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

Advances in PID Control

Since the foundation and up to the current state-of-the-art in control engineering, the problems of PID control steadily attract great attention of numerous researchers and remain inexhaustible source of new ideas for process of control system design and industrial applications. PID control effectiveness is usually caused by the nature of dynamical processes, conditioned that the majority of the industrial dynamical processes are well described by simple dynamic model of the first or second order. The efficacy of PID controllers vastly falls in case of complicated dynamics, nonlinearities, and varying parameters of the plant. This gives a pulse to further researches in the field of PID control. Consequently, the problems of advanced PID control system design methodologies, rules of adaptive PID control, self-tuning procedures, and particularly robustness and transient performance for nonlinear systems, still remain as the areas of the lively interests for many scientists and researchers at the present time. The recent research results presented in this book provide new ideas for improved performance of PID control applications

Development of a New Adaptive Backstepping Control Design for a Non-Strict and Under-Actuated System Based on a PSO Tuner

In this work, a new adaptive block-backstepping control design algorithm was developed for an under-actuated model (represented by a ball–arc system) to enhance the transient and steady-state behaviors and to improve the robustness characteristics of the controlled system against parameter variation (load change and model uncertainty). For this system, the main mission of the proposed controller is to simultaneously hold the ball at the top of the arc and retain the cart at the required position. The stability of a controlled system based on the proposed adaptive controller was analyzed, and its globally asymptotic stability was proven based on the Lyapunov theorem. A comparative study of adaptive and non-adaptive block-backstepping controllers was conducted in relation to the transient, steady-state, and robustness characteristics. The effectiveness of the controller was verified via simulation within a MATLAB/SIMULINK environment. The simulated results show that the proposed adaptive control strategy could successfully stabilize the under-actuated ball–arc system, regardless of both the regulation problem and the tracking problem. This provides a better dynamic performance and a better load rejection capability, and it performs well in solving the uncertainty problem in the model parameter