Application of high power amplifier in inverse system control of hyperbolic function model of Antai Electronics
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Experiment name: Preisach type hysteresis nonlinear modeling and inverse control based on hyperbolic function
Experimental content:
Drivers made of smart materials such as piezoelectric ceramics and magnetostrictive materials are widely used in the field of precision positioning. However, the inherent hysteresis nonlinearity of these smart materials seriously restricts the control accuracy of the positioning system and may cause system instability. In order to reduce the adverse effects of hysteresis nonlinearity on the system, a control method based on hysteresis model is usually used.
This paper describes the hysteresis nonlinearity of the Preisach class based on hyperbolic functions. Two hyperbolic functions are used to describe the rising and falling segments of the hysteresis main loop, and the first-order curve attached to the main loop is fitted through coordinate transformation. Then, according to the memory erasure of the Preisach model and the consistency principle of the secondary loop, the first-order rising curve is used to describe the rising segment of the secondary loop, and the first-order falling curve simulates the falling segment of the secondary loop. Based on this hysteresis model, an inverse controller is designed to compensate for the hysteresis nonlinearity of the piezoelectric dual-chip driver, thereby improving the accuracy of positioning control.
Experimental process:
In order to verify the effectiveness of the hyperbolic function model, an inverse controller was designed for the precision positioning system of the piezoelectric dual-chip driver. The experimental system: a computer equipped with a dSPACE system applies the driving voltage to the piezoelectric dual-chip through a power amplifier , measures the displacement of the piezoelectric dual-chip through an optical fiber displacement sensor, and transmits the signal back to the dSPACE board. In order to compare the control effect and obtain the identification data of the hysteresis model, the response of the piezoelectric dual-chip driver under the action of a 1Hz, 50V peak sinusoidal signal was measured.
 
Before control:
In order to test the control results of the hysteresis primary loop and the secondary loop at the same time, it is expected to use a sinusoidal signal with a variable amplitude of 1 Hz.
After control: If the hysteresis inverse model is accurate enough, it will cancel out the hysteresis nonlinearity of the piezoelectric bimorph actuator, making the desired displacement and the response displacement linear.
Experimental results:
This paper describes the hysteresis nonlinearity of the Preisach class based on hyperbolic functions. Two hyperbolic functions are used to describe the rising and falling segments of the hysteresis main loop respectively, and the first-order rising and falling curves attached to the main loop are fitted by transforming the coordinates. Then, the arbitrary secondary loop of the hysteresis nonlinearity is described according to the memory erasure and the consistency of the secondary loop. The model parameters required by this modeling method are much smaller than those of the classic Preisach model, and the parameters are easy to identify. The premise of using this model is that the hyperbolic function can fit the main loop of the hysteresis nonlinearity, which is suitable for controlling the hysteresis nonlinearity of smart materials such as piezoelectric actuators. Based on this hysteresis model, an inverse controller of the piezoelectric dual-chip actuator is designed, which reduces the maximum positioning error after control by 44.26% compared with that before control, and can effectively suppress the error caused by hysteresis nonlinearity.
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