Nonlinear Controller Design For Piezoelectric Nano-Positioning Actuator

Nanotechnology will produce revolutionary changes in all aspects of human life, it has been widely used in various fields of human life. Nano-positioning technology is the basis for the applications of nanotechnologyPiezoelectric ceramic displacement drive can achieve nano-scale displacements, but the presence of hysteresis, creep and other nonlinear properties greatly deteriorate its positioning performance. This paper will study the issue of hysteresis compensation for piezoelectric ceramics from three perspectivesFirstly introduced is the classical model-based control method. With the input-output data of the piezoelectric ceramic actuator, the Prandtl-Ishlinkii model is adopted to describe the hysteresis. To compensate for the difference between the ideal Prandtl-Ishlinkii model and the actual hysteresis loop, we extend the classical Prandtl-Ishlinkii model with OSD-operator. Then the piezoelectric actuator system is linearized with the inverse model of the extended Prandtl-Ishlinkii model, so that we can implement a traditional control design method on the system to compensate the modeling error.While the modeling procedure is rather complicated, a novel L1, adaptive control algorithm is adopted in the next chapter, which eliminates the process of hysteresis modeling. The overall system is modeled as a decoupled linear sub-system with a nonlinear hysteresis as input, while the nonlinear hysteresis is modeled in the hysteresis subsystem. The L1 adaptive control algorithm is implemented after some transformation of hysteresis, which transform the hysteresis into the disturbance of the linear system. Through theoretical analysis, the proof of stability of the system is obtained. Then the algorithm is implemented on the experiment platform, with a PID control algorithm as a comparison.Combining the advantages of the previous two methods, we use a Prandtl-Ishlinkii model-based L1 control algorithm in the last approach. The system is still described by the decoupled system in section 2. And the hysteresis is compensated with inverse Prandtl-Ishlinkii model in section 1. Compared to L1 adaptive controller in section 2, this method is not only to reduce the L1 adaptive controller uncertain number of parameters, but also reduce the range of uncertain parameters, making the choice of an ideal system parameters broader conducive to further reduce small control error, get better control effect.