Hybrid STSMC-Backstepping Control for Nonlinear System Stabilization under Uncertainties

Abstract

This paper presents a comparative study of a hybrid Super-Twisting Sliding Mode Control (STSMC) combined with Backstepping against a Linear Quadratic Regulator (LQR) for stabilizing a nonlinear pendulum under parameter uncertainties and external disturbances. The pendulum represents a classic nonlinear system subject to parameter variations in mass and length, with disturbances included in both torque and velocity. The hybrid controller integrates the robust disturbance rejection of STSMC with the adaptive stabilization of Backstepping, augmented by integral action to eliminate steady-state error. In contrast, the LQR relies on a linearized model with optimal gains. Simulations are conducted in MATLAB and performance is evaluated through overshoot, steady-state error, and control effort. Results demonstrate that the hybrid controller achieves lower overshoot and negligible steady-state error compared to LQR, which exhibits persistent oscillations following disturbances.