From Linear to Nonlinear Control Means: A Practical Progression

With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology

From Linear to Nonlinear Control Means: A Practical Progression

With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology

θ-D Approximation Technique for Nonlinear Optimal Speed Control Design of Surface-Mounted PMSM Drives

This paper proposes nonlinear optimal controller and observer schemes based on a θ-D approximation approach for surface-mounted permanent magnet synchronous motors (PMSMs). By applying the θ-D method in both the controller and observer designs, the unsolvable Hamilton–Jacobi–Bellman equations are switched to an algebraic Riccati equation and statedependent Lyapunov equations (SDLEs). Then, through selecting the suitable coefficient matrices, the SDLEs become algebraic, so the complex matrix operation technique, i.e., the Kronecker product applied in the previous papers to solve the SDLEs is eliminated. Moreover, the proposed technique not only solves the problem of controlling the large initial states, but also avoids the excessive online computations. By utilizing a more accurate approximation method, the proposed control system achieves superior control performance (e.g., faster transient response, more robustness under the parameter uncertainties and load torque variations) compared to the state-dependent Riccati equation-based control method and conventional PI controlmethod. The proposed observer-based control methodology is tested with an experimental setup of a PMSM servo drive using a Texas Instruments TMS320F28335 DSP. Finally, the experimental results are shown for proving the effectiveness of the proposed control approac

θ-D Approximation Technique for Nonlinear Optimal Speed Control Design of Surface-Mounted PMSM Drives

This paper proposes nonlinear optimal controller and observer schemes based on a θ-D approximation approach for surface-mounted permanent magnet synchronous motors (PMSMs). By applying the θ-D method in both the controller and observer designs, the unsolvable Hamilton–Jacobi–Bellman equations are switched to an algebraic Riccati equation and statedependent Lyapunov equations (SDLEs). Then, through selecting the suitable coefficient matrices, the SDLEs become algebraic, so the complex matrix operation technique, i.e., the Kronecker product applied in the previous papers to solve the SDLEs is eliminated. Moreover, the proposed technique not only solves the problem of controlling the large initial states, but also avoids the excessive online computations. By utilizing a more accurate approximation method, the proposed control system achieves superior control performance (e.g., faster transient response, more robustness under the parameter uncertainties and load torque variations) compared to the state-dependent Riccati equation-based control method and conventional PI controlmethod. The proposed observer-based control methodology is tested with an experimental setup of a PMSM servo drive using a Texas Instruments TMS320F28335 DSP. Finally, the experimental results are shown for proving the effectiveness of the proposed control approac

High performance disturbance observer based control system design for permanent magnet synchronous AC machine applications

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonAn electrical machine is one of the main workforces in different industries and serves them in various applications. Machine drive control design involves many technical issues for efficient and robust exploitation. Over several decades, Permanent Magnet Synchronous Motor (PMSM) is getting preferred for industrial applications over its counterpart Squirrel Cage Induction Motor (SCIM) drive, because of their higher efficiency, power density, and higher torque to inertia ratio. In the prospective that PMSM drives are considered the drives of the future, there are still technical challenges and issues related to PMSM control. Many studies have been devoted to PMSM control in the past, but there are still some open research areas that bring worldwide researchers’ interests back to PMSM drive control. One of the approaches that may facilitate better performance, higher efficiency, and robust and reliable work of the control system is the disturbance observer-based control (DOBC) with linear and nonlinear output feedback control for PM synchronous machine applications. DOBC is adopted due to its ability to reject external and internal disturbances with improving tracking performance in the variable speed wind energy conversion system (WECS) to maximize power extraction. The high order disturbance observer (HODO) is utilized to estimate the aerodynamic torque-based wind speed without the use of a traditional anemometer, which reduces the overall cost and improves the reliability of the whole system. Also, this method has been designed to improve the angular shaft speed tracking of the PMSM system under load torque disturbance and speed variations. The model-based linear and nonlinear feedback control are used in the proposed control systems. The sliding mode control (SMC) with switching output feedback control law and integral SMC with linear feedback and state-dependent Riccati equation (SDRE) based approaches have been designed for the systems. The SDRE control accounts for the nonlinear multivariable structure of the WECS and is approximated with Taylor series expansion terms. The chattering inherited from SMC is eliminated by the continuous approximation technique. The sliding mode is guaranteed by eliminating the reaching mode in the proposed integral SMC. The model-free cascaded linear feedback control system based on the proportional-integral (PI) controllers use a back-calculation algorithm anti-windup scheme. The proposed speed controllers are synthesized with HODO to compensate for the external disturbance, model uncertainty, noise, and modelling errors. Moreover, servomechanism-based SDRE control, a near-optimal control system is designed to suppress the model uncertainty and noise without the use of disturbance observers. The proposed control systems for PMSM speed regulation have demonstrated a significant improvement in the angular shaft speed-tracking performance at the transients. Their performances have been tested under speed, load torque variations, and model uncertainty. For example, HODO-based SMC with switching output feedback control law (SOFCL) has demonstrated improvement by more than 78% than the PI-PI control system of the PMSM. The performance of the HODOs-based Integral SMC with SDRE nonlinear feedback is improved by 80.5% under external disturbance, model uncertainty, and noise than Integral SMC with linear feedback in the WECS. The HODO-based SDRE control with servomechanism has shown an 80.2% improvement of mean absolute percentage error under disturbances than Integral SMC with linear feedback in the WECS. The PMSM speed tracking performance of the proposed HODO-based discrete-time PI-PI control system with back-calculation algorithm anti-windup scheme is improved by 87.29% and 90.2% in the speed commands and load torque disturbance variations scenarios respectively. The simulations for testing the proposed control system of the PMSM system and WECS have been implemented in Matlab/Simulink environment. The PMSM speed control experimental results have been obtained with Lucas-Nuelle DSP-based rapid control prototyping kit.Center for International Program “Bolashak” of the Ministry of Education and Science Republic of Kazakhsta

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Derivative-free Kalman Filter-based Control of Nonlinear Systems with Application to Transfemoral Prostheses

Derivative-free Kalman filtering (DKF) for estimation-based control of a special class of nonlinear systems is presented. The method includes a standard Kalman filter for the estimation of both states and unknown inputs, and a nonlinear system that is transformed to controllable canonical state space form through feedback linearization (FL). A direct current (DC) motor with an input torque that is a nonlinear function of the state is considered as a case study for a nonlinear single-input-single-output (SISO) system. A three degree-of-freedom (DOF) robot / prosthesis system, which includes a robot that emulates human hip and thigh motion and a powered (active) transfemoral prosthesis disturbed by ground reaction force (GRF), is considered as a case study for a nonlinear multi-input-multi-output (MIMO) system. A PD/PI control term is used to compensate for the unknown GRF. Simulation results show that FL can compensate for the system\u27s nonlinearities through a virtual control term, in contrast to Taylor series linearization, which is only a first-order linearization method. FL improves estimation performance relative to the extended Kalman filter, and in some cases improves the initial condition region of attraction as well. A stability analysis of the DKF-based control method, considering both estimation and unknown input compensation, is also presented. The error dynamics are studied in both frequency and time domains. The derivative of the unknown input plays a key role in the error dynamics and is the primary limiting factor of the closed-loop estimation-based control system stability. It is shown that in realistic systems the derivative of the unknown input is the primary determinant of the region of convergence. It is shown that the tracking error asymptotically converges to the derivative of the unknown input

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering