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

Linear matrix inequality based synthesis of PI controllers for PMSM with uncertain parameters

This paper addresses the design of robust PI controllers for permanent magnet synchronous motors in terms of a linear matrix inequality based problem. A polytopic model of the plant is obtained and validated for the motor uncertain parameters belonging to intervals. The design procedure proposed here encompasses: i. suitable plant uncertainties inclusion and the use of practical design control constraints; ii. robust PI computation based on linear matrix inequalities with a very fast solution; iii. simulation analyses; and iv. experimental evaluations. The robust PI controller can produce superior speed regulation than a PI controller designed only for the nominal parameters, including better disturbance rejection and H-infinity performance. Experimental results confirm the viability of the proposal, which can be seen as an efficient alternative to trade off performance and robustness for PI controllers in this application233310319CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES306197/2015-4não te

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

Adaptive control of sinusoidal brushless DC motor actuators

Electrical Power Assisted Steering system (EPAS) will likely be used on future automotive power steering systems. The sinusoidal brushless DC (BLDC) motor has been identified as one of the most suitable actuators for the EPAS application. Motor characteristic variations, which can be indicated by variations of the motor parameters such as the coil resistance and the torque constant, directly impart inaccuracies in the control scheme based on the nominal values of parameters and thus the whole system performance suffers. The motor controller must address the time-varying motor characteristics problem and maintain the performance in its long service life. In this dissertation, four adaptive control algorithms for brushless DC (BLDC) motors are explored. The first algorithm engages a simplified inverse dq-coordinate dynamics controller and solves for the parameter errors with the q-axis current (iq) feedback from several past sampling steps. The controller parameter values are updated by slow integration of the parameter errors. Improvement such as dynamic approximation, speed approximation and Gram-Schmidt orthonormalization are discussed for better estimation performance. The second algorithm is proposed to use both the d-axis current (id) and the q-axis current (iq) feedback for parameter estimation since id always accompanies iq. Stochastic conditions for unbiased estimation are shown through Monte Carlo simulations. Study of the first two adaptive algorithms indicates that the parameter estimation performance can be achieved by using more history data. The Extended Kalman Filter (EKF), a representative recursive estimation algorithm, is then investigated for the BLDC motor application. Simulation results validated the superior estimation performance with the EKF. However, the computation complexity and stability may be barriers for practical implementation of the EKF. The fourth algorithm is a model reference adaptive control (MRAC) that utilizes the desired motor characteristics as a reference model. Its stability is guaranteed by Lyapunov’s direct method. Simulation shows superior performance in terms of the convergence speed and current tracking. These algorithms are compared in closed loop simulation with an EPAS model and a motor speed control application. The MRAC is identified as the most promising candidate controller because of its combination of superior performance and low computational complexity. A BLDC motor controller developed with the dq-coordinate model cannot be implemented without several supplemental functions such as the coordinate transformation and a DC-to-AC current encoding scheme. A quasi-physical BLDC motor model is developed to study the practical implementation issues of the dq-coordinate control strategy, such as the initialization and rotor angle transducer resolution. This model can also be beneficial during first stage development in automotive BLDC motor applications

Robust fault tolerant control of induction motor system

Research into fault tolerant control (FTC, a set of techniques that are developed to increase plant availability and reduce the risk of safety hazards) for induction motors is motivated by practical concerns including the need for enhanced reliability, improved maintenance operations and reduced cost. Its aim is to prevent that simple faults develop into serious failure. Although, the subject of induction motor control is well known, the main topics in the literature are concerned with scalar and vector control and structural stability. However, induction machines experience various fault scenarios and to meet the above requirements FTC strategies based on existing or more advanced control methods become desirable. Some earlier studies on FTC have addressed particular problems of 3-phase sensor current/voltage FTC, torque FTC, etc. However, the development of these methods lacks a more general understanding of the overall problem of FTC for an induction motor based on a true fault classification of possible fault types.In order to develop a more general approach to FTC for induction motors, i.e. not just designing specific control approaches for individual induction motor fault scenarios, this thesis has carried out a systematic research on induction motor systems considering the various faults that can typically be present, having either “additive” fault or “multiplicative” effects on the system dynamics, according to whether the faults are sensor or actuator (additive fault) types or component or motor faults (multiplicative fault) types.To achieve the required objectives, an active approach to FTC is used, making use of fault estimation (FE, an approach that determine the magnitude of a fault signal online) and fault compensation. This approach of FTC/FE considers an integration of the electrical and mechanical dynamics, initially using adaptive and/or sliding mode observers, Linear Parameter Varying (LPV, in which nonlinear systems are locally decomposed into several linear systems scheduled by varying parameters) and then using back-stepping control combined with observer/estimation methods for handling certain forms of nonlinearity.In conclusion, the thesis proposed an integrated research of induction motor FTC/FE with the consideration of different types of faults and different types of uncertainties, and validated the approaches through simulations and experiments

Discrete-time sliding mode control based on disturbance observer applied to current control of permanent magnet synchronous motor

This paper proposes a robust current control technique based on a discrete-time sliding mode controller and a disturbance observer for high-performance permanent magnet synchronous motor (PMSM) drives. This scheme is applied in the PMSM current control loops to enable the decoupling between the dq current axes, rejection of disturbances caused by mechanical load changes and robustness under parametric uncertainties. In order to ensure the discrete-time sliding mode properties, which make the system cross the sliding surface at each sampling period, the PMSM model is extended, including the digital implementation delay resulting from the discrete-time algorithm execution. The development of this method allows direct implementation in microcontrollers and digital signal processors. Stability and convergence analysis are developed in the discrete-time domain. Simulation and experimental results demonstrate the effectiveness and good performance of the proposed current control approach

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