A Comparative Study of Pole Placement and LQR in Cart Inverted Pendulum Controller Design

The inverted pendulum systems have been well recognized as agreeable benchmarks for evaluating various aspects in control systems. It also mimics numerous real-world important physical systems. Many control algorithms have been implemented for the inverted pendulum system. This paper is presented to conduct the comparative study of the pole placement and linear quadratic regulator (LQR) control designs for the cart inverted pendulum system. The dynamic model of the cart inverted pendulum system, including the belt drive system as an actuator, is modelled. Its linearized model is adopted in the controller design based on the pole placement and LQR methods. Simulations were carried out using the full nonlinear model. The control responses from 5 different controllers designed by the two control techniques are simulated to comprehend the benefits of LQR over the pole placement. The simulation results show higher degrees of freedom in the LQR method in manipulating control performance in the individual states.