Some mathematical aspects of fuzzy systems

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion and additive inversion, are proposed. Based on these tools, the relationship among fuzzy vectors in fuzzy space is studied. Analytical expressions of maximum and mean solutions for FREs, and an optimal algorithm for calculating minimum solutions are developed. Second, the possibility of applying functional analysis theory to Takagi-Sugeno (T-S) fuzzy systems design is investigated. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling. Third, the mathematical aspects of model-based fuzzy control (MBFC) are investigated. MBFC theory is not suitable for general nonlinear systems, due to an implicit linearity assumption. This assumption limits fuzzy controller design to a special case of linear time-varying systems control. To apply MBFC in general nonlinear control, a new stability criterion for general nonlinear fuzzy system is proposed. The mathematical aspects investigated in this research, provide a systematic guidance on issues such as efficient fuzzy systems modelling, balanced "soft" and "hard" computing in fuzzy system design, and applicability of fuzzy control to general nonlinear systems. They serve as a theoretical basis for further development of fuzzy systems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Development of dc-dc converter for dc motor using fuzzy logic controller

When the DC motor is turned on, the start dc motor speed will experience overshoot at the starting speed of the motor. This overshoot will affect the current rise high as if connected to a load. The use of conventional controllers has long been used to control the dc motor and reduce overshoot starting. Fuzzy logic controller is one controller that can be used to control the speed of a dc motor including motor control overshoot starting. To see the effectiveness of fuzzy logic controller in dc motor speed control, a study done by designing a conventional two-Integrated controllers of proportional controller (PI) and proportional-Integrated-Derivatives controller (PID) and compared with fuzzy logic controller. The design of Fuzzy Logic Controller (FLC) does not require an exact mathematical model. Instead, it is design based on general knowledge of the plant. Both three controllers are connected to a dc motor as a load to control the motor speed to the required level. The effectiveness of the designed FLC is compared with designed conventional controllers to examine aspects of starting overshoot, settling time and ripple factor for dc motor speed

Multiple-input multiple-output proportional-integral-proportional-derivative type fuzzy logic controller design for a twin rotor system

A new multiple-input multiple-output (MIMO) proportional-integral-proportional-derivative (PIPD) type fuzzy logic controller (FLC) is proposed for pitch and yaw motion control of a twin rotor system in this study. A fuzzy feedforward compensator for gravity effects on pitch motion of the twin rotor is also designed. Fuzzy logic was preferred for controller design since it can be applied to nonlinear systems and do not require the mathematical model of the system. The twin rotor system is a highly nonlinear system that includes coupling effects between pitch and yaw motions and has similar dynamics to that of a helicopter in certain aspects. Experimental results demonstrate that the proposed controller is able to stabilize the system along with good trajectory tracking performance

Some mathematical aspects of fuzzy systems

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion and additive inversion, are proposed. Based on these tools, the relationship among fuzzy vectors in fuzzy space is studied. Analytical expressions of maximum and mean solutions for FREs, and an optimal algorithm for calculating minimum solutions are developed. Second, the possibility of applying functional analysis theory to Takagi-Sugeno (T-S) fuzzy systems design is investigated. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling. Third, the mathematical aspects of model-based fuzzy control (MBFC) are investigated. MBFC theory is not suitable for general nonlinear systems, due to an implicit linearity assumption. This assumption limits fuzzy controller design to a special case of linear time-varying systems control. To apply MBFC in general nonlinear control, a new stability criterion for general nonlinear fuzzy system is proposed. The mathematical aspects investigated in this research, provide a systematic guidance on issues such as efficient fuzzy systems modelling, balanced 'soft' and 'hard' computing in fuzzy system design, and applicability of fuzzy control to general nonlinear systems. They serve as a theoretical basis for further development of fuzzy systems

Intelligent STATCOM Voltage Regulation using Fuzzy Logic Control

Reactive power compensation is a very important and challenging task in electrical power systems today. Future trends foreseen in power systems such as high interconnectivity and the integration of renewable energy resources produce even more issues related to power system control and stability. Flexible AC transmission systems are vastly used in power systems in order to mitigate several performance aspects found in typical power systems. One shunt connected device in particular, STATCOM, is very powerful and commonly used in voltage regulation at the power transmission level. STATCOM uses voltage sourced converters to inject or absorb reactive power from the power grid as commanded to stabilize the transmission line voltage at the point of connection. The control of STATCOM has relied historically on using traditional PI controllers, however, since the dynamic response of STATCOM highly affects its ability to perform its task, improving the capabilities of STATCOM using more advanced control approaches has become vital for both manufacturers and power systems operators. Fuzzy logic control, as one area of artificial intelligence techniques, has been emerging in recent years as a complement to the conventional methods in various areas of power systems control. The most significant advantage of fuzzy controller as an intelligent controller is that it doesn’t require mathematical modelling. It is robust and nonlinear in its nature, and expert’s knowledge can be utilized in generating control rules. The main contribution is to use fuzzy logic control theory to design a pure fuzzy logic control and another fuzzy adaptive PI control strategies for STATCOM that are superior in performance to traditional PI control approach. This will increase STATCOM’s ability to seamlessly perform their task in voltage regulation. This work investigates the performance of classical PI controlled STATCOM then compares it with fuzzy logic based STATCOM and fuzzy adaptive PI controlled STATCOM. Simulations done using MATLAB on a three generator test system show that adaptive fuzzy PI control technique is faster in responding to voltage variations and better in tracking the reactive current reference. Results also show that a direct control using fuzzy logic provides even faster voltage regulation and acts almost as a perfect tracker for reference reactive current

Extruder for food product (otak–otak) with heater and roll cutter

Food extrusion is a form of extrusion used in food industries. It is a process by which a set of mixed ingredients are forced through an opening in a perforated plate or die with a design specific to the food, and is then cut to a specified size by blades [1]. Summary of the invention principal objects of the present invention are to provide a machine capable of continuously producing food products having an’ extruded filler material of meat or similarity and an extruded outer covering of a moldable food product, such as otak-otak, that completely envelopes the filler material

Fuzzy Logic Path Planning System for Collision Avoidance by an Autonomous Rover Vehicle

Systems already developed at JSC have shown the benefits of applying fuzzy logic control theory to space related operations. Four major issues are addressed that are associated with developing an autonomous collision avoidance subsystem within a path planning system designed for application in a remote, hostile environment that does not lend itself well to remote manipulation of the vehicle involved through Earth-based telecommunication. A good focus for this is unmanned exploration of the surface of Mars. The uncertainties involved indicate that robust approaches such as fuzzy logic control are particularly appropriate. The four major issues addressed are: (1) avoidance of a single fuzzy moving obstacle; (2) back off from a dead end in a static obstacle environment; (3) fusion of sensor data to detect obstacles; and (4) options for adaptive learning in a path planning system

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks

A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued

An evaluation methodology for ergonomic design of electronic consumer products based on fuzzy axiomatic design

This article is posted with permission of OCP Science imprint. Copyright @ 2008 Old City Publishing Group.The development life cycle of software and electronic products has been shortened by the growth of rapid prototyping techniques. The evaluation of electronic consumer products should consider hardware and software as well as the ergonomic usability, emotional appeal and aesthetic integrity of the design. This research follows a systematic approach to develop an evaluation methodology for electronic mobile products on ergonomic design. The proposed methodology is based on fuzzy multi attribute decision making and fuzzy axiomatic design realized in three steps; determination of ergonomic attributes for electronic consumer products, determination of a representative set of alternatives, and selection of the best alternative in terms of ergonomic design by utilizing fuzzy axiomatic design. A case study is also provided to support the proposed methodology