Modified inverted pendulum on a cart system with four-bar mechanism

In this study, the inverted pendulum on cart system, classic problem of control theory has been modified and an experimental control design has been proposed to maintain balance of a four-bar mechanism instead of a traditional pendulum rod system. Both the inverted pendulum on cart system and the four-bar mechanism are commonly used systems that have been the subject of many control theory problems. Therefore, the combination of these two widely studied systems, which is the focus of this research paper, could very well be integrated for various practical problems such as Segway transportation systems, robotic applications, and rocket guidance systems. With this motivation the modified system has been designated as the "four-bar on a cart system", and dynamic equations of motion have been obtained using the Lagrange method. Furthermore, the performance of the system has been validated through an established experimental setup, and the experimental results for a Lyapunov type backstepping controller are presented. The utilization of a four-bar mechanism instead of a pendulum rod has led to greater challenges in the derivation of the motion of equation due to the additional link position variables in the system. However, despite the modifications on the system, the total degrees of freedom remain unchanged, and the system continues to exhibit dynamic behavior similar to inverted pendulum on cart system. For the completeness of the proposed topic, the inverted pendulum on cart system was initially investigated in this study, and its experimental results were presented. Subsequently, the focus shifted to the four-bar on a cart system.