When a complex task has to be performed by multiple systems, it imposes functional dependencies b... more When a complex task has to be performed by multiple systems, it imposes functional dependencies between the states and outputs of the systems. These functional dependencies create a system of 'virtually' interconnected subsystems, even though they may be physically separated. The component subsystems within the overall system we call 'functionally related systems', since nature of the task of the system is defining functional relations between the system components. This dissertation deals with motion control design for functionally related systems. The design is based on identifying functions to be executed within a task and design of control to make these functions follow their references. The main goal is to obtain unit control distribution matrix in the function space and enforce a desired dynamics for each of the identified functions. However, the decoupling is not based on physical separation, but rather on the functions. By transforming the configuration space dynamics of the controlled system to the function space, it is shown that by properly selected transformation one can obtain the desired structure of the dynamics in the function space which has identity control distribution matrix. This was done by projecting the configuration space velocities to the function space by the function Jacobian matrix, and having transformation of the control signals from the function space back to the configuration space by a right pseudoinverse of the function Jacobian matrix. In the presented approach, any right pseudoinverse of the function Jacobian matrix can be used. A weighted pseudoinverse is proposed in this dissertation; thus, a weighting matrix can arbitrarily be selected. While any appropriate control method can be used for control input synthesis in the function space, three control methods were employed in this dissertation. These are disturbance-observer-based control, sliding mode control, and control based on the equivalent control estimation. All these methods provide stable and robust control in the function space. The proposed approach for control design is tested in experiments and simulations. Experimental results on a piezoelectric walker showed that nanometric precision positioning can be achieved. In experiments for tasks including two pantograph manipulators, results validated the presented approach allowing simultaneous grasping force and motion control. Simulation results for different tasks including different robotic manipulators and for the formation control of mobile robots showed the potential of our proposed methods in some other interesting scenarios as well.
This paper describes an embedded system for the automation of scheduling systems such as school b... more This paper describes an embedded system for the automation of scheduling systems such as school bells, factory shift changes, military drills etc. The system consists of two parts: a remote node used for remote control and setup of the system and the real time actuator node which controls a physical object, for example, a bell system. The hardware and software structure are illustrated in detail for both parts of the system through the implementation as an automatic school bell system.
Measurement of ambient conditions in homes is one of the main preconditions for their control wha... more Measurement of ambient conditions in homes is one of the main preconditions for their control what represents one of the steps toward the complete implementation of smart homes. The objective of this study is to implement a system for distributed measurement of temperature, illuminance and humidity. In this work, all parameters to be measured will be analyzed, and applied sensors will be described. In order to have better insight in the measured parameters, measurements on different locations are made and all data are sent to one place. One of the main purposes of the project is to accomplish low price of the implemented system. In addition, a simple software application is made, and it allows visualization of the measurement results and their statistical analysis.
The main goal of this study is comparative analysis of different methods used in design of digita... more The main goal of this study is comparative analysis of different methods used in design of digital fractional-order differentiator and integrator. The fractional-order digital differentiator or integrator can be described (in continuous time domain) with a transfer function H(s)=s^ɑ, where ɑ is a real number. To implement digital differentiators and integrators of arbitrary order the main step is the discretization. There are two common approaches of discretization. In this paper the direct and indirect discretization are presented but the emphasis will be on the indirect method, where the generating functions can be obtained through bilinear transformation, Al-Alaoui operator, Euler's backward operator and stable Simspon operator. The main differences between alternatives will be provided through analysis and comparison of their frequency responses - magnitude-frequency response, phase-frequency response and Nyquist diagrams.
This work presents functional description of a walking piezoelectric motor and its control in nan... more This work presents functional description of a walking piezoelectric motor and its control in nanometer precision. For this purpose a dynamical model of the actuator is derived based on simple mass spring damper system. Model parameters are estimated from step response plot and the system is expressed with second order transfer function. Additional identification experiments verified the theoretical kinematics of the bimorph legs. These experiments demonstrate approximately linear relation between the legs displacement in x and y directions to the applied voltages. Based on derived system model and identification results a PI controller followed by Hadamard transformation is proposed as a controller scheme. Experimental results for staircase and sinusoidal references reveal precise positioning capabilities of the system with the proposed control scheme down to few nanometers.
The paper presents a concept of universal motion controller. The controller merges both position ... more The paper presents a concept of universal motion controller. The controller merges both position and force control into a single control structure. Therefore, it gives a possibility to use the same control algorithm, both for position tracking tasks as well as for the interaction force control. The universal motion controller can be used not only to make the interaction force track its reference, but also for the limiting of the interaction force, so that safety is ensured. This makes it very useful for human-robot interaction applications.
In this paper implementation of a control system for high precision applications is presented. Th... more In this paper implementation of a control system for high precision applications is presented. The control system is developed for a Piezo LEGS motor, which is a walking piezo motor that can be employed in nanometric precision applications. In the control system structure, two main components are digital signal controller which executes control algorithm and power driver that is generating driving voltages for the motor. The waveforms of the driving voltages are designed using a recently presented coordinate transformation. This transformation enables synthesis of driving waveforms according to design requirements regarding force imposed to the motor's rod and rod's x-direction trajectory profile. In this work, the waveforms are selected to ensure no relative motion between the motor's legs and rod, and constant velocity of the rod within one step. Control algorithm is named as virtual time control. Despite its simplicity, the algorithm allows high precision positioning which is very close to theoretically achievable one.
ABSTRACT In this paper a novel design for three-dimensional (3-D) contour controller is proposed.... more ABSTRACT In this paper a novel design for three-dimensional (3-D) contour controller is proposed. This design relies on dynamics projection to the moving Frenet-Serret frame defined for each point on reference trajectory. Contour controller consists of independent joint controller and additional sliding mode controller, added as corrective term. Control task is defined as contour tracking with constant tangential velocity. Contour controller was compared with independent joint controller designed as acceleration controller with first order disturbance observer. Reference trajectory is generated using time based spline approximation to provide smooth reference trajectory. Experimental results showed significant improvement that contour controller provides over independent joint control with relatively high velocity references.
International Journal of Control Automation and Systems, Mar 1, 2022
The main research topic of this paper is to apply the sliding mode based soft actuation to smooth... more The main research topic of this paper is to apply the sliding mode based soft actuation to smooth transition between position, force, and impedance control, and realize bilateral control and reproduction of the haptic motion. The proposed design rests on the sliding mode two steps procedure: in the first step, the generalized error — the sliding mode function — is selected in such a way that a closed loop system exhibits a desired dynamics. In the soft actuation method, the generalized error depends on the position and the force, thus allowing the modification of the position tracking if interaction with the environment appears. In the second step, the control is selected to enforce the desired convergence rate and the stability of the closed loop dynamics. The control allows “natural — human-like” behavior. The application to the bilateral control and reproduction of the haptic motion is discussed in detail and verified by experiments.
When a complex task has to be performed by multiple systems, it imposes functional dependencies b... more When a complex task has to be performed by multiple systems, it imposes functional dependencies between the states and outputs of the systems. These functional dependencies create a system of 'virtually' interconnected subsystems, even though they may be physically separated. The component subsystems within the overall system we call 'functionally related systems', since nature of the task of the system is defining functional relations between the system components. This dissertation deals with motion control design for functionally related systems. The design is based on identifying functions to be executed within a task and design of control to make these functions follow their references. The main goal is to obtain unit control distribution matrix in the function space and enforce a desired dynamics for each of the identified functions. However, the decoupling is not based on physical separation, but rather on the functions. By transforming the configuration space dynamics of the controlled system to the function space, it is shown that by properly selected transformation one can obtain the desired structure of the dynamics in the function space which has identity control distribution matrix. This was done by projecting the configuration space velocities to the function space by the function Jacobian matrix, and having transformation of the control signals from the function space back to the configuration space by a right pseudoinverse of the function Jacobian matrix. In the presented approach, any right pseudoinverse of the function Jacobian matrix can be used. A weighted pseudoinverse is proposed in this dissertation; thus, a weighting matrix can arbitrarily be selected. While any appropriate control method can be used for control input synthesis in the function space, three control methods were employed in this dissertation. These are disturbance-observer-based control, sliding mode control, and control based on the equivalent control estimation. All these methods provide stable and robust control in the function space. The proposed approach for control design is tested in experiments and simulations. Experimental results on a piezoelectric walker showed that nanometric precision positioning can be achieved. In experiments for tasks including two pantograph manipulators, results validated the presented approach allowing simultaneous grasping force and motion control. Simulation results for different tasks including different robotic manipulators and for the formation control of mobile robots showed the potential of our proposed methods in some other interesting scenarios as well.
This paper describes an embedded system for the automation of scheduling systems such as school b... more This paper describes an embedded system for the automation of scheduling systems such as school bells, factory shift changes, military drills etc. The system consists of two parts: a remote node used for remote control and setup of the system and the real time actuator node which controls a physical object, for example, a bell system. The hardware and software structure are illustrated in detail for both parts of the system through the implementation as an automatic school bell system.
Measurement of ambient conditions in homes is one of the main preconditions for their control wha... more Measurement of ambient conditions in homes is one of the main preconditions for their control what represents one of the steps toward the complete implementation of smart homes. The objective of this study is to implement a system for distributed measurement of temperature, illuminance and humidity. In this work, all parameters to be measured will be analyzed, and applied sensors will be described. In order to have better insight in the measured parameters, measurements on different locations are made and all data are sent to one place. One of the main purposes of the project is to accomplish low price of the implemented system. In addition, a simple software application is made, and it allows visualization of the measurement results and their statistical analysis.
The main goal of this study is comparative analysis of different methods used in design of digita... more The main goal of this study is comparative analysis of different methods used in design of digital fractional-order differentiator and integrator. The fractional-order digital differentiator or integrator can be described (in continuous time domain) with a transfer function H(s)=s^ɑ, where ɑ is a real number. To implement digital differentiators and integrators of arbitrary order the main step is the discretization. There are two common approaches of discretization. In this paper the direct and indirect discretization are presented but the emphasis will be on the indirect method, where the generating functions can be obtained through bilinear transformation, Al-Alaoui operator, Euler's backward operator and stable Simspon operator. The main differences between alternatives will be provided through analysis and comparison of their frequency responses - magnitude-frequency response, phase-frequency response and Nyquist diagrams.
This work presents functional description of a walking piezoelectric motor and its control in nan... more This work presents functional description of a walking piezoelectric motor and its control in nanometer precision. For this purpose a dynamical model of the actuator is derived based on simple mass spring damper system. Model parameters are estimated from step response plot and the system is expressed with second order transfer function. Additional identification experiments verified the theoretical kinematics of the bimorph legs. These experiments demonstrate approximately linear relation between the legs displacement in x and y directions to the applied voltages. Based on derived system model and identification results a PI controller followed by Hadamard transformation is proposed as a controller scheme. Experimental results for staircase and sinusoidal references reveal precise positioning capabilities of the system with the proposed control scheme down to few nanometers.
The paper presents a concept of universal motion controller. The controller merges both position ... more The paper presents a concept of universal motion controller. The controller merges both position and force control into a single control structure. Therefore, it gives a possibility to use the same control algorithm, both for position tracking tasks as well as for the interaction force control. The universal motion controller can be used not only to make the interaction force track its reference, but also for the limiting of the interaction force, so that safety is ensured. This makes it very useful for human-robot interaction applications.
In this paper implementation of a control system for high precision applications is presented. Th... more In this paper implementation of a control system for high precision applications is presented. The control system is developed for a Piezo LEGS motor, which is a walking piezo motor that can be employed in nanometric precision applications. In the control system structure, two main components are digital signal controller which executes control algorithm and power driver that is generating driving voltages for the motor. The waveforms of the driving voltages are designed using a recently presented coordinate transformation. This transformation enables synthesis of driving waveforms according to design requirements regarding force imposed to the motor's rod and rod's x-direction trajectory profile. In this work, the waveforms are selected to ensure no relative motion between the motor's legs and rod, and constant velocity of the rod within one step. Control algorithm is named as virtual time control. Despite its simplicity, the algorithm allows high precision positioning which is very close to theoretically achievable one.
ABSTRACT In this paper a novel design for three-dimensional (3-D) contour controller is proposed.... more ABSTRACT In this paper a novel design for three-dimensional (3-D) contour controller is proposed. This design relies on dynamics projection to the moving Frenet-Serret frame defined for each point on reference trajectory. Contour controller consists of independent joint controller and additional sliding mode controller, added as corrective term. Control task is defined as contour tracking with constant tangential velocity. Contour controller was compared with independent joint controller designed as acceleration controller with first order disturbance observer. Reference trajectory is generated using time based spline approximation to provide smooth reference trajectory. Experimental results showed significant improvement that contour controller provides over independent joint control with relatively high velocity references.
International Journal of Control Automation and Systems, Mar 1, 2022
The main research topic of this paper is to apply the sliding mode based soft actuation to smooth... more The main research topic of this paper is to apply the sliding mode based soft actuation to smooth transition between position, force, and impedance control, and realize bilateral control and reproduction of the haptic motion. The proposed design rests on the sliding mode two steps procedure: in the first step, the generalized error — the sliding mode function — is selected in such a way that a closed loop system exhibits a desired dynamics. In the soft actuation method, the generalized error depends on the position and the force, thus allowing the modification of the position tracking if interaction with the environment appears. In the second step, the control is selected to enforce the desired convergence rate and the stability of the closed loop dynamics. The control allows “natural — human-like” behavior. The application to the bilateral control and reproduction of the haptic motion is discussed in detail and verified by experiments.
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