Mann, George K. I.

Systematic Analysis and Design of Fuzzy Logic Controllers for Process Control

[PhD thesis]. St. John's, NL: Memorial University of Newfoundland

Gosine, Raymond G. (supervisor)

September 1999

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- Abstract
Fuzzy Logic is relatively a recent development in the field of artificial intelligence. Since 1975. research and development in this field has had significant impact on industrial control including applications in many consumer products. A survey of the literature suggests that the majority of fuzzy control applications belong to the class of fuzzy PID-like or simply fuzzy PID controllers. Also the literature reveals that the existing design criteria require trial and error methods involving many computer simulations and need time to achieve satisfactory optimum control. This thesis presents a systematic study and analysis of fuzzy PID-type controllers with particular attention to process control. The work aims to remove the ad-hoc procedures and multi-dimensional complexity in the conventional fuzzy control designs and to present an analytical framework for the systematic design of fuzzy logic controllers.

The work investigates different fuzzy PID control structures including the conventional Mamdani-type controller. By expressing the fuzzy rules in different forms, each PID structure is distinctly identified. The rules are written in terms of the feed back error signals of a closed- loop control system. Therefore a general fuzzy PID controller output may be produced with three-, two- or one-input rule inference. A simple analytical procedure is developed to deduce the closed form expressions for generating outputs for general fuzzy PID controllers. The analysis starts with a linear-like fuzzy controller. Nonlinear fuzzy controllers are then systematically developed. The solution algorithm has the capability to generate the closed- form expressions to the general three-input fuzzy inference. The two- and one-input inferences are obtained as special cases of the general solution. The linear-like fuzzy output is used to identify the fuzzy PID actions in a dissociated form. The design of fuzzy controllers is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear PID gains. By assigning a minimum number of rules to each PID structure, the linear and nonlinear gains are explicitly presented. The tuning characteristics of each structure are evaluated with respect to their functional behaviours. The rule de- coupled and one-input rule structures proposed in this thesis provide greater flexibility and better functional properties than the conventional fuzzy controllers.

Non-linearity analysis is used to assess and rank the different fuzzy systems for fuzzy control. The normalized fuzzy output characteristics are identified for two-point control. Thus, a performance criterion is developed to identify the non-linearity tuning properties of the fuzzy controllers. For each fuzzy PID type, a basis for non-linearity-tuning is developed. Using the new evaluation approach, different fuzzy systems are assessed. The min-max- gravity fuzzy reasoning has shown better nonlinear properties for fuzzy control applications. An alternative nonlinear control using spline-based functions is proposed. The geometrically based nonlinear controller has better nonlinear properties for PID control.

Linear PID controllers are analyzed in detail. The study is narrowed to process systems whose dynamics can be roughly approximated to first-order plus dead-time plant systems. The PID analysis covers the process systems having normalized time delay ranging from zero to any higher value. The time-domain-based analysis produces new PID tuning expressions for each case. The proposed tuning rules accommodate actuator saturation limits and avoid integral wind-up during the control. Numerical studies are made for higher order processes having monotonic open-loop characteristics. With the new tuning rules better performance is observed than with other commonly available tuning methods.

Fuzzy PID controllers are then evaluated for process control. A novel two-level tuning scheme is proposed for designing and tuning fuzzy controllers. For comparisons, three tuning methods are evaluated: (a) design based on a genetic algorithm (b) design based on a trial and error method of tuning and (c) design based on two-level tuning rules. The off-line design methods, such as genetic based tuning and trial and error based tuning, are unable to produce any improved control compared to linear PID controllers. The two-level tuning strategy uses the available linear control knowledge, and the resulting design always guarantees better performance than the linear controllers. The numerical simulations prove the new tuning method can be effectively used for any fuzzy PID controller type. Finally the two-level tuning is effectively implemented in a real time control problem. With the systematic two- level tuning, the fuzzy controllers are able to produce superior and improved performance to linear PID controllers. The design and tuning is simple and therefore the method can be extended to any process control problem.