ECE 460: Solutions to Homework 6
Instructor: Stan Baek
Due: Monday, March 7, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (50 points) Sketch the root
ECE 460
Lecture 14
Root Locus Continued
Last lecture
Basic rules
This lecture
Rule refinement
Multiple examples
It is impossible to verify this for every s. Instead, we seek a locus of the pole
ECE 460
Lecture 18
Compensating a deficient open loop system (plant)
%OS
epos()
Lag compensation using root locus
1
Consider the following closedloop system
Suppose that we wish that this syst
ECE 460
Lecture 10
System stability
A system is stable if x(t) is bounded (energy or power signal) implies that y(t) is also bounded
X(s)
+

G(s)
Y(s)
1
How do we ensure that a closed system is st
ECE 460
Lecture 20
1
The transfer function of the various system components is not always known !
In others words we may dealing with a closed loop control system:
For which we do not know the plant
ECE 460
Lecture 11
Recall the antenna position control system
1
A case study of unityfeedback closedloop control
system
A system whose behavior can be dramatically
altered by just changing the va
ECE 460
Lecture 13
System performance
1
Adjust K in order to achieve
Desired %OS ?
Desired Ts
?
Desired e()
Stability
2
Lets look at %OS
Closedloop poles should lie at a (no more than) desired an
ECE 460
Lecture 12
System classified by their tracking ability
1
Classification examples
X(s)
+
G(s)

Y(s)
K
1. G ( s )
( s 1)(s 5)
K
2. G ( s )
s( s 5)
K
3. G ( s)
s 2 ( s 5)
4. G ( s )
K
s3 (
ECE 460
Lecture 15
Lecture 13  basics of root locus
Lecture 14  first refinement of the root locus
Breakaway/in point(s)
This lecture is about additional refinements and special cases
Complex
ECE 460
Lecture 22
R(s)
+

K.G(s)
C(s)
We used the Bode plot of the openloop G(s) to adjust K so that the closedloop system meets certain performance requirements
%OS, epos(), Stability
Estimati
ECE 460
Lecture 16
Further review of gain adjustment (calibration) using root locus
%OS
Ts ?
Stability ?
1
Stability Using RootLocus
Consider the following closedloop system
Suppose that we w
ECE 460
Lecture 17
Further review of gain adjustment (calibration) using root locus
%OS
Ts ?
Stability ?
1
Stability Using RootLocus
Consider the following closedloop system
Suppose that we w
ECE 460
Lecture 21
R(s)
+

K.G(s)
C(s)
We want this system to perform:
%OS, epos(), Ts, Stability
But G(s) is unknown !
We do have an experimentally obtained frequency response of G(s)
Bode plot
Solutions to Homework 5
ECE 460: Automatic Control
Due: Monday, February 22, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (30 points) Given the system
ECE 460: Solutions to Homework 7
Instructor: Stan Baek
Due: Wednesday, March 16, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Note 2. This homework set includes
Solutions to Homework 3
ECE 460: Automatic Control
Due: Monday, February 1, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. Figure 1 shows a DC motor wit
ECE 460: Solutions to Homework 9
Instructor: Stan Baek
Due: Monday, April 11, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (25 points) Find a statesp
Solutions to Homework 4
ECE 460: Automatic Control
Due: Monday, February 8, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (20 points) Reduce the block
ECE 460: Homework 8
Instructor: Stan Baek
Due: Wednesday, March 30, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. ( 40 points) Sketch the asymptotes of
Solutions to Homework 2
ECE 460: Automatic Control
Due: Wednesday, January 20, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (20 Points) Find the Lapla
Solutions to Homework 1
ECE 460: Automatic Control
Due: Wednesday, January 13, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. (40 Points) Using Eulers f
ECE 460: Solutions to Homework 10
Instructor: Stan Baek
Due: Monday, April 18, at 2:10pm
Note 1. Your solutions should be neat and legible; always show your work.
Problem 1. Consider the following sys
ECE 460
Lecture 19
1
We want the closed loop system, with proper gain (K) adjustment, to meet all four of these performance requirements:
Ts = 1s
%OS = 20%
Stable
epos() = 102
2
Root Locus of
An
ECE 460
Lecture 20
1
The transfer function of the various system
components is not always known !
In others words we may dealing with a closed loop
control system:
R(s)
K.G(s)
+
C(s)

For which we
ECE 460
Lecture 14
Root Locus Continued
Last lecture
Basic rules
This lecture
Rule refinement
Multiple examples
It is impossible to verify this for every s. Instead, we
seek a locus of the pole
ECE 460
Lecture 13
System performance
1
Adjust K in order to achieve
Desired %OS
Desired Ts
Desired e()
Stability
?
?
2
Lets look at %OS
Closedloop poles should lie at a (no more than)
desired an
ECE 460
Lecture 10
System stability
X(s)
+

G(s)
Y(s)
A system is stable if x(t) is bounded (energy or
power signal) implies that y(t) is also bounded
1
How do we ensure that a closed system is st