Study on discrete acceleration feedback control with time delay

This paper addresses the design problem of a discrete controller with time delay and acceleration feedback. The delta operator is firstly used to describe the discrete acceleration signal and convert the delayed continuous-time state equation into the delayed discrete-time system. Then the delayed discrete-time system is transformed into the delay-free one by applying a discrete reduction method. Based on the delay-free discrete-time system, the optimal output delta state feedback controller is designed by minimizing a discrete non-standard quadratic performance index and the feedback gain of the controller is obtained by a convergent algorithm. On the basis of the optimal output delta state feedback controller, the discrete time-delayed acceleration feedback controller is achieved by using the inverse reduction method, and the corresponding recursive control algorithm is developed. The controller saves the process of performing numerical integration and eliminating direct current and trend term in designing the displacement or velocity feedback control, so as to make the closed-loop system become simpler. Moreover, it can solve the problem of phase shift of the measured signal caused by time delay. The proposed controller with a low order model-based control algorithm is implemented on a smart cantilever beam with an accelerometer and piezoelectric actuator for different controller gain-delay combinations, and the control performance is evaluated. Simulation and experimental results demonstrate that the controller can effectively reduce the free vibration response of the smart cantilever beam.