The Research Of The Control System Of The Ball And Plate System Using Active Disturbance Rejection Control

The ball and plate system is constituted by a two-dimensional plate and a ball rolling on it. The ball rolls on the plate because of the gravity. This paper focuses on the Ball and Plate System based on the 3-DOF parallel mechanism built in our laboratory and analysis it. And do some research on the active disturbance rejection control. What is more, some simulations and experiments are done to validate the controller.First, the movement of the ball on the plate and the requirement of the ball moving on the plate are analyzed. The model of the movement of the ball on the plate is built. The actuator of the ball and plate system studied in this paper is the 3-DOF parallel mechanism which constituted by three linear motion actuator. This paper decouples with the geometrical relationship of the 3-DOF parallel mechanism for the coupling of mechanism. And the relationship between the attitude of the 3-DOF parallel mechanism and the length of the linear motion actuator is calculated. So the attitude of the 3-DOF parallel mechanism can be controlled by the linear motion actuator. Then the movement of the ball can be controlled. After that the motor and the driver is analyzed and identified to build the model of the Ball and Plate System.Secondly, the uncertain disturbance, friction between the ball and plate, centripetal force and coupling term in the system is analyzed. The Extended State Observer(ESO) is applied to estimate the total disturbance including the uncertain disturbance, the friction, centripetal force and coupling term. It will be eliminated from the control. The Active Disturbance Rejection Control(ADRC) is applied to control the ball to track the trajectory. The simulation is completed.Thirdly,when getting the position of the ball, the measurement noise will be introduced into the output of the system. So a low-pass first filter is designed to filter the output of the system with measurement noise. Then the ESO with a first-order inertia element is designed for the compound system constituted by the original system and the filter. The noise-resistant ability of the ESO with a first-order inertia element is satisfactory and the phase lag of the low frequency signal is small. In order to change the angle of the plate in a small range, the control is introduced into the performance index and the LQR controller is designed. According to the ADRC, ADRC with acceleration feed-forward is a type of LQR. Moreover, the simulation of set-point and circle trajectory tracking are completed.In the end, the experimental platform is completed containing the hardware and the software. And some experiments are completed on it, which proves effectiveness of the controller. With the peaking phenomenon caused by the ESO, we analyze it and initialize the initial state of the ESO with the actual value of the system. And it reduces the Peaking phenomenon and makes the performance much better.