Double inverted pendulum sliding mode variation structure control based on fractional order exponential approach law

Rotary double inverted pendulum system is a typical nonlinear, much variable, high order and unstable underactuated system. Currently, common sliding mode variable structure control method made system being vibration, long adjusting time and large overshoot, and so on. Aiming at these problems, fractional order improvement is proposed in this paper. Simulating on rotary double inverted pendulum system, the result´s comparison indicates that fractional-order method has obvious superiority, like overshoot decreasing, adjusting time shortening, and vibration weakening. The simulation result provides theory for a hardware-in-loop simulation for rotary double inverted pendulum system.