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MECH523: Intelligent Control
Lecture 18
Fuzzy model reference learning control
(FMRLC)
Dr. Ryozo Nagamune
Department of Mechanical Engineering
University of British Columbia
Fall 2008 MECH523 : Intelligent Control 1

Review
• Fuzzy controller design methods
• Construction of rules via heuristic information
• Fuzzy identification via numerical I/O data
Fuzzy controller
r(t)
Fuzzification
Inference
mechanism
Rule-base
Defuzzification
u(t)
Plant
y(t)
Fall 2008 MECH523 : Intelligent Control 2

Issues in fuzzy controllers
• Hard to choose some controller parameters (e.g.
in membership functions and rule-base) to meet
specified performance.
• How to automatically synthesize the initial fuzzy
controller for the nominal condition?
• The fuzzy controller designed for a nominal plant
may perform inadequately if plant parameters
vary, or if some condition (noise, disturbance,
environment) changes significantly.
• How to automatically tune the fuzzy controller so that
it can adapt to different plant conditions?
Fall 2008 MECH523 : Intelligent Control 3

Direct and indirect adaptive control
• Direct adaptive control
(Sections 6.2-6.5)
6.5)
• Indirect adaptive control
(Section 6.6)
Plant parameters
Adaptation
mechanism
Controller
designer
System ID
Controller parameters
Controller
Plant
Controller
Plant
Fall 2008 MECH523 : Intelligent Control 4

Fuzzy model reference learning
control (FMRLC)
• Direct model reference adaptive controller
• FMRLC will tune controller parameters, and will
memorize to some extent the parameter values
that it had tuned in the past.
• On the contrary, many conventional adaptive
control techniques
• would not have such memorizing scheme,
• and have to retune each time a new operating
condition is encountered.
• Note the difference of “learning” and “adaptive”.
Fall 2008 MECH523 : Intelligent Control 5

Block diagram of FMRLC
Reference
model
Knowledge-base
modifier
Learning mechanism
Fuzzy inverse model
Plant
Fuzzy controller
Fall 2008 MECH523 : Intelligent Control 6

Fuzzy controller
• PD fuzzy controller with inputs
• Error
• Change-in
in-error
• Scaling gains ge, gc, gu
• Rule-base
• Ex: If error is PL and change-in
in-error is NS
then plant input is PL.
• MF
Fall 2008 MECH523 : Intelligent Control 7

Fuzzy controller (cont’d)
• FMRLC will automatically synthesize or tune
output MFs. . (Input MFs are fixed.)
• Initialization is necessary for output MFs. . Make a
best guess, or just choose the triangular ones.
• Method selections
• Fuzzification: : singleton fuzzification
• Premise “and”:: minimum or product
• Implication: minimum or product
• Defuzzification: : COG method, center average method
Fall 2008 MECH523 : Intelligent Control 8

Reference model
• Reference model characterizes design criteria:
• Rise time
• Overshoot, etc.
• Example
Discrete-time
time
implementation
Discretization
Fall 2008 MECH523 : Intelligent Control 9

Performance evaluation
• Desired performance of the closed-loop loop system
is achieved if the error signal
remains very small for all time no matter what
• reference signal is.
• plant parameter variations occur.
• Error signal
• Small Learning mechanism will not make
significant modifications to the fuzzy controller.
• Large Learning mechanism will adjust FC.
Fall 2008 MECH523 : Intelligent Control 10

Learning mechanism
• Tuning of rule-base of fuzzy controller s.t. . the
C.L. system behaves like reference model.
• The learning mechanism consists of:
• Fuzzy inverse model: : Function to map ye(kT) ) to
changes in the plant input p(kT) ) that are necessary to
force ye(kT) ) to be zero, or small. (next lecture)
• Knowledge-base modifier: : Function to modify fuzzy
controller’s s rule-base to affect the needed changes in
the plant inputs. (following slides)
Fall 2008 MECH523 : Intelligent Control 11

Knowledge-base modifier
Fuzzy
controller
Plant
• If fuzzy controller had generated control input
then ye(kT) would have been zero.
• Next time when we have similar value of e and
c, plant input will be u(kT-T)+p(kT
T)+p(kT). ).
Fall 2008 MECH523 : Intelligent Control 12

Modification of output MFs
• Example: Assume fuzzy inverse model produced
p(kT)=0.5, for e(kT-T)=0.75,
T)=0.75, c(kT-T)=
T)=-0.2.
Output MF
for R1R
Output MF
for R2R
Fuzzy
controller
Move the corresponding
output MFs by p(kT).
Two rules (R1 & R2)
are active in this case.
Fall 2008 MECH523 : Intelligent Control 13

Some comments
• Local learning: : Only output MFs relevant to
active rules (not entire rule-base!) are modified.
• Local learning is important for memorizing the
changes in the past in fuzzy controllers.
• The controller adapts to new situations and also
memorize how it has adapted past situations.
• Various alternative knowledge-base modifiers to
modify output MFs are presented in Section
6.2.4. Read the section.
Fall 2008 MECH523 : Intelligent Control 14

Summary
• FMRLC: Fuzzy model reference learning control
• Plant
• Fuzzy controller
• Reference model (desired closed-loop loop system)
• Learning mechanism
• Fuzzy inverse model (next lecture)
• Knowledge-base modifier (today’s s lecture)
• Learning mechanism memorizes and tunes
information in fuzzy controllers.
• Read the textbook until page 330.
Fall 2008 MECH523 : Intelligent Control 15