Fractional PID based stability control for a single link rotary inverted pendulum

Fractional order based stability control for the system of the single link rotary inverted pendulum is presented. The mathematical model is derived using Lagrange Equation and the G-L fractional calculus. Then the integer order PID controller and fractional order PID controller are designed respectively. Under the condition of the same parameters K
_p
, K
_I
, and K
_D
, the integrator of order λ and a differentiator of order μ of the fractional order PID controller are adjusted adaptively. Finally, comparing with the integer order PID controller, the results show the system of fractional order PID controller is more quickly swigged, and the stability control performance is more effective.