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Accurate tracking of ball trajectories on a platform using a 2-DOF balancer system poses significant challenges in the existing literature due to its inherent nonlinearity and instability. This research addresses these challenges through a two-fold approach. Firstly, we focus on designing a robust 2-DOF ball balancer system model. Secondly, we perform a comparative study of three control techniques: Linear Quadratic Regulator-based Proportional (LQRP), Full State Feedback-based Proportional (FSFP), and Classical Proportional Derivative-based Proportional (PDP) control. To evaluate the effectiveness of the designed controllers, we conduct both simulation and experimental tests using MATLAB Simulink integrated with Quarc software and the 2DOF ball balancer system Quanser hardware. The results demonstrate that the Linear Quadratic Regulator-based proportional control exhibits superior performance in terms of transient response, including percentage overshoot, settling time, and peak time. Moreover, it showcases excellent steady-state response, achieving a minimum steady-state error of 0. 641mm, outperforming the other techniques investigated in this study.
Sidi et al. (Sun,) studied this question.