Modeling and Control of Underactuated System Using LQR Controller Based on GA

Cart-pole system is the benchmark for the study of controls. Literature ensures the availability of various controllers to control an underactuated system at an unstable position. Due to its simplicity, LQR optimal control is mostly used to cart-pole system despite challenges in the selection of LQR parameters. The dynamic model of the cart-pole system is derived using the Euler–Lagrangian method and controllability analysis is considered. According to optimal determination problem of the weighting matrix Q and R in LQR, the genetic algorithm (GA) is adopted and the optimal parameter values are used to stable the system at the unstable equilibrium position. From the results, it has been found that the system is stable, robust than the unoptimized LQR controller. This algorithm can avoid heavy and complicated work, improve work efficiency, and has strong practicability.