T-S fuzzy controller design for Rotary Inverted Pendulum with input delay using Wirtinger-based integral inequality

This paper investigates a Takagi-Sugeno fuzzy descriptor approach for designing a input delay controller for a rotary inverted pendulum. The rotary inverted pendulum, under-actuated system, is considered a benchmark for verifying the performance of linear or nonlinear control laws in control system theory because this system has nonlinearities, such as gravity and centripetal force. The Takagi-Sugeno fuzzy modeling technique transformed the rotary inverted pendulum system into several local linear models, and a parallel distributed compensation (PDC) based fuzzy controller was designed. By constructing suitable Lyapunov-Krasovskii functionals and utilizing some mathematical techniques, a stabilization criterion for a T-S fuzzy system with input delay was derived in linear matrix inequalities. Finally, the designed controller was experimented on the `Quanser SRV-02' platform compared to the linear controller designed using LMI Toolbox of MATLAB under the same conditions.