Modeling, H^∞ control and stability analysis for structural systems using Takagi-Sugeno fuzzy model

This article proposes a design method for producing H^∞ control performance for structural systems using the Tagagi-Sugeno (T-S) fuzzy model. A structural system with a tuned mass damper is modeled using a T-S type fuzzy model. Using the parallel distributed compensation (PDC) scheme, we design a nonlinear fuzzy controller for the tuned mass damper system. A sufficient stability condition for the control system is derived in terms of Lyapunov theory and this control problem is reformulated into solving the linear matrix inequalities (LMI) problem. Finally, the tuned mass damper is designed based on the first modal frequency of the control system and a fuzzy controller to stabilize the structural system is then found using the Matlab LMI toolbox. A simulation example is given to show the feasibility of the proposed fuzzy controller design method.