CONTROL SYSTEM
AN INTRODUCTION
Contents
1. An Motion Control System
2. Purpose of Closed-Loop Control
3. Servo and Regulation Systems
4. Controller
5. How to Identify System
6. Summary
1. An Motion System
Plant: Input-output relationship (transfer function) may
vary 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: real
“speed”, its output: “readable data” of speed
Actuator: Its input: “readable data” of the voltage of the
power source.
Its output: voltage, with needed current
Decision Making: Controller
Analog Controller
Digital Controller
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.
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 and
accuracy.
• Regulation Systems: the desired speed does not
changes very fast. It may be constant. Major
concern: substantial uncertainties/disturbances and
high accuracy.
4. Controller
• What does a controller do? Decides how to respond to the
observed difference between the measured speed and the
desired speed set-point.
• How should the controller respond? Primarily based on
the model, which describes the relationship between the
input (voltage) and the output(speed)
Robust
Control: 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.
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
SYSTEM IDENTIFICATION
INTRODUCTION
Contents
1. System
2. System Identification
3. Importance
4. Why Specific Techniques?
5. Example
6. Summary
1. System
• System: an object in which variables of
different kinds interact and produce
observable signals
• Control engineers’ views:
Process producing outputs from inputs
Outputs:
Inputs: manipulated to change the outputs
Disturbances:
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
3. Importance
• Control algorithms & system dynamics
• First principles
4. Why Specific Techniques?




Model structure:
y(t )  ay(t  1)  bu(t  1)
Given:
{u(1), y(1)},{u(2 ), y(2 )},...,{u( N ), y( N )}
To determine: a and b
Equation system
 y(2)  ay(1)  bu(1)


 y(3)  ay(2)  bu(2)
 y( 2 ) 
 y(3)  


 y(1) u(1)  a 
 y ( 2 ) u( 2 )   b 

 
Problem:
y(t )  ay(t  1)  bu(t  1)  e(t )
a  0.95, b  2
u(0)  0, y(0)  0
u(1)  1, u(2)  1.2
y(1)  0, y(2)  2, y(3)  4.3
 a, b: 0.95, 2
e(1)  0.1813, e(2)  0.1205, e(3)  0.3318
y(1)  0.1813, y(2)  2.0517, y(3)  4.6809
 a, b: 1.2097, 1.8324
5. Example

Model Structure
y(t )  ay(t  1)  bu(t  1)  e(t )

Given:
{u(1), y(1)},{u(2), y(2)},...,{u( N ), y( N )}

To determine:
a and b

Prediction
y (t )  ay(t  1)  bu(t  1)

Prediction Error
y(t )  y (t )  y(t )  ay(t  1)  bu(t  1)

Cost Function
N
J ( a, b)   {y(t )  ay(t  1)  bu(t  1)}2
t 2

Results
 a 
 
 b
 y( 2 ) 


y(3) 
1
T
T
    
 ... 


 y( N )
u(1) 
 y(1)


y
(
2
)
u
(
2
)


 ......



 y( N  1) u( N  1)
for y(t )  ay(t  1)  bu(t  1)  e(t )
6. Summary
•
•
•
•
Data Generation (Experiment Design)
Model Structure Determination
Parameters Estimation
Model Validation