Adaptive Control
#0F Lectures 28 h
#0F Read the book in advance!!
#0F Exercises 14h
#0F Labs
1,Indirect STR
2,Direct STR
3,Auto-tuning
#0F Project 30 h
#7B Combine with real-time systems
#7B Presentation
#0F Computer simulation
#7B Start tomorrow!!!
#0F Examination
#0F Feedback
#0F Use the web!
Contents
#0F Introduction L1
#0F Parameter Estimation L1,L2
#0F Self-tuning Regulators STR L3,L4
#0F Model Reference Adaptive Systems L5,L8
#0F Nonlinear Stability Theory L6,L7
#0F Analysis of Adaptive Systems L9,,L11
#0F Automatic Tuning L12
#0F Gain Scheduling L12
#0F Implementation L13
#0F Products L13
#0F APerspective L14
What is Adaptive Control?
#0F Introduction
#0F LinearFeedback
#0F E#0Bects of Process Variations
#0F Adaptive Schemes
#0F The Adaptive Control Problem
#0F Conclusions
Semantics
Adapt to adjust behavior to new circum-
stances.
Any alteration in structure or function of an
organism to make it better #0Ctted to survive
and multiply in its environment.
Change in response of sensory organs to
changed environmental conditions.
A slow usually unconscious modi#0Ccation of
individual and social activity in adjustment to
cultural surroundings.
Learn to acquire knowledge or skill by study,
instruction or experience.
Problem,Adaptation and feedback?
c#0D K,J,#C5str#F6m and B,Wittenmark 1
Adaptive Control
#0F Adaptation and feedback
#0F Truxal 1959:Designed from an adaptive
view point
#0F IEEE CSS Committee 1973:
#7B Self-organizing control process SOC
#7B Parameter adaptive SOC
#7B Performance adaptive SOC
#7B Learning control system
#0F Pragmatically,A special class of nonlinear
control systems
Brief History
#0F Early #0Dight control systems 1955 #7B
#0F Dynamic programming Bellman 1957
#0F Dual control Feldbaum 1960
#0F System identi#0Ccation 1965 #7B
#0F Learning control Tsypkin 1971
#0F Algorithms MRAS STR 1970 #7B
#0F Stability analysis 1980 #7B
#0F Robustness 1985 #7B
#0F Industrial products 1982 #7B
An Adaptive Control System
Parameter
adjustment
Controller Plant
Controller
parameters
Control
signal
Output
Setpoint
Notice two loops
#0F Regular feedback loop
#0F Parameter adjustment loop
LinearFeedback - 2DOF
Feedforward Process
uy
Feedback
- 1
u
c
y
m
G
fb
G
p
G
ff S
Two-degree-of-freedom structure #28FB+FF#29
The sensitivity function and complementary
sensitivity function
S =
1
1+G
p
G
fb
=
1
1+L
=
Y
cl
#28s#29
Y
ol
#28s#29
T =
G
p
G
fb
1+G
p
G
fb
=
L
1+L
L = G
p
G
fb
is the loop transfer function,
S + T =1and
dT
T
=
1
1+G
p
G
fb
dG
p
G
p
= S
c#0D K,J,#C5str#F6m and B,Wittenmark 2
JudgingProcess Variations from
Open Loop Data
Open loop changes drastically but little change
in closed loop.
G
0
#28s#29=
1
#28s+ 1#29#28s + a#29
0 100 200 300
0
100
200
300
0510
0.0
0.5
1.0
Time
Time
JudgingProcess Variations from
Open Loop Data
10
3
10
2
10
1
10
0
10
1
10
2
10
0
10
2
10
4
Magnitude
10
3
10
2
10
1
10
0
10
1
200
100
0
Frequency [rad/s]
Phase [deg]
10
3
10
2
10
1
10
0
10
1
10
1
10
0
10
1
Magnitude
10
3
10
2
10
1
10
0
10
1
200
100
0
Frequency [rad/s]
Phase [deg]
JudgingProcess Variations from
Open Loop Data
Open loop response changes little but drastic
change in closed loop.
G
0
#28s#29=
400#281,sT#29
#28s + 1#29#28s + 20#29#281 + Ts#29
012345
0.0
0.5
1.0
0 0.2 0.4 0.6 0.8 1
0
1
Time
Time
JudgingProcess Variations from
Open Loop Data
10
1
10
0
10
1
10
2
10
3
10
2
10
0
10
2
Magnitude
10
1
10
0
10
1
10
2
10
3
400
200
0
Frequency [rad/s]
Phase [deg]
10
1
10
0
10
1
10
2
10
3
10
2
10
0
10
2
Magnitude
10
1
10
0
10
1
10
2
10
3
400
200
0
Frequency [rad/s]
Phase [deg]
c#0D K,J,#C5str#F6m and B,Wittenmark 3
Nonlinear Actuators
y
- 1
uv
S
Valve ProcessPI controller
f( )
G
0
(s)
K 1 +
1
T
i
s
- 1
u
c
Valve characteristics
v = f#28u#29=u
4
u#150
010203040
0.2
0.3
010203040
1.0
1.1
010203040
5.0
5.2
Time
Time
Time
u
c
y
u
c
y
y
u
c
Flow and SpeedVariations
c
in
V
d
V
m
c
V
m
dc#28t#29
dt
= q#28t#29#28c
in
#28t,#1C#29,c#28t#29#29
where #1C = V
d
=q#28t#29 and T = V
m
=q#28t#29
0 5 10 15 20
0.0
0.5
1.0
0 5 10 15 20
0.0
0.5
1.0
1.5
Time
Time
FlightControl
a
V
q
q =
˙
q
N
z
d
e
dx
dt
=
0
@
a
11
a
12
a
13
a
21
a
22
a
23
0 0,a
1
A
x +
0
@
b
1
0
a
1
A
u
0 0.4 0.8 1.2 1.6 2.0 2.4
80
60
40
20
0
1 2
3 4
Mach number
Altitude (x1000 ft)
Changing Disturbances
b
0
s
2
+ b
1
s + b
2
s
2
+ w
e
2
1
s+ 1
y
White noise
w s
s
2
+ 2zw s + w
2
S
0 200 400 600
1
1
0 200 400 600
1
1
0 200 400 600
1
1
Time
Time
Time
#28a#29 Output error
#28b#29 Output error
#28c#29 Output error
c#0D K,J,#C5str#F6m and B,Wittenmark 4
AdaptiveSchemes
#0F Gain Scheduling
#0F Model Reference Adaptive Control MRAS
#0F Self-tuning Regulator STR
#0F Certainty Equivalence
#0F Dual Control
Gain Scheduling
Process
schedule
Gain
Output
Control
signal
Controller
parameters
Operating
condition
Command
signal
Controller
Example of scheduling variables
#0F Production rate
#0F Machine speed
#0F Mach number and dynamic pressure
Model Reference Adaptive Control
MRAS
Adjustment
mechanism
u
Model
Controller parameters
Plant
y
Controller
y
m
u
c
Linear feedback from e = y,y
m
is not
adequate forparameter adjustment!
The MIT rule
d#12
dt
=,#0De
@e
@#12
Self-TuningRegulator STR
Process parameters
Controller
design
Estimation
Controller
Process
Controller
parameters
Reference
Input Output
Specification
Self-tuning regulator
Certainty Equivalence
Parameter estimation
#0F Gradient methods
#0F Least squares
Control design methods
#0F PID
#0F Pole placement
#0F LQG
c#0D K,J,#C5str#F6m and B,Wittenmark 5
Dual Control
uy
Nonlinear
control law
Process
Calculation
of hyperstate
Hyperstate
u
c
#0F No certainty equivalence
#0F Control should be directing as well as
investigating!
#0F Intentional perturbation to obtain better
information
#0F Conceptually very interesting
#0F Unfortunately very complicated
The Adaptive Control Problem
#0F Principles
#7B Certainty Equivalence
#7B Caution
#7B Dual Control
#0F Controller structure
#7B Linear Nonlinear
#7B State Model
#7B Input Output Model
#0F Control Design Method
#0F Parameter Adjustment Method
#0F Speci#0Ccations
#7B Situation dependent?
#7B Optimality
Applications
Process dynamics
Varying Constant
Use a controller with
varying parameters
Use a controller with
constant parameters
Unpredictable
variations
Predictable
variations
Use an adaptive
controller
Use gain scheduling
#0F Automatic Tuning
#0F Gain Scheduling
#0F Continuous Adaptation
#0F Feedback and Feedforward
Conclusions
#0F Adaptive control deals with
#7B Variations in process dynamics
#7B Variations in disturbances
#0F Adaptive systems are nonlinear
#0F Reasonably well understood theoretically
#0F Emerging as an industrially viable technol-
ogy
#0F Applications
#7B Automatic tuning
#7B Gain scheduling
#7B Continuous adaptation #28FB and FF#29
#0F Many challenging problems remain
#7B Dual control
#7B Nonlinear systems
#7B Adaptation rates
c#0D K,J,#C5str#F6m and B,Wittenmark 6