Discrete-time sliding mode control of flexible smart structures with piezofilm actuators

In this study, a new discrete-time sliding mode controller is proposed and applied to active vibration control of a flexible smart structure featuring a piezofilm actuator. After deriving the governing equation of motion for the smart structure, a discrete-time control model with system uncertainties is constructed in a state space. A stable sliding surface is then designed followed by the formulations of a discrete-time sliding mode controller which consists of a discontinuous part and an equivalent part. For the design of the discontinuous part, a time-varying control gain is adopted to increase system robustness to the uncertainties. In the design of the equivalent part, a so called equivalent controller separation method is employed to achieve faster reaching to the sliding surface without extension of the sliding region in which undesirable vibration chattering may be arisen. Controlled responses of transient and forced vibrations are evaluated through computer simulation and experimental realization.