Hybrid proportional derivative/repetitive control for active vibration control of smart piezoelectric structures

Abstract

This paper presents a hybrid control method for active vibration control of smart piezoelectric structures. The proposed controller consists of a proportional derivative (PD) controller for broadband disturbance rejection and a repetitive controller for narrowband disturbance rejection. The proposed design embeds the repetitive controller by solving a Bezout identity satisfying deterministic constraint into an existing PD feedback control loop. The applied method has two main advantages: (1) each controller design is modularized with an “add-on” property for performance improvement; (2) it achieves superior vibration suppression for both impulse and persistent excitation. Experimental results on a piezoelectric cantilever beam demonstrate the effectiveness of the proposed hybrid controller design method.

Robust µ control and repetitive control for precision motion control of a pneumatic actuating table

“…The transfer function of the discrete-time m controller C m WB for real implementation is represented as C m WB = 0:04929z 6 À 0:2407z 5 + 0:4709z 4 À 0:4624z 3 + 0:2287z 2 À 0:0465z + 0:000593 z 6 À 5:74z 5 + 13:73z 4 À 17:52z 3 + 12:58z 2 À 4:821z + 0:7699 ð9Þ The applied W p is a transfer function that can be treated as an approximated integrator. Before showing the experimental results, the following inequality 21 should first be checked to satisfy the robust stability…”

Active Vibration Suppression of a Motor-Driven Piezoelectric Smart Structure Using Adaptive Fuzzy Sliding Mode Control and Repetitive Control

“…The AFSMC processes complex vibrations in the thin flexible plate generated in the application of rotary motion. We used a hybrid RC framework [14] incorporating RC to reduce the influence of periodic disturbances created by the periodic motions introduced by the motor.…”

“…In the hybrid control framework used in this study, we designed the controllers separately with the aim of having them work synergistically. The controller designs are similar to those in [14]; however, we replace PD control with AFSMC control to handle the complex vibration behaviors found in actual flexible structures more effectively. Periodic disturbances from the external environment or the motions of mechanical structures can damage the system via resonance.…”

“…They combined neural-fuzzy control with a genetic algorithm to achieve active vibration suppression control; however, the system was limited to static positioning and did not take into account the vibration responses created by dynamic tracking [13], Lin et al established a mathematical model to facilitate modal analysis of the large flexible structure in [12]. They also applied a hybrid PD/repetitive control framework [14] for the active suppression of vibrations produced in a thin plate undergoing periodic movement. Their simulation results demonstrated the effectiveness of a hybrid repetitive control (RC) algorithm in suppressing vibration responses in a motor-driven structure.…”

“…This control method can effectively handle nonlinear systems with uncertain parameters and achieve the expected control performance [15][16][17]. To minimize the influence of the periodic disturbances caused by the periodic motions of the motor, we adopted a hybrid RC framework [13,14] to combine RC with AFSMC and enhance piezoelectric vibration-suppression control. Experimental results demonstrate the effectiveness of the proposed hybrid intelligent control method in suppressing the complex vibrations generated in flexible structures subjected to periodic motor-driven rotations.…”