lecture-slides chapter 04
TRANSCRIPT
-
7/25/2019 Lecture-Slides CHAPTER 04
1/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
-
7/25/2019 Lecture-Slides CHAPTER 04
2/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Feedback Control System
Characteristics
Chapter 4
-
7/25/2019 Lecture-Slides CHAPTER 04
3/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Introduction
Error signal analysis
Sensitivity of control systems to variations in process
parameters
Disturbance rejection
Steady state error
Outline
-
7/25/2019 Lecture-Slides CHAPTER 04
4/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Open-loop control system
utilizes an actuating device to control the process (plant)directly without using feedback.
Closed-loop control system
uses a measurement of the output and feedback of this signal
to compare it with the desired input (reference or command).
Also called as feedback control system
Introduction
-
7/25/2019 Lecture-Slides CHAPTER 04
5/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Notation:R(s): Input signal;
U(s): Control or actuating signal;
Y(s): Output signal;
E(s): Error signal;
Gc(s): Transfer function of the controller;
G(s): Transfer function of the process or plant;
H(s): Transfer function of the sensor.
Feedback Control System
Controller Process
Sensor
Measured output
_
+ sY sR
sE sU
sG c sG
sH
-
7/25/2019 Lecture-Slides CHAPTER 04
6/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Why feedback control system:
Advantages: Decreased sensitivity of the system to variations in the parameters of
the process
Improved disturbance rejection
Improved steady-state error reduction Easy control and adjustment of the transient response of the system
Disadvantages:
Increased cost Increased system complexity
Now we examine how feedback improves system performance
Feedback Control System (FCS)
-
7/25/2019 Lecture-Slides CHAPTER 04
7/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Tracking error:
Where L(s)=Gc(s)G(s)H(s) is the loop gain
Error Signal Analysis
Controller Process
Sensor
Measured output
_
+ sY sR
sE sU
sG
c sG
sH
sRsL
sE
1
1
sRsHsGsG
sE
c
1
1
sYsHsRsE
-
7/25/2019 Lecture-Slides CHAPTER 04
8/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Sensitivity function: S(s)
Consider a unity feedback system H(s)=1:
To minimize the tracking error (for a given G(s)):
We need S(s) to be small
We need loop gain L(s) to be large, where
Error Signal Analysis continued
sL
sS
1
1
sGsGsL
sS
c
1
1
1
1
sGsGsLc
-
7/25/2019 Lecture-Slides CHAPTER 04
9/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Tracking error:
Disturbance Rejection
Controller Process
Sensor
Measured output
_
+ sY sR sE sGc
sG
1sH
++
sD
sYsHsRsE
sDsD
sYsR
sR
sYsY
sRsD 00
sD
sL
sGsR
sL
sE
11
1
-
7/25/2019 Lecture-Slides CHAPTER 04
10/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
For R(s)=0; the disturbance D(s) is related to E(s) as:
To minimize the effect of disturbance (for a given G(s)):
We need loop gain L(s) to be large, where
Disturbance Rejection continued
sDsL
sGsD
sGsG
sE
c
11
1
sGsGsLc
-
7/25/2019 Lecture-Slides CHAPTER 04
11/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
G(s): Transfer function of the process
G(s) includes the process parameters subjected to variationsdue to changing environment, non-exact values of
parameters, other errors, etc.
In open-loop systems, these errors and changes result in
inaccurate output Closed-loop system senses the changes in output and
attempts to correct the output (an advantage of FCS)
FCS has an ability to reduce systems sensitivity
Sensitivity of FCS to process parameters
-
7/25/2019 Lecture-Slides CHAPTER 04
12/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
System sensitivity:
The ratio of the percentage change in the system transferfunction (T(s)) to the percentage change in the process
transfer function (G(s))
Where T(s) is the transfer function of the system
In the limit for small incremental changes:
Sensitivity of FCS to process parameters
sG
sG
sT
sT
S
T
G
G
T
sG
sG
sT
sT
S
-
7/25/2019 Lecture-Slides CHAPTER 04
13/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Tracking error for unity feedback system
With changes in the process parameters:
As GcG>>GcG, and for large values of L, 1+LL then
Sensitivity of FCS to process parameters
sRsGsG
sE
c
1
1
sRGGGGGG
GGsE
ccc
c
11
sRsGsGsG
sEsE
c )(1
1
sRG
G
L
sE
1
-
7/25/2019 Lecture-Slides CHAPTER 04
14/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
For changes in a certain parameter K of the process:
where
Sensitivity of FCS to process parameters
T
G
G
TS
T
G
G
K
T
G
T
K SSS
G
K
K
GS
G
K
-
7/25/2019 Lecture-Slides CHAPTER 04
15/16
-
7/25/2019 Lecture-Slides CHAPTER 04
16/16
ME464-Sys Dyn & Ctrl Spring-2013 Dr. Shaukat Ali
Error of a unity feedback system
For open-loop system
For closed loop system
According to the final value theorem (properties of LT
chapter2)
Open-loop:
Closed-loop:
4.6: Steady State Error
sRsTsRsTsRsEc
1
sYsRsE
ssEtest 0
limlim
sRsGsRsGsRsEo
1
sRsGses
o
1lim0
sRsGses
c
1lim0