Controls Quiz 1 Solutions
Signals & Systems
April 25, 2014
1
1. (25 pts) Consider the transfer function H(s) =
s+3
s2 +6s+18 .
(a) (5 pts) Compute the nite-valued poles and zeros.
Solution:
At zeros numerator s + 3 = 0 so z = 3
At poles denominator s2 + 6
Chapter 4 - Solutions to Exercises
April 19, 2013
1. (30 Points) Transient Behavior Revisited
Consider the following open loop transfer function for a second order system with an added zero:
G(s) =
2
n s + n
.
2
s2 + 2n s + n
Remember that for second orde
Homework 1
(100 pts)
April 1, 2014
1.
(a) (15 pts) Compute the LaPlace transform of f (t) = t et sin(3t)us (t). Show your steps and logic.
sin(3t)us (t)
3
Re(s) > 0
s2 + 9
(1a)
(differentiation in s property)
tsin(3t)us (t)
d
ds
s2
3
+9
=
(s2
6s
(6 pts
Homework 4 Solutions
May 7, 2014
1. (30 Points) Transient Behavior Revisited
Consider the following open loop transfer function for a second order system with an added zero:
G(s) =
2
n s + n
.
2
s2 + 2n s + n
Remember that for second order system with com
Homework 7
April 9, 2014
1. (30 pts) Draw a block diagram using only gains, adders, and integrators (no derivative operators as they are not
necessarily causal!) of the following causal LTI systems:
(a) H(s) =
10
s+6
1
(b) H(s) =
10(s+3)
(s+1)(s1)
Alterna
Quiz 2 (Final)
May 1, 2012
Have a great summer holiday! 1. (20 points) Consider an LTI system with transfer function H (s) = (Fi. -~:. Wég'lé 3)
o (5 pts) What are the poles and zeros of H(s)?
FOLES ; Z, LI
asses: \, w:
o (5 pts) What R.O.C. would give r
Chapter 2 - Solutions to Exercises )
April 16, 2013
1. (30 points) Let us (t) be the unit step function. Find the Laplace transform and region of convergence of the
following time functions.
(a) (10 points) f (t) = (tet + 2t sin t)us (t)
(b) (10 points) f
Practice Problems
May 7, 2012
1. Consider the following input-output model of an LTI system:
y + 3y + 2y = u + 7u + 12u
2. Compute the transfer function, H(s) from u to y.
3. What are the poles and zeros of H(s)?
4. What R.O.C. gives rise to a BIBO stable
Chapter 5 - Solutions to Exercises
1. (25 points) Consider the linear system with the following state-space representation.
0 1
0
0
1 x(t) + 0 u(t), x(0) = 0,
x(t) = 0 0
0 6 5
1
y(t)
1
=
0
1 x(t).
Answer:
(a) (5 points) Recall that the transfer function
Chapter 6 - Solutions to Exercises
April 19, 2013
1. (15 points) Imagine that as you are reading this question, you decide to reach for a pencil. You lift your
eyes from the paper and try to locate the target. The usual human reach-to-grasp movement thus