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
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History of Fuzzy Control
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•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
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Comfort is true(1)
Label
Comfort is false(0)
Crisp Set
Hot
1
00 10 20 30 40
Comfort
Room Temperature ℃
25℃
25.1℃
Cool
Label & Grade of Membership
Comfort is 0.70
Comfort is 0.65
Fuzzy Set
1.0
0.00 10 20 30 40
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
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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
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Fuzzy Control by Linguistic Variable (1)
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Fuzzy Control by Linguistic Variable (2)
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Fuzzy Control for Water Tank(1)*
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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)
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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.
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-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
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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.
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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.
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・ 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.
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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)
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-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
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Intelligent Control Based on Human Knowledge(1)
- Single Pendulum, Swing Up and Stabilize -
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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 ]
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 -
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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
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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
Step3:Simulation
Step4:Actual experiment
Step3:Simulation → Step4:Actual experiment
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exp1
exp2
Simulation
Swing Up and Stabilize for Double Pendulum
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
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Fuzzy Decision, Selection.(Predictive Fuzzy Control )
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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)
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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
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・Acceleration to Target Speed
・Keeping a Target Speed
・Stopping Accurately at Target Position
Automatic Train Operation by PID Control(Conventional Control)
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Performance is defined by the fuzzy sets
(Ex: Stop Accuracy)
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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
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: 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
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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
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Operate trains as skillfully as expert operators
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Sendai subway,Tokyo metro,..
In Practical Use, Since 1987.ATOvideo
ATO & ATP controllers
Result of Real Train
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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.
:
Summary of Field Test Results(Stopping Accuracy)
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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.
Auto-driving by Fuzzy Decision(PFC)
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⇒ 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
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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
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
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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”
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