<title>Vibration and tracking control of piezoceramic-based smart structures via quantitative feedback theory</title>

Abstract

This paper presents robust vibration and position tracking control of a flexible smart structure featuring a piezoceramic actuator. A cantilever beam structure with a surface-bonded piezoceramic actuator is proposed, and its governing equation of motion and associated boundary conditions are derived from Hamilton's principle. The transfer function from control input voltage to output displacement is then established in Laplace domain in order to formulate a robust controller using the quantitative feedback theory (QFT). A robust QFT compensator is designed on the basis of a stability criterion which prescribes a bound on the peak value of an M-contour in the Nichols chart. In the formulation of the compensator, disturbance rejection specification and tracking performance bounds are specified to guarantee the robustness of the system to plant uncertainties and external disturbances. A prefilter is also designed for the improvement of step and sinusoidal tracking control performances. Vibration and position tracking control performances are evaluated through computer simulation and experimental implementation in order to demonstrate the efficiency and robustness of the proposed control methodology.