Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

Abstract

In this paper, a combined feedback-feedforward control design scheme is presented to enhance the tracking performance of a piezo-actuated micropositioning stage by compensating the nonlinear hysteretic behavior of the piezoelectric actuator and model uncertainties of the system. Detailed investigation of the presented control scheme is performed not only in simulation by analyzing the robust stability and robust performance but also in real-time with motion trajectories of multiple frequencies. To design the presented control scheme, first of all, the dynamic model of the system is identified from the real-time experimental data by using the recursive least squares parameter adaptation algorithm. Then, Dahl hysteresis model is considered to represent the nonlinear hysteretic behavior of the piezoelectric actuator. To deal with this hysteresis nonlinearity, Dahl feedforward compensator is designed without involving inverse model calculations to avoid any computational complexity. This feedforward compensator is then combined with µ-synthesis robust feedback controller which is designed in the presence of model uncertainties of the system. The presented control scheme ensures the boundedness of the closed-loop signals and the desired tracking performance of the considered micropositioning stage. Finally, experimental tests are conducted with motion trajectories of multiple frequencies for the validation of the control scheme. An average improvement of 95% in compensating the hysteresis nonlinearity and 80% in reducing the tracking error is achieved which demonstrates the efficacy of the presented control scheme. INDEX TERMS Dahl feedforward compensator, hysteresis nonlinearity, micropositioning, model uncertainties, piezoelectric actuator, µ-synthesis robust feedback controller.

Design and disturbance rejection control of a piezoelectric nanopositioning stage

“…29,30 Among feedback controllers, robust control with excellent stability and positioning accuracy plays a vital role in nanopositioning systems. 31,32 Several comprehensive controllers with excellent robustness were designed and applied, such as those combining feedforward compensation and µ-synthesis methods 31,33 and anti-windup compensators 32,34 based on robust H ∞ control. Usually, high control gains can guarantee enough positioning accuracy for feedback control.…”

Parameter identification of Duhem model based on antlion-fish swarm hybrid algorithm and robust backstepping sliding mode control for rate-dependent hysteresis of piezoelectric actuators

“…Piezoelectric actuators (PEA) has the advantages of small size, high precision, fast response, low energy consumption and so on. 1 So it has been widely used in micro-positioning systems such as high precision metal cutting systems 2 and other high precision fields. The flight inchworm actuators (FIA) which is composed of PEA stacks is used to position various optical elements in highly sensitive optical instruments.…”

Dynamic modeling and disturbance rejection compensation for hysteresis nonlinearity of high voltage piezoelectric stack actuators

“…However, there are some drawbacks to using these models, such as complex model construction, high calculation costs for parameter identification and difficulty in solving inverse models in the application of these models [27]. Nonlinear differential equations are used in the second type of hysteresis model, which includes the Bouc-Wen model [28][29][30][31], the Duhem model [32,33], the Dahl model [34,35], and the Jiles-Atherton model [36,37]. When compared with operatorbased hysteresis models, these models regard the hysteresis characteristic as the input/output relationship of a dynamic system, and the model parameters to be identified are greatly reduced.…”