Effectiveness Comparison of Balance Control Strategies in Nonlinear Systems Considering Disturbances

Nowadays, the control of underactuated systems is an emerging trend in high-tech products, including self-balancing robots, humanoid robots, and spacecraft. However, most real-world oscillatory systems, and underactuated systems in particular, exhibit inherent instabilities, nonlinearities, and external disturbances, posing significant challenges to effective control. Conventional linear control methods often yield suboptimal performance due to their reliance on linear models. To overcome these limitations, advanced nonlinear control techniques have been developed. This paper addresses the effectiveness comparison of balance control strategies in nonlinear systems. The system's dynamic model is first established, followed by the formulation of the PD-LQR and HSMC control strategies and their theoretical validation through Lyapunov stability analysis. Next, a comparative study between the conventional PD-LQR and HSMC controllers is demonstrated. Finally, the oscillatory disturbances affecting the system performance are presented and evaluated using graphs and harmonic analysis. The results underscore that HSMC effectively mitigates issues such as vibrations and chattering, ensuring enhanced robustness, response speed, and stability in controlling underactuated nonlinear systems.