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CONTROL SYSTEM
AN INTRODUCTION
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Contents
1. An Motion Control System
2. Purpose of Closed-Loop Control
3. Servo and Regulation Systems
4. Controller
5. How to Identify System6. Summary
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1. An Motion System
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Plant: Input-output relationship (transfer function) mayvary
uncertainties (including time-varying) and
Disturbances
Nominal Model G(s)=5/(s+1)
Actual Model G(s)=5.9/(s+1.3)
Sensor: output may be digital or analog. Its input: realspeed,
its output: readable data of speed
Actuator: Its input: readable data of the voltage of thepower
source.
Its output: voltage, with needed current
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Decision Making: Controller
Analog Controller
Digital Controller
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2. Purposes
Open-loop: speed varies with the motor and
load for a given drive voltage
Closed-loop: Compensates for the influence
of the variations in the motor and the load
(uncertainties and disturbances) on the
speed.
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3. Types of Systems
Servo Systems: the desired speed (set-point)
changes fast. Major requirement: to follow the
changing set-point at an acceptable speed andaccuracy.
Regulation Systems: the desired speed does not
changes very fast. It may be constant. Major
concern: substantial uncertainties/disturbances andhigh
accuracy.
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4. Controller
What does a controller do? Decides how to respond to theobserved
difference between the measured speed and thedesired speed
set-point.
How should the controller respond? Primarily based onthe model,
which describes the relationship between theinput (voltage) and the
output(speed) RobustControl: also largely based on the
uncertainties
An important Step in System Design: Find the model(system
identification)
Design: compromise between the uncertainties/disturbance and the
response speed.
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5. How to Identify the System
Analyze the input-output data pairs to fit the parameters in
the used model (structure)
How to analyze and how to generate the data pairs for
analysis:
System Identification
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6. Summary
This class: Part One: Identification
Part Two: Control Design Based on ModelPart Three: Discrete
Control
Project 1: Parts One and Two
Project 2: Part Three
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SYSTEM IDENTIFICATION
INTRODUCTION
Dr. YuMing Zhang
College of Engineering
University of Kentucky
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Contents
1. System
2. System Identification
3. Importance
4. Why Specific Techniques?
5. Example6. Summary
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1. System
System: an object in which variables ofdifferent kinds interact
and produce
observable signals Control engineers views:
Process producing outputs from inputs
Outputs:
Inputs: manipulated to change the outputs
Disturbances:
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2. System Identification
End products: empirical models of systems
Model: description of relationship among related
variables
Theoretical Models: from first principles
Empirical models:
Observations of system variables
==>Relationship among variables
==> Models linking the variables
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3. Importance
Control algorithms & system dynamics
First principles
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4. Why Specific Techniques?
Model structure:y t ay t bu t( ) ( ) ( ) 1 1
Given:{ ( ), ( )},{ ( ), ( )},...,{ ( ), ( )}u y u y u N y N 1 1
2 2
To determine: a and b Equation system
y ay bu
y ay bu
y
y
y u
y u
a
b
( ) ( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )
( ) ( )
2 1 1
3 2 2
2
3
1 1
2 2
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Problem:
y t ay t bu t e t( ) ( ) ( ) ( ) 1 1
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a b
u y
u u
y y y
a b
e e e
y y y
a b
0 95 2
0 0 0 0
1 1 2 1 2
1 0 2 2 3 4 3
0 95
1 0 1813 2 0 1205 3 0 3318
1 0 1813 2 2 0517 3 4 6809
. ,
( ) , ( )
( ) , ( ) .
( ) , ( ) , ( ) .
, : . ,
( ) . , ( ) . , ( ) .
( ) . , ( ) . , ( ) .
, : ,
2
1.2097 1.8324
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5. Example Model Structure
y t ay t bu t e t( ) ( ) ( ) ( ) 1 1
Given:{ ( ), ( )},{ ( ), ( )},...,{ ( ), ( )}u y u y u N y N 1 1
2 2
To determine:a
andb
Prediction( ) ( ) ( )y t ay t bu t 1 1
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Prediction Errory t y t y t ay t bu t( ) ( ) ( ) ( ) ( ) 1 1
Cost FunctionJ a b y t ay t bu t
t
N
( , ) { ( ) ( ) ( )}
2
21 1
Results
( )( )
...
( )
( ) ( )
( ) ( )
......
( ) ( )
a
b
yy
y N
y u
y u
y N u N
T T
1
23
1 1
2 2
1 1
fory t ay t bu t e t( ) ( ) ( ) ( ) 1 1
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6. Summary
Data Generation (Experiment Design)
Model Structure Determination
Parameters Estimation
Model Validation
