ABSTRACT
The Single Input Rule Modules (SIRMs) dynamically connected fuzzy inference model transform multi-dimension fuzzy control into single-dimension fuzzy control which can greatly reduce the number of fuzzy rules. In the control system, the effects of all input variable on the system are different. For example, the angle and angular velocity of the pendulum directly affect the success in the stability control of inverted pendulum system, and the effects of the position and speed of the cart are relatively weak. That is to say, the pendulum control should take priority over the cart control before the pendulum reach equilibrium; the cart position control can only start when the pendulum is in equilibrium. As a result, each input variable corresponding to a SIRM and a dynamic importance degree, and the dynamic importance degrees will change with the control conditions. Each input variable in the SIRM has
SIRM-i : j
(1)
Here, SIRM-i expresses the ith input item, and Ri
j is the jth rule in the SIRM-i. xi is the ith input
1 INTRODUCTION
The inverted pendulum system is a typical multivariable, nonlinear, strong coupling and nonminimum phase system with natural instability characteristics, which can effectively reflect many key problems such as stabilization, nonlinear, robustness and tracking in the controlling process. It is an ideal model to verify the different control theories and techniques in teaching and scientific research. In engineering applications, the inverted pendulum system has similarities with satellite attitude control, the joint motion of robot control and steady hook device of lifting machinery. Therefore, as typical experimental equipment, the inverted pendulum system becomes a bridge from theory to practice. The study has important engineering background and practical significance.
