Advanced Control
Introduction to
Fuzzy Logic
Æ
Performance
Monitoring and
optimization
Dra. Doris Sáez
Æ
Unit and plant-level
applications - offer
high value to
customer operations
.
Teacher: Doris Sáez H., Ph.D
1
Slide 2
Advanced Control
.
Teacher: Doris Sáez H., Ph.D
Æ
The Control Foundation in DeltaV
- Traditional tools e.g. override, cascade, ratio
- Improvements provided by advanced control
Æ
DeltaV Inspect
- Detection of abnormal conditions
- Variability index, utilization
Æ
DeltaV Tune
- Tuning response, robustness
- Expert options e.g. Lambda, IMC
Æ
DeltaV Fuzzy
- Principals of fuzzy logic control
- FLC function block, tuning
Æ
DeltaV Neural
- Creation of virtual sensor
- Data screening, training
Æ
DeltaV Predict
- MPC for multi-variable control
- Model identification, data screening
- Simulation of response, tuning
Æ
DeltaV Simulate
- Operator training and engineering
- Using High fidelity process simulation
Slide 3
DeltaV Redefines Advanced Control
High
Classic Advanced Control
Lower Cost
Low
Greater Benefits
DeltaV Advanced Control
Product
Price
Cost of
Services
ROI
Ease
of Use
Stability
Over
Time
Ongoing
Problem
Solving
.
Teacher: Doris Sáez H., Ph.D
Slide 4
DeltaV Fuzzy
Æ
Improved response to process disturbances and
setpoint changes, especially for loops with long
time constants
Æ
May replace PID for most applications
Æ
Configuration is Easy - exactly like PID
Æ
Quick tuning with DeltaV Autotuner
.
Fuzzy Logic Fundamentals
Æ
The fuzzy logic associates uncertainty to the data
set structure (Zadeh, 1965).
Æ
The elements of a fuzzy set are order pair data
which gives the element value and membership
grade
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 5
Slide 6
1
Fuzzy Logic Fundamentals
–
Fuzzy Logic Fundamentals
Example
Low: “a velocity around 40 km/h”
Medium : “a velocity around 55 km/h”
High: “a velocity over 70 km/h aprox.”
µ
Low
High
Medium
1
Æ
For a fuzzy set, an element x belong to a set
A with a membership grade µA (x), which is
between 0 and 1
Æ
A variable could be characterized with
different linguistic values, each one
represents a fuzzy set
0.66
0.33
0
–
40 45
70
55
Velocity
Thus, if the velocity is 45 km/h, the membership
grades are 0, 0.33 and 0.66 belong to the fuzzy sets
Low, Medium, High, respectively
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 7
Slide 8
DeltaV Fuzzy
Basic Operations of Fuzzy Logic
Æ
.
Given two fuzzy sets A and B in the same
universe X, with membership functions uA
and uB respectively, the following basic
operations are defined
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 9
Slide 10
Basic Operations of Fuzzy Logic
µ(x)
1
z
Union
Basic Operations of Fuzzy Logic
u A ∪ B = max{(u A (x), u B (x))}
z
B
A
Complement
u A (x) = 1 − u A (x)
µ(x)
1
0
x
A
µ(x)
1
z
0
Intersection u A ∩ B = min{(u A (x), u B (x))}
x
B
A
0
x
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 11
Slide 12
2
Basic Operations of Fuzzy Logic
Æ
Fuzzy Models
Given the fuzzy sets A1, ..., An with
universes X1, ..., Xn respectively, the product
Cartesian is defined as a fuzzy set in X1...Xn
with the following membership function:
Æ
Linguistic fuzzy
models
Æ
Takagi & Sugeno
fuzzy models
u A1x..xAn (x1 ,..., x n ) = min{u A1 (x1 ),..., u An (x n )}
Mamdani (1974)
u A1x..xAn (x1 ,..., x n ) = u A1 (x1 ) ⋅ u A2 (x 2 ) ⋅ ⋅ ⋅ u An (x n )
Larsen (1980)
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 13
Slide 14
Linguistic Fuzzy models
Æ
Æ
Linguistic Fuzzy models
The linguistic fuzzy models are based on
heuristic rule sets where the input and output
linguistic variables are represented by fuzzy sets
Knowledge
Base
Example
“If temperature is High then fun velocity is Slow”
µ(x)
U
Fuzzification
Defuzzification
Inteface
Interface
Y
Fun velocity
1
Inference
Slow
Medium
Motor
Fast
0
x
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 15
Slide 16
Fuzzyfication Interface
Æ
This element transform the input variables to fuzzy
variables
Example: 70 º → “Low with membership grade 0.7”
µ(x)
1
Æ
It contains the linguistic rules and the membership
function information of the fuzzy sets
Æ
Calculates the output variable fuzzy sets from the
input variables by using the rules and the fuzzy
inference
Example: x1 (temperature) = 10 and
0.7
x2 (pressure) = 26
Low
0
70º Temperature
.
Knowledge base
→ y (speed)?
R1:
If x1 is A1 and x2 is B2 then y is C2
R2:
If x1 is A1 and x2 is B1 then y is C1
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 17
Slide 18
3
Knowledge base
A
0 10
1
A
Defuzzification Interface
B
2
100
Temperature
-50
1
B
C
2
26 50 y
Pressure
0
1
C
100 z
Speed
C
1
0
Æ
2
C
From output variable fuzzy sets, obtained by
fuzzy inference, provides the non fuzzy
output
2
100 z
C’.
0
40
10 z
C .
.
Teacher: Doris Sáez H., Ph.D
0
40
100 z
Slide 19
Slide 20
Takagi & Sugeno Fuzzy Models
Æ
.
Teacher: Doris Sáez H., Ph.D
These models are characterized by fuzzy rules,
where each premise represents a fuzzy subspace
and the consequences are linear relation of inputoutput
Takagi & Sugeno Fuzzy Models
Æ
Linear models for the consequences
y
Example
If x is A1 Then y = Cx + D
u
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 21
Slide 22
Takagi & Sugeno Fuzzy Models
Æ
Example: Batch Fermentator
In general,
Ri : If X1 is Ali and K and Xk is Ak i
Then Yi = p0i + p1i X 1 + K + pki Xk
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 23
Slide 24
4
Example: Batch Fermentator
Æ
Membership functions
.
Control Strategies Based
on Fuzzy Models
Æ
Fuzzy expert control
Æ
PID fuzzy control
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 25
Slide 26
Fuzzy Expert Control
Æ
These controllers are based on heuristic rules
where the input and output linguistic variables are
represented by fuzzy sets
Æ
Example:
Fuzzy Expert Control
Knowlogment
base
y
Fuzzification
Interface
Controlled
variable
Teacher: Doris Sáez H., Ph.D
Slide 27
Slide 28
Æ
Example: Washing machine
– The dirtiness is determined by the transparency of the
water.
– Type of dirt is given from the saturation time.
Saturation is the point at which the change in water
transparency is close to zero
Process
Manipulated
variable
.
Teacher: Doris Sáez H., Ph.D
Fuzzy Expert Control
u
Inference
Motor
– If temperature is high then fun velocity is fast
.
Defuzzification
Interface
Fuzzy Expert Control
Æ
Example: Washing machine
Rules
if dirtness_of_clothes is Large and type_of_dirt is Greasy then wash_time
is VeryLong;
if dirtness_of_clothes is Large and type_of_dirt is Medium then wash_time
is Long;
if dirtness_of_clothes is Medium and type_of_dirt is Medium then
wash_time is Medium;
if dirtness_of_clothes is Large and type_of_dirt is NotGreasy then
wash_time is Medium;
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 29
Slide 30
5
Fuzzy Expert Control
Æ
Fuzzy Expert Control
Example: Washing machine
Æ
Input membership functions
Example: Washing machine
Output membership functions
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 31
Slide 32
Fuzzy PID Control
Fuzzy PID Control
Æ
Characteristics:
– Two or seven fuzzy sets for the input variables
e(k)
GE
ref
GR
de(k)
– Two or seven fuzzy sets for the output variables
Controller
du(k)
GU
Process
y(k)
– Triangular membership functions
– Fuzzyfication with continuous universes
– Inference based on fuzzy implicance
– Desfuzzyfication by the maximum mean method
e(k) = r - y(k)
de(k) = e(k) - e(k-1)
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 33
Slide 34
Fuzzy PID Control
Fuzzy PID Control
y(k)
a1
a2
a3
a4
ref
e(k)
>0
<0
<0
>0
de(k)
<0
<0
>0
>0
a1 a2 a3 a4
e(k) + - - +
de(k) - - + +
.
b1
b2
b3
b4
b5
b6
e(k)
=0
=0
=0
=0
=0
=0
de(k)
<<<0
<<0
<0
>0
>>0
>>>0
c1
c2
c3
c4
c5
c6
de(k) e(k)
=0 <<<0
=0 <<0
=0 <0
=0 >0
=0 >>0
=0 >>>0
time
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 35
Slide 36
6
Fuzzy PID Control
Fuzzy PID Control
c3
y(k)
ref
b1
c2
c1
y(k)
b2
b3
b4
b5
ref
c4
c5
b6
c6
time
time
(a)
NB
NB a2
NM a2
NS a2
e(k) ZE b1
PS a1
PM a1
PB a1
NM
a2
a2
a2
b2
a1
a1
a1
NS
a2
a2
a2
b3
a1
a1
a1
de(k)
ZE
c1
c2
c3
ZE
c4
c5
c6
PS
a3
a3
a3
b4
a4
a4
a4
PM
a3
a3
a3
b5
a4
a4
a4
PB
a3
a3
a3
b6
a4
a4
a4
(b)
.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 37
Slide 38
Fuzzy PID Control
Fuzzy Logic Control vs PID
de(k)
NB NM NS ZE
NB NB NB NB NB
NM NB NB NM NM
NS NB NM NS NS
e(k) ZE NM NM NS ZE
PS NM NS ZE PS
PM NS ZE PS PM
PB ZE PS PM PB
Setpoint Change
PS
NM
NS
ZE
PS
PS
PM
PB
PM
NS
ZE
PS
PM
PM
PB
PB
PB
ZE
PS
PM
PM
PB
PB
PB
– “If the error is Negative Small and the incremental
error is Positive Medium then the increment control
variable is Positive Small”
.
Load Disturbance
FLC
FLC
PID
FLC
PID
FLC
PID
PID
Notice at both SP change and at load disturbance the FLC output change is more dramatic
than PID. Resulting in faster return to SP. Also notice as PV approaches SP, the FLC
exhibits less overshoot.
.
Teacher: Doris Sáez H., Ph.D
Teacher: Doris Sáez H., Ph.D
Slide 39
Slide 40
DeltaV Tune - Fuzzy Logic Commissioning
Transfer recommended
constants to fuzzy control
.
Teacher: Doris Sáez H., Ph.D
Slide 41
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