Abstract:
The use of smart structures provides more efficient solutions to most of the active vibration control problems in flexible systems due to the significant advances in sensor and actuator technologies. This paper presents a novel design approach of a gain scheduling H∞ controller for a parameter varying smart beam having surface bonded piezoelectric sensors and actuators. The robust approach intends to suppress the vibrations of the first flexural resonance of the smart beam which has a servo actuated end mass. The smart beam studied is a cantilever aluminum beam with four surface bonded Lead-Zirconate-Titanate (PZT) patches in bimorph configuration. In the design procedure, first, the parameter uncertain modeling of the flexible cantilever aluminum beam with a piezoelectric sensor and actuator is created by means of an analogical approach. Hence, the uncertain model was achieved from the simulation of the experimentally obtained beam model with a mass-spring-damper system having the equivalent smart beam characteristics. Then, the generalized plant model of the uncertain model is constituted, and a Linear Time Invariant (LTI) H∞ controller is computed. Finally, a gain scheduling H∞ controller was obtained by adapting a variable parameter filter to the LTI H∞ controller. The developed gain scheduling H∞ controller and its corresponding conventional H∞ controller are applied on the smart system with parameter varying. The obtained experimental results in time and frequency domain reveal that the proposed controller is able to suppress the vibrations of the smart beam at the first flexural mode. In addition to this, the experimental results show that proposed gain scheduling H∞ controller's performance is superior then conventional LTI H∞ controller. © 2017 International Center for Numerical Methods in Engineering. All rights reserved.