An Enhanced Fuzzy Repetitive-Control Design and Optimisation Method based on 2D Performance Index

This paper concerns the design and optimisation of two-dimensional (2D) repetitive control of nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model. First, a continuous-discrete 2D model of nonlinear repetitive-control systems based on T-S fuzzy model is constructed by utilizing the 2D characteristics of continuous control and discrete learning actions in the repetitive-control process. Next, a fuzzy Lyapunov-Krasovskii functional derives the linear-matrix-inequality-based stability condition with a low conservatism. Two positive and two nonzero parameters in the fuzzy Lyapunov-Krasovskii functional tune the control and learning actions. Then the particle swarm optimisation algorithm based on a 2D performance index searches for the best parameter combination, resulting in the optimal 2D controller gains. A numerical example is given to demonstrate the effectiveness of the method.