Let's Build a Fuzzy Logic Control System

8/7/2019 Let's Build a Fuzzy Logic Control System

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FUZZY LOGIC FOR "JUST PLAIN FOLKS "

Chapter 3. Let's Build a Fuzzy Logic Control System

Building a System to Gain Understanding and Familiarity

The easiest and quickest way to understand fuzzy logic control is to build a fuzzy

logic control system; following is one example:

This is a fuzzy logic speed control example, using the same techniques as used by

Professor Mamdani, that you can build for yourself to get experience with fuzzy

logic control. I recommend you do build some kind of system. I found I began

more and more to understand what fuzzy logic was all about as I tried to make

the system work. The following example system has been reduced in complexity

to make it easier to understand, but the concepts are the same as those used by

Mamdani.

If your application is more demanding than the following example, you add

inputs and "rules"; you do not have to learn new things or change the approach.

In considering this reduced complexity example, it may be observed that control

could have been effected without going through the fuzzy control exercise we are

about to go through. This would be correct, but only because we are working

with a simple system, only one input and no discontinuities or aberrations

requiring patching.

Following is a system diagram, Figure 3, for a "getting acquainted with fuzzy"

project that provides speed control and regulation for a DC motor. The motor

maintains "set point" speed, controlled by a stand-alone converter-controller,

directed by a BASIC fuzzy logic control program in a personal computer.


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Parts List

(1) IBM or compatible personal computer equipped to run Microsoft Quick

BASIC. IBM is a registered trademark of IBM Corporation. Microsoft and

Quick BASIC are registered trademarks of Microsoft, Inc.

(2) Controller (see below).

(3) Signal conditioner (transistor amplifier to adjust levels as needed).

(4) Transistor - 2N3053.

(5) DC motor, 1.5 V to 3.0 V, 100 ma., 1100 Rpm to 3300 Rpm, and compatible

generator.

The above speed control system is low cost and suitable for learning at home

where being rigorously, mathematically correct is not required. It is important

to be aware that this speed controller is only an experimental controller to get

familiar with the fuzzy logic concept. It is not what engineers call a rigorous,

technically correct application of fuzzy logic. The difference is in the fact that

this approach does not add triangles to compute center of mass as specified byDr. Bart Kosko (Fuzzy Thinking, Chapter 10). Adding triangles can be done,

but is difficult and time consuming, however that is the way a truly professional

application would be designed. There are ICs that do it all and commercially

available fuzzy logic controllers that do everything correctly.


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This fuzzy logic controller project was done under pressure of very limited

money available, resulting in an inexpensive approach. What is needed is an

analog to digital converter, which connects to a PC, and a digital to analog

output device from the PC to the transistors and DC motor-generator being

controlled. Often this is all in one plug-in card that goes inside the PC. Plug in

the A to D and D to A converter in the PC and write a program to measure the

input and control the output according to fuzzy logic principles. This approach

can be somewhat expensive and was not used in this case.

For this experiment, the controller was a 40-8 controller manufactured by

Prairie Digital Company. Click on the following Web page to see this controller.

http://www.prairiedigital.com/PDI_Website/PDI_Model40.htm (The author

has no connection at all with Prairie Digital.) The 40-8 controller is external to

the computer, connecting to the PC via a standard RS-232 serial port. The

serial port connects to the 40-8 controller via a serial cable. A BASIC program

is used to communicate with the 40-8 controller. The Prairie Digital instruction

book has sample programs showing how to do this. Through a BASIC program,

you can read the analog voltage level on one of the 40-8 analog input lines, then

tell the 40-8 to output a pulse-width-modulated signal. By controlling the pulse

width of the 40-8 output, the average value of the output is the equivalent of

varying the level of the output in an analog fashion.

If not constrained by cost, a 12 bit, A to D unit should be used, rather than the 8

bit unit. This would provide improved control. This approach, using the 40-8

controller, is low cost, in the range of $100 to buy the 40-8. Purchasing the items

Prairie Digital offers to accompany the controller, that is the connector, cables,

software, etc., is recommended. It costs very little extra, but is well worth it.

With regard to the other hardware, only low cost transistors, resistors,

capacitors, etc., were used for the signal conditioner providing input to the

motor-generator. The DC motor and DC generator were small, low power units

purchased from a surplus catalog. The motor output shaft was connected to the

generator input shaft with a small section of shrink insulation tubing; cheap,

simple and effective. The power supply for everything, including the 40-8, was a

12 Volt DC power supply removed from an old Apple computer.

National Instruments, www.natinst.com, sells a fuzzy logic system where the

fuzzy control action is accomplished by the software. National Instruments

applications engineers recommend one of their several analog/digital in,

digital/analog out converters for your application and provide a mathematically

correct software program to produce fuzzy control action. Their system also

provides attractive screen display color graphics. Needless to say, cost of the


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National Instruments system is considerably above the $100 range. One would

use the National Instruments approach for a large, complex system where

flexibility and changes down the road are involved, such as automating a

processing plant.

Where using a personal computer is not practical because of space and weightlimitations, fuzzy logic control is also available utilizing microchips

manufactured by Motorola. These microchips are suitable for fuzzy control

applications, www.mcu.motsps.com. One would use this approach if developing,

for example, a fuzzy logic anti-lock braking system (see "Fuzzy Logic,

Revolutionizing Automotive Engineering; Circuit Cellar INK magazine,

November 1997; www.circuitcellar.com).

(Please note, this note added January 1, 2008: A reader sent the following

information. The author has not personally pursued this, but this information

could be very useful. FUDGE is a fuzzy logic development tool for the Motorola68hc11 microcontroller that enables the user to graphically design a fuzzy

system, run fuzzy logic simulations, and generate C and assembly source code.

FUDGE can be downloaded from the Internet:

http://users.sdsc.edu/~decastro/home/projects/fudge/ Fudge.exe is a visual

program that shows the crisp inputs and outputs as well as the fuzzified inputs

and the fuzzified outputs. You can change the input and observe the output .

KBG11C.EXE is the .asm file for the 68hc11 fuzzy engine. If you open this with

notepad you can actually see the code for the fuzzification process. In FUDGE

click on >Balance.fdg then click on >Evaluate, then click on > Fuzzy Logic

Evaluator. Input and output is displayed graphically and all the input and output

membership functions are shown as well as the rules, all on one screen. End of

note added January 1, 2008.)

The steps in building our system are:

1. Determine the control system input. Examples: The temperature is the

input for your home air conditioner control system. Speed of the car is the input

for your cruise control.

In our case, input is the speed in Rpm of the DC motor, for which we are going to

regulate the speed. See Figure 3 above. Speed error between the speed

measured and the target speed of 2,420 Rpm is determined in the program.

Speed error may be positive or negative. We measure the DC output voltage

from the generator. This voltage is proportional to speed. This speed-

proportional voltage is applied to an analog input channel of our fuzzy logic


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controller, where it is measured by the analog to digital converter and the

pesonal computer, including appropriate software.

2. Determine the control system output. For a home air conditioner, the output

is the opening and closing of the switch that turns the fan and compressor on and

off. For a car's cruise control, the output is the adjustment of the throttle thatcauses the car to return to the target speed.

In our case, we have just one control output. This is the voltage connected to the

input of the transistor controlling the motor. See Figure 3.

3. Determine the target set point value, for example 70 degrees F for your home

temperature, or 60 Miles per hour for your car.

In our case, the target set point is 2,420 Rpm.

4. Choose word descriptions for the status of input and output.

For the steam engine project, Professor Mamdani used the following for input:

Positive Big

Positive Medium

Positive Small

Almost No Error

Negative Small

Negative MediumNegative Big

Our system is much less complicated, so let us select only three conditions for

input:

Input Status Word Descriptions

Too slow

About right

Too fast

And, for output:

Output Action Word Descriptions


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Speed up

Not much change needed

Slow down

RULES

Translate the above into plain English rules (called "linguistic" rules by Dr.

Zadeh). These Rules will appear in the BASIC computer program as "If-Then"

statements:

Rule 1: If the motor is running too slow, then speed it up.

Rule 2: If motor speed is about right, then not much change is needed.

Rule 3: If motor speed is to fast, then slow it down.

The next three steps use a charting technique which will lead to a computer

program. The purpose of the computer program is to determine the voltage tosend to the speed controlled motor. One function of the charting technique is to

determine the "degree of membership" (see Ch. 1) of the Too slow, About right

and Too fast triangles, for a given speed. Further, the charting technique helps

make the continuous control feedback loop easier to visualize, program and fine

tune.

5. Associate the above inputs and outputs as causes and effect with a Rules

Chart, as in Figure 4, below. The chart is made with triangles, the use of which

will be explained. Triangles are used, but other shapes, such as bell curves,

could also be used. Triangles work just fine and are easy to work with. Widthof the triangles can vary. Narrow triangles provide tight control when operating

conditions are in their area. Wide triangles provide looser control. Narrow

triangles are usually used in the center, at the set point (the target speed). For

our example, there are three triangles, as can be seen in Figure 4 (three rules,

hence three triangles).


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6. Figure 4 (above) is derived from the previously discussed Rules and results in

the following regarding voltage to the speed controller:

a. If speed is About right then Not much change needed in voltage to the speed

controller.

b. If speed is Too slow then increase voltage to the speed controller to Speed up.

c. If speed is Too fast then decrease voltage to the speed controller to Slow

down.

7. Determine the output, that is the voltage that will be sent from the

controller/signal conditioner/transistor to the speed controlled motor. This


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calculation is time consuming when done by hand, as we will do below, but this

calculation takes only thousandths of a second when done by a computer.

Assume something changes in the system causing the speed to increase from the

target speed of 2,420 Rpm to 2,437.4 Rpm, 17.4 Rpm above the 'set point."

Action is needed to "pull" the speed back to 2,420 Rpm. Intuitively we know weneed to reduce the voltage to the motor a little. The "cause" chart and vertical

speed line appear as follows, see Figure 5 below:

The vertical line intersects the About right triangle at .4 and the Too fast triangle

at .3. This is determined by the ratio of sides of congruent triangles from PlaneGeometry:

Intersect point / 1 = 11.6/29 = .4

Intersect point / 1 = 17.4/58 = .3

8. The next step is to draw "effect" (output determining) triangles with their

height "h" determined by the values obtained in Step 7, above. The triangles to

be drawn are determined by the rules in Step 6. Since the vertical 2,437.4 Rpm

speed line does not intersect the Too slow triangle, we do not draw the Speed up

triangle. We draw the Not much change and the Slow down triangles becausethe vertical speed line intersects the About right and Too fast triangles. These

"effect" triangles will be used to determine controller output, that is the voltage

to send to the speed control transistor. The result is affected by the widths we

have given the triangles and will be calculated. See Figure 6, below. The Not

much change triangle has a height of .4 and the Slow down triangle has a height


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of .3, because these were the intersect points for their matching "cause"

triangles; see Figure 4, above.

The output, as seen in Figure 6 (above), is determined by calculating the point at

which a fulcrum would balance the two triangles, as follows:

The Area of the Not much change triangle is: 1/2 X Base X Height = .5 X .04 X .4

= .008. Area of the Slow down triangle is .5 X .08 X .3 = .012.

Compute the controller output voltage by finding the point on the output voltage,

Vdc, axis where the "weight" (area) of the triangles will balance. Assume all the

weight of the Not much change triangle is at 2.40 Vdc and all the weight of the

Slow down triangle is at 2.36 Vdc. We are looking for the balance point.

Find the position of the controller output voltage (the balance point) with the

following calculation:

(Eq. 1) .008 X D1 = .012 X D2

(D1 is the fulcrum distance from 2.4 V. D2 is the fulcrum distance from 2.36 V.)

(Eq. 2) D1 + D2 = .04 (from Figure 6)

D1 = .04 - D2

Solving the above by substituting (.04-D2) for D1 in Equation 1 gives D2 = .016

and D1 = .024, therefore the balance point is a voltage of 2.376 Vdc, and this is

the voltage which we have determined should be applied to return speed to the

target value. See Figure 6, above.


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Keep in mind that we are only discussing one sample at one instant in time, with

a resulting controller output voltage; the controller is sampling several times

each second with a resulting "correction" output following each sample.

The above system was tested with changing loads on the rotating shaft, and

returned the speed of the motor to within 2 % of the 2,420 Rpm set point in lessthan 1.5 seconds. The accuracy with which the set point speed can be

maintained is determined by the resolution of the analog to digital and digital to

analog conversion circuits in the fuzzy logic controller. Typical "low cost"

resolution is "8 bit", 256 increments. Higher cost "12 bit" units provide 4,096

increments.

Please note: The above is a very effective, but much simplified, version of

computer based fuzzy logic control systems actually in use commercially. If

your application is of a more demanding, complex or commercial nature, we

suggest you refer to Fuzzy Thinking, a book by Bart Kosko, Ph.D., Chapter 10,Hyperion, New York, 1993. Dr. Kosko is one of the world's leading proponents

of fuzzy control and among the most knowledgeable regarding fuzzy control

theory. In the Kosko method, the intersecting triangles are added, then the total

area of the added triangles determined by integration. Fulcrum location is

determined by computer integration of area "under the curve" to the point of

one half the total area. This sounds complicated, but only requires a few

thousandths of a second for a computer, once the program is set up.

For more complex systems with additional inputs (for example, using rate of

change as an input in addition to speed error), the approach is as above, but

there are two or more "sub-outputs" to be considered in arriving at one crisp

output to control the system. This is handled by averaging these sub-outputs

with a weighting determined by the system designer and inserted in the program.

This weighting may be based on theoretical prediction, previous experience

with a similar manual system and/or experimentation and "tuning" of the

system, once it is assembled.

Patch It

For an individual control channel, fuzzy rules cover control requirements during

a certain "range" of operation. In our example speed control system, one rule

covered about right. There was an actual numerical upper limit and lower limit

for about right. Our control rule for this range is sometimes referred to in fuzzy

logic literature as a "patch." As you can see, the more patches we have over the

control range, the better the control. Fortunately, most system control problems

can be solved with relatively few patches. A patch, or rule, may be anything that


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solves the problem. If the system required it, you could even mix continuous

feedback loop control and off-on control over a channel's control range, if that

solved the problem.

The Program

The fuzzy logic program in the computer directs sending messages to and

receiving messages from the controller, thereby directing the measurement and

control operation and causing target and actual speed to be displayed. The

fuzzy logic controller receives messages from the computer via BASIC language

commands. Reply messages to the computer from the fuzzy logic controller are

acquired via BASIC.

In this case, the computer was an IBM PC/XT. The programming language was

Microsoft Quick BASIC. The program was compiled with Microsoft's compiler,

but compiling is not essential. Compiling increases speed of execution andperformance. Ideal computers for fuzzy logic control systems are often ancient

IBM PC-XT computers, available in garage sales for $50. These computers are

of no value for today's software, but work very adequately for fuzzy logic

measurement and control applications. IBM is a trademark of IBM

Corporation. Microsoft and Quick BASIC are trademarks of Microsoft, Inc.

The portion of the program for the above system system which examines the

input and performs the "triangle" calculations to arrive at a crisp output

follows:

910 IF MS = 2420 THEN MIV = 2.4 : GOTO 5000 'MS-MEASURED SPEED,

MIV-MOTOR INPUT VOLTAGE

920 IF MS < 2420 THEN 2000 ELSE 1000

1000 ' LINES 1010-1110; GREATER THAN 2420 RPM, SLOW DOWN

1010 IF MS > 2449 THEN MIV = 2.36 : GOTO 5000

1020 ' COMPUTE INTERSECT POINT, IPA, FOR 'ABOUT RIGHT'TRIANGLE

1030 IPA = (2449-MS) / 29

1040 IF IPA =< 0 THEN IPA = .0001


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1050 ' COMPUTE INTERSECT POINT, IPS, FOR 'SLOW DOWN'

TRIANGLE

1060 IPS = (MS-2420) / 58

1070 ' COMPUTE MOTOR (TRANSISTOR) INPUT VOLTAGE (MIV)

1080 AAR = .5 * .04 * IPA 'AAR - AREA OF 'ABOUT RIGHT' TRIANGLE

1090 ASD = .5 * .08 * IPS 'ASD - AREA OF 'SLOW DOWN' TRIANGLE

1100 D1 = .04 * (ASD / (ASD+AAR))

1110 MIV = 2.4 - D1 : GOTO 5000

2000 ' LINES 2010-2110; LESS THAN 2420 RPM, SPEED UP

2010 IF MS < 2362 THEN MIV = 2.44 : GOTO 5000

2020 ' COMPUTE INTERSECT POINT, IPA, FOR 'ABOUT RIGHT

'TRIANGLE

2030 IPA = (MS-2391) / 29

2040 IF IPA =< 0 THEN IPA = .0001

2050 ' COMPUTE INTERSECT POINT, IPF, FOR 'SPEED UP' TRIANGLE

2060 IPF = (2420-MS) / 58

2070 ' COMPUTE MOTOR INPUT VOLTAGE (MIV)

2080 AAR = .5 * .04 * IPA 'AAR - AREA OF 'ABOUT RIGHT 'TRIANGLE

2090 ASU = .5 * .08 * IPF 'ASU - AREA OF 'SPEED UP' TRIANGLE

2100 D1 = .04 * (ASU / (ASU+AAR))

2110 MIV = 2.4 + D1

5000 '


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The remainder of the program would be determined by the program

requirements of the analog to digital/digital to analog controller in use.

Program statements would be specific to the hardware selected. Almost any

controller should be usable with the above BASIC statements, so long as the

controller could be programmed in BASIC to measure inputs and send control

output signals. Program execution would cycle in the sequence: 1. Measure

input. 2. Analyze with the fuzzy logic program statements. 3. Send the

output signal.

End Chapter 3.

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