Lecture Notes: Week 7a
Topic: (Youla) Controller parameterization
ECE/MAE 7360
Optimal and Robust Control
( Fall 2003 Offering)
Instructor: Dr YangQuan Chen, CSOIS, ECE Dept.,
Tel. : (435)797-0148.
E-mail: [email protected] or, [email protected]
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Lecture Notes: Week 7a - Controller Parameterization in Optimal and Robust Control, Study notes of Mechanical Engineering
A set of lecture notes from a university course on optimal and robust control, specifically for week 7a, which covers the topic of controller parameterization. The notes include information on feedback and feedforward control, cascade control, model following, filters, and various control schemes. The instructor's contact information is also provided.
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Lecture Notes: Week 7a
Topic: (Youla) Controller parameterization
ECE/MAE 7360
Optimal and Robust Control
(Fall 2003 Offering)
Instructor : Dr YangQuan Chen, CSOIS, ECE Dept.,
Tel. : (435)797-0148.
E-mail: [email protected] or, [email protected]
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÷ 1C&E
Lecture 16 - Controller Structures
K. J. Åström
- Introduction2. Feedback and Feedforward3. Linear Schemes4. Nonlinear Schemes5. Gain Scheduling and Adaptation6. Summary Theme: Building complex control systems.
Introduction
Many common issues in design of machines, electronics,computer software, mechatronics
How to deal with complexity
Modularization
Standardization
Structures
Paradigms, Design principles
Top Down and Bottom Up
Bottom Up Design
A way to view systems
A number of building blocks
Ideas to combine them
What are the building blocks of control?
What principles can be used to select and combine them?
The danger: Can it be done better?
Commissioning: Close loops one by one.
Bottom Up Design of Control Systems
Components
Controllers
Observers
Estimators
Filters
Limiters
Dead zones
Selectors
System principles
Feedback
Feedforward
Model following
Cascade
Split range
Gain scheduling
Adaptation
c &
K. J. Åström August, 2001
Combination of Feedback and Feedforward
y
G
p
1
Σ
v
y
c
e
−
1
Process
u
Σ
y
sp
Feedforward
Σ Σ
G
m
G
ff
2
G
ff
1
G
fb
G
p
2
Linear Schemes
Model following - Systems with two degrees of freedom(2DOF)
Filters
Cascade control
State feedback
Observers
Attenuation of disturbances with specific character
The Smith Predictor
Model Predictive Control
Model Following - 2DOF
u
Σ
Model
e
y
Controller
Process
y
sp
y
c y
c
u
Σ
Model
e
y
−
1
Process
y
sp
Feedforward
Σ
Controller
u
ff
Applications of Model Following
Coordination in multi-axis motion control
Robotics
Path following
Mixing in chemical processes
Coordinated production changes
c &
K. J. Åström August, 2001
Filters
Typical filters
Low pass
High pass
Band pass
Notch
Body bending filters
Typical applications
Reduce disturbances
Improve robustness (high frequency roll-off)
Smooth reference signals
Cascade Control
How to use several sensors. State feedback is the ultimatecase!
Process
Inner loop
y
u
P 1
P 2
y^ sp
y s
Outer loop C
s
C
p
0
10
20
30
0
0
10
20
30
− −0.
0
When is Cascade Control Useful?
Key idea: make tight feedback around essential places wherethere are essential perturbations (disturbances or uncertain-ties)Guidelines:
Well defined relation between primary and secondaryvariables
Essential disturbances and process variations in inner loop
Inner loop faster
Tight feedback (high gain and high bandwidth) in innerloop
When is Cascade Control Useful? T
=
10
T
=
1
y
s y
s y
s
T
=
10
T
=
1
y y y
u u u
y
s
v
u
y y s
u
y
v
v
v v
A
D
B C
E
c &
K. J. Åström August, 2001
State Feedback and Observers
∑
∑
x m
u
ff
ˆ x^
Observer
L
Process
−
u
fb
y
u
c
Model and Feedforward
Generator
Use model to estimate variables that are not directlymeasurable
States are the variables required to account for storage ofmass, momentum and energy
Estimate the state
Feedback from full state deviation
Feedforward to generate
u
m
and
y
m
Nonlinear Schemes
Limiters
Split range
Ratio control
Selectors
Fuzzy control
Gain scheduling
Neural networks
Adaptation
Limiters
Limiters are often used
To avoid saturation
An element in circuits for windup protection
To protect equipment to rapid changes
A simple amplitude limiter
u
l
u
h
u
y
Rate Limiter
y
u
Σ
1 s − 1
e
0
1
2
3
4
(^10) −
vlim=2, k=5, 100
A rate limiter causes delays (JAS)
c &
K. J. Åström August, 2001
Jump and Rate Limiter
0
1
2
3
4
(^10) −
vlim=2, alim=0.
Commonly used in the power industry for load changes to saveboilers.
Split Range
A simple way to use one controller to control two actuators.Commonly used for heating and cooling.
Open Closed
0
Cooling valve1.
Heating valve
Ratio Control
Arrangement to obtain two flows that are proportional to eachother, e.g. oil and air in boilers
a(y
k
b)
Σ
y
k
Π
y
PI
SPPV
u
b
a
a
y
y k Div
y
PI
SPPV
u
k y
A
B
The scheme B is preferable! Why?
Selector Control
Scheme used to achieve several control objectives, e.g. controltemperature unless pressure is too high. A way to constrainprocess variables during operation.
MAX
MI N
C
min C
max
C
u
l
z
min z
max
y
u
h
Process
u
z
G
2
G
1
u
n
SPPV
y
sp
PV SP
c &
K. J. Åström August, 2001
Gain Scheduling
schedule^ Process
Gain
Output
Controlsignal
Controllerparameters
Operatingcondition
Commandsignal
Controller
Example of scheduling variables
Production rate
Machine speed
Mach number and dynamic pressure
Room occupancy
Uses of Gain Scheduling
Many uses
-
Linearization of actuators
-
Surge tank control
-
Control over wide operating regions
Important issues
-
Choice of scheduling variables
-
Granularity of scheduling table
-
Interpolation schemes
-
Bump-less parameter changes
-
Man machine interfaces
Importance of auto-tuning
Adaptation
Process
parameters
Controller
design
Estimation
Controller
Process
Controllerparameters
Reference
Input
Output
Specification
Self-tuning regulator
Certainty Equivalence
Many control and estimation schemes
Dual control
-
Control should be directing as well as investigating!
Uses of Adaptation
Tuning Tools
Automatic Tuning
Gain Scheduling
Adaptive feedback
Adaptive feedforward
Integrated systems
Process dynamics
Varying
Constant
Use a controller withvarying parameters
Use a controller withconstant parameters
Unpredictablevariations
Predictablevariations
Use an adaptivecontroller
Use gain scheduling
c &
K. J. Åström August, 2001