Abstract
In this paper, a discrete second order linear equation with the Krasnosel’skii-Pokrovskii (KP) operator is used to describe the piezoelectric actuated stage. The weights of the KP operators are identified by the gradient descent algorithm. To suppress the hysteresis nonlinearity of the piezoelectric actuated stage, this paper proposes an adaptive tracking control with the hysteresis decomposition on the designed error surface. The proposed adaptive tracking controller dispenses with any form of the feed-forward hysteresis compensation and the unknown parameters of the discrete second order linear equation are adaptively adjusted. Some simulations are implemented to verify the effectiveness of the KP operators, then a series of modeling and control experiments are carried out on the piezoelectric actuated stages experimental systems. The comparative experimental results verify the feasibility of the KP operators modeling method and the adaptive tracking control method.
Highlights
Piezoelectric actuated stages are extensively applied in the high-precision imaging mechanism and ultra-precision positioning field, such as optical alignments, scanning tunneling microscope, and photoelectric imaging tracking systems, because of their high response speed, big work-distance and strong stress [1,2]
We used three KP kernel with the different weights as the actual system, the gradient descent algorithm was used to identify the unknown weights for verifying the validity of the proposed KP operator modeling method
To avoid the contingently of the simulation results, the sine wave signal was used as the input signal; the output of the KP operators based on the gradient descent algorithm was consistent with the output of actual system after a period from the Figure 4
Summary
Piezoelectric actuated stages are extensively applied in the high-precision imaging mechanism and ultra-precision positioning field, such as optical alignments, scanning tunneling microscope, and photoelectric imaging tracking systems, because of their high response speed, big work-distance and strong stress [1,2]. The hysteresis of the piezoelectric materials damages the positioning accuracy of the stage [3] To solve this problem, numerous modeling methods have been proposed to capture hysteresis of the piezoelectric actuated stage, which mainly include the differential equations-based models and operator-based models. In [7], the Bouc-Wen model was used to represent the hysteresis nonlinearity of the piezoelectric actuated stage and it got the great results. The element operator of KP model overcomes the drawback of the jump discontinuities of Preisach operators. It includes minor loops within its major loop which make it more closed to the actual behaviors of the hysteresis nonlinearity [16,17]. The simulation results show the proposed hysteresis model can describe the hysteresis loop with the different frequencies driving input of the piezoelectric-driven platform
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