ME 3600 Control Systems
Homework Assignments
No.
Chapter/
Set #
Assignment
E 1.4, 1.13 and P 1.2, 1.5, 1.8, 1.18
#1
1/1
#2
2/1
Draw a block diagram for each system and identify the input, output, actuator, plant (or process), and
sensor. Be specific.
Find approximate linear models for the systems of: E 2.2, 2.11, 2.18, P 2.5
Find only the differential equations of motion for the systems of: E 2.26, P 2.2, 2.3, 2.34
#3
2/2
See page 2 below.
#4
2/3
Find the required transfer functions for: E 2.26, P 2.9, 2.10, 2.34
E 2.7, 2.8, 2.9, 2.12, 2.14, 2.23, 2.24, 2.27, 2.29, P 2.33.
#5
2/4
For each of these problems, (a) Draw a block diagram for the system, and (b) Use block diagram
reduction to find the required transfer function.
#6
2/5
E 2.16 (See page 3 below.)
#7
4/1
E 4.2, 4.4, 4.8, 4.9 and P 4.3, 4.6, 4.15
#8
5/1
E 5.2, 5.3, 5.4, 5.7, 5.9, 5.15 and P 5.4, 5.6, 5.7(a, b)
#9
6/1
E 6.1, 6.4, 6.6 and P 6.1(e), 6.1(g), 6.3, 6.9, 6.10, 6.19
#10
7/1
E 7.2, 7.4, 7.6, 7.8, 7.9, 7.17 and P 7.1(b), P 7.1(d), 7.6, 7.12(a, b, c)
Make sure to include a detailed sketch of the root locus diagram as part of your solution.
E 8.2, 8.3, 8.4*, 8.6, 8.8**, 8.11. Make sure to include a Bode magnitude diagram for each problem.
Sketch the Bode magnitude diagram for K  400 and a  2 , only.
100( s  2)
**
Use Gc G(s)  2
.
( s  10s  100)
*
#11
8/1
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ME 3600 Control Systems
Homework #3 (Solving differential equations using Laplace transforms)
1. E 2.4
a) as required in text
b) use the final value theorem to find the limit of y (t ) as t  
c) compare the value of part (b) with lim( y(t ))
t 
2. E 2.19 a) as required in text
b) use the final value theorem to find the limit of y (t ) as t  
c) compare the value of part (b) with lim( y(t ))
t 
Solve the following differential equations using Laplace transforms. Use the final value
theorem to find the limit of x( t ) as t  . Compare that value to lim( x(t )) .
t 
3. x  3x  us (t ) with the initial values a) x(0)  0 and b) x(0)  2
( us (t ) is the unit step function).
4. x  5x  e3t cos(2t ) with the initial value x(0)  0 .
5. x  8x 15x  us (t ) with the initial values
a) x(0)  x(0)  0 , and
b) x(0)  0 and x(0)  3 .
6. x  4x 15x  e3t with the initial values x(0)  x(0)  0 .
7. P 2.36 – Do part (a) only and assume r(t) is the unit step function.
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ME 3600 Control Systems
Homework #6
For the system described in problem E 2.16, complete the following.
a) Draw the block diagram for the system. Identify transfer functions for each equation
given.
b) Find the transfer function P(s) R( s) using block diagram reduction.
c) MATLAB simulation:
i) Replace the amplifier gain equation "v2=7v1" with the equation "v2=Kv1".
ii) Plot the step response of the system using MATLAB, for the following gains:
K = 1, 2, 6, 13, 17. All responses should be plotted from 020 seconds.
Print the plots.
iii) Classify each response (over-damped or under-damped, stable or unstable).
iv) Compare the responses. Which gets to the commanded value first? Which gets
to and remains within 10% of the command in the shortest time? Which do you
think provides the best solution? Why?
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