Two degree-of-freedom hysteresis compensation for a dynamic mirror with antagonistic piezoelectric stack actuation
Abstract
A dynamic mirror actuator (DMA) with antagonistic piezoelectric stack actuation (PESA) is considered for laser beam dot placement error reduction in electrophotographic processes. The DMA is required to meet tracking error specifications below 500~Hz to reduce low-frequency process noise and base vibration. In addition, the DMA is desired to compensate repeatable high-frequency tracking errors due to polygon mirror facet-to-facet misalignment. This high-frequency error correction is a new and novel problem. The development of the DMA is approached in two steps: development of a linear model and low-computation, high-bandwidth hysteresis control. First, a methodology for development of the best linear model to represent the DMA is presented. The DMA is known to exhibit hysteresis and other nonlinearities which are represented by additive input uncertainty and feedback uncertainty elements, respectively, connected to the linear plant model. The proposed linear model employs explicit PESA charging dynamics and incorporates two drive modes for mapping a single control input to the two PESA drive voltages. The proposed linear model is compared to constitutive models from literature and shown to exhibit less frequency response error when compared to experimental data. As a further validation, simulated step response data is shown to agree with experimental data. Second, a methodology for designing a low-computation, high-bandwidth strategy for closed-loop hysteresis control of the DMA without a priori knowledge of the desired trajectory is presented. The resulting hysteresis control is applied to the DMA. A hysteresis compensator is created as a finite state machine switching among polynomials for hysteresis inversion along rising or falling curves. Residual hysteresis error after compensation is further corrected by an LQR feedback controller. Experimental results demonstrate effectiveness of the hysteresis compensator and closed-loop system under the proposed hysteresis control strategy. For the triangular input signal tested, the closed-loop system achieves a 91.5% reduction in hysteresis uncertainty.
Degree
Ph.D.
Advisors
Chiu, Purdue University.
Subject Area
Mechanical engineering
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