Erratum to: Robust motion control of a two-wheeled inverted pendulum with an input delay based on optimal integral sliding mode manifold

Abstract

This paper presents a robust integral sliding mode controller for the back-and-forth motion of a two-wheeled inverted pendulum. The control design of this nonlinear system is based on the linearized system with bounded uncertainty and with an input delay taken into account, where the uncertainty is the integrated effect of the linearization error and bounded system uncertainties. Firstly, a trajectory tacking target is selected according to the control task. Secondly, a quadratic performance criterion with large weight of tilt angle error for optimal control is introduced to “force” the tilt angle of inverted pendulum small enough and in turn to make the linearization error small. Thirdly, a new integral state transformation is used to convert the delayed error system with uncertainty into a delay-free one, and a key relationship between the original state variable and the new state variable is founded. Finally, the robust optimal integral sliding mode controller represented in the form of predictor state is designed by choosing the optimal state of the nominal error system as the integral sliding mode manifold. Numerical simulation shows that the designed controller not only works well in implementing the control task, but also has strong robustness against system uncertainties.