Dynamic modeling and validation of a novel 3-DOF flexible thin sheet nano-manipulator with piezoelectric material bonded

Abstract

In this paper, we investigate a 3-DOF (degree-of-freedom) piezoelectric nano-manipulator designed with flexible flexures and unimorph piezoelectric thin sheet actuators, allowing for high-precision motions with a compact size and fast dynamics response. Based on the Lagrange's equations, the dynamic model of the proposed motion system is established by equivalent approximations of the distributed parameter dynamics and the piezoelectricmechanical coupling effect. Comprehensive simulations and experiments are also conducted on the flexible piezoelectric nano-manipulator with piezoelectric thin sheets (PZT-5A) under various electric fields, where the proposed model agrees well with simulations and experiments. The proposed modeling approach provides the basis for the model-based feedback controller design of such systems.

Dynamic Modeling and Attitude Decoupling Control for a 3-DOF Flexible Piezoelectric Nano-Positioning Stage Based on ADRC

“…Moreover, the attitude decoupling control method using LADRCs simultaneously allows the proposed system the obtain high-speed and high-position accuracy, where it effectively eliminates and compensates for the errors caused by the hysteresis and creep of piezoelectric thin-sheet micro-actuators. The simulation results of the piezoelectric nano-positioning stage have been shown in [ 22 ], where the uniaxial tracking error is approximately 0.86% in tracking a sinusoidal signal (50 Hz) with this ADRC method.…”

“…T and V are the equivalent kinetic energy and potential energy of the continuous distributed system, respectively. The distributed-parameter piezoelectric nano-positioning stage is transformed into a lumped-parameter system as depicted in Figure 4 , and then the equivalent kinetic energy and potential energy of the piezoelectric nano-positioning stage are obtained as follows: where k and m are the equivalent stiffness and the equivalent mass of PZT micro-actuators, which can be obtained from Appendix A and [ 22 ], respectively. is the equivalent moment of inertia of such a flexible system, and ( ) are the equivalent deformations of piezoelectric thin-sheet micro-actuators under external forces in [ 28 ].…”

“…As depicted in Figure A1 , the equivalent force F of the flexible piezoelectric thin-sheet micro-actuators of the piezoelectric nano-positioning stage under electric fields can be obtained obtained in [ 22 ], and we define the equivalent force ( F ) as follows:

Figure A1 Deflection of the piezoelectric beam.

where …”

“…In spite of a twisting control scheme with a PID sliding surface applied to a torsional micro-mirror to enhance the transient response and high-positioning performance, the chattering problem still exists in closed-loop control systems [ 20 ]. Note that the flexible systems present new challenges to the modeling and control on account of the distributed-parameter characteristics and the coupling effect of flexible micro/nano-actuators, which is significantly different from the traditional micro/nano-motion systems driven by PZT stack actuators [ 21 , 22 , 23 ]. In addition, active disturbance rejection control (ADRC) becomes a popular control method in robot applications, with advantages of simple implementation, strong robustness [ 24 , 25 ], and ability to suppress various uncertainties and disturbances [ 26 , 27 ].…”