Asynchronous hysteresis compensation-linear quadratic H-infinity control method and system for piezoelectric deformable mirror

Abstract

The invention discloses an asynchronous hysteresis compensation-linear quadratic H-infinity control method and system for a piezoelectric deformable mirror. The method comprises the steps of measuringthe relationship between an output displacement hysteresis component and input voltage of each piezoelectric ceramic actuator; establishing an asynchronous rate-dependent asynchronous Bouc-Wen hysteresis model; identifying model parameters according to the measurement result by adopting a contraction type particle swarm optimization algorithm; designing a hysteresis compensation feedforward controller according to the hysteresis model; and carrying out overall modeling on the hysteresis compensation feedforward controller and the piezoelectric ceramic actuators, and designing a linear quadratic H-infinity feedback controller. The hysteresis model describes the asymmetry, rate dependence and asynchroneity of hysteresis, and is higher in accuracy; the hysteresis compensation feedforward controller does not require the reversibility of the hysteresis model, so that the hysteresis compensation based on a differential equation hysteresis model is enabled to be realized; and the linear quadratic H-infinity feedback controller solves the contradiction among requirements of the system for the adjustment time, accuracy, energy consumption and robustness, and enables the performance indexesto reach comprehensively optimum.

Description

technical field [0001] The invention belongs to the technical field of control, and in particular relates to an asynchronous hysteresis compensation-linear quadratic type H of a piezoelectric deformable mirror. ∞ Control method and system. Background technique [0002] Piezoelectric deformable mirrors are commonly used wavefront correctors in adaptive optics systems. They are mainly composed of piezoelectric ceramic actuator arrays and thin mirrors. Different voltages are applied to each piezoelectric ceramic of the driver array, and each piezoelectric ceramic produces a deformation displacement, thereby pushing and pulling the thin mirror surface to produce a surface shape that is conjugate to the wavefront to be corrected. The linear relationship between the output displacement of piezoelectric ceramics and the input voltage is the basis for establishing the theory of wavefront correction of adaptive optical systems, but the actual response characteristics of piezoelectri...

AI Technical Summary

Problems solved by technology

This method uses the asymmetric rate-dependent asynchronous Bouc-Wen model to describe the hysteresis characteristics, and makes an effective estimate of the asymmetry, rate-dependence, and asynchrony of the hysteresis; uses the hysteresis compensation feedforward controller to correct the hysteresis, and solves the differential equation The problem that the inverse model controller cannot be designed because there is no analytical inverse in the model model; the linear quadratic H ∞ The feedback controller further improves the performance of the piezoelectric deformable mirror, making the system adjustment time, precision, energy consumption and robustness reach the comprehensive optimization

Images