Fuzzy Control and Fuzzy Decision for Practical Human ...

Fuzzy Control and Fuzzy Decision for

Practical Human-Friendly System

Seiji YASUNOBUUniversity of Tsukuba

[email protected] SCIS&ISIS 2014@Kitakyushu

Outline・History of fuzzy control and feature of fuzzy set

1) Fuzzy control (FC)

An easy non-linear control element as enhancing

the linear PD control.

・Single/Double pendulum control

2) Fuzzy decision (Predictive fuzzy control (PFC) )

Decides gentle human-friendly operation

・Automatic train operation (ATO) system

[email protected] SCIS&ISIS 2014@Kitakyushu [2]

History of Fuzzy Control

[email protected] SCIS&ISIS 2014@Kitakyushu[3]

•Automatic Train Operation System

'80

'85

'95

'90

Predictive Fuzzy Control

Home Appliance•Washing Machine•Video Cameras•Air Conditioner

Sendai Subway in Practical Use

Process Control•Iron Plant•Gas Plant

'65

'70

Fuzzy Logic Control(Mamdani)(State Evaluate)

•Steam Engine•Cement Kiln Plants

Linguistic Variable, Fuzzy If-Then rule (Zadeh)

Water Purification Process

2nd IFSA in Tokyo

Machine Control•Automobile•Robot

‘89

Japan

Fuzzy Set was proposed by Prof. Zadeh (UCB)

2000

‘05

‘87

‘10

Design Support System•Fuzzy tool box / MATLAB

Control & Support for Human Life With Prof. Zadeh (2011)‘15

The fuzzy set treats a grade of membership with the computer


Comfort is true(1)

Label

Comfort is false(0)

Crisp Set

Hot

１

００１０２０３０４０

Comfort

Room Temperature ℃

25℃

25.1℃

Cool

Label & Grade of Membership

Comfort is 0.70

Comfort is 0.65

Fuzzy Set

1.0

0.0０１０２０３０４０

Cool Comfort

Room Temperature ℃

25℃

25.1℃

Hot

In the case, “Room temperature is 25 ℃”,

a grade of comfort is 0.7 and a grade of hot is 0.8.

μ

Fuzzy Reasoning Achieves a Flexible Functionwith The Computer


Fuzzy Control & DecisionControl know-how : Skilled human operator

Control engineer, Control theory

Algorithm: fuzzy sets and If-then & Do-if rules

(1) Fuzzy Control

Observed system states → Control command

• Water Level Control

• Pendulum, Swing Up and Stabilize


Fuzzy Control by Linguistic Variable (1)


Fuzzy Control by Linguistic Variable (2)


Fuzzy Control for Water Tank(1)*


If level is * and rate is * then valve is *.

okay

okay

okay

low

high

charge

positive

negative

close

discharge

small charge

small discharge

Output “charge”

Input-Outputlevel x

XT

＋ー

dx/dt Reasoning

Valve

No accurate model

*Demo of fuzzy toolbox MATLAB by the MathWorks, Inc.

Fuzzy Control for Water Tank(2)


FuzzyControlWRule

yasutank_FLC with Ruleviewer

tank max

inflow

0.5

tank 2

WATER

TANK

error

change

scope

change

XY Graph

Sum1

Subsystem

VALVE

Signal

Generator

Scope4

Scope2

Scope1

S-Function

animtank

PID

Controller

PID

Mux2

Mux

Mux1

Mux

Manual Switch

Derivative

du/dt

Constant

1

-1

0

1

-0.1

0

0.1

-0.5

0

0.5

levelratevalveFuzzy control is a non-linear control element.

However, a flexible design is difficult.

Simplified Fuzzy Inference[Feature]

Fuzzy Control by Linguistic Variable,

Enhancing the linear function Ex: y = a*x1 + b*x2,

And, it can be freely transformed.

[Rule form]

If-part: Triangle fuzzy sets

(Linear interpolation)

Then-part: Real number rmExample of rules for N-input, 1-output.

R1: if x1 is F11 and x2 is F12 and ・・ and xN is F1N then y=r1.

…

RM: if x1 is FM1 and x2 is FM2 and ・・ and xN is FMN then y=rM.


-1.0 0.0

μ

1.0

0.0

NB NM ZO PM PB

1.0-0.5 0.5

0.50.25

Inference process of simplified fuzzy inference

b22

a11

b11

0.0

1.0

X1 r10.0

1.0

Y

r2

推論結果：y

0.0

1.0

r1

a12

b120.0

1.0

X2

a21

b21

0.0

1.0

X1 r20.0

1.0

a220.0

1.0

X2 Y

Y

x1 x2

p11

p21

p12h1= p11*p12

h1

h2

p22h2=p21*p22

y = h1 + h2

h1*r1+h2*r2

If x1 is F11 and x2 is F12 then y = r1

If x1 is F21 and x2 is F22 then y = r2


At fuzzy tool box of MATLAB

FIS Type: sugeno

And.method : Prod

Or.method: Max

Defuzzification: Wtsum

Output variable ：Constant

Output: y

Input range[-1.0,1.0]

Fuzzy Inference Rules(3x3)Fuzzy rules for y = 0.5*x1 + 0.5*x2.

Each input x1,x2 have 3 fuzzy sets N, Z, and P.

Nine(9=3x3) rules are prepared.


x10-1.0 1.0

x2

(R1)-1.0

0

1.0

(R2)

(R3)

(R4)

(R5)

(R6)

(R7)

(R8)

(R9)

Rule (R2) If x1 is N and x2 is Z,Center values of input: x1=-1.0, x2=0.0y = 0.5*(-1.0)+0.5*0.0 = -0.5.

Therefore, y = -0.5.

(R1) if x1 is N and x2 is N then y = -1.0(R2) if x1 is N and x2 is Z then y = -0.5(R3) if x1 is N and x2 is P then y = 0.0(R4) if x1 is Z and x2 is N then y = -0.5(R5) if x1 is Z and x2 is Z then y = 0.0(R6) if x1 is Z and x2 is P then y = 0.5(R7) if x1 is P and x2 is N then y = 0.0(R8) if x1 is P and x2 is Z then y = 0.5(R9) if x1 is P and x2 is P then y = 1.0

0.0

μ

1.0

0.0

N Z P

-1.0 1.0

0.50.5

The Fuzzy Control has the ability of Linear PD control: u=0.5・x+0.5・dx.


・ Rule view and Surface view of fuzzy toolbox MATLAB by the MathWorks, Inc.

Fuzzy Inference Rules(5x5)

(R1) if x1 is N1 and x2 is N1 then y = -1.0.

(R2) if x1 is N1 and x2 is N.5 then y = -0.5.

(R3) if x1 is N1 and x2 is Z then y = 0.0.

(R4) if x1 is N1 and x2 is P.5 then y = 0.5.

(R5) if x1 is N1 and x2 is P1 then y = 1.0.

:

(R13) if x1 is Z and x2 is Z then y = 0.0.

:

(R24) if x1 is P1 and x2 is P.5 then y = 0.5.

(R25) if x1 is P1 and x2 is P1 then y = 1.0.


x1-1.0 1.0

x2

(R1)-1.0

0

1.0

0.0

μ1.0

0.0

N1 Z P1

-1.0 1.00.5-0.5

Fuzzy rules for y = 0.5*x1 + 0.5*x2.

Each input x1, x2, there are 5 fuzzy sets

N1, N.5, Z, P.5 and P1.

25(=5x5) rules are prepared.

0

(R2)

(R3)

(R4)

(R5)

(R6)

(R7)

(R8)

(R9)

(R10)

(R11)

(R12)

(R13)

(R25)

(R24)

N.5 P.5

x1

(R14) (R19)

Inputx1=0.3,x2=0.2

From (R13)(R14)(R18)(R19)

Output: y = 0.25

From 25 rules, moreover, 49(7x7), 121(11x11),output value is calculated by adjacent 4 rules. => Low calculation cost

(R18)

Fuzzy Control (Multi-input, 1 output)


-1-0.5

00.5

1

-1-0.5

00.5

1-1

-0.5

0

0.5

1

入力 x1

入力 x2

出力 y

Input：x1

Input：x2

Output：y

Fuzzy sets IF-then rulesIf x1 is P, x2 is N then y = 0.0.

If x1 is P, x2 is P then y = 1.0.

:

-1

0

1

-0.1

0

0.1

-0.5

0

0.5

levelrate

valve

Linear and Non-linear

Control elementFuzzy control enhancing

the linear PD control.

0.0

1.0

X-1.0 0.0 1.0

0.5

μ

1

2

4

3

Intelligent Control Based on Human Knowledge

- Pendulum, Swing Up and Stabilize -

Acquirement of knowledge for the system which is difficult

to operate in real-time.

Step2 Constructing the

control system based on

operating knowledge

Step3 Simulation Step4 Actual experiment

Step1 Acquirement of operating knowledge

Operating the model on computer at extended simulation-time

The method for development of the intelligent control system


[17]

Intelligent Control Based on Human Knowledge(1)

- Single Pendulum, Swing Up and Stabilize -


Stabilize

Swing Up

24cm

Sampling interval：10ms

Control instruction：－10V～＋10V

“If the pendulum is standing, moves the cart in the

direction that pendulum seems to fall.”

“If the pendulum is hanging, moves the cart in opposite

direction of the pendulum.”

[Linguistic Rules ]

E:/1pptmovie/Spend_GA/sPendGairan2.mpg

E:/1pptmovie/Spend_GA/sfuriage.mpg

2nd pendulum

1st pendulum

cart

"Swing Up Intelligent Control of Double Inverted Pendulum Based on Human Knowledge", Proc. of SICE Annual Conference 2004 in Sapporo, pp.1869-1873, 2004.

Intelligent Control Based on Human Knowledge(2)

- Double Pendulum -


Controller

Human

or

Pendulum

Pendulum

au Fx

u

2

1 2nd

1st

x x

1, 1

2, 2

,

.

.

.

xController

Human

or

Pendulum

Pendulum

au Fx

u

2

1 2nd

1st

x x

1, 1

2, 2

,

.

.

.

x

Double Pendulum

• Suitable Control by Judging state of Double Pendulum

Step1:Acquirment of Operating Knowledge


SimMechanics(The Math Works Inc.).

2 2

2 1 21 2

2 211 1 1 1

2 2 2

[{ ( sin )} { ( cos )} ]2

M J JT x

m d dx l l

dt dt

No equation

Step2:

Configuration of Control System

Operation by joystick

The model is constructed on computer

Operation by input with joystick many times

at extended simulation-time

• Moment of Inertia

• Mass of 1st & 2nd Pendulum

• Center of Mass etc

E:/1pptmovie/dpend/dPendJoystick2.mpg

Step3:Simulation

Step4:Actual experiment

Step3:Simulation → Step4:Actual experiment


[21]

exp1

exp2

Simulation

Swing Up and Stabilize for Double Pendulum

E:/1pptmovie/dpend/dPendjikki2.mpg

E:/1pptmovie/dpend/2g3_3.mpg

E:/1pptmovie/dpend/dPendAnime2.mpg

Fuzzy Control & DecisionControl know-how : Skilled human operator

Control engineer, Control theory

Algorithm: fuzzy sets and If-then & Do-if rules

(2) Fuzzy Decision (Predictive Fuzzy Control)

System purpose → Good operation

• Automatic Focusing Camera

• Automatic Train Operation

• Automatic Car-Drive & Support


Fuzzy Decision, Selection.(Predictive Fuzzy Control )


Rule 1: Do u=c1, if X(c1) is Good and Y is Big.

Rule n: Do u=cn, if X(cn) is Very Good and Y is Small.

Rule N: Do u=cN, if X(CN) is Very Good and Y is Medium.

c1cncN

X(c1)X(cn)X(cN)

c*

Y

ControlAlternatives

Good Control

c1 cn cN

Fuzzy Decision for Automatic Focusing Camera

(With no system model)


Control Rules

1. Do Focus on Left, if Left is Near.

:

n. Do Focus on Center, if Left is far & Center is medium & Right is near.

Focus on Right

Focus on LeftCenter

Right

Good focus

Intelligent Control for Real Train

Do accelerate, If the speed will be slow.

Do brake, If the speed will be fast.

Gentle control by soft rules

X in

Y out

y

x

Fuzzy inference

Control

purpose

Intelligent (soft)

control system

Formulate

Controlled

train

Instruction

Control

knowledge

Sendai subway (since 1987)

State X

Train

model

Fuzzy set

1.0

0.0

μ0.3

slow

Speed

Compute using human’s word

The intelligent control achieves human’s good train operation. [25]yasunobu [a] iit.tsukuba.ac.jp SCIS & ISIS 2014@Kitakyushu

Purpose of Train Operation


・Acceleration to Target Speed

・Keeping a Target Speed

・Stopping Accurately at Target Position

Automatic Train Operation by PID Control(Conventional Control)


Performance is defined by the fuzzy sets

(Ex: Stop Accuracy)


0.5m-0.5m

In the case “Stopping error is 0.2m”,

a grade of Good Stop is 1.0

a grade of Very Good Stop is 0.6.

Train Dynamics ModelPredict Performances from

Control Alternative and Train States


: Control AlternativeNp

: Current Control CommandtN

: Train Accelerationt

: Train Speedtv

: Train Positiontx

Train ModelMotor, Brake, ..

+ ( )tv Np TPredicted Train Speed

( )p p t Tv N

0

Predicted Stop Position

( )p p vx N

Predicted Running Time

Tz

2

2 ( )

tv

Np

-T t

t

x x

v

Fuzzy Decision (PFC) Rules

From Human Know-how


Example: The rule for accurate stopping

Do the control command is changed by n steps, ⇒ Do ΔN is n,

if if

・Riding comfort is “Good” ⇒ Riding comfort is good

・”No” Running time margin ⇒ Running time is good

・Stopping seems to be done with “Very good”. ⇒ Stop gap is very good.

[TASC Predictive Fuzzy Control Rules]

(T-1) Do N is B7+, if Safety is very bad. (Emergency brake)

(T-2) Do N is B7, if Safety is bad. (Maximum brake)

(T-3) Do N is P7, if Riding comfort is good, and Running time is long.

(T-4) Do N is P4, if Riding comfort is good, and Running time is short.

(T-5) Do N is P0, if Riding comfort is good, and Running time is medium.

(T-6) Do N is B2, if Riding comfort is good, and Running time is good.

(T-7) Do ΔN is 0, if Running time is good, and Stop gap is good.

(T-8,12) Do ΔN is n, if Riding comfort is good, and Running time is good,

and Stop gap is very good. (n= ±1, ±2, ±3)

Predictive Fuzzy Control for Stopping Control

[31][email protected] SCIS&ISIS 2014@Kitakyushu

Operate trains as skillfully as expert operators


Sendai subway，Tokyo metro，．．

In Practical Use, Since 1987.ATOvideo

ATO & ATP controllers

E:/1pptmovie/ATO_VTR.mpg

Result of Real Train


Run

Do accelerate, If the speed will be slow, comfort.Do hold, If the speed will be good, safety, (comfort).Do brake, If the speed will be fast, comfort.

:

E:/1pptmovie/83ATO_RUN2m07.mpg

Summary of Field Test Results（Stopping Accuracy)


2,000

1,500

1,000

500

-50cm 0 +50cmStop Gap

Frequency Number of Trials 11,395

Average +3.57 cm

Standard Deviation 10.61 cm

StopFuzzy ATO achieved a comfortable(no shock), accurate stop and short driving time.

E:/1pptmovie/84ATO_Stop30.mpg

Auto-driving by Fuzzy Decision(PFC)


⇒ Output the best control instruction

Target

Current

Position

u=C1

u=C3

Wall

u=C2

Distance to wall

u=C0(Keep current operation)

Future States

Error to target

Seiji Yasunobu, Ryota Sasaki: Intelligent Auto-Driving System for an Electric Four-Wheeled Cart,

Proceedings of SCIS & ISIS 2004( TUP-4-1), pp.1-4 (2004), (IEEE-FUZZ'94)

Keep

Center

Turn RightTurn Left

C1 C0 C3C2

Good Operation

Automatic parking control

Car-driving by Intelligent Fuzzy Support


Guidance

member

Driver（Supported person）

State

Operation

Support for a cart Operation

Support for a real vehicleOperation

SimulationAutomatic parking control

(IEEE-FUZZ'94 - SCIS&ISIS2004) (IEEE-CIRA2003)

(IEEE-SMC2004)

Keep

Center

Turn RightTurn Left

C1 C0 C3C2

Good Operation

E:/1pptmovie/4ParkSupportEcar.mpg

E:/1pptmovie/5ParkSupportCar.mpg

E:/1pptmovie/4a_muto_mpg1.mpg

E:/1pptmovie/3AutoparkEcar.mpg

Summary・The fuzzy set can handle man's concept with the computer

1) The fuzzy control (FC) method

• An easy non-linear control element as enhancing the

linear PD control

• Low calculation cost by Simplified FC

2) Fuzzy decision (Predictive fuzzy control (PFC)) method

Decides gentle human-friendly operation for practical

system.

• Automatic train operation (ATO) system

• Drive support for four-wheel car


If I (system) wasn‘t hard, I (system) wouldn’t be alive. If I (system) couldn‘t ever be

gentle, I (system) wouldn’t deserve to be alive. “By Raymond Chandler”

Fuzzy Control and Fuzzy Decision for Practical Human ...

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