Research On Piezoelectric Stack Control Method Based-on Fractional Order PI~λD~μ

As precision displacement actuator, piezoelectric actuators has the advantages of high response frequency, less heat and strong stiffness.which makes it is widely applied in the field of biological engineering, aerospace, electronic packaging, optical imaging, etc.The piezoelectric stack is an important role of the piezoelectric actuators,it has bigger output displacement because it consists of fold piezoelectric pieces. But the piezoelectric stack has the common faults of piezoelectric materials—hysteresis characteristics. The hysteresis characteristics causes nonlinearity between the input voltage and output displacement, which is unfavorable for precision positioning in the engineering.To overcome the hysteresis nonlinearity of the piezoelectric stack and control displacement of piezoelectric stack precisely, this paper carried out research work on the modeling and control of the piezoelectric stack with fractional order calculus.Main work content is as follows:1. This paper built up a displacement acquisition and control platform for piezoelectric stack based on x PC target prototype environment, then used the platform to collect displacement of piezoelectric stack and used wavelet transform for denoising displacement data. The collected piezoelectric stack displacement intuitively show the hysteresis nonlinearity of the piezoelectric stack.2. Fractional order model for piezoelectric stack. Through the study of fractional order calculus and analysis of the influence between parameters of transfer fractional order function and the output signal, this paper built the fractional order correction equation between the output force and driving voltage of piezoelectric stack, hence the fractional order model of piezoelectric stack was established. Fractional order model parameters was calculated by particle swarm optimum algorithm under the ISE error rule, And accuracy of model was verified through comparing the model output displacement to the measured displacement of the piezoelectric stack.3. In order to achieve precise displacement control, This paper designed particle swarm optimum fractional order PI~λD~μ controller for fractional order model of the piezoelectric stack, this method used particle swarm algorithm to calculate controlparameters of fractional order PI~λD~μ under ITAE error criterion. Then, this paper controlled piezoelectric stack by fractional order PI~λD~μ controller with the same control parameters on the piezoelectric stack displacement acquisition and control platform, and compared with the integer order PID. Experimental results show that the control result of fractional order PI~λD~μ controller had better dynamic property and higher control accuracy.4. RBF neural network fractional order PI~λD~μ control algorithm was designed for controlling the piezoelectric stack. RBF neural network was used to provide Jacobain information for fractional order PI~λD~μ to set control parameters in this algorithm.This algorithm made a good use of model information and avoided uncertainty of manual tuning, on addition it also benefited from flexibility and robustness of fractional order PI~λD~μ controller. The experimental results show that the RBF neural network fractional order PI~λD~μ controller proposed in this paper can achieve the high precision displacement control for the piezoelectric stack.