle time of pneumatic actuators of the assembly machine resulting from external piston-side leakage in chamber A before and after the throttle valve; below: corresponding fault recognition paths of the algorithms.</p>
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25 pages, 20721 KiB  
Article
Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations
by Marek Moravič, Daniela Marasová, Peter Kaššay, Maksymilian Ozdoba, František Lopot and Piotr Bortnowski
Appl. Sci. 2024, 14(22), 10164; https://doi.org/10.3390/app142210164 - 6 Nov 2024
Viewed by 394
Abstract
The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim [...] Read more.
The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim of the paper is to control the dangerous vibration of a mechanical system actuator using a pneumatic elastic coupling using different approaches such as analytical calculations, experimental measurement results, and simulation models. Based on the known mechanical properties of the laboratory system, its dynamic model in the form of a twelve-mass chain torsionally oscillating mechanical system is developed. Subsequently, the model is reduced to a two-mass system using the method of partial frequencies according to Rivin. The total load torque of the piston compressor under fault-free and fault conditions is simulated to obtain the amplitudes and phases of the harmonic components of the dynamic torque. After calculating the natural frequency and the natural shape of the oscillation, the Campbell diagram is processed to determine the critical revolutions. There is a pneumatic flexible coupling between the rotating masses, which changes the dynamic torsional stiffness. The dynamic torque curves transmitted by the coupling are compared with different dynamic torsional stiffnesses during steady-state operation and one cylinder failure. The monitored values are the position of the critical revolutions, the natural frequency, the natural shape of the oscillation, and the RMS of the dynamic load torque. The experimental model is verified by the simulation model. The accuracy of the developed simulation model with the experimental data are apparently very good (even more than 99% of the critical revolutions value obtained by calculation); however, it depends on the dynamic stiffness of the coupling. In this study, a detailed, comprehensive approach combining analytical procedures with simulation models is presented. Experimental data are verified with simulation results, which show a good agreement in the case of 700 kPa coupling pressure. The inaccuracy of some of the experiments (at 300 and 500 kPa pressures) is due to the interaction of the coupling’s apparent stiffness and the level of the damped vibration energy in the coupling, which is manifested by its different heating. Based on further experiments, a solution to these problems will be proposed by introducing this phenomenon effectively into the simulation model. Full article
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Figure 1
<p>Research methodology.</p>
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<p>Experimental model of a mechanical system: 1—electric motor, 2—gearbox, 3—torque sensor, 4—bearing housing, 5—pneumatic flexible coupling, 6—three-cylinder piston compressor, 7—rotation supply.</p>
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<p>Time record from an experiment measurement in the CatmanEasy program.</p>
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<p>A complete replacement dynamic piston compressor drive model.</p>
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<p>A twelve-mass chain mechanical system.</p>
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<p>Two-mass reduced mechanical system.</p>
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<p>Mode shape of the strain curve for <span class="html-italic">Ω</span><sub>0</sub> = 201.431 rad·s<sup>−1</sup>.</p>
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<p>Campbell diagram of the mechanical system studied.</p>
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<p><span class="html-italic">p</span>-<span class="html-italic">V</span> diagram of piston compressor cylinder.</p>
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<p>The total load torque <span class="html-italic">M<sub>C</sub></span> vs. the rotation angle of the crankshaft of the piston compressor and its static component <span class="html-italic">M<sub>S</sub></span>.</p>
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<p>Development over time of dynamic torque transmitted by a pneumatic flexible coupling at pressure 700 kPa.</p>
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<p>Hysteresis loop of flexible pneumatic coupling at pressure 700 kPa.</p>
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<p>Dynamic load torque transmitted by the flexible pneumatic coupling at pressure 700 kPa.</p>
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<p>The effective value of the dynamic component of the torque <span class="html-italic">RMS M<sub>D</sub></span> transmitted by the pneumatic flexible coupling at pressure 700 kPa.</p>
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<p>Total load torque <span class="html-italic">M<sub>C</sub></span> depending on the angle of rotation of the <span class="html-italic">α</span> crankshaft when the cylinder of the piston compressor is out of operation and its static component <span class="html-italic">M<sub>S</sub></span>.</p>
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<p>Development over time of the dynamic torque <span class="html-italic">M<sub>DS</sub></span> transmitted by a pneumatic flexible coupling at pressure 700 kPa with the cylinder out of operation.</p>
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<p>Pneumatic flexible coupling hysteresis loop at pressure 700 kPa with the cylinder out of operation.</p>
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<p>Dynamic torque <span class="html-italic">M<sub>DS</sub></span> transmitted by pneumatic flexible coupling at pressure 700 kPa with the cylinder is out of operation.</p>
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<p>Effective value of the dynamic component of the load torque <span class="html-italic">RMS M<sub>DS</sub></span> transmitted by a pneumatic flexible coupling at pressure 700 kPa with the cylinder out of operation.</p>
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<p>Signal (<b>a</b>) and Hamming window (<b>b</b>) at coupling pressure <span class="html-italic">p<sub>S</sub></span> = 700 kPa and revolutions <span class="html-italic">n</span> = 500 min<sup>−1</sup>.</p>
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<p>Spectrum from the signal (<b>a</b>) and Hamming window (<b>b</b>).</p>
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<p>Campbell diagram of the mechanical system from the measured values.</p>
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<p>Development of the static component of load torque <span class="html-italic">M<sub>S</sub></span> depending on the engine revolutions <span class="html-italic">n</span> at pressure 700 kPa.</p>
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<p>Effective value of the dynamic component of the load torque <span class="html-italic">RMS M<sub>D</sub></span> of the pneumatic flexible coupling at pressure 700 kPa vs. the engine revolutions <span class="html-italic">n</span> – steady state.</p>
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<p>Effective value of the dynamic component of the load torque <span class="html-italic">RMS M<sub>D</sub></span> of the pneumatic flexible coupling at pressure 700 kPa vs. the engine revolutions <span class="html-italic">n</span> with the cylinder out of operation.</p>
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<p>Frequency analysis using a Hamming window at <span class="html-italic">n</span> = 500 min<sup>−1</sup> at steady operation.</p>
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<p>Frequency analysis using a Hamming window at <span class="html-italic">n</span> = 500 min<sup>−1</sup> and one cylinder out of operation.</p>
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<p>Comparison of the characteristics at steady operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 700 kPa.</p>
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<p>Comparison of the characteristics at one cylinder out of operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 700 kPa.</p>
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<p>Comparison of the characteristics at steady operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 500 kPa.</p>
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<p>Comparison of the characteristics at one cylinder out of operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 500 kPa.</p>
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<p>Comparison of the characteristics at steady operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 300 kPa.</p>
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<p>Comparison of the characteristics at one cylinder out of operation of a piston compressor—pressure in the elastic element of the coupling <span class="html-italic">p<sub>S</sub></span> = 300 kPa.</p>
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29 pages, 4318 KiB  
Article
Adaptive Integral Sliding Mode Control with Chattering Elimination Considering the Actuator Faults and External Disturbances for Trajectory Tracking of 4Y Octocopter Aircraft
by Samir Zeghlache, Hilal Rahali, Ali Djerioui, Hemza Mekki, Loutfi Benyettou and Mohamed Fouad Benkhoris
Processes 2024, 12(11), 2431; https://doi.org/10.3390/pr12112431 - 4 Nov 2024
Viewed by 715
Abstract
This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control [...] Read more.
This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings. Full article
(This article belongs to the Special Issue Fuzzy Control System: Design and Applications)
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Figure 1
<p>The 4Y octocopter aircraft configuration [<a href="#B16-processes-12-02431" class="html-bibr">16</a>], (<b>a</b>) Real 4Y octocopter (<b>b</b>) 4Y octocopter configuration.</p>
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<p>Controlling the motion of the 4Y octocopter aircraft utilizing virtual control.</p>
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<p>Overview of the developed fault-tolerant control.</p>
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<p>Architecture of a type-2 fuzzy logic system.</p>
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<p>Interval type-2 Gaussian membership functions for the antecedent sets.</p>
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<p>The membership functions of input variables <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> </mrow> </semantics></math> and output <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mo> </mo> <msub> <mi>u</mi> <mi>i</mi> </msub> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>6</mn> </mrow> </semantics></math>.</p>
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<p>Block diagram of the proposed control algorithm.</p>
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<p>(<span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span>) positions and yaw angle (<span class="html-italic">ψ</span>) outputs of the 4Y octocopter aircraft in the presence of actuator faults and external disturbances (Scenario 1)). (<b>a</b>) Evolution of x real vs. x desired (<b>b</b>) Evolution of x real vs. y desired (<b>c</b>) Evolution of z real vs. z desired (<b>d</b>) Evolution of ksi real vs. ksi desired.</p>
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<p>Roll and pitch angles (<span class="html-italic">φ</span>, <span class="html-italic">θ</span>) of the 4Y octocopter aircraft in the presence of actuator faults and external disturbances (Scenario 1).(<b>a</b>) Evolution of phi angle (<b>b</b>) Evolution of theta angle.</p>
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<p>The input forces of the 4Y octocopter aircraft (Scenario 1). (<b>a</b>) Evolution of input F1 (<b>b</b>) Evolution of input F2 (<b>c</b>) Evolution of input F3 (<b>d</b>) Evolution of input F4 (<b>e</b>) Evolution of input F5 (<b>f</b>) Evolution of input F6 (<b>g</b>) Evolution of input F7 (<b>h</b>) Evolution of input F8.</p>
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<p>3D position tracking result of the 4Y octocopter aircraft (Scenario 1).</p>
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<p>3D position tracking result of the 4Y octocopter aircraft (Scenario 1). (<b>a</b>) Evolution of x real vs. x desired (<b>b</b>) Evolution of x real vs. y desired (<b>c</b>) Evolution of z real vs. z desired (<b>d</b>) Evolution of ksi real vs. ksi desired.</p>
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<p>Roll and pitch angles (<span class="html-italic">φ</span>, <span class="html-italic">θ</span>) of the 4Y octocopter aircraft in the presence of actuator faults and external disturbances (Scenario 2). (<b>a</b>) Evolution of phi angle (<b>b</b>) Evolution of th et a angle.</p>
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<p>The input forces of the 4Y octocopter aircraft (Scenario 2). (<b>a</b>) Evolution of input F1 (<b>b</b>) Evolution of input F2 (<b>c</b>) Evolution of input F3 (<b>d</b>) Evolution of input F4.</p>
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<p>3D position tracking result of the 4Y octocopter aircraft (Scenario 2).</p>
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24 pages, 14320 KiB  
Article
Localized Bearing Fault Analysis for Different Induction Machine Start-Up Modes via Vibration Time–Frequency Envelope Spectrum
by Jose E. Ruiz-Sarrio, Jose A. Antonino-Daviu and Claudia Martis
Sensors 2024, 24(21), 6935; https://doi.org/10.3390/s24216935 - 29 Oct 2024
Viewed by 562
Abstract
Bearings are the most vulnerable component in low-voltage induction motors from a maintenance standpoint. Vibration monitoring is the benchmark technique for identifying mechanical faults in rotating machinery, including the diagnosis of bearing defects. The study of different bearing fault phenomena under induction motor [...] Read more.
Bearings are the most vulnerable component in low-voltage induction motors from a maintenance standpoint. Vibration monitoring is the benchmark technique for identifying mechanical faults in rotating machinery, including the diagnosis of bearing defects. The study of different bearing fault phenomena under induction motor transient conditions offers interesting capabilities to enhance classic fault detection techniques. This study analyzes the low-frequency localized bearing fault signatures in both the inner and outer races during the start-up and steady-state operation of inverter-fed and line-started induction motors. For this aim, the classic vibration envelope spectrum technique is explored in the time–frequency domain by using a simple, resampling-free, Short Time Fourier Transform (STFT) and a band-pass filtering stage. The vibration data are acquired in the motor housing in the radial direction for different load points. In addition, two different localized defect sizes are considered to explore the influence of the defect width. The analysis of extracted low-frequency characteristic frequencies conducted in this study demonstrates the feasibility of detecting early-stage localized bearing defects in induction motors across various operating conditions and actuation modes. Full article
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<p>(<b>a</b>) Expanded deep-groove ball bearings view, (<b>b</b>) bearing geometry including numbering of rolling elements (i.e., 1 to 9 numbers) and main dimensions.</p>
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<p>Defect ratio graphic description.</p>
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<p>Bearing defect vibration signal <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and its envelope.</p>
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<p>Signal processing pipeline graphic description with an inner race defect example.</p>
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<p>Induction motor specimen cross-section.</p>
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<p>Test bench graphic description. (1) Induction machine including faulty bearing, (2) DC generator imposing constant resistant torque, (3) flexible coupling.</p>
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<p>Accelerometer locus description. (<b>a</b>) Vertical xy-plane, (<b>b</b>) horizontal xz-plane.</p>
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<p>Bearing defect description. (<b>a</b>) Healthy, (<b>a</b>) 0.5 mm inner race defect, (<b>c</b>) 1 mm inner race defect, (<b>d</b>) 0.5 mm outer race defect, (<b>e</b>) 1 mm outer race defect.</p>
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<p>Line-fed induction machine startup vibration signal at 12 o’clock for (<b>a</b>) rated line-to-line voltage, (<b>b</b>) 50% rated line-to-line voltage.</p>
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<p>Vibration envelope spectrum analysis acquired at 12 o’clock position at rated slip, (<b>a</b>) healthy, (<b>b</b>) 0.5 mm outer race defect, (<b>c</b>) 1 mm outer race defect, (<b>d</b>) 0.5 mm inner race defect, (<b>e</b>) 1 mm inner race defect.</p>
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<p>Vibration amplitude comparison among two defect widths. Signals acquired at 12 o’clock at rated slip. (<b>a</b>) Outer race defects, (<b>b</b>) inner race defects.</p>
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<p>Healthy bearing at rated slip, (<b>a</b>) line-started 100% rated voltage, (<b>b</b>) line-started 50% rated voltage, (<b>c</b>) VFD-fed 20 s ramp, (<b>d</b>) VFD-fed 5 s ramp.</p>
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<p>Outer race 0.5 mm defect at rated slip, (<b>a</b>) line-started 100% rated voltage, (<b>b</b>) line-started 50% rated voltage, (<b>c</b>) VFD-fed 20 s ramp, (<b>d</b>) VFD-fed 5 s ramp.</p>
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<p>Outer race 1 mm defect at rated slip, (<b>a</b>) line-started 100% rated voltage, (<b>b</b>) line-started 50% rated voltage, (<b>c</b>) VFD-fed 20 s ramp, (<b>d</b>) VFD-fed 5 s ramp.</p>
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<p>Inner race 0.5 mm defect at rated slip, (<b>a</b>) line-started 100% rated voltage, (<b>b</b>) line-started 50% rated voltage, (<b>c</b>) VFD-fed 20 s ramp, (<b>d</b>) VFD-fed 5 s ramp.</p>
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<p>Inner race 1 mm defect at rated slip, (<b>a</b>) line-started 100% rated voltage, (<b>b</b>) line-started 50% rated voltage, (<b>c</b>) VFD-fed 20 s ramp, (<b>d</b>) VFD-fed 5 s ramp.</p>
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<p>Load dependency steady-state analysis. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>B</mi> <mi>F</mi> <mi>O</mi> </mrow> </msub> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>f</mi> <mrow> <mi>B</mi> <mi>F</mi> <mi>O</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>B</mi> <mi>F</mi> <mi>I</mi> </mrow> </msub> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>f</mi> <mrow> <mi>B</mi> <mi>F</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Load variation analysis during the line-started excitation mode at 50% rated line-to-line voltage. Vibration signals acquired at 12 o’clock. (<b>a</b>) Healthy bearing, (<b>b</b>) outer race 0.5 mm defect, (<b>c</b>) outer race 1 mm defect, (<b>d</b>) inner race 0.5 mm defect, (<b>e</b>) inner race 1 mm defect.</p>
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<p>Load variation analysis during the VFD-fed excitation mode with 20 s ramp duration. (<b>a</b>) Healthy, (<b>b</b>) outer race 0.5 mm defect, vibration signals acquired at 12 o’clock, (<b>c</b>) outer race 1 mm defect, (<b>d</b>) inner race 0.5 mm defect, (<b>e</b>) inner race 1 mm defect.</p>
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<p>HUST dataset experimental test bench description [<a href="#B53-sensors-24-06935" class="html-bibr">53</a>].</p>
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<p>VFD-fed start-ups for inner and outer race defects, (<b>a</b>) HUST dataset inner race defect, (<b>b</b>) custom dataset inner race defect, (<b>c</b>) HUST dataset outer race defect, (<b>d</b>) custom dataset outer race defect.</p>
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18 pages, 1971 KiB  
Article
Comprehensive Analysis and Reconstruction of Sensor Faults in Interleaved Buck Converters Using Sliding Mode Observers
by Eduardo Maximiliano Asensio, Ken King Man Siu, Juan Carlos Astrada, Federico Martín Serra and Cristian Hernán De Angelo
Electronics 2024, 13(21), 4202; https://doi.org/10.3390/electronics13214202 - 26 Oct 2024
Viewed by 539
Abstract
This paper presents a fault signal reconstruction method for current sensors in an interleaved buck DC–DC converter, utilizing a sliding mode observer (SMO). A filter bank is used to design the observer within an extended-order system, effectively treating sensor faults as actuator faults, [...] Read more.
This paper presents a fault signal reconstruction method for current sensors in an interleaved buck DC–DC converter, utilizing a sliding mode observer (SMO). A filter bank is used to design the observer within an extended-order system, effectively treating sensor faults as actuator faults, which enables precise estimation of the fault signal. Thus, the proposed approach allows for the identification of the faulty sensor and supports the implementation of fault-tolerant strategies. The paper provides an in-depth analysis of current sensor faults, verifies their impact on current balancing control, and demonstrates the challenge of achieving error-free current estimation in one phase using observers. A comprehensive set of simulation results is carried out, validating the method’s effectiveness and showing a strong correlation with theoretical principles. Full article
(This article belongs to the Section Power Electronics)
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<p>Diagram of an N-phase interleaved buck converter.</p>
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<p>Trajectory of adopted sliding mode control.</p>
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<p>Impact of sensor failure on current balancing control.</p>
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<p>Effects of the fault in current estimation of <math display="inline"><semantics> <msub> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>: (<b>a</b>) measured phase 1 current <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math>, actual phase 1 current <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, reference current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>ref</mi> </msub> </semantics></math>, and estimated current <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </mrow> </semantics></math>; (<b>b</b>) measured and actual phase 2 current, <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics></math>, respectively; (<b>c</b>) faults induced in the phase 1 and phase 2 sensors, <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>2</mn> </msub> </semantics></math>, respectively.</p>
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<p>Scheme of the Fault Reconstruction Strategy.</p>
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<p>Fault reconstruction when a failure in sensor 1 occurs: (<b>a</b>) measured phase 1 current <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math>, actual phase 1 current <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, reference current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>ref</mi> </msub> </semantics></math>, and estimated current <math display="inline"><semantics> <msub> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>; (<b>b</b>) measured and actual phase 2 current, <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics></math>, respectively; (<b>c</b>) measured and actual phase 3 current, <math display="inline"><semantics> <mrow> <msup> <mi>i</mi> <mi>M</mi> </msup> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </msub> </semantics></math>, respectively; (<b>d</b>) fault induced in the phase 1 <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math> and its reconstruction <math display="inline"><semantics> <msub> <mover accent="true"> <mi>γ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Fault reconstruction when a simultaneous failure occurs in sensors 1 and 2: (<b>a</b>) measured phase 1 current <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math>, actual phase 1 current <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, reference current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>ref</mi> </msub> </semantics></math>, and estimated current <math display="inline"><semantics> <msub> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>; (<b>b</b>) measured and actual phase 2 currents, <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics></math>, respectively; (<b>c</b>) measured and actual phase 3 currents, <math display="inline"><semantics> <mrow> <msup> <mi>i</mi> <mi>M</mi> </msup> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </msub> </semantics></math>, respectively; (<b>d</b>) faults induced in phases 1 (black line) and 3 (black dashed line), <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>3</mn> </msub> </semantics></math> and their reconstruction <math display="inline"><semantics> <msub> <mover accent="true"> <mi>γ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </semantics></math> (red line) and <math display="inline"><semantics> <msub> <mover accent="true"> <mi>γ</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> </semantics></math> (red dashed line).</p>
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<p>Tolerant strategy when a failure in sensor 1 occurs: (<b>a</b>) measured phase 1 current <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math>, actual phase 1 current <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, reference current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>ref</mi> </msub> </semantics></math>, and estimated current <math display="inline"><semantics> <msub> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>; (<b>b</b>) measured and actual phase 2 currents, <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics></math>, respectively; (<b>c</b>) measured and actual phase 3 currents, <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </msub> </semantics></math>, respectively; (<b>d</b>) fault induced in the phase 1 <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math> and its reconstruction <math display="inline"><semantics> <msub> <mover accent="true"> <mi>γ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Results under parametric variations and load change: (<b>a</b>) measured phase 1 current <math display="inline"><semantics> <msubsup> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> </semantics></math>, actual phase 1 current <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, reference current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>ref</mi> </msub> </semantics></math>, and estimated current <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>L</mi> <mo>,</mo> <mn>1</mn> </mrow> </mrow> </semantics></math>; (<b>b</b>) measured and actual phase 2 currents, <math display="inline"><semantics> <mrow> <msup> <mi>i</mi> <mi>M</mi> </msup> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics></math>, respectively; (<b>c</b>) measured and actual phase 3 currents, <math display="inline"><semantics> <mrow> <msup> <mi>i</mi> <mi>M</mi> </msup> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>L</mi> <mo>,</mo> <mn>3</mn> </mrow> </msub> </semantics></math>, respectively; (<b>d</b>) fault induced in the phase 1 <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math> and its reconstruction <math display="inline"><semantics> <msub> <mover accent="true"> <mi>γ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </semantics></math>.</p>
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30 pages, 858 KiB  
Article
Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay
by Omayma Mansouri, Ali Ben Brahim, Fayçal Ben Hmida and Anis Sellami
Math. Comput. Appl. 2024, 29(6), 96; https://doi.org/10.3390/mca29060096 - 26 Oct 2024
Viewed by 536
Abstract
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states [...] Read more.
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the H criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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<p>Separated Design FTC.</p>
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<p>Integrated design of FTC.</p>
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<p>The air path system of diesel engines.</p>
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<p>Estimation of actuator fault: Actuator fault estimation without FTC (blue line), actuator fault estimation with the separated FTC (red line), and actuator fault estimation with the integrated FTC (green line).</p>
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<p>First closed-loop system output response: output response with the separated FTC (red line) and output response with the integrated FTC (green line).</p>
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<p>Second closed-loop system output response: output response with the separated FTC (red line) and output response with the integrated FTC (green line).</p>
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<p>First output estimation error: First output estimation error with the separated FTC (red line) and the first output estimation error with the integrated FTC (green line).</p>
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<p>Second output estimation error: Second output estimation error with the separated FTC (red line) and second output estimation error with the integrated FTC (green line).</p>
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<p>Effect of increasing constant <math display="inline"><semantics> <mi>τ</mi> </semantics></math> on actuator fault reconstruction (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> red line), (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> green line), (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> brown line).</p>
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<p>Actuator fault estimation without FTC (blue line), actuator fault estimation with state feedback in [<a href="#B26-mca-29-00096" class="html-bibr">26</a>] (red line), and actuator fault estimation with the integrated FTC (green line).</p>
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24 pages, 5970 KiB  
Article
Adaptive Fault-Tolerant Control of Mobile Robots with Fractional-Order Exponential Super-Twisting Sliding Mode
by Hao Wu, Shuting Wang, Yuanlong Xie and Hu Li
Fractal Fract. 2024, 8(10), 612; https://doi.org/10.3390/fractalfract8100612 - 19 Oct 2024
Viewed by 583
Abstract
Industrial mobile robots easily experience actuator loss of some effectiveness and additive bias faults due to the working scenarios, resulting in unexpected performance degradation. This article proposes a novel adaptive fault-tolerant control (FTC) strategy for nonholonomic mobile robot systems subject to simultaneous actuator [...] Read more.
Industrial mobile robots easily experience actuator loss of some effectiveness and additive bias faults due to the working scenarios, resulting in unexpected performance degradation. This article proposes a novel adaptive fault-tolerant control (FTC) strategy for nonholonomic mobile robot systems subject to simultaneous actuator lock-in-place (LIP) and partial loss-of-effectiveness (LOE) faults. First, a nominal fractional-order sliding mode controller based on the designed exponential super-twisting reaching law is investigated to reduce the reaching phase time and eliminate the chattering. To address the time-varying LIP faults and uncertainties, a novel barrier function (BF)-based gain is explored to assist the super-twisting law. An estimator is designed to estimate the lower bound of the time-varying partial LOE fault coefficients, thus without requiring the boundary information of faults that is commonly requested in traditional FTC schemes. Combined with the nominal controller clubbed with BF and estimator-based LOE fault compensation term, the fault-tolerant controller is finally constructed. The proposed FTC scheme achieves fast convergence and the sliding variables can be confined in a predetermined neighborhood of the sliding manifold under actuator faults. The results show that the proposed controller has superior tracking performance under faulty conditions compared with other state-of-the-art adaptive FTC approaches. Full article
(This article belongs to the Section Engineering)
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<p>Overall control framework of the proposed adaptive FTC scheme.</p>
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<p>The prototype of the developed NMR.</p>
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<p>Hardware architecture of the developed NMR.</p>
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<p>The implementation procedure of the proposed CFSMC BF-FOESTSMC scheme.</p>
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<p>Case 1: Position tracking performance of compared schemes and the proposed FTC.</p>
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<p>Case 1: State tracking errors. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>x</mi> <mi>e</mi> </msub> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>y</mi> <mi>e</mi> </msub> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>ς</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Case 1: Sliding variables. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>|</mo> <mi>σ</mi> <mo>|</mo> <mo>|</mo> </mrow> </semantics></math>.</p>
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<p>Case 1: Control outputs. (<b>a</b>) MESFTC. (<b>b</b>) SFTSMC. (<b>c</b>) proposed controller.</p>
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<p>Case 2: Position tracking performance of compared schemes and the proposed FTC.</p>
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<p>Case 2: State tracking errors. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>x</mi> <mi>e</mi> </msub> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>y</mi> <mi>e</mi> </msub> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>ς</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Case 2: Sliding variables. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>|</mo> <mi>σ</mi> <mo>|</mo> <mo>|</mo> </mrow> </semantics></math>.</p>
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<p>Case 2: Control outputs. (<b>a</b>) MESFTC. (<b>b</b>) SFTSMC. (<b>c</b>) proposed controller.</p>
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29 pages, 12513 KiB  
Article
UAV Trajectory Tracking Using Proportional-Integral-Derivative-Type-2 Fuzzy Logic Controller with Genetic Algorithm Parameter Tuning
by Oumaïma Moali, Dhafer Mezghani, Abdelkader Mami, Abdelatif Oussar and Abdelkrim Nemra
Sensors 2024, 24(20), 6678; https://doi.org/10.3390/s24206678 - 17 Oct 2024
Viewed by 642
Abstract
Unmanned Aerial Vehicle (UAV)-type Quadrotors are highly nonlinear systems that are difficult to control and stabilize outdoors, especially in a windy environment. Many algorithms have been proposed to solve the problem of trajectory tracking using UAVs. However, current control systems face significant hurdles, [...] Read more.
Unmanned Aerial Vehicle (UAV)-type Quadrotors are highly nonlinear systems that are difficult to control and stabilize outdoors, especially in a windy environment. Many algorithms have been proposed to solve the problem of trajectory tracking using UAVs. However, current control systems face significant hurdles, such as parameter uncertainties, modeling errors, and challenges in windy environments. Sensitivity to parameter variations may lead to performance degradation or instability. Modeling errors arise from simplifications, causing disparities between assumed and actual behavior. Classical controls may lack adaptability to dynamic changes, necessitating adaptive strategies. Limited robustness in handling uncertainties can result in suboptimal performance. Windy environments introduce disturbances, impacting system dynamics and precision. The complexity of wind modeling demands advanced estimation and compensation strategies. Tuning challenges may necessitate frequent adjustments, posing practical limitations. Researchers have explored advanced control paradigms, including robust, adaptive, and predictive control, aiming to enhance system performance amidst uncertainties in a scientifically rigorous manner. Our approach does not require knowledge of UAVs and noise models. Furthermore, the use of the Type-2 controller makes our approach robust in the face of uncertainties. The effectiveness of the proposed approach is clear from the obtained results. In this paper, robust and optimal controllers are proposed, validated, and compared on a quadrotor navigating an outdoor environment. First, a Type-2 Fuzzy Logic Controller (FLC) combined with a PID is compared to a Type-1 FLC and Backstepping controller. Second, a Genetic Algorithm (GA) is proposed to provide the optimal PID-Type-2 FLC tuning. The Backstepping, PID-Type-1 FLC, and PID-Type-2 FLC with GA optimization are validated and evaluated with real scenarios in a windy environment. Deep robustness analysis, including error modeling, parameter uncertainties, and actuator faults, is considered. The obtained results clearly show the robustness of the optimal PID-Type-2 FLC compared to the Backstepping and PID-Type-1 FLC controllers. These results are confirmed by the numerical index of each controller compared to the PID-type-2 FLC, with 12% for the Backstepping controller and 51% for the PID-Type-1 FLC. Full article
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<p>UAV classification.</p>
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<p>Quadrotor configuration [<a href="#B18-sensors-24-06678" class="html-bibr">18</a>].</p>
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<p>Control architecture of the quadrotor [<a href="#B21-sensors-24-06678" class="html-bibr">21</a>].</p>
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<p>Global model proposed for controller system for quadrotor.</p>
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<p>Type-1 fuzzy logic controller.</p>
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<p>Membership function of Type-1-FLC: (<b>a</b>) first input (e); (<b>b</b>) second input (de).</p>
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<p>Model of membership function for Type-2 FLC.</p>
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<p>Type-2 fuzzy logic controller.</p>
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<p>Membership function of Type-2-FLC: (<b>a</b>) first input (e); (<b>b</b>) second input (de).</p>
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<p>Quadrotor control scheme with GA optimization.</p>
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<p>Generic algorithm cycle.</p>
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<p>Architecture of optimization strategy for Type-1 FLC and Type-2 FLC using GA.</p>
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<p>GA optimization step diagram.</p>
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<p>Trajectory of simulation.</p>
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<p>Quadrotor commands of Backstepping control.</p>
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<p>Motor velocities of Backstepping control.</p>
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<p><span class="html-italic">x</span>, <span class="html-italic">y</span>, z errors evolution of Backstepping control.</p>
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<p>Quadrotor angles of Backstepping control.</p>
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<p>Quadrotor commands of Type-1 FLC.</p>
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<p>Motor velocities of Type-1 FLC.</p>
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<p><span class="html-italic">x</span>, <span class="html-italic">y</span>, z error evolution of Type-1 FLC.</p>
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<p>Quadrotor angles of Type-1 FLC.</p>
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<p>Quadrotor commands of Type-2 FLC.</p>
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<p>Motor velocities of Type-2 FLC.</p>
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<p><span class="html-italic">x</span>, <span class="html-italic">y</span>, z error evolution of Type-2 FLC.</p>
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<p>Quadrotor angles of Type-2 FLC.</p>
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<p>Quadrotor trajectory for proposed controllers.</p>
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<p>The errors of X, Y, and Z position using the PID-Type-1 FLC controller with GA.</p>
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<p>Quadrotor angles of PID-Type-1 FLC controller with GA.</p>
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<p>Quadrotor commands of PID-Type-1 FLC controller with GA.</p>
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<p>Motor velocities of PID-Type-1 FLC controller with GA.</p>
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<p>The errors of X, Y, and Z for the PID-Type-2 FLC controller with GA.</p>
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<p>Quadrotor angles of PID-Type-2 FLC controller with GA.</p>
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<p>Quadrotor commands of PID-Type-2 FLC controller with GA.</p>
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<p>Motor velocities of PID-Type-2 FLC controller with GA.</p>
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<p>Quadrotor trajectory for PID-Type-1 FLC and PID-Type-2 FLC controllers with GA optimization.</p>
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<p>Wind velocity for scenario 2.</p>
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<p>Quadrotor trajectory for scenario 2.</p>
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<p>The errors of X, Y, and Z for PID-Type-2 FLC scenario 2.</p>
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<p>The errors of X, Y, and Z for PID FLC scenario 2.</p>
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<p>The errors of X, Y, and Z for Backstepping controller scenario 2.</p>
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18 pages, 5244 KiB  
Article
Unified Fault-Tolerant Control and Adaptive Velocity Planning for 4WID-4WIS Vehicles under Multi-Fault Scenarios
by Ao Lu and Guangyu Tian
Actuators 2024, 13(10), 407; https://doi.org/10.3390/act13100407 - 7 Oct 2024
Viewed by 772
Abstract
Four-wheel independent drive and four-wheel independent steering (4WID-4WIS) vehicles provide increased redundancy in fault-tolerant control (FTC) schemes, enhancing heterogeneous fault-tolerant capabilities. This paper addresses the challenge of maintaining vehicle safety and maneuverability in the presence of actuator faults in autonomous vehicles, focusing on [...] Read more.
Four-wheel independent drive and four-wheel independent steering (4WID-4WIS) vehicles provide increased redundancy in fault-tolerant control (FTC) schemes, enhancing heterogeneous fault-tolerant capabilities. This paper addresses the challenge of maintaining vehicle safety and maneuverability in the presence of actuator faults in autonomous vehicles, focusing on 4WID-4WIS systems. A novel unified hierarchical active FTC strategy is proposed to handle various actuator failures. The strategy includes an upper-layer motion controller that determines resultant force requirements based on trajectory tracking errors and a middle-layer allocation system that redistributes tire forces to fault-free actuators using fault information. This study, for the first time, considers multi-fault scenarios involving longitudinal and lateral coupling, calculating FTC boundaries for each fault type. Additionally, a fault tolerance index is introduced for 256 fault scenarios, using singular value decomposition to linearly represent the vehicle attainable force domain. Based on this, an adaptive velocity planning strategy is developed to balance safety and maneuverability under fault conditions. Matlab 2021a/Simulink and Carsim 2019 co-simulation results validate the proposed strategies, demonstrating significant improvements in fault-tolerant performance, particularly in complex and emergency scenarios. Full article
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<p>The vehicle dynamic model and the trajectory tracking model.</p>
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<p>The hierarchical architecture of unified FTC.</p>
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<p>The ratio of vehicle attainable force volumes under different numbers of faults. The fault index is arranged in lexicographical order from 1 to 255, based on the number of faults and the order of actuators, from smallest to largest.</p>
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<p>Fitting results of the attainable force volume ratio and the fault tolerance index under static load conditions for various vehicle fault states.</p>
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<p>Tracking performance in DLC under fault 1-3-4.</p>
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<p>Course angle tracking error in DLC under fault 1-3-4.</p>
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<p>Sideslip angle tracking error in DLC under fault 1-3-4.</p>
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<p>Four-wheel torque commands under four control strategies. (<b>a</b>) Front left wheel. (<b>b</b>) Front right wheel. (<b>c</b>) Rear left wheel. (<b>d</b>) Rear right wheel.</p>
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<p>Four-wheel steering angle commands under four control strategies. (<b>a</b>) Front left wheel. (<b>b</b>) Front right wheel. (<b>c</b>) Rear left wheel. (<b>d</b>) Rear right wheel.</p>
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<p>Target and actual velocities under no AVP.</p>
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<p>Target and actual velocities under AVP.</p>
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<p>The DLC trajectory tracking performance under no FTC.</p>
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<p>The DLC trajectory tracking performance under FTC-Comparison.</p>
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<p>The DLC trajectory tracking performance under FTC.</p>
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<p>The DLC trajectory tracking performance under FTC-AVP.</p>
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17 pages, 4904 KiB  
Article
Development of a Digital Twin Driven by a Deep Learning Model for Fault Diagnosis of Electro-Hydrostatic Actuators
by Roman Rodriguez-Aguilar, Jose-Antonio Marmolejo-Saucedo and Utku Köse
Mathematics 2024, 12(19), 3124; https://doi.org/10.3390/math12193124 - 6 Oct 2024
Viewed by 678
Abstract
The first quarter of the 21st century has witnessed many technological innovations in various sectors. Likewise, the COVID-19 pandemic triggered the acceleration of digital transformation in organizations driven by artificial intelligence and communication technologies in Industry 4.0 and Industry 5.0. Aiming at the [...] Read more.
The first quarter of the 21st century has witnessed many technological innovations in various sectors. Likewise, the COVID-19 pandemic triggered the acceleration of digital transformation in organizations driven by artificial intelligence and communication technologies in Industry 4.0 and Industry 5.0. Aiming at the construction of digital twins, virtual representations of a physical system allow real-time bidirectional communication. This will allow the monitoring of operations, identification of possible failures, and decision making based on technical evidence. In this study, a fault diagnosis solution is proposed, based on the construction of a digital twin, for a cloud-based Industrial Internet of Things (IIoT) system contemplating the control of electro-hydrostatic actuators (EHAs). The system was supported by a deep learning model using Long Short-Term Memory (LSTM) networks for an effective diagnostic approach. The implemented study considers data preparation and integration and system development and application to evaluate the performance against the fault diagnosis problem. According to the results obtained, positive results are shown in the construction of the digital twin using a deep learning model for the fault diagnosis problem of an active EHA-IIoT configuration. Full article
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<p>A general scheme regarding the solution implemented.</p>
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<p>Architecture of Long-Short Term Memory (LSTM) [<a href="#B74-mathematics-12-03124" class="html-bibr">74</a>].</p>
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<p>A general scheme for the control of an electro-hydrostatic actuator (EHA) [<a href="#B29-mathematics-12-03124" class="html-bibr">29</a>].</p>
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<p>The general system structure: (<b>a</b>) IIoT approach, (<b>b</b>) LSTM localization, (<b>c</b>) digital twin user interface, (<b>d</b>) sample state graphics seen in real time for <math display="inline"><semantics> <mrow> <mi>I</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>r</mi> <mi>s</mi> </mrow> </semantics></math> (green: normal state, blue; minor fault state, orange: medium fault state, red: mjor fault state), (<b>e</b>) optimization module, and (<b>f</b>) simulation module (AnyLogic<sup>®</sup>).</p>
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<p>Fault state values by training–testing data sets.</p>
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<p>LSTM model results (Data Set A). The green color corresponds to a correct classification and the red color to a classification in the incorrect category.</p>
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<p>LSTM model results (Data Set B). The green color corresponds to a correct classification and the red color to a classification in the incorrect category.</p>
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<p>LSTM model results (Data Set C). The green color corresponds to a correct classification and the red color to a classification in the incorrect category.</p>
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<p>LSTM model results (Data Set D). The green color corresponds to a correct classification and the red color to a classification in the incorrect category.</p>
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<p>LSTM model results (Data Set E). The green color corresponds to a correct classification and the red color to a classification in the incorrect category.</p>
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15 pages, 8345 KiB  
Article
Fault Diagnosis of Maritime Equipment Using an Intelligent Fuzzy Framework
by L. F. Mendonça, J. M. C. Sousa and S. M. Vieira
J. Mar. Sci. Eng. 2024, 12(10), 1737; https://doi.org/10.3390/jmse12101737 - 2 Oct 2024
Viewed by 598
Abstract
The task of automatically and intelligently diagnosing faults in marine equipment is of great significance due to the numerous duties that shipboard professionals must handle. Incorporating automated and intelligent systems on ships allows for more efficient equipment monitoring and better decision-making. This approach [...] Read more.
The task of automatically and intelligently diagnosing faults in marine equipment is of great significance due to the numerous duties that shipboard professionals must handle. Incorporating automated and intelligent systems on ships allows for more efficient equipment monitoring and better decision-making. This approach has attracted considerable interest in both academia and industry because of its potential for economic savings and improved safety. Several fault diagnosis methods are documented in the literature, often involving mathematical and control theory models. However, due to the inherent complexity of some processes, not all characteristics are precisely known, making mathematical modeling highly challenging. As a result, fault diagnosis often depends on data or heuristic information. Fuzzy logic theory is particularly well suited for processing this type of information. Therefore, this paper employs fuzzy models to diagnose faults in a marine pneumatic servo-actuated valve. The fuzzy models used in fault diagnosis are obtained from the data. These fuzzy models are identified for the normal operation of the marine pneumatic servo-actuated valve, and for each fault, predicting the system’s outputs from the inputs and outputs of the process. The proposed fault diagnosis framework analyzes the discrepancy signals between the outputs of the fuzzy models and the actual process outputs. These discrepancies, known as residuals, help in detecting and isolating equipment faults. The fault isolation process uses an intelligent decision-making approach to determine the specific fault in the system. This method is applied to diagnose abrupt faults in a marine pneumatic servo-actuated valve. The approach presented was used to detect and diagnose three very important faults in the operation of a marine pneumatic servo-actuated valve. The three faults were correctly detected and isolated, and no errors were detected in this detection and isolation process. Full article
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<p>Fault detection approach.</p>
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<p>Fault detection and isolation approach.</p>
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<p>Diagram of the pneumatic servo-actuated valve.</p>
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<p>Fault F1 detection.</p>
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<p>Fault F1 detection.</p>
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<p>Fault F1 isolation.</p>
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<p>Fault F2 isolation.</p>
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<p>Fault F3 isolation.</p>
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<p>Process data without fault.</p>
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<p>Process data without fault.</p>
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<p>Process data with fault F1.</p>
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<p>Process data with fault F1.</p>
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<p>Process data with fault F2.</p>
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<p>Process data with fault F3.</p>
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19 pages, 972 KiB  
Article
Robust H Control for Autonomous Underwater Vehicle’s Time-Varying Delay Systems under Unknown Random Parameter Uncertainties and Cyber-Attacks
by Soundararajan Vimal Kumar and Jonghoek Kim
Appl. Sci. 2024, 14(19), 8827; https://doi.org/10.3390/app14198827 - 1 Oct 2024
Viewed by 491
Abstract
This paper investigates robust H-based control for autonomous underwater vehicle (AUV) systems under time-varying delay, model uncertainties, and cyber-attacks. Sensor and actuator cyber-attacks can cause faults in the overall AUV system. In addition, the behavior of the system can be affected [...] Read more.
This paper investigates robust H-based control for autonomous underwater vehicle (AUV) systems under time-varying delay, model uncertainties, and cyber-attacks. Sensor and actuator cyber-attacks can cause faults in the overall AUV system. In addition, the behavior of the system can be affected by the presence of complexities, such as unknown random uncertainties that occur in system modeling. In this paper, the robustness against unpredictable random uncertainties is investigated by considering unknown but norm-bounded (UBB) random uncertainties. By constructing a proper Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) techniques, new stability criteria in the form of LMIs are derived such that the AUV system is stable. Moreover, this work is novel in addressing robust H control, which considers time-varying delay, cyber-attacks, and randomly occurring uncertainties for AUV systems. Finally, the effectiveness of the proposed results is demonstrated through two examples and their computer simulations. Full article
(This article belongs to the Section Robotics and Automation)
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<p>Schematic diagram of AUV system in the presence of cyber-attacks and external disturbances.</p>
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<p>State trajectories of AUV for Theorem 1.</p>
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<p>Simulation results for Theorem 1. (<b>a</b>) Comparison of randomly occurring uncertainties <math display="inline"><semantics> <mover accent="true"> <mi>α</mi> <mo>¯</mo> </mover> </semantics></math>. (<b>b</b>) Controller (<a href="#FD2-applsci-14-08827" class="html-disp-formula">2</a>) compared with actuator attack and [<a href="#B19-applsci-14-08827" class="html-bibr">19</a>].</p>
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<p>Simulation results for Theorem 1. (<b>a</b>) Comparison of output y(t). (<b>b</b>) Disturbance.</p>
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<p>Simulation results for Theorem 3.</p>
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<p>State trajectories of AUV for Theorem 2.</p>
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<p>Simulation results for Theorem 2. (<b>a</b>) Comparison of actuator attack <math display="inline"><semantics> <mrow> <msub> <mi>χ</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Comparison of controller (<a href="#FD2-applsci-14-08827" class="html-disp-formula">2</a>).</p>
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<p>Simulation results for Theorem 2. (<b>a</b>) Comparison of output y(t). (<b>b</b>) Time-varying delay <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Simulation results for Theorem 4.</p>
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18 pages, 737 KiB  
Article
Enhancing Reliability and Performance of Load Frequency Control in Aging Multi-Area Power Systems under Cyber-Attacks
by Di Wu, Fusen Guo, Zeming Yao, Di Zhu, Zhibo Zhang, Lin Li, Xiaoyi Du and Jun Zhang
Appl. Sci. 2024, 14(19), 8631; https://doi.org/10.3390/app14198631 - 25 Sep 2024
Viewed by 603
Abstract
This paper addresses the practical issue of load frequency control (LFC) in multi-area power systems with degraded actuators and sensors under cyber-attacks. A time-varying approximation model is developed to capture the variability in component degradation paths across different operational scenarios, and an optimal [...] Read more.
This paper addresses the practical issue of load frequency control (LFC) in multi-area power systems with degraded actuators and sensors under cyber-attacks. A time-varying approximation model is developed to capture the variability in component degradation paths across different operational scenarios, and an optimal controller is constructed to manage stochastic degradation across subareas simultaneously. To assess the reliability of the proposed scheme, both Monte Carlo simulation and particle swarm optimization techniques are utilized. The methodology distinguishes itself by four principal attributes: (i) a time-varying degradation model that broadens the application from single-area to multi-area systems; (ii) the integration of physical constraints within the degradation model, which enhances the realism and practicality compared to existing methods; (iii) the sensor suffers from fault data injection attacks; and (iv) an optimal controller that leverages particle swarm optimization to effectively balance reliability and system performance, thereby improving both stability and reliability. This method has demonstrated its effectiveness and advantages in mitigating load disturbances, achieving its objectives in just one-third of the time required by established benchmarks. The case study validates the applicability of the proposed approach and demonstrates its efficacy in mitigating load disturbance amidst stochastic degradation in actuators and sensors under FDIA cyber-attacks. Full article
(This article belongs to the Special Issue Recent Advances in Smart Microgrids)
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<p>Control block diagram of area <span class="html-italic">i</span>.</p>
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<p>Structure of the control system subject to degradation and FDIA.</p>
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<p>Dynamic model of the control area <span class="html-italic">i</span> with degraded components considering FDIA.</p>
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<p>Diagram of the proposed MCS-PSO approach.</p>
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<p>A schematic framework of the 3-area LFC system.</p>
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<p>The quality parameters for each area.</p>
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<p>The comparison of system reliability with and without optimization.</p>
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