Modelling and simulation of the inverted pendulum based on granular hybrid system

The inverted pendulum is a multi-variable, nonlinear, inherently unstable and non-minimum phase system. There are two main problems considered in controlling the inverted pendulum: one is how to swing up fast; the other is to stabilize the inverted pendulum at the operating position. From the viewpoint of granular computing theory, the inverted pendulum can be regard as a hybrid system of different granularity worlds, which exploits controllers switching between the discrete events in order to swing up the pendulum from the initial position and to stabilize at the target position. A granular hybrid automaton was proposed in the paper and the granular hybrid system, as a controller of inverted pendulum, was simulated in Matlab and the results show that the inverted pendulum can be swung up rapidly and then be stabilized in the balance area.