Fuzzy Sliding Mode Variable Structure Control Algorithm On Planar Double Inverted Pendulum

Inverted pendulum device is an absolute unstable system, it has high-order, nonlinear and strong coupling characteristics, so research on inverted pendulum control can effectively reflect many problems. Research on inverted pendulum have both important theoretical value and application value.This paper first describes the research background of inverted pendulum, then derives the mathematical model of planar double inverted pendulum system by use of Lagrange modeling method. After partial linearization, we can arrive at the pendulum's equation of state space, which is a controlable, observeable, but absolute unstable system after analysising.We have designed planar double inverted pendulum's SMC(Sliding Mode Controler) and FSMC(Fuzzy Sliding Mode Controller) controller. SMC's simulating results tells us that SMC can stable the pendulum, but we can not eliminate chattering by adjusting the controller's parameters; On the contrary, FSMC's simulating results proves that FSMC can weaken SMC's chattering, improve the system's dynamic response and anti-disturbance performance.The results show that FSMC inherits the characteristics of sliding mode variable structure control algorithm it not only weakened SMC's chattering, but also smooths the pendulum's stabling process is more stable and accelerates the dynamic response.