312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #12
(1) Nise Chapter 9, Problem 27.
(2) Nise Chapter 10, Problem 1.
For the following closed-loop transfer functions, sketch the b
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #7
(1)
a) poles: -2, no zeros; c(t) = A + Be2t ; first-order response.
b) poles: -3, -6, no zeros; c(t) = A + Be3t + Ce6t ; overd
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #9
(1)
(2)
(3)
(4)
(5)
Nise
Nise
Nise
Nise
Nise
Ch.
Ch.
Ch.
Ch.
Ch.
8,
8,
8,
8,
8,
Problem
Problem
Problem
Problem
Problem
1.
2.
3
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #11
(1) Obtain the step response for the following system in a unity feedback loop. K = 10
K(s + 1)
(1)
s2
(2) For the following s
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #8
(1) Nise Ch. 5, Problem 4.
(2) Nise Ch. 5, Problem 8.
(3) Nise Ch. 5, Problem 11.
(4) Nise Ch. 5, Problem 12.
(5) Nise Ch. 5, P
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #10
(1)
(2)
(3)
(4)
(5)
(6)
Nise
Nise
Nise
Nise
Nise
Nise
Ch.
Ch.
Ch.
Ch.
Ch.
Ch.
8,
8,
8,
9,
9,
9,
Problem
Problem
Problem
Proble
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #4
(1)
Figure 1: Problem 1.
Note there are two locations with distinct pressures, the bottom of the tank, with PC and the
just befo
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #2
(1) B-3-4
Note that = 2f , f = 20Hz, J = 50Kg m2 and t = 5s.
J = step
(1)
step
step
(t) = (t = 0) +
t=
t
J
J
step
(t = 5) =
5s
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #6
(1) B-9-1
This problem was also solved on page 433. The equations of motion are,
m
x + kx = P sin(t)
(1)
Then, taking the Laplac
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #8
(1)
T (s) =
G3 + G1 G 2
1 + H[G3 + G1 G2 ] + G2 G4
(1)
(2)
22 (s)
G 1 G2 G4 G5 G6 G7
=
11 (s)
1 G4 G5 + G4 G5 G6 + G1 G 2 G3 G
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #10
(1)
characteristic polynomial: s3 + 13s2 + 40s + K = 0
s = j j 3 13 2 + j40 + K = 0
(K 13 2 ) + j(40 2 ) = 0
from the real po
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2015
Solution Set #11
(1)
KG(s) =
10(s + 1)
s2
(1)
The closed-loop transfer function is,
Gcl (s) =
s2
10(s + 1)
10(s + 1)
=
+ 10s + 10
(s + 1.127)(s
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #5
(1) There are three pressure drops: from atmosphere to the bottom of the tank, (PC ), from the
tank to just before (to the lef
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #1
(1)
1.c f (t) = sin(t) t 0
Z
sin(t)e
F (s) =
0
Z
=
=
=
=
=
=
st
Z
dt =
0
1 jt
(e ejt )est dt
2j
1 (sj)t
(e
e(s+j)t )dt
2j
0
"
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #4
(1) a) For springs in series the forces are equivalent, but each has a different displacement, , which
sums to the total displ
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2016
Solution Set #2
(1) Note that R1 is in parallel with the two resistors, R2 and R3 , which are in series (so R2 and R3
add).
1
1
1
R1 + R2 + R3
R
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #3
(1) a) The mesh equations are:
I1 (s)(R1 + Ls) I2 (s)Ls = Vi (s)
(1)
I2 (s)(R2 + Ls) I1 (s)Ls = 0
(2)
Use second equation to s
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #6
(1) a) We begin with our node and loop laws,
iR = iL = im
(1)
Vs = VR + VL + Vm
(2)
Then,
Vm = Vs VR VL
Vm = Vs Rim L
(3)
dim
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #9
(1) a. No: Not symmetric; On real axis to left of an even number of poles and zeros.
b. No: On real axis to left of an even nu
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #3
(1) B-6-1
Note that R1 is in parallel with the two resistors, R2 and R3 , which are in series (so R2 and R3
add).
1
1
R1 + R2 +
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #5
(1) Shown is a diagram for a DC motor. The resistance is that of the armatures coils. For now,
assume the inductance, L is negli
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Fall 2014
Solution Set #1
Find the Laplace transform of the following functions:
(1)
f (t) = 3 + cos(t) + e3t sin(5t)
s
5
3
+ 2
+
F (s) =
s s + 1 (s + 3)
MIE 312 Fall 2013 Assignment 7 Page 1 of 2
1. The open loop transfer function of a dynamic system is given as
5+1
WW
Using Rouths criterion determine the range of the gain K for which the system is stable when
the characteristic equation is 1 + KG(s) = 0.
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #7
(1) Nise Ch. 4, Problem 8.
(2) Nise Ch. 4, Problem 9.
(3) Nise Ch. 4, Problem 12.
(4) Nise Ch. 4, Problem 13.
(5) Nise Ch. 4, P
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical & Industrial Engineering Spring 2016
Problem Set #6
(1) Shown is a diagram for a DC motor. The resistance R and the inductance, L are that of
the armatures coils. Use
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #5
(1) Find the transfer function defining the volumetric flow out as a function of the source, Qo (s)/QS (s).
(2) Find the transf
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #4
(1) a) Derive the equivalent spring stiffness for two springs in series. b) What is the general expression for n springs in ser
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #2
(1) Obtain the resistance between points A and B.
R2
R3
A
R1
B
(2) Obtain the resistance between points A and B.
10
20
A
B
100
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Problem Set #3
(1) Nise Ch. 2, Problem 17, but use impedance modeling techniques.
(2) Nise Ch. 2, Problem 18, use Kirchhoffs current and volta
312 DYNAMIC SYSTEMS AND CONTROL
University of Illinois, Chicago
Department of Mechanical Engineering Spring 2016
Solution Set #12
(1)
G(s) =
K
(s + 4)(s + 6)(s + 10)
(1)
a) 25% OS corresponds to zeta p
= 0.4037, and n = 4/Ts = 2, so n = 4.954. Thus our de
MIE 312 Fall 2013 Assignment 5 SOLN Page 1 of4
Assignment 5:
1. B-7_3 in your text. For the two tank fluid flow system shown in the following figure determine
the transfer function relating the flow from the first tank to the flow of the second tank.
,1,
ME/IE 312 Fall 2012 Exam 2 Page 1 of 6
Print Name: 3% LU
The exam is closed book and closed notes. You may have an 8% by 11 sheet of paper with any notes
that you think appropriate. Show all equations, work and units. Answers without equations will not
be
MIE 312 Fall 2013 Assignment 6 Page 1 of 2
Assignment 6:
1. A block diagram of a dynamic system is shown below.
Disturbance, w
Measurement noise. v
The command input is the reference speed.
D(s)=K
10
GHZW
a. With a zero command input, zero measureme