LQR control with refined PID to balance rotary inverted pendulum with time-varying uncertainty

Inverted pendulum is a nonlinear dynamical system with a strong implication in studying human balance, developing bipedal robot or rehabilitation. The rotary type of the inverted pendulum showed rather complicated to implement its control and maintain its stability than a linear one. Design and implement the control law of such a complicated system is quite difficult and challenging. The paper thus proposed a policy by using combination of LQR and refined PID control to maintain the inverted balance of the pendulum. Together with a swing up control, the full control of the pendulum was practically implemented, and realized to be more robust to outside interference.