Modeling piezoelectric actuators

H.J.M.T.S. Adriaens, W.L. De Koning, R. Banning
2000 IEEE/ASME transactions on mechatronics  
The piezoelectric actuator (PEA) is a well-known device for managing extremely small displacements in the range from 10 pm (1 pm = 10 12 m) to 100 m. When developing a control system for a piezo-actuated positioning mechanism, the actuator dynamics have to be taken into account. An electromechanical piezo model, based on physical principles, is presented in this paper. In this model, a first-order differential equation is adopted to describe the hysteresis effect, and a partial differential
more » ... al differential equation is used to describe the mechanical behavior. Since, in practice, a PEA is most often used as an actuator for positioning mechanisms, we considered the influence of such a mechanism on the overall mechanical behavior of PEA and positioning mechanism together. For a well-designed mechanism, the overall mechanical behavior practically equals that of a single mass-spring-damper system, of which the undamped eigenfrequency and the relative damping can be designed favorably. With respect to traditional voltage steering, charge steering has the advantage that no hysteresis is encountered between electrical input and elongation. Electrical steering configurations for both cases of steering are presented. Finally, for the case of charge steering, we derived the total model of a piezo-actuated positioning mechanism. This model is dominated by the mechanical model, which could be designed favorably. Therefore, this model gives a broad range of possibilities for model-based controller design. in 2000. He is currently with ASM Lithography, Veldhoven, The Netherlands, where machines for semiconductor manufacturing are developed and produced. His main research interest is in applied mathematics, with a focus on nonlinear systems and control, and on measurement systems. Willem L. de Koning was born in Leiden, The Netherlands, in 1944. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Delft University of Technology, Delft, The Netherlands in 1975 and 1984, respectively. From 1969 to 1975, he was a Research Engineer of power electronics and control in the Department of Electrical Engineering, Delft University of Technology. From 1975 to 1987 , he was an Assistant Professor of process dynamics and control in the Department of Applied Physics, Delft University of Technology. Since 1987, he has been an Associate Professor of mathematical system theory in the Department of Information Technology and Systems, Delft University of Technology. He has also held a visiting position at the Florida Institute of Technology, Melbourne. His research interests include control of distributed-parameter systems, reduced-order control, adaptive predictive control, digital optimal control, and applications.
doi:10.1109/3516.891044 fatcat:to6konwilreejkeap2bketf6kq