Stabilization Control of Double Inverted Pendulum Systems by the SIRMs Dynamically Connected Fuzzy Inference Model

Abstract

The SIRMs(Single Input Rule Modules)dynamically connected fuzzy inference model is applied to double inverted pendulum systems. The design methods of stabilization fuzzy controllers are presented, and the model is proved to be effective even in systems with six input items. For series-type double inverted pendulum system, a stabilization fuzzy controller is constructed, which handles six input items to cover the angular controls of the two pendulums and the position control of the cart. The method of determining each SIRM and each dynamic importance degree so that the angular control of the upper pendulum takes priority over the other two controls is discussed. It is made clear that by using the SIRMs and the dynamic importance degrees, the angular controls of the two pendulums and the position control of the cart are executed in parallel, and the priority orders of the three controls are automatically adjusted according to control situations. The simulation results show that the fuzzy controller has a high generalization ability to stabilize completely series-type double inverted pendulum systems of different parameter values in about 10 seconds. For parallel-type double inverted pendulum system, the angle and angular velocity of the two pendulums and the position and velocity of the cart are taken as input items, and a stabilization fuzzy controller is built which is similar to that of series-type double inverted pendulum system. By using the fuzzy controller, a parallel-type double inverted pendulum system can be stabilized completely within 10 seconds. This is the first time for a fuzzy controller to realize successfully complete stabilization control of a parallel-type double inverted pendulum system.