Vibration Control of Macro and Micro Mechanical Systems With Piezoelectric Transducers

2002 Fiscal Year Final Research Report Summary

• Project/Area Number: 13650256
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Dynamics/Control
• Research Institution: Akita Prefectural University
• Principal Investigator: TSUCHIYA Takao Akita Prefectural University, Department of Electronics and Information Systems, Associate Professor, システム科学技術学部, 助教授 (20217334)
• Co-Investigator(Kenkyū-buntansha): WAKATSUKI Naoto Akita Prefectural University, Department of Electronics and Information Systems, Assistant, システム科学技術学部, 助手 (40294433) ; KAGAWA Yukio Akita Prefectural University, Department of Electronics and Information Systems, Professor, システム科学技術学部, 教授 (10019200)
• Project Period (FY): 2001 – 2002
• Keywords: Piezoelectricity / Feedback System / Modal Analysis / Finite Element Method / Electrical Equivalent Circuit Model

Research Abstract

The vibration control with piezoelectric transducer is presented. Based on the finite element expression for a vibration system with electromechanical coupling included, the discretized equation of motion is derived. Modal Analysis is then applied to develop the corresponding electrical equivalent circuit model. Some numerical demonstrations are made for simple vibrators with and without piezoelectricity, which are assumed to be one-dimensional vibratory systems. It is confirmed that the solutions based on the equivalent model well agree with the analytical ones. The passive damping control is then demonstrated for a simple cantilever beam which is assumed to be two-dimensional. To evaluate the damping effect, the loss factor is calculated based on the circuit parameters of the equivalent circuit. For effective damping, there is the optimum value of the electrical resister which is connected to the electrodes of the piezoelectric transducer. It is found that the damping is mainly caused due to the adhesive layer between the cantilever and the transducer. The active control is lastly demonstrated for the cantilever beam system. To evaluate the stability of the system, the transfer function for the feedback system is derived based on the equivalent circuit. It is shown that the stability of the system is determined by the amplification factor and the force factors of the sensor and the actuator. In other words, the choice of the position of the sensor and actuator is very important for the stable feedback control. Our next project could be to verify the model in comparison with the experiment.