Stability Analysis and Sliding-Mode Controller Design for a Nonlinear Second-Order System: A Tutorial
Keywords:
sliding mode control, nonlinear control, stability of equilibrium point, Lyapunov’ s stabilityAbstract
This article is an academic article in the form of a tutorial that introduces the design of a sliding mode controller for a nonlinear second-order system. Traditional controllers induce high-frequency oscillations due to discontinuous functions, making them impractical for real-world applications. To reduce chattering and improve efficiency, a high-slope saturation function is used. The sliding mode control scheme consists of two phases: the reaching phase and the sliding phase. By designing the sliding surface and switching function, the system trajectory moves towards the sliding surface and stays within the boundary layer until reaching the origin. Estimating the region of attraction allows for defining a compact set of boundary layer that confines zig-zag motion. Additionally, Lyapunov's stability theory is used to prove that the closed-loop system’s equilibrium point is globally asymptotically stable. This validation highlights the robustness and reliability of the proposed control design.
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