ME 360: Modeling, Analysis, and Control of Dynamic Systems
Professor Tilbury, University of Michigan, Winter 2009 Linearization Handout September 10, 2009 Basic idea: The local behavior of a nonlinear system can be approximated by its linearization about
ME360 - Dynamic Systems
Prof. Gillespie - Fall 2010
HW 4 - Due Sept 30
Problem 1 Problem 2.13, page 70. (Same in the previous book edition). Problem 2 Property No. 3 in Table 3.3.2 on page 104 of your book is a property that I did not derive in lecture. D
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 6 solution
Assigned: Thurs. Oct. 8, 2015
Due: October 23, 2015
1. Problem 5.12
Let x1 = y, x2 = y, x3 =
y
1
x3 = ( f (t) 7x1 4x2 5x3 )
2
2. Problem 5.14
Y (s)
6
= 2
F(s) 3s + 6s + 10
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 8 solution
Assigned: Thurs. Oct. 29, 2015
Due: November 5, 2015
1. Problem 6.21
Because and are parallel, the equivalent impedance is
Total impedance for the circuit is:
So the required tra
ME 360: Modeling, Analysis and Control of Dynamic
Systems
Homework 2 Solution
Assigned: Thursday, Sept. 10, 2015
Due: Sept. 17, 2015
Problem 1
Problem 2
() 0 0
Alternatively, using
() 16 +
1
216
() = 4 +
() 0 16
1
8
Problem 3
(a)
Take x 0 and then x 0 or
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 5 solution Assigned:
Thurs. Oct. 1, 2015
October 8, 2015
1
Problem 3.15, page 158
Given:
I1 = 0.3kg m2 ; I2 = 0.5kg m2 ; T1 = 0.5N m; T2 = 0.3N m;
Question: compute the equivalent inertia o
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 7 solution Assigned:
Thurs. Oct. 23 ,2015 October
30, 2015
1
Problem 6.3, page 386
Let i1 be the current through R1 , R4 , i2 be the current through R2 , R3 .
Then,
Vs = (R1 + R4 )i1 = (R2
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 8 solution
Assigned: Thurs. Oct. 29, 2015
Due: November 5, 2015
1. Problem 6.21
Because and are parallel, the equivalent impedance is
Total impedance for the circuit is:
So the required tra
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 4 solution
Assigned: Thurs. Sept. 24,
2015 October 1, 2015
1. Problem 2.20b
5
C
C2
C
1
3
2
2
(s 4) (s 1) s 4 ( s 4)
s 1
C1 C3 0
5
15
5
=> C1 , C2 , C3
5C1 C2 8C3 0
9
9
9
4C C 16C 5
1
2
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 3 solution Assigned:
Thurs. Sept. 17, 2015
September 24, 2015
1
Problem 2.6, page 109, parts a,b,d
a. L cfw_x(t)=10+t2 :
X(s) = 10 + s23
s
b. L cfw_x(t)=6te5t + e3t :
6
1
X(s) = (s+5)2
ME 360
Modeling, Analysis and Control of Dynamic Systems
W 2016
Homework Set #6
(Due by start of class on Thu 2/25/15)
Please show your work in solving all the problems below. Print out any Matlab files and plots
that you use with your name on each file.
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 10 solution
Assigned: Thurs. Nov. 6, 2014
Due: November 13, 2014
1. Problem 10.6
(a)
!
= ! ! ! ! , ! is the resistance of motor
!
(b)
(c)
is the answer
!(!)
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 9 solution
Due: Thurs. Nov. 12, 2015
1
Problem 8.7, page 517
According to the equation (8.1.3) in page 475, the time constant of the rotational system:
1 =
100
= 20s
5
The time constant of
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 8 solution
Assigned: Thurs. Oct. 24, 2013
Due: October 31, 2013
1. Problem 6.21
Because and are parallel, the equivalent impedance is
Total impedance for the circuit is:
So the required tra
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 6 solution
Assigned: Thurs. Oct. 9, 2014
Due: October 16, 2014
1. Problem 5.12
Let x1 = y, x2 = y, x3 =
y
1
x 3 = ( f (t) 7x1 4x2 5x3 )
2
2. Problem 5.14
Y (s)
6
= 2
F(s) 3s + 6s + 1
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 9 solution
Assigned: Thurs. Oct. 30,2014
Due: Thurs. Nov. 6, 2014
November 7, 2014
1
Problem 8.7, page 517
According to the equation (8.1.3) in page 475, the time constant of the rotational
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 7 solution
Assigned: Thurs. Oct. 16,2014
October 20, 2014
1
Problem 6.3, page 386
Let i1 be the current through R1 , R4 , i2 be the current through R2 , R3 .
Then,
Vs = (R1 + R4 )i1 = (R2 +
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 4 solution
Assigned: Thurs. Sept. 18,
2014 September 25, 2014
1. Problem 2.20b
5
C
C2
C
1
3
2
2
(s 4) (s 1) s 4 ( s 4)
s 1
C1 C3 0
5
15
5
=> C1 , C2 , C3
5C1 C2 8C3 0
9
9
9
4C C 16C 5
ME 360: Modeling, Analysis and Control of Dynamic
Systems
Homework 1 Solution
Assigned: Thursday, Sept. 4, 2014
Due: Sept. 11, 2014
Problem 1
Problem 2
Problem 3
(a)
Take x 0 and then x 0 or x M .
(b)
Let x f ( x) ax 1
x
M
x f
x axo 1 o
M x
x
axo 1 o
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 5 solution
Assigned: Thurs. Oct. 3,2013
October 9, 2013
1
Problem 3.15, page 158
Given:
I1 = 0.3kg m2 ; I2 = 0.5kg m2 ; T1 = 0.5N m; T2 = 0.3N m;
Question: compute the equivalent inertia on
ME 360: Modeling,Analysis and Control of Dynamic
Systems
Homework 3 solution Assigned:
Thurs. Sept. 11, 2014
September 18, 2014
1
Problem 2.6, page 109, parts a,b,d
a. L cfw_x(t)=10+t2 :
+ s23
X(s) = 10
s
b. L cfw_x(t)=6te5t + e3t :
6
1
X(s) = (s+5)
2
ME 360: Modeling, Analysis and Control of Dynamic Systems
Professor J.L. Stein
University of Michigan, Fall 2015
Homework #1
Assigned: Tue. Sept. 8, 2015
Due: Thurs. Sept. 10, 2015
Students may work together on the homework assignments, but individually p
ME 360: Modeling, Analysis, and Control of Dynamic Systems
Professor Stein
University of Michigan
Fall 2015
Exam #75 1
Wednesday, October 14, 2015
M
This exam is closed book and closed notes. One sheet of handwritten notes (8.5X11), one side is
allowed. N
ME 360
Modeling, Analysis and Control of Dynamic Systems
W 2016
Homework Set #9
(Due by start of class on Thu 3/31/16)
Please show your work in solving all the problems below. Print out any Matlab files and plots
that you use with your name on each file.
ME 360
Modeling, Analysis and Control of Dynamic Systems
W 2016
Homework Set #4
(Due by start of class on Thu 2/04/16)
Please show your work in solving all the problems below. Print out any Matlab files and plots
that you use with your name on each file.
ME 360
Modeling, Analysis and Control of Dynamic Systems
W 2016
Homework Set #10
(Due by start of class on Tuesday 4/12/16)
Please show your work in solving all the problems below. Print out any Matlab files and plots
that you use with your name on each f