Theoretical Advancements and Implementations of Discrete-Time Sliding Mode Control with Higher Relative Degree Sliding Variable

Abstract

Thethesis delves into the domain of control systems, focusing on uncertainties that drive engineers to establish the intricate relationship between stability and performance, lead ing to the exploration of robustness and adaptability. These uncertainties are categorized into parametric or structured uncertainties included in the system, and unmodeled or un structured uncertainties arising from intentional underestimation of system order. These uncertainties significantly impact system performance during operation, prompting the use of robust and adaptive control approaches. Thereportexploresrobustcontroltechniques, particularly Sliding ModeControl(SMC), knownforits successful applications across various industries. While many SMC strate gies rely on state feedback, the thesis emphasizes the practicality of an output feedback based SMC, especially in scenarios where complete state measurement is infeasible. The multirate output feedback (MROF) approach is introduced, leveraging the output for controller design, particularly beneficial in systems with limited sensor availability and observability challenges. The study focuses on implementing fast output sampling (FOS) in MROF-based SMC, where states are computed from output information and previous control input, converg ing to the actual states of the system in finite time. The thesis also examines sliding variable approaches, emphasizing the relative degree two (RD2) sliding variable, show casing improved robustness and performance in comparison to the conventional relative degree one (RD1) approach. The thesis extends its application to practical systems, such as the buck converter and DC motor, demonstrating the effectiveness of the developed strategies in discrete-time sliding mode control (DTSMC). Additionally, the report introduces a novel inverse hy perbolic sine (IHS) reaching law, enhancing robustness and convergence without gener ating excessive control signals.