Comprehensive Case Study: A Novel Design, Modeling, Simulation, and Experimental Implementation and Evaluation of Control Strategies for a 9-DOF Ball on Plate System

Abstract

This comprehensive case study examines the Ball on Plate (BnP) system, a critical component of our prototype involving multiple systems. The BnP system features a complex 9 Degrees of Freedom (DOF) nonlinear mechanical setup, comprising three independent Ball and Beam (BnB) systems that collectively enhance functionality. The primary objective was to model, simulate, and control this system using various control algorithms, including PI, PD, and PID controllers. The methodology involved designing and theoretically modeling each aspect of the BnP system, followed by extensive simulations and practical experiments for performance validation. The study aims to achieve several goals: analyzing hardware components and their mechanisms; modeling the three BnB systems with nonlinear mathematical models and linearizing them; implementing a control loop using Simulink and Arduino IDE; analyzing software components, including vision measurement and image processing; designing controllers with trial-and-error tuning for precise ball positioning; simulating the theoretical system with applied PID; and investigating practical results compared to theoretical outcomes. The embedded system actuates three servos based on webcam feedback with DSP control. Initial PID implementation resulted in high overshooting, which was mitigated by adjusting error gain. The study also explored alternative controllers (PI1, PI2, PD), revealing the PD controller's effective balance of stability and responsiveness. This research validates the efficacy of PID controllers in achieving stable system responses, emphasizing the influence of nonlinear and coupling factors on stability and performance. The complexities of controlling a multi-DOF nonlinear system underscore its significance in automatic control labs, aerospace engineering, and beyond.