VARIABLE UNIVERSE FUZZY CONTROLLER FOR STABILIZATION OF DOUBLE INVERTED PENDULUM USING SIGNED DISTANCE INPUT VARIABLE

Abstract

Inverted Pendulum (IP) system has the property of unstable, higher order, multivariable and highly coupled which can be considered as a typical non linear system. A more interesting and complicated problem in terms of controller design is the Double Inverted Pendulum (DIP) system, in which one pendulum is mounted over the other pendulum on the cart. Due to its complex structure it is a favorite problem in the field of control theory, computer control and robotics. Fuzzy control, variable structure control and robust control are some of the methods commonly used to solve this problem. In this dissertation a conventional fuzzy controller with rule base of forty nine rules is designed to stabilize the double inverted pendulum. Traditional fuzzy controller has many advantages, but its control accuracy is low. Therefore it is not advised to use this method in such applications which require high precise control. So the variable universe technique is used to vary the universe of discourse of fuzzy controller with the help of contraction-expansion factor. By adjusting scaling gains (contraction-expansion factors), the universe is changed automatically and the rules are dynamically adjusted. The basic concept behind the variation of universe of discourse is that if the input variable is large then its weight should be increased and when it is small then its weight should be decreased. After obtaining a variable fuzzy controller its rule base is reduced by the use of signed distance method. By this method rule base has been reduced to only seven rules without affecting the performance of the controller. In this method, the signed distance is taken as sole input at the place of the error and the change-in-error. The simulation results of variable universe fuzzy controller are compared with conventional fuzzy controller and a significant improvement in response time is observed. Further, the results of conventional fuzzy controller are compared with the results of single input variable universe fuzzy controller and it has been observed that while reducing the number of rules, time response remains unaltered. After verifying the technique in MATLAB SIMULATION it is also implemented on real time on 1-stage inverted pendulum in the laboratory.