Nonlinear Backstepping Control for Stabilizing and Trajectory Tracking Double Inverted Pendulum on Cart

Abstract

This study implemented a nonlinear control method on a higher-Degree-of-Freedom (DOF) underactuated model, namely a Double Inverted Pendulum (DIP) on a cart. The high-DOF underactuated nonlinear model is well known for its control challenges. Thus, in this research, a nonlinear Backstepping (BSP) controller was successfully designed and applied to address this issue. To evaluate the control quality and feasibility, the BSP controller was compared with the Linear Quadratic Regulator (LQR) in two cases: regulating the system to maintain balance near the equilibrium point and tracking a sine-wave trajectory. The results showed that LQR excels in stabilizing around the equilibrium position, whereas BSP proves superior in trajectory tracking due to its solid mathematical foundation.