FUZZY LOGIC SYSTEMS
James Vernon: Visiting Consultant Scientist, control uk2017年高考
ABSTRACT: This is one of a ries of white papers on systems modelling, analysis and
control, prepared by Control uk to give insights into important
principles and process in control. In control systems there are a number of generic
systems and methods which are encountered in all areas of industry and technology. The
white papers aim to explain the important systems and methods in straightforward terms.
The white papers describe what makes a particular type of system/method important, how
it works and then demonstrates how to control it. The control demonstrations are performed
using models of real systems designed by our founder - Peter Wellstead, and developed for
manufacture by TQ Education and Training Ltd in their CE range of equipment. Where
possible, results from the real system are shown. This white paper is about the very simple,
but very uful method of fuzzy logic and fuzzy control.
1. Why Fuzzy Logic?
公共管理硕士Normally in logic we have a ries of statements which are either true or fal, yes or no, 0 or 1. In this context, the statement ‘the temperature is 25 degrees Celsius’ is an objective one and is either true or fal. However, for many situations the answer is more like ‘Errr’ – ‘not sure’ – ‘maybe’ – ‘that depends’ and so on. For example, on a pleasant summer’s day the statement ‘the temperature is too high’ is neither true nor fal. The statement is a qualitative one – it reprents an opinion rather than an objective fact. For example, it needs to be a bright sunny day on the beach for me to feel warm. On the other hand, I could mention some visiting scientists at Control Systems Principles who feel comfortable in a snow storm on top of a mountain. Do you e what I mean? There is no certainty to the situation – it depends upon the context.
Fuzzy logic deals with uncertainty in engineering by attaching degrees of certainty to the answer to a logical question. Why should this be uful? The answer is commercial and practical. Commercially, fuzzy logic has been ud with great success to control machines and consumer products. In the rig
ht applications fuzzy logic systems are simple to design, and can be understood and implemented by non-specialists in control theory. In most cas someone with a intermediate technical background can design a fuzzy logic controller. The control system will not be optimal but it can be acceptable. Control engineers also u it in applications where the on-board computing is very limited and adequate control is enough. Fuzzy logic is not the answer to all technical problems, but for control problems where simplicity and speed of implementation is important then fuzzy logic is a strong candidate. A cross ction of applications that have successfully ud fuzzy control includes:
Environmental Control
• Air Conditioners
• Humidifiers
Domestic Goods
• Washing Machines/Dryers
• Vacuum Cleaners
• Toasters
• Microwave Ovens
• Refrigerators
Consumer Electronics
totolook• Television
• Photocopiers
• Still and Video Cameras – Auto-focus, Exposure and Anti-Shake
• Hi-Fi Systems
Automotive Systems
•
Vehicle Climate Control •
Automatic Gearboxes •
Four – Wheel Steering • Seat/Mirror Control Systems
This is an impressive list, and gives an idea of the key application areas. In general you will not find a fuzzy controller in a safety critical application, unless the practical and theoretical performance has been completely studied.
2. Engineering Motivation
报考研究生A traditional logic decision block produces an outcome bad upon binary logic. A firm YES or NO emerges as an output of the decision block. However, the inventor of fuzzy logic, Lofi Zadeh, noted that human decision making incorporates shades of meaning in which the binary YES/NO might be replaced by:
DEFINITELY YES,
PROBABLY YES,fishermen
MAYBE,
PROBABLY NO,
DEFINITELY NO.
instruction是什么意思Fuzzy logic copies this feature of human decision making using levels of possibility in a number of uncertain (or fuzzy) categories. For example, think about the Coupled Tanks System (See Elke’s white paper on Coupled Tanks Systems on the download page uk for full details) in which the object is to adjust the input voltage, u, to the pump motor (Figure 1) so that the level in Tank 2 is held at a steady value. The measured output is the level in Tank 2, denoted by the signal . My colleague Elke would apply a PI controller to this system as fast you could say ‘the hills are alive with the Sound of Music’. But if the 2y exact level is not important then why not u a simpler controller? For example, a common n controller could u the following fuzzy control rules:
IF {level too high} THEN {reduce pump voltage}
IF {level too low} THEN {increa pump voltage}
IF {level correct} THEN {t pump voltage zero}
The controller performance would not be as good as a PI controller, but it might be acceptable – and
that is what we are after – the simplest and cheapest possible controller for a given application. Sorry about that Elke.
Figure 1. Coupled Tanks System
3. How to Do Fuzzy Logic
3.1. Classification - Turning a Real Signal into a Set of Fuzzy Variables
The first step in fuzzy logic is to convert the measured signal x (which might be the error signal in a c
ontrol system) into a t of fuzzy variables. This is called fuzzy classification or fuzzification . It is done by giving values (the will be our fuzzy variables) to each of a t of membership functions. The values for each membership function are labelled µ(x), and are determined by the original measured signal x and the shapes of the membership functions. A common fuzzy classifier splits the signal x into five fuzzy levels as follows:-
a) LP: x is large positive
b) MP: x is medium positive
c) S: x is small
d) MN: x is medium negative e) LN: x is large negative
Membership functions for three of the five fuzzy levels are shown in Figures 2a. So, for example, the value (or fuzzy variable) for the MP membership function and a signal value of is 2.5v x =5.0)5.2(=mp µ.
Figure 2a. Membership Functions for Zero Membership (S: x is small), Medium Positive
Membership (MP), Large Positive Membership (LP).
Figure 2a only shows the zero (or small S), medium positive (MP), and large positive (LP) memberships. The remaining two (MN, LN) are the same as the MP and LP shapes, but with the x axis reverd. Figure 2b shows all five membership functions on the same axis.
Figure 2b. The Complete Set of Membership Functions for Five Level Fuzzification
The shape of the membership functions in Figures 2a and 2b is termed ‘triangular’ – this is only one of many choices of membership function shapes. I u triangular shapes becau they are widely ud, simple to implement and give good results.
A practical fuzzifier would have a measured signal from a nsor at its input and would provide at its output the values (fuzzy variables) corresponding to the membership functions. For example, if a nsor signal with an output voltage of 2V is applied to a five level fuzzifier, the resulting t of fuzzy variables is:
4
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LN =====LP MP S MN µµµµµ
As the input to the fuzzifier changes in the range –10v to +10v, then the corresponding fuzzy variables will also change.
In a controller the fuzzifier is ud to determine the level of membership by connecting a measured signal from the system to the fuzzifier input. For example, if the five level fuzzifier is connected to the Coupled Tanks System, then the membership value associated with a statement like: "the level in Tank 2 is large positive " is obtained by connecting the signal for level in Tank 2 () to the input of the fuzzifier and monitoring the LP output of the classifier as in Figure 3.
2y
混血儿英语Figure 3. Measuring the Membership Value ‘Level 2 is Large and Positive’.
3.2. Fuzzy Decisions Blocks
Fuzzy control us fuzzy equivalents of logical AND, OR and NOT operations to build up fuzzy logic rules. The definitions of the are: AND : If αµ is the membership of class α for a measured variable βµand is the membership of class β for another measured variable, then the fuzzy AND is obtained a
s the minimum of the two membership values:
),min(A β回答英语
µαµβηαµβαµ=∧=ND Where the symbol ∧ is ud to denote the fuzzy AND operation. An alternative definition of the fuzzy AND is that is the product of the two membership values:
β
µαµβµαµβαµ×=∧=ND A We have ud both in practical applications and there is not much difference, so I generally recommend the first definition of fuzzy AND. OR : The previously given definitions of βαµµ apply again, and the fuzzy OR function is defined as:
),max(β
µβµβµαµβαµ=∨=OR NOT : For membership α
µ the fuzzy NOT operation is defined by: α
µαµαµ−=¬=1NOT Where the symbol ¬ is ud to denote the fuzzy NOT operation.
3.3. Defuzzification - Turning a Set of Fuzzy Variables into a Real Signal
The last step in building a fuzzy logic system is turning the fuzzy variables generated by the fuzzy logic rules into a real signal again. The fuzzy logic process which does this is called defuzzification becau it combines the fuzzy variables to give a corresponding real (crisp or non-fuzzy) signal which can then be ud to perform some action. For example, in the ca of a coupled tanks control system the crisp signal would be a voltage which can be ud to actuate the pump drive amplifier.
A five level defuzzifier block (Figure 4) will have inputs corresponding to the following five actions:
a) LP: Output signal large (positive)
b) MP: Output medium (positive)
c) S: Output signal small
d) MN: Output signal medium (negative) e) LN: Output signal large (negative)
Figure 4. Block Diagram of a Defuzzifier
The defuzzifier combines the information in the fuzzy inputs to obtain a single crisp (non-fuzzy) output variable. There are a number of ways of doing. This is the simplest and most widely ud method and is called the centre of Gravity Method. It works as like this: If the fuzzy LN have membership values that are labelled µ1.....µ5, then the crisp output signal u is defined as:-
∑∑===51
51
i i i i i
u u µ
µ
初中英语教案模板Where the values of the are, i u V - V, u -V, u V, u V, u u 105051054321=====, and correspond to the central points of the fuzzy class LP: MP: S: MN: LN at the input to the defuzzifier. Defuzzifier input terminals which have no connections have fuzzy input values of zero.
4. Developing Fuzzy Logic Control Rules
Many rearch papers have been written on how to create fuzzy rule ts. Most of the methods are mathematical and require analytical knowledge to understand them. In our view this defeats the purpo of fuzzy logic. The main motivation for fuzzy logic is that by simply writing down common n rules it is possible to build a reasonable control strategy without deep theoretical knowledge of control. This means that we will have no knowledge of the stability properties of the controller, and so the scope of applications is restricted to fairly simple control applications. This is fine becau there are simple control problems that just want a simple solution. I have mentioned already the domestic products market, but we can add to this some of the simpler industrial control loops.
A fuzzy control system is obtained by writing a t of rules of the form:
IF {situation} THEN {action}
The procedure is to write down the basis rules and add and refine them bad upon experience. In the example of the coupled tanks system, a fuzzy rule which forms part of a control system might be: IF {error small} AND {control signal large positive}
不可忽视THEN {control signal small} (#1)
