Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum

Abstract

In this paper, a sliding mode controller (SMC) is proposed for control of a wheeled inverted pendulum (WIP) system, which consists of a pendulum and two wheels in parallel. The control objective is to use only one actuator to perform setpoint control of the wheels while balance the pendulum around the upright position, which is an unstable equilibrium. When designing the SMC for the WIP system, various uncertainties are taken into consideration, including matched uncertainties such as the joint friction, and unmatched uncertainties such as the ground friction, payload variation, or road slope. The SMC proposed is capable of handling system uncertainties and applicable to general underactuated systems with or without input coupling. For switching surface design, the selection of the switching surface coefficients is in general a sophisticated design issue because those coefficients are nonaffine in the sliding manifold. In this work, the switching surface design is transformed into a linear controller design, which is simple and systematic. By virtue of the systematic design, various linear control techniques, such as linear quadratic regulator (LQR) or linear matrix inequality (LMI), can be incorporated in the switching surface design to achieve optimality or robustness for the sliding manifold. To further improve the WIP responses, the design of reference signals is addressed. The reference position for the pendulum is adjusted according to the actual equilibrium of the pendulum, which depends on the size of the friction and slope angle of the traveling surface. A smooth reference trajectory for the setpoint of the wheel is applied to avoid abrupt jumps in the system responses, meanwhile the reaching time of the switching surface can be reduced. The effectiveness of the SMC is validated using intensive simulations and experiment testings.