PERFORMANCE COMPARISON AND OPTIMIZATION OF BALL AND BEAM SYSTEM USING DIFFERENT CONTROLLERS

Abstract

The Ball and Beam system (BBS) is a nonlinear and unstable system which resembles with many real-time complicated systems, such as aircraft take off, aircraft turning in the space and robot walking with load in one arm. Its simple structure offers the easy modeling and testing different intelligent control techniques. Providing an appropriate beam angle to give the stability to the ball on the beam in a specific position with certain specifications, is a challenging task for the control system researchers. The performance of the system is greatly dependent on the accuracy of the control action. In this research work a very good and intelligent controller, single input fuzzy logic controller has been designed. This single input fuzzy logic controller has been designed based on signed distance method and theory of fuzzy logic control. Signed distance method makes the controller with less number of tuning parameters and less number of linguistic rules. In the sense of transient and steady state performance, single input fuzzy logic controller is capable of giving satisfactory performance. The power of signed distance method is used to design an interval type-2 fuzzy logic controller that is single input interval type-2 fuzzy logic controller. This controller also has less number of rules and less number of tuning parameters. The membership function of a type-2 fuzzy set is three dimensional, where third dimension is the value of membership function at each point on its two dimensional domain that is called its footprint of uncertainty. The advantage of footprint of uncertainty helps the single input interval type-2 fuzzy logic controller to give satisfactory performance of the system in the presence of disturbance and parameter-variation. This robustness of this controller is the most remarkable and acceptable property of the single input interval type-2 fuzzy logic controller. Then an optimized full state feedback controller powered by linear quadratic regulator theory and Genetic Algorithm, has been designed for the ball and beam system. Genetic Algorithm is coded for three types of fitness function, such as Integral Time and Absolute Error (ITAE), Integral Square Error (ISE) and Integral Absolute Error (IAE). The optimum performance is obtained by the ITAE fitness function. The simulation work is carried out in simulink environment of MATLAB (7.8.0) software. The simulation results are also validated in the real-time implementation of the ball and beam system, designed by Googol Technology. The results in chapter-6 show the superiority of the designed controllers over the existing controllers.