Design and simulation of fractional order PID controller for an inverted pendulum system

The paper proposed the design scheme for a FOPID-based controller and implemented its simulation according to the non-linearity, multivariate, strong coupling and instability of the inverted pendulum system. First, the paper built a mathematical model for the system and derived the transfer function of the pendulum's angle and displacement of the car. The appropriate closed-loop dominant poles were selected to satisfy the frequency domain stable performance requirements for the given system and the system can get the desired dynamic performance and stability after stabilization. And the parameters of the fractional order controller were tuned with the horizontal phase algorithm at the cutoff frequency. Comparing simulation of the IOPID-based controller with that of the FOPID-based controller shows that the FOPID-based controller can achieve better control effect with small overshoot and fast convergence.