Hierarchical sliding mode control with oscillation compensation for low-cost inverted pendulum systems using hardware-in-loop

This research presents three major contributions to the nonlinear control of underactuated systems. First, the identification and characterization of a 2.5 Hz oscillatory phenomenon in the low-cost inverted pendulum system, addressing challenges from mechanical elasticity and electrical delays, is reported. Second, the Hierarchical Sliding Mode Control (HSMC) framework is developed to control this underactuated system considering its unwanted oscillatory phenomenon. This HSMC control system is used to achieve superior disturbance rejection, maintaining cart position within ± 0.05 m compared to PD-LQR's ± 0.35 m under pure oscillatory disturbances, while reducing energy consumption by 32%. Third, a comprehensive Hardware-in-the-Loop (HIL) implementation using the F28379D microcontroller, which provides real-time parameter adjustment capabilities, is established. The stability of the system is theoretically validated through Lyapunov analysis and homoclinic orbit characterization. Experimental results demonstrate the effectiveness of the HSMC controller in maintaining pendulum angular oscillations within ± 2.5°, significantly outperforming PD-LQR's ± 5° range under combined disturbances.