Application of Fuzzy-model-based Control to Nonlinear Structural Systems with Time Delay: an LMI Method

Abstract

In this study we present a fuzzy robust control design which combines H ∞ control performance with Tagagi-Sugeno (T-S) fuzzy control for the control of delayed nonlinear structural systems under external excitations. We design a nonlinear fuzzy controller based on parallel distributed compensation schemes. The controller design problem is reformulated as a linear matrix inequality (LMI) problem as derived from the Lyapunov theory. This robust method is designed to overcome the modeling error that can occur between delayed nonlinear structural systems with T-S fuzzy models. Given the fuzzy-model-based H ∞ control and the stability conditions, the stability of a delayed nonlinear structural system under external excitation is ensured. Furthermore, the delayed nonlinear structural system is equipped with a tuned mass damper designed according to the first mode of frequency. The feedback gain of the fuzzy controller is found via the Matlab LMI toolbox. The proposed method is then applied to a delayed nonlinearly tuned mass damper system. The simulation results show that not only is the proposed method able to stabilize delayed nonlinear structural systems, but also has strong robustness in terms of preventing modeling errors and external excitations.