Development and Application of a Gradient Descent Method in Adaptive Model Reference Fuzzy Control Aous Thabit Naman Prof. Mohd. Zaki Abdulmuin Dr. Hamzah Arof Electrical Engineering Dept., Mechanical Engineering Dept., Electrical Engineering Dept., Universiti Malaya, Universiti Malaya, Universiti Malaya, 50603 KL, Malaysia. 50603 KL, Malaysia. 50603 KL, Malaysia. e-mail: zakin,fl<.iiin.edu.ii~y e-mail: aous72@,hotmai I.com e-mail: hamza hfi3 tk. tin1 .edii.m\ Abstract: This paper presents an adaptive model- reference fuzzy controller (AMRFC) to control the water level of a water tank. It derives the AMRFC and compares its performance with the more conventional methods of proportional-integral (PI) control and model- reference adaptive control (MRAC). The gradient descent method is chosen to adapt the AMRFC. Unlike most of the papers reviewed, which use the error and error change as inputs to the fuzzy system, this paper uses the theoretical background developed for MRAC in choosing these inputs. Although the controller uses many inference rules (441 rules), it is shown that the required mathematical calculations are not much, making implementation on a low-end microcontroller feasible. The control algorithm is implemented in simulation and real-time using an 8-bit microcontroller. It is found that the AMRFC and MRAC have approximately similar performance, however they compare favorably to the PI controller. This similarity in performance is due to the linearity of the plant, and it is expected that the AMRFC would have a much performance if the plant had a stronger non-linearity. Keywords: Fuzzy Control, Adaptive Control, Model-Based Control. I. Introduction Fuzzy control has evolved over the years to become one of the most active and fruitful areas of research in the application of fuzzy set theory. Although, Lee [l] gives many applications of fuzzy controllers, fuzzy controllers are still finding newer applications, like using them in DC/DC converters [2], in air-conditioning systems [3], and in fast valving control [4]. Ying [5] asserts that there are two major different types of fuzzy controllers: the Mamdani type [6] and the Takagi- Sugeno-Kang (Sugeno, for short) type [7]. The Mamdani control rules are significantly more linguistically intuitive while Sugeno rules appear to have more interpolation power even for a relatively small number of control rules. Both types of fuzzy control have been successfully applied to solve practical control problems. Many adaptation schemes have been implemented to optimize fuzzy systems. Some authors use intuition [8,9] and some use direct or indirect Model Reference Adaptive System (MRAS) among other schemes. The use of direct and indirect MRAS (Model Reference Adaptive System) allows the on-line adjustments of different parameters of the fuzzy inference engine’s rules [3,10]. The gradient descent method is one of the most favored adjustment methods due to its simplicity [2,1 I]. Although many of the papers reviewed implement model- reference adaptation, none of them relies, in choosing the controller inputs, on the theory developed for MRAC [ 121, which specifies the necessary controller inputs to achieve exact model following. In this paper, we try to make use of the theoretical background of MRAC in choosing the inputs to the controller. This controller is a Sugeno fuzzy system adapted online by utilizing a direct adaptation method based on the gradient descent method. The objective of the controller is to control the level of water in a tank. The next section discusses the plant to be controlled, whereas section three derives the adaptive model- reference fuzzy controller (AMRFC). Section four explains how the system is implemented and illustrates the results. Finally, section five is devoted to discussions and conclusions. 11. The Plant For every controller there must be a plant where the controller can be applied. In this paper, a simple water level system is used. Although this system is a typical academic first-order system, the lack of good understanding of the system dynamics results in an improper model, leading to a complicated design of the controller, which might not satisfy the requirements. A good model of the system is a basic starting point. Fig. 1 depicts a graphical block diagram of the overall system that is used for experimenting. To obtain a linearized model of the water level system, the pump must be calibrated against the input voltage, the physical model for the water tank including the drainage should be extracted. and finally the level transducer should be calibrated. The mathematical relation that governs the water tank is given by [13,14] to be 0-7803-63 5 5-8/00/$10.0002000 IEEE 111-358