Switching TS fuzzy model-based dynamic sliding mode observer design for non-differentiable nonlinear systems

Abstract

This paper presents four sliding mode observers (SMOs) based on a novel approach in Takagi–Sugeno (TS) fuzzy modeling of multi-input multi-output (MIMO) non-linear systems that have non-differentiable operating points. A comprehensive approach is proposed to using the TS fuzzy model (TSFM) in the field of non-differentiable nonlinear systems, where the TSFM is an approximation with high accuracy and a negligible error (2ε) of the nonlinear model. Furthermore, the considered system can be with measurable or unmeasurable premise variables. The observers are synthesized for the above two cases and dynamic observers for state estimations of MIMO non-linear Lipschitz systems. The dynamic gain of the observer is established from inspiring state-space representation of an LTI system with error as input, internal states, and the gain of the observer as output. The dynamics used in the gain of the observer will increase the degrees of freedom in the design procedure and a generalization to the one used in previous works. The proposed method is applicable for continuous-time, but not necessarily differentiable, nonlinear systems. Considering the inherent strongly nonlinear and coupling performance of the plant, the switching method driven by states is presented. This paper presents a comparison of four SMOs and multiple-model adaptive estimation (MMAE) for benchmark hydraulic wind power transfer (HWPT). Simulation results demonstrate improvement in the state observation convergence rate and simplicity and universality of the proposed approach.