Prescribed performance-based hierarchical fast terminal sliding mode control for a rotary inverted pendulum: Design and experimental validation

Abstract

This paper presents a prescribed performance-based hierarchical fast terminal sliding mode control (PP-HR-FTSMC) approach for stabilizing a rotary inverted pendulum (RIP). The proposed controller ensures finite-time convergence while enforcing a prescribed performance bound on the system tracking error. A hierarchical recursive control structure is designed to handle the highly nonlinear and underactuated dynamics of the RIP, enhancing robustness against uncertainties and disturbances. By utilizing an error transformation function, the constrained control problem is converted into an unconstrained one, ensuring compliance with the preset performance of tracking errors. The fast terminal sliding mode (FTSM) framework guarantees rapid error convergence while mitigating chattering effects. To optimize the controller gains, a multi-objective golden eagle optimization (MO-GEO) algorithm is employed, balancing key performance metrics such as convergence speed, control effort, and robustness. The proposed control strategy is validated through high-fidelity simulations in Simscape, followed by real-time experiments on a custom-built RIP platform. The results demonstrate superior tracking accuracy, robustness, and finite-time stabilization compared to linear quadratic Gaussian (LQG) controller, adaptive super-twisting sliding mode controller (ASTSMC), and proportional integral derivative (PID) controller.