Research On Identification Method For A Ball And Plate System Using V-gap Optimization

A Ball and Plate System(BPS)is a classical verification platform to verify the validity of control algorithm.It can be regarded as a two-dimensional extension of the ball-and-rod system and a typical non-linear control system with complex,multi-variable and under-actuated characteristics.This subject takes a BPS produced by Shenzhen Yuanchuangxing Technology Co.,Ltd.as the research object.Due to the long-term use,mechanical wear,device aging,temperature change and other reasons,the control accuracy and control effect of the BPS have been reduced.In order to make the system continue to work as a verification platform,it is necessary to improve the control accuracy and control effect of the BPS.The most direct way to improve the control accuracy and effect is to get the high-precision model of the system.In this paper,we will use the identification method of v-gap metric to identify the BPS model to obtain the high-precision model.Around this research,this paper mainly carries out research from the following four aspects.Firstly,in order to identify the BPS,its mechanism model needs to be given.The differential equation of the BPS is established by using Lagrange equation.The linearized model of the BPS can be established at the equilibrium point.The linearized model of the BPS is established by using the differential equation.Then,according to the linear model,the simulation model of the BPS is built by using MATLAB software.The characteristics of the mechanism model of BPS are analyzed,which provides the model basis for the parameterization of BPS model.Secondly,the v-gap metric optimization identification method studied by previous scholars is improved to improve the computational efficiency and reduce the identification time.There are two main ways: using sequential quadratic programming(SQP)to optimize parameters to improve identification speed;improving the constraints of normality,reciprocity and Nyquist winding conditions of the nominal model to reduce the number of constraints.Thirdly,the M-sequence of continuous excitation is designed as input signal,and the input and output data are collected to provide experimental data for the research of identification methods.Due to the v-gap identification method uses the frequency domain signal,the BPS directly collects the time domain signal.It is necessary to transform the time domain signal into the frequency domain signal by Fourier transform.Finally,the validity and high accuracy of the identification method are verified by the simulation function of MATLAB software and the BPS experiment.In this paper,the input and output data are used to identify the model of the BPS.By comparing the identified model with the original model,the feasibility of the proposed identification method is proved.