Experimental study of active control for a flexible beam with nonlinear hysteresis and time delay

Abstract

In this paper, an active controller for a nonlinear and hysteretic structure with time delay is studied. The nonlinear and hysteretic behavior of the system is illustrated by the Bouc-Wen model. The genetic algorithm is used to identify the optimal parameters of the Bouc-Wen model in order to describe the hysteresis phenomenon of the experimental system. By specific transformation and augmentation of state parameters, the motion equation of the system with explicit time delay is transformed into the standard state space representation without any explicit time delay. Then the fourth-order Runge-Kutta method and instantaneous optimal control method are applied to the controller design with time delay. Finally, numerical simulation and experimental results of a flexible beam using the proposed time delay controller are carried out. The results indicate that the control performance will deteriorate if time delay is not taken into account in the controller design. The time delay controller proposed in this paper can not only effectively compensate time delay to get better control effectiveness, but also work well with both small and large time delay problems.