This introductory chapter covers the journey of control system theory research from classical control towards variable structure control. Control system theory is crucial for regulating dynamic systems across various applications, ensuring stability, performance, and robustness against disturbances. It covers both continuous-time and discrete-time systems, each serving different domains. Feedback mechanisms are central to this theory, enabling systems to maintain desired outputs by minimizing discrepancies between actual and reference signals. Conventional control methods, such as PID controllers, rely on continuous actions and frequency domain analysis, excelling in linear time-invariant systems. In contrast, Variable Structure Control (VSC) utilizes discontinuous actions, with Sliding Mode Control (SMC) being a prominent method that effectively handles nonlinearities and uncertainties, despite challenges like chattering. With the rise of digital technology, Discrete-Time Sliding Mode Control (DSMC) has emerged, adapting SMC principles for discrete systems. While DSMC is efficient for digital control, it faces challenges such as quasi-sliding modes, where the system’s behavior only approximates ideal sliding motion. To address this, higher-order discrete sliding modes have been developed, offering enhanced robustness and precision by reducing the quasi-sliding mode band. Overall, control system theory provides a versatile framework for analyzing, designing, and optimizing dynamic systems, with ongoing advancements like DSMC and higher-order methods continuing to refine its applicability across various fields.

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A Journey from Classical Control Towards Variable Structure Control

  • Shyam Kamal,
  • Parijat Prasun

摘要

This introductory chapter covers the journey of control system theory research from classical control towards variable structure control. Control system theory is crucial for regulating dynamic systems across various applications, ensuring stability, performance, and robustness against disturbances. It covers both continuous-time and discrete-time systems, each serving different domains. Feedback mechanisms are central to this theory, enabling systems to maintain desired outputs by minimizing discrepancies between actual and reference signals. Conventional control methods, such as PID controllers, rely on continuous actions and frequency domain analysis, excelling in linear time-invariant systems. In contrast, Variable Structure Control (VSC) utilizes discontinuous actions, with Sliding Mode Control (SMC) being a prominent method that effectively handles nonlinearities and uncertainties, despite challenges like chattering. With the rise of digital technology, Discrete-Time Sliding Mode Control (DSMC) has emerged, adapting SMC principles for discrete systems. While DSMC is efficient for digital control, it faces challenges such as quasi-sliding modes, where the system’s behavior only approximates ideal sliding motion. To address this, higher-order discrete sliding modes have been developed, offering enhanced robustness and precision by reducing the quasi-sliding mode band. Overall, control system theory provides a versatile framework for analyzing, designing, and optimizing dynamic systems, with ongoing advancements like DSMC and higher-order methods continuing to refine its applicability across various fields.