FUZZY CONTROLLER: INTELLIGENT DESIGN APPROACHES WITH REDUCED RULE SET

Abstract

The ever increasing technological demands of today call for very complex systems, which in turn require highly sophisticated controllers to ensure that high performance can be achieved and maintained under adverse conditions. There are needs in the control of these complex systems, which cannot be met by conventional approaches to control. Therefore in recent years, soft computing approaches in control applications have emerged as an integrated, active and fruitful area of research and development. The improved technology in this area, explore alternative solutions based on artificial intelligence (AI) and intelligent control techniques and specifically in the field of fuzzy systems. Fuzzy Logic Controllers (FLCs) have proved to be more robust and their performances are less sensitive to parameter variations than conventional controllers. Unlike conventional control, which is based on mathematical model ofa plant, a FLC usually embeds the intuition and experience of human operator. Even combinations between FLCs and conventional controllers have also been designed. Among the various types, Proportional-Integral (PI), Proportional-Derivative (PD), Proportional-Integral- Derivative (PID) type FLCs are used like conventional controllers in process control system. PI type FLCs are most common and practically followed by the PD type FLCs because it can be seen in the facts that human, generally, are not so sensitive to absolute values of data in their sensing and actuation, and besides sometimes it is not possible to remove out steady state error with PD type controllers for large class ofsystems. Afuzzy controller has a fixed set of control rules, usually derived from expert's knowledge. Trial and error has been anatural choice to design fuzzy systems since their origin. The design of FLC is, therefore, developed by determining the rule base and some suitable fuzzy sets over the controller's input and output ranges. In the present study, efforts have been devoted to extract appropriate rule base and observed that increasing the rules and number of membership functions beyond a certain limit is fruitless as it increases the complexity of FLC and has almost no effect on output response on the system. Fuzzy rules can be easily and directly formulated by experts in the form oflinguistic rules. The selection of fuzzy "if-then" rules often relies on a substantial amount of heuristic observations to express knowledge of proper strategy. Obviously, it is difficult for human experts to examine all the input/output data from a complex system to find the proper number of rules for fuzzy system. So, in this work, different intelligent approaches are used to extract rule set covering the whole input/output space as well as membership functions for each input variable. The approaches are fuzzy curves, fuzzy subtractive clustering (FSC), neural networks and neurofuzzy technique. The objective of using these approaches is to design a fuzzy logic controller with less number of rules leading to a smaller amount of computational time and memory. The author investigates how fuzzy curves and FSC approach, modelled from a set of input/output data, can be applied to the area of control theory for linear and nonlinear dynamic systems. Both noisy and noise-free data have been considered. Simulation shows the effectiveness of the proposed FLC as compared to existing FLC. In FSC approach, it is found that some membership functions projected from different clusters have high degree of similarity. A similarity measure is used to eliminate the closely spaced membership functions for each input variable. Although the number of rules is automatically determined by this method, a user-specified parameter ra (the radius of influence of cluster center) strongly affects the number of rules that will be generated. A suggestion to choose the value of ra is also given. A set of fuzzy rules often needs to be manually adjusted on a trial-and-error basis before it reaches the desired level of performance. Hence, it is desirable to develop an auto-tuning method that can improve its performance based on its experience, and to adapt its response in relation to variations in the process dynamics. A simple and effective method for tuning of fuzzy PI controller based on fuzzy logic is proposed. Here the input scaling factors are tuned online by gain updating factors whose values are determined by rule base with the error and change in error as inputs according to the required controlled process. The auto-tuning method is applied to PI type FLC for simulation experiments with various types of linear and nonlinear processes including well-known example of coupled tank and first order delayed process. A number of performance indices such as peak overshoot, settling time, rise time and integral square error, are computed for a detailed performance comparison of the auto-tuned FLC with conventional FLC. It is observed that the performance is good using the proposed tuning

mechanism but due to three fuzzy reasoning blocks the computational time and memory used is higher. FSC approach is then used to reduce the fuzzy inference rules ofthe three fuzzy reasoning blocks which is shown to minimize the computational time and amount of memory used. Aneural network tuned fuzzy controller is also proposed for controlling multi-input multi-output (MIMO) systems. For the convenience of analysis, the structure ofMIMO fuzzy controller is divided into single-input single-output controllers for controlling each degree of freedom. According to the characteristics of the system's dynamics coupling, an appropriate coupling fuzzy controller is incorporated to improve the performance. The simulation analysis on a two-level mass-spring MIMO vibration system is carried out and results show the effectiveness of the proposed fuzzy controller. The performance though improved, the computational time and memory used is comparatively higher, due to the four fuzzy reasoning blocks and this number may increase if number of input/output increases. To reduce the computational burden during implementation, a fuzzy neural network is designed from a set of input-output training data. Besides reducing fuzzy rules, computational time and consuming less memory, this control strategy also simplifies the implementation problem of fuzzy control. A fuzzy neural network is then used to predict the future values of a chaotic time series and to estimate the number ofautomobile trips generated from an area based on demographics factors. Furthermore, the well-known examples of linear and nonlinear systems are also simulated. In this dissertation, the design of fuzzy controller has been achieved with reduced rule set using different approaches. The approaches are fuzzy curve, FSC, neural networks and neurofuzzy algorithm. The results show that the controller designed, using these approaches, has minimum amount of computational time, memory and gives satisfactory performance. The performance of FLC can further improve by making it adaptive. It is also illustrated by the proposed auto-tuning method when applied to a variety of linear and nonlinear systems.