DORDT COLLEGE ENGINEERING DEPARTMENT
CONTROL SYSTEMS -- EGR 362
(Spring 2003)
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PROBLEM SETS (Last update:
------------ 5/06/03 8:03 am)
+===============================================================+
|PS|ASSIGNED| DUE |RETURNED| Problems Assigned (In Ogata |
| #| / \ | (unless otherwise noted) |
|==+=======+=======+=======+====================================|
| 1| 1/15 | 1/17 | 1/20 | Prove line 7 on page 17 using the |
| | | | | def'n of the Laplace Transform. |
| | | | | B-2-6, B-2-9 via tables |
|--+-------+-------+-------+------------------------------------|
| 2| 1/17 | 1/24 | 1/28 | B-2-13, B-2-18, B-2-20 assume |
| | | | | zeta > 1, B-2-21, B-2-22, B-2-23 |
|--+-------+-------+-------+------------------------------------|
| 3| 1/24 | 1/31 | 2/07 | B-2-20 assume zeta = 1, B-3-1, |
| | | | | B-3-2, B-3-3 |
|--+-------+-------+-------+------------------------------------|
| 4| 2/03 | 2/07 | 2/10 | B-3-9, B-3-10, B-3-14, B-3-26 |
|--+-------+-------+-------+------------------------------------|
| 5| 2/07 | 2/14 | 2/19 | B-3-5 hint: use superposition, |
| | | | | B-3-15 hint: (Write a sum-of-forces|
| | | | | equals ma equation for each mass. |
| | | | | then choose state variables which |
| | | | | relate to energy storage--spring |
| | | | | displacements and mass velocities. |
| | | | | re-write the original equations in |
| | | | | terms of the state variables. Then|
| | | | | write state variable equations and |
| | | | | output equations.) |
| | | | | B-3-22, B-4-1, B-4-2 |
|--+-------+-------+-------+------------------------------------|
| 6| 2/14 | 2/21 | 2/24 | B-3-12 hint: page 75, B-3-13 and |
| | | | | prove your result or prove general |
| | | | | theorems for series and parallel |
| | | | | dampers and apply your theorems. |
| | | | | B-3-29, B-4-11 tip: "show" means |
| | | | | "prove" or in other words, find a |
| | | | | math relationship between the two |
| | | | | angles. Use either degrees or |
| | | | | radians consistently in your |
| | | | | calculations. Assume both levers |
| | | | | (the handle and the elevator |
| | | | | support) are initially vertical, |
| | | | | and then get moved to the angles |
| | | | | shown. Correction 1) the length of|
| | | | | the support lever for the elevator |
| | | | | should be "m," dimensioned between |
| | | | | the two black dots that represent |
| | | | | the hinge pins. Correction 2) The |
| | | | | handle (lever with dimension "l" |
| | | | | on it) is shown leaning in the |
| | | | | wrong direction. It should lean |
| | | | | to the left and angle theta should |
| | | | | increase in the counterclockwise |
| | | | | direction. A corrected figure |
| | | | | 4-58 is available (click here). |
| | | | | |
| | | | | B-5-1 (On 2/19 problem B-5-2 was |
| | | | | removed from this assignment.) |
|--+-------+-------+-------+------------------------------------|
| 7| 2/24 | 2/28 | 3/10 | B-5-2, B-5-4, B-5-5 Prove that it |
| | | | | can be stopped by an impulsive |
| | | | | force. Hints 1) find an input made|
| | | | | from the sum of an impulse and a |
| | | | | delayed impulse. Show that for the|
| | | | | right delay and after a certain |
| | | | | amount of time the output is zero. |
| | | | | 2) Is the system linear? What are |
| | | | | the consequences of your answer? |
| | | | | |
| | | | | B-5-6 Find a formula for the |
| | | | | solutions. Plot the formula via |
| | | | | Mathcad, Matlab, or neatly by hand.|
| | | | | |
| | | | | B-5-9 Find formulae for the step |
| | | | | responses. Plot the formulae via |
| | | | | Mathcad, Matlab, or neatly by hand.|
| | | | | Put the two formulae on the same |
| | | | | plot or on two plots with identical|
| | | | | axes so that proportions are |
| | | | | visually comparable. |
|--+-------+-------+-------+------------------------------------|
| 8| 2/28 | 3/7 | 3/10 | B-5-10, B-5-13 Note: here "obtain" |
| | | | | means "generate a plot of." |
| | | | | B-5-14, B-5-15 Note: do not forget |
| | | | | to make the requested comparisons. |
| | | | | B-5-19, B-5-22 here "obtain" means |
| | | | | solve for an analytical answer. |
| | | | | You may check your answer via |
| | | | | a computer simulation (MATLAB) or |
| | | | | a symbolic algebra program on your |
| | | | | calculator or computer. |
| | | | | B-5-23 |
|--+-------+-------+-------+------------------------------------|
| | 3/7 | --- | --- | No problem set this week--study |
| | | | | for the test. |
|--+-------+-------+-------+------------------------------------|
| | To be | --- | --- | If you want to work ahead during |
| | assigned | | spring break, these problems will |
| | after | | | be assigned on Wednesday, 3/26 and |
| | spring| | | due on Friday, 3/28: |
| | break | | | From the text we used in EGR 221, |
| | | | | Lindner 12.1.1, 12.1.3. (Click on |
| | | | | either problem to see it in a |
| | | | | Word document.) |
|--+-------+-------+-------+------------------------------------|
| 9| 3/26 | 3/28 | 4/02 | From the text we used in EGR 221, |
| | | | | Lindner 12.1.1, 12.1.3. (Click on |
| | | | | either problem to see it in a |
| | | | | Word document.) |
|--+-------+-------+-------+------------------------------------|
|10| 3/28 | 4/04 | 4/16 | B-5-20, After doing B-5-20, find |
| | | | | the transfer function for the |
| | | | | system in B-5-20 and apply the |
| | | | | the final value theorem to find |
| | | | | the steady state error for a ramp |
| | | | | input. (The result should agree |
| | | | | with the Matlab simulation.) |
| | | | | B-5-30 |
| | | | | B-5-30 |
|--+-------+-------+-------+------------------------------------|
|11| 4/04 | 4/11 | 4/16 | B-6-3 Be sure to find the portion |
| | | | | of the locus on the real axis, |
| | | | | centroid, and angles of asymptotes.|
| | | | | Assume a breakaway point at about |
| | | | | s = -0.4. Sketch the locus on a |
| | | | | big enough plot. Check your result|
| | | | | via Matlab. See your text section |
| | | | | 6-4 on page 358 and Matlab Program |
| | | | | 6-1 on page 360. (Turn in hand |
| | | | | calculations, hand sketch based on |
| | | | | calculations, Matlab code, Matlab |
| | | | | plot.) |
|--+-------+-------+-------+------------------------------------|
|12| 4/14 | 4/18 | 4/23 | B-6-5 Recommended: First use Matlab|
| | | | | to plot the locus. The plot will |
| | | | | be graded. Make sure that the |
| | | | | interesting area of the plot is big|
| | | | | enough (e.g. open-loop poles are |
| | | | | spread out far enough so that they |
| | | | | cannot be covered with a thumb- |
| | | | | print.) Calculations for angles of|
| | | | | asymptotes and the centroid are |
| | | | | optional and will not be graded. |
| | | | | Calculations to show the exact |
| | | | | points, s = ñjw and the |
| | | | | corresponding value for K will be |
| | | | | graded. |
| | | | | |
| | | | | B-6-6 Recommended: First use Matlab|
| | | | | to plot the locus. The Matlab plot|
| | | | | will not be graded. Calculations |
| | | | | for the angles of departure and |
| | | | | arrival will be graded. Optional: |
| | | | | use a protractor to check your |
| | | | | calculations against your Matlab |
| | | | | plot. Finally, use what you know |
| | | | | about the closed-loop system to |
| | | | | PROVE the closed loop poles are on |
| | | | | the circle described in the problem|
| | | | | statement. (The root locus is |
| | | | | not directly used in the PROOF.) |
|--+-------+-------+-------+------------------------------------|
| | 4/21 | --- | --- | No assignment this week to give you|
| | | | | time to do your project. |
|--+-------+-------+-------+------------------------------------|
|13| 4/28 | 5/02 | 5/06 | B-7-1, B-7-7 (There is no single |
| | | | | uniquely correct answer.), |
| | | | | B-7-11 (There is no single |
| | | | | uniquely correct answer.) |
| | | | | B-8-1 |
| | | | | Extra Credit: (8 points) |
| | | | | B-8-3--except sketch the Bode plot |
| | | | | (magnitude and phase) by hand and |
| | | | | then verify your result using |
| | | | | Matlab. |
| | | | | |
| | | | | (On Wed. 4/30 problem B-8-3 was |
| | | | | deleted from this assignment. You |
| | | | | may still do it for extra credit.) |
| | | | | |
+---------------------------------------------------------------+
PROJECT last update 3/28/03
-------
Assigned on 3/28. Due on Friday, 4/25.
There are five different projects to choose from. Samples
are posted on the white board in the hallway across from
the computer lab, S236. After you choose a project you may
pick up a copy of it from one of the plastic bins in the
hallway near the engineering pod. Also there is a sign-up
sheet where you should note the project you have chosen.
At most three people may work on the same project. Each
project is to be done individually and each person should
turn in a report.
The projects are ordinary homework problems which you need
to extend. Principle results (answers) should be computed
by more than one method. Analytic results should be
reconciled with computer results. You should also develop
a thesis statement, possibly around a "What if?" question,
and defend your thesis. For example, you might ask "What
if the gain is adjusted to eliminate overshoot?" This
could lead to the thesis that, "At least 10% overshoot will
need to be tolerated in order to get adequatly small
steady-state error responses."
Your final report should follow the guidelines in the
handout "Writing a Laboratory Report." If you need a paper
copy of this handout, ask Prof. De Boer. The grading
rubric is also included in that handout.
TESTS (Last update:
----- 5/02/03 7:55 am)
Test #1, Wednesday, 2/12. Covered Chapters 1-3, except for
sections 3-6 and 3-10. Tables 2-1 and 2-2 (pages 17-18 and
31) from your text were given to you at the test. One
crib sheet was allowed. No calculators were allowed.
Handed back on 2/14/03.
Raw scores: high=100, average=74, low=59 (100 possible)
Frequency distribution: 2 A's, 3 B+'s, 5 B's, 2 B-'s (n=12)
Test #2, Wednesday, 3/12. Covered Section 3-10 in Chapter 3,
Chapter 4, and Sections 5-1 through 5-4 in Chapter 5.
One crib sheet was allowed. No calculator was allowed.
Tables 2-1 and 2-2 (pages 17-18 and 31) from your text were
given with the test. Handed back on 3/26.
Raw socres: high = 100, average = 79, low = 51.
Frequency Distribution: 2 A's, 4 A-'s, 4 B's, 1 C+, 1 D+.
Final exam, 3:30 - 5:30 PM Tuesday, May 6.
Will cover the entire course. Specifically, The exam will
cover all the topics from Test #1, Test #2, plus
convolution plus Sections 5-7 through 5-9 in Chapter 5,
Sections 6-1 through 6-6 in Chapter 6, Sections 7-1 through
7-4 in chapter 7, and section 8-1 in Chapter 8. You may
have three crib sheets. No calculators will be allowed.
Tables 2-1 and 2-2 (pages 17-18 and 31) from your text will
be provided to you with the exam.
offering of this course by Professor De Boer
Back to Prof. De Boer's home page