Research On H_∞Loop-shaping Robustly Stabilizing Controller Design For A Ball And Plate System

A ball and plate system(BPS) is two-dimensional extension of ball-beam system, which is a typical multi-variable, under-actuated and nonlinear control system. So it is often taken as a typical experiment platform to verify advanced control methods. Its main control object is to achieve the position control and trajectory tracking of the ball on the plate by the way of controlling the two degree of plate. The topic of this paper will take the BPS produced by ShenZhen Yuan Chuang Xing Technology Co. Ltd. as a research object. With prolonged use of the BPS, due to mechanical wear, device aging and other reasons, its control performance and control accuracy may decline. In order to improve its robust stability, anti-perturbation performance and control accuracy, the topic will make use of the method of H∞loop-shaping to design a robustly stabilizing controller for the BPS. Around this task, this topic mainly researches from the following three aspects.First, we need to obtain the math model of the BPS in order to design a robust controller. So, The nonlinear model of the BPS is linearized to obtain a linear model which is easy to control and biaxial decoupling system in the BPS equilibrium operating point. And then this topic will make use of the MATLAB to build simulation models of the BPS and study its controllability and stability according to the linear model of the BPS.Second, we will design a robustly stabilizing controller for the BPS employing the method of H∞loop-shaping. The shaping weighting functions play a decisive role in the loop-shaping, which is designed to have a direct impact on robust stability and immunity performance of the BPS. So, this topic proposes a new method to design the weighting functions, which makes use of the classical control theory lead-lag compensations to design the shaping weighting functions which make open-loop model of the BPS shaped the desired crossover frequency and phase margin based on the time-domain performance requirements. And then, this topic designs a robustly stabilizing controller for the BPS employing the improved method of static H∞loop-shaping based on the designed weighting functions. The advantages of the designed robustly stabilizing controller are to achieve closed-loop control in the manners of the lowest order output feedback, therefore which can improve the stability of the discrete robustly stabilizing controller.Finally, it verifies the effectiveness of the robustly stabilizing controller by the MATLAB simulations and the BPS experiments. This topic using MATLAB simulations studies the design of weighting functions and static H∞loop-shaping robust controller. Then, this topic applies the obtained discrete robustly stabilizing controller to the BPS experiment control and compares control effect with the original LQR controller of the BPS. The experimental results show that the designed static H∞robustly stabilizing controller is better than the original LQR controller obviously, thus validating the proposed design method of weighting functions and robustly stabilizing controller effectiveness.