Design and implementation of fractional PID controller for rotary inverted pendulum

As for the stability control problem for rotary inverted pendulum, the two closed-loop fractional order PID control scheme is used to control the pendulum. First, the mathematical model of rotary inverted pendulum is established according to the Euler-Lagrange equation. Then, a fractional order PID controller is designed based on the Bode ideal transfer function. Finally, the fractional order PID (FOPID) controller, fractional PD (FOPD) controller and integer order PD (IOPD) controller are applied to the rotary inverted pendulum system which based on the Quanser company loop simulation experiment platform. The results show that the FOPID controller is better than the FOPD and IOPD controller in stabilizing the system and the angle of the pendulum is closest to the stable equilibrium point.