Equivalent dynamic fuzzy controllers and their application to engine control
Kalmanje S. Krishnakumar, N. Kulkarni · 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit · 1998
In this paper a fuzzy logic control scheme that combines the power of linear dynamic controllers with fuzzy set theory is developed. Theoretical analysis of the technique is presented to illustrate the benefits of this particular scheme. This technique uses a linear dynamic compensator designed for a specific operating condition as the inferencing engine. The ability of this hybrid controller in maintaining robust operation of an aircraft engine model has been investigated. The results of this study reveal that the controller maintains plant stability even when the plant open-loop model is varied substantially. Also, performance to sensor noise shows the superior ability of the controller to accommodate noise. Introduction Fuzzy Logic controllers have been successfully used in several applications in the past few years [1-4]. However, synthesis of FL controllers to a large extent does not rely on sound mathematical principles. It is entirely based on the nature of problem in hand and the ability of the engineer to translate his experience into meaningful rules and fuzzy sets. Although this approach works well for simple problems or problems with single input and single output, it is almost impossible to manually arrive at fuzzy controllers for more complex problems. Several approaches based on parameter optimization, neural networks, clustering, etc [5-7] have been proposed to solve this problem. All of these methods require a good model of the system and a great deal of computing power to realize the controller. Also, proving stability becomes difficult if not an impossible task using the above techniques. One of the benefits of fuzzy logic is the fuzzy granularization that is obtained by defining fuzzy sets for the inputs and outputs. It could be claimed that this is the most important contribution of fuzzy logic to the control community rather than the logic (inferencing) part of fuzzy controllers. Towards this appreciation, we have approached to combine this granularization advantage with the power of linear dynamic controllers to arrive at a powerful hybrid technique. In this technique, we start with a linear dynamic controller that has been designed to meet certain specifications (stability and performance). We then fuzzify the inputs and use the dynamics of the controller as the inferencing engine. This results in a fuzzy output that is defuzzified to arrive at a crisp control. In the following pages, we first present the equivalency between a linear dynamic controller and a fuzzified dynamic controller. Then, we show that by manipulating the membership function (or granularization) definition one can achieve better controller robustness. We end the paper by presenting results of the hybrid controller for an engine control problem. Equivalent Fuzzy Dynamic Controller For the present problem we consider the control architecture presented in Figure 1. For this architecture we have the closed-loop transfer function as, //„•> X*) y(s)«(s) d(s) u(s) d(s) Now, and d(s~) implying,