Experimental study of H∞ control for a flexible plate

Abstract

This paper presents theoretical and experimental studies of H∞ control for a flexible plate. Firstly, the dynamic equation of the plate with time delay is established with consideration of external disturbance. Then the standard state equation without explicit time delay is deduced by using a particular integral transformation to the time-delay equation. Finally, a H∞ time-delay controller is designed based on the standard state equation using the method of linear matrix inequality. In the controller designed, it contains not only the current step of state feedback but also the linear combination of some former steps of control. In the experiment, piezoelectric patches are used as actuators and sensors. The experiment system is structured based on the DSP TMS320F2812. Single time delay and double time delay are both considered in the experiment. The robustness of H∞ controller against the structural parameter of the plate and time delay is experimentally investigated. Simulation and experimental results indicate that the control system may suffer from instability if time delay is not treated in control design. The time-delay controller presented in this paper can effectively deal with time delay in the system, and is available for small-time delay and large-time delay as well. Furthermore, this delay controller is robust to the variance of structural parameter of the plate and time delay.