A Chattering-Reduction Sliding Mode Control Algorithm for Affine Systems With Input Matrix Uncertainty

This paper aims to develop a chattering-reduction sliding mode control (SMC) approach for affine systems with input matrix uncertainty. Input matrix uncertainty poses adverse effects on systems, such as aggravating the chattering effect, and even causing instability for systems. To solve this problem, a two-step controller design method is proposed in this paper. In the first step, a general sliding mode controller is designed for the system without input matrix uncertainty. To suppress the effect of input matrix uncertainty, in the second step, a control term is specially developed to compensate for input matrix uncertainty. This term is obtained by solving a nonlinear equation, in which the directional characteristics of the control vector in the first step are integrated into the control term. By adding up the control terms obtained from the above two steps, a refined controller is obtained whose control gain is significantly reduced, especially facing with large input matrix uncertainty. In addition, the efficacy of the designed controller was verified in the simulation of a nonlinear plant. Upon drawing a comparison of the proposed method with a state-of-the-art SMC algorithm, it is learnt that the proposed controller is able to provide the closed-loop system with a more desired performance in which the amplitude of chattering is greatly reduced.