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Predictive Dynamic Matrix Control (DMC) for Ball and Plate System Used in a Stewart Robot

Abstract:

This paper presents the development of a predictive dynamic matrix controller (DMC) on a Stewart platform with 6 degrees of freedom for the ball and plate application that consists of controlling the position of a ball on a rotating plane surface. Prior to implementation, the construction characteristics of the system and its kinematic analysis are established. Obtaining the position of the ball on the platform is carried out by means of digital signal processing of the images from a camera by means of algorithms implemented in a Raspberry Pi 3B microcomputer. It also includes the description of the identification process of the mathematical model of the system, which starts from an excitation of the closed-loop system with a pseudo-random binary signal (PRBS). The qualities of this type of controllers are detailed, as well as the considerations necessary for their application and design. The device that runs the control algorithm is a STM32F4 Discovery development board. The results show that the proposed controller stabilizes the ball in an average time of less than 6 s and reacts to disturbances by re-stabilizing the system in a similar time with an expected error of 10%.