Comparison of fuzzy logic and classical controller designs for nonlinear systems

The design of controllers for nonlinear systems in industry is a complex and difficult task. The development of nonlinear control techniques has been approached in many different ways with varied results. One approach which has been shown promise for solving nonlinear control problems is the use of fuzzy logic control. Fuzzy controllers have proven suitable for many nonlinearly modeled industrial processes (as have been successfully demonstrated in Japan and Europe) such as linguistically controlled devices and systems that cannot be precisely described by mathematical formulae. A unified approach for comparing the performance of fuzzy and nonfuzzy (classical) controller designs for nonlinear systems is presented in this dissertation; also, two fuzzy controllers are presented and compared with classical controllers and then compared with each other. These two fuzzy controllers are the Mamdani (for the two dimensional inverted pendulum problem), and the Sugeno (for the four dimensional inverted pendulum problem) models. The classical controllers used in this dissertation are the proportional-integral-derivative (PID) and the state variable feedback (SVF). A design of fuzzy and classical controllers for an example of nonlinear systems is presented (inverted pendulum). A comparison of state variable feedback and Sugeno fuzzy control are discussed. Also a full discussion of the advantages and disadvantages of fuzzy and classical controllers are presented.; In this dissertation, fuzzy logic control demonstrated good performance. Furthermore, fuzzy logic offers the advantage of faster design, and it is easy to understand, because fuzzy logic emulates human control strategies. Also fuzzy control works well for higher-order and nonlinear system and shows the efficiency over the PID and state variable feedback controllers. In PID, controller parameters must be continuously tuned in order to meet the performance criteria. The same process will apply to the state variable feedback control: the gain matrix k_i has to be modified in order to meet the performance criteria. It is shown that by applying the obtained consequent coefficients from the rules of the Sugeno model to the state-variable feedback, we get the root locus based on the Sugeno model (all the poles of the system are in the left half plane). Therefor, the Sugeno model provides a strong basis for stability analysis of fuzzy systems. The advantages of the Mamdani and Sugeno models are presented.