ECE 360 System Modeling and Control
Design Project
Due: Monday, December 10, 2007
I. System Description
The IP-02 inverted pendulum from Quanser Consulting, Inc., consists of a motor-driven cart
which is equipped with two encoders. One encoder measures th
Solutions HW 7
Fall 2014 ECE/ME 360
October 21, 2014
1
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8 Rotational Motion
Write down the equations of motion for the box of mass mb in Figure 8. The cylinder of radius R has ma
Solutions HW 9
Fall 2014 ECE/ME 360
November 5, 2014
1
Problem 1 Block Diagram Reduction
A block diagram of a control system is shown in Figure 1 below.
G1( s)
R(s)
G2 (s)
C (s)
FIGURE 1.
Compute the transfer function ()() using block diagram reduction me
Solutions HW 2
Fall 2014 ECE/ME 360
September 23, 2014
ii
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12 Laplace Transform
Let
() =
1
(2 + 1)( + 1)
(a) Find () = L1 cfw_ () using
Solutions HW 3
Fall 2014 ECE/ME 360
September 18, 2014
1
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
6
(d) Find a solution to the system of part () using the phasor
Solutions HW 10
Fall 2014 ECE/ME 360
November 5, 2014
1
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6 Proportional Feedback
Consider a satellite tracking antenna whose equation of motion is given by
2
+
=
2
where is the angle of elevation
Solutions HW 4
Fall 2014 ECE/ME 360
September 22, 2014
ii
Problem 1 Vertical Spring-Mass System
Consider the spring-mass-damper system in the figure below.
k
m
f(t)
x
FIGURE 1.
(a) Write down the equations of motion of the mass using Newtonss laws of moti
Solutions HW 8
Fall 2014 ECE/ME 360
October 28, 2014
1
Problem 1
Problem 2
Problem 3
Problem 4 The Linear DC Motor
~ = B^
Consider the simple linear motor in Figure 4 where the magnetic eld B
z (B > 0) is up out of the page.
Closing the switch causes a cu
Solutions HW 1
Fall 2014 ECE/ME 360
September 2, 2014
ii
Problem 1 Inverse Laplace Transform
Let
F (s) =
and compute f (t) = L
We have
1
3s2 + s + 4
s3
fF (s)g.
F (s) =
3
4
3s2 + s + 4
1
= + 2+ 3
s3
s s
s
so that
f (t) = 3us (t) + tus (t) + 4
Problem 2 In
HW 6 Solutions
Problem 1 Faradays Law
Consider the gure below where the magnet is moving up into a square planar loop of copper wire.
CW CCW
z
n1
y
x
n2
r
vm
N
S
(a) Using the normal n
^ 1 , compute the ux and roughly sketch it as a function of t. Is the
Solutions HW 8
Fall 2014 ECE/ME 360
November 10, 2014
1
Problem 1 Block Diagram Reduction
Use the block diagram reduction method to compute the transfer function ()(). Show work!
b1
C (s)
1
s
R(s)
1
s
b2
a1
a2
FIGURE 1.
We first rewrite it as the equivale
Comparison of a P and a PI Controller for the Cart and Track System
Andres Valdepea Delgado, John Chiasson
Boise State University
Due Date: Sunday April 23rd 11:59pm
Simulation Work: Consider both the proportional and proportional plus integral controller
ECE360
EXAM #2
FALL 2007
Instructions:
1. Closed-book, closed-notes, open-mind exam. You may only use the exam objectives and the
two tables of Laplace transforms distributed in class.
2. Work each problem on the exam booklet in the space provided.
3. Wri
ECE360
EXAM #3
FALL 2007
Instructions:
1. Closed-book, closed-notes, open-mind exam.
2. Work each problem on the exam booklet in the space provided.
3. Write neatly and clearly for partial credit. Cross out any material you do not want graded.
4. Leave on
ECE360
HOMEWORK #5
DUE: FRIDAY, OCTOBER 12, 2007
Problem 5.1 (Problem B-5-7 p. 242) Problem 5.2 (Problem B-5-8 p. 242) Problem 5.3 (Problem B-8-16 p. 429) Problem 5.4 (Problem B-8-17 p. 429)
ECE360
HOMEWORK #1
DUE: FRIDAY, SEPTEMBER 7, 2007
Problem 1.1
R1 v1 R2 v2 + + vi (t) C1 C2 vo (t)
Derive a state-space model for the above electric circuit in the form: v1 v2 = vo = Problem 1.2 Using the results of Problem 1.1, derive the input-output di
ECE360
HOMEWORK #2
DUE: FRIDAY, SEPTEMBER 14, 2007
Problem 2.1 (Problem B-2-9 p. 50) Problem 2.2 (Problem B-2-10 p. 50) Problem 2.3 (Problem B-2-13 p. 51) Problem 2.4 (Problem B-2-14 p. 51) Problem 2.5 (Problem B-2-18 p. 51) Problem 2.6 (Problem B-2-19 p.
ECE360
HOMEWORK #3
DUE: FRIDAY, SEPTEMBER 21, 2007
Problem 3.1
R1 v1 R2 v2 + + vi (t) C1 C2 vo (t)
(a) Assuming that both capacitors are deenergized at time t = 0, draw the Laplace equivalent of the above circuit. (b) Solve for the node voltages V1 (s) a
ECE360
PRACTICE EXAM #3
FALL 2007
Instructions:
1. Closed-book, closed-notes, open-mind exam.
2. Work each problem on the exam booklet in the space provided.
3. Write neatly and clearly for partial credit. Cross out any material you do not want graded.
4.
ECE360
PRACTICE EXAM #1 SOLUTIONS
FALL 2007
Instructions:
1. Closed-book, closed-notes, open-mind exam. You may only use the exam objectives and the
two tables of Laplace transforms distributed in class.
2. Work each problem on the exam booklet in the spa
HW 6 Solutions
Problem 1 Moment of Inertia of a Uniform Solid Sphere
4
4
3 as its volume is 3 .
3
3
Show that the moment of inertia of the sphere about any axis through its center (about any diameter of the sphere)
2
is given by = 3 . Hint: Use spherical