An investigation on the design and performance assessment of double-PID and LQR controllers for the inverted pendulum

The widespread application of inverted pendulum principles requires better dynamic performance and steady state performance of the inverted pendulum system. The objective of this paper is to design and investigate the time specification performance of the inverted pendulum controllers. Two control methods are proposed in this paper, an innovative double PID control method and a modern LQR (liner quadratic regulator) control method. Dynamic performance and steady state performance are investigated and compared of the two controllers. This paper proves that the LQR controller can guarantee the inverted pendulum a faster and smoother stabilizing process and with better robustness and less oscillation than the double-PID controller. The novelty of this paper is the design of the two controllers, and the adoption of limits cycles as the performance assessment method for the inverted pendulum, which not only makes the steady state performance assessment available, but also, provides an effective way for the evaluation of any equilibrium control problem with friction involved.