A ball-on-wheel system is a recently developed model in the field of automatic control. It serves as a simple model, meeting the learning and algorithmic research needs of students. With this model, there are various algorithms available for system control, such as PID controllers, fuzzy PID controllers, and sliding mode controllers, among others. In this paper, we construct a mechanical model for the system. We choose the Linear Quadratic Regulator (LQR) algorithm to design for this system. Simulation and experimental results demonstrate the effective operation of the LQR controller for the inverted pendulum on a cart system. Additionally, tuning experiments indicate that the parameters have been verified and confirmed to be consistent with the theoretical tuning principles of the LQR controller.
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Nguyen et al. (2024) studied this question.
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