A Novel sliding mode control method for an inertia wheel pendulum system

For practical mechanical systems, including inertia wheel pendulums, they unavoidably suffer from the unexpected influences brought about by frictions and extraneous disturbances. Hence, it is essential for the developed control approach to be capable of overcoming these unfavorable factors. In the present paper, we consider the problem of controlling underactuated inertia wheel pendulum systems in the presence of parametrical uncertainties and external disturbances. To this end, we present a novel robust sliding mode control (SMC) law without linearizing the original dynamics. More precisely, the system dynamics are first transformed, via several coordinate changes, into a quasi-chained form. Based on this, we construct a new sliding manifold, on which the state variables vanish asymptotically towards the equilibrium point. Then, a nonlinear controller is presented to keep the system state always staying on the fabricated sliding manifold. Lyapunov-based analysis, without performing any linearizations/approximations to the nonlinear dynamics, is provided to demonstrate that the equilibrium point of the closed-loop system is asymptotically stable. We include a series of numerical simulation results to examine its superior performance and strong robustness against uncertainties and extraneous disturbances.