Improved robustness and performance of discrete time sliding mode control systems

Area of Science:

• Control Systems Engineering
• Discrete-Time Systems Analysis
• Nonlinear Control Theory

Background:

• Sliding mode control (SMC) is a robust control technique widely used in various engineering applications.
• Standard discrete-time sliding mode control (DSMC) systems often face challenges with robustness and performance limitations.
• The choice of sliding variable and its relative degree significantly impacts the system's dynamic behavior.

Purpose of the Study:

• To investigate the impact of relative degree on the robustness of discrete-time sliding mode control systems.
• To theoretically analyze and simulate the performance of DSMC systems with relative degree two outputs.
• To compare the robustness and stability properties against standard DSMC systems with relative degree one.

Main Methods:

• Theoretical analysis of discrete-time sliding mode control systems.
• Development of mathematical models for relative degree one and relative degree two outputs.
• Computer simulations to validate the theoretical findings and assess system performance under various conditions.

Main Results:

• Selecting a relative degree two sliding variable demonstrably increases the robustness of discrete-time sliding mode control systems.
• The ultimate bound of the sliding variable is successfully reduced compared to standard relative degree one systems.
• The reduced-order system exhibits finite-time stability in the absence of disturbances and finite-time ultimate boundedness with disturbances.

Conclusions:

• Utilizing relative degree two outputs offers a significant enhancement in robustness for discrete-time sliding mode control.
• The proposed method provides improved performance by reducing the sliding variable's ultimate bound.
• Finite-time stability properties are achieved, offering predictable and bounded system behavior even under external disturbances.