## Homework Assignments
## Summer 2014
MAE 4310 - Introduction to Automatic Control
Last Updated
The following problems are assigned as practice for better understanding the material presented in class and identify areas where more help is needed. The problem numbers are from the textbook **Modern Control Engineering by K. Ogata, 5th edition used for Summer 2014 semester**.
Note that you are responsible only for homework with due date 2014.
Homework 1 - Chapter 2 (Due Wed June 11, 2014 at beginning of class)
Homework 2 - Chapter 5 (Due Monday June 30, 2014 at beginning of class)
Homework 3 - Chapter 6 (Due Monday July 14, 2014 at beginning of class)
Homework 4 - Chapter 6 (Due Monday July 19, 2010 at beginning of class)
Homework 5 - Chapter 7 (Due Monday July 26, 2010 at beginning of class)
Homework 6 - Chapter 7 (Due Wednesday August 4, 2010 at beginning of class)
**Homework # 1 - Chapter 2 - Due Wed June 16, 2014 ****(beginning of class) **
**Study all problems A-2.xx**
Solve and turn in the problems designated as **B-2: 1, 2, 3, 6, 7, 8, 9, 10, 11** (10 and 11 must be solved by hand showing your work - verify with computer tools if you like).
Homework # 2 - Chapter 5 - Due Monday June 30, 2014 (beginning of class)
The problems to work out and turn in from course textbook are the following (B_5_xx)
** 3, 9, 12, 14, 19, 20, 21, 22, 24**
Make sure you understand the procedures and evaluate your results.
I strongly advice to study the solved problems in chapter 5 (i.e. A-5 problems) related to the material covered in class.
Note some of them are very basic where others require a little more analysis.
If the problem statement says Matlab, you could use any software package you desire but make sure you understand the commands and how they are used.
The GTA will be a good resource to get help with software (Matlab). Make sure you take your scripts with your if you need help.
If you want to solve additional problems for practice, go ahead and if you have difficulty, let me know or talk with the GTA.
Homework # 3 - Chapter 6 - Due Wednesday July 14, 2014 (beginning of class)
This HW set will count as two HWs, i.e. double the number of allocated points.
Homework # 3 - Chapter 6 - Due Monday July 14, 2014 (beginning of class), also study all problems A-5.xx.
Make sure you understand the procedures and be able to discuss the information in the plots as discussed in class.
You do not need to perform this discussion on the HW but you must be able to do so for the exam.
Solve and turn in the problems designated as B-6: **2, 4, 5, 6, 7, 8 , 9, 14, 15, 16, 17, 24, 26, 28**
Solve by hand showing your work and verify with computer tools if you like.
Some of the problems you can solve exclusively by hand and some you will need to use computer tools.
Homework solutions that are exclusively simulations will not be graded.
If the problem statement says use MATLAB, you can use any computer tool that you like.
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**Homework # - Chapter 5 - Due Monday June 21, 2010 (beginning of class) **
The problems to work out and turn in from course textbook are the following (B_5_xx)
**18, 19, 20, 21, 22, 23, 24**
I strongly advice to study the solved problems in chapter 5 (i.e. A-5 problems).
Note some of them are very basic where others require a little more analysis.
If the problem statement says Matlab, you could use any software package you desire.
If you want to solve additional problems for practice, go ahead and if you have difficulty, let me know or talk with the GTA.
**Note** – I saw some of you having the fourth edition of the same book. The theory might be there but the material is reorganized and the problem statements are not the same.
**Assigned Reading:**
**Study the last special case for Routh-Hurwitz stability criterion (when a row full of zeros is encountered).**
** Read the section on Steady State Error.**
**Homework # 3 - Chapter 6 - Due Wednesday July 7, 2010 (beginning of class) **
The problems to work out and turn in from course textbook are the following (B_6_xx)
**2, 4, 5, 6, 7, 8 , 9, 12, 13, 14**
I strongly advice to study the solved problems in chapter 6 (i.e. A-6 problems).
If the problem statement says Matlab, you could use any software package you desire such as SCILAB or Mathematica, Maple etc as discussed in the Simulations page.
If you want to solve additional problems for practice, go ahead and if you have difficulty, let me know or talk with the GTA.
Homework # 4 - Chapter 6 - Due Wednesday July 19, 2010 (beginning of class)
Homework on Root Locus and Compensation
The problems to work out and turn in from course textbook are the following (B_6_xx)
**16, 17, 18, 19, 20, 22, 24, 27, 28**
If the problem indicates MATLAB, you can use any software package you like.
I strongly advice to study the solved problems in chapter 6 (i.e. A-6 problems).
Homework # 5 - Chapter 7 - Due Monday July 26, 2010 (beginning of class)
Strongly encourage you to study the related solved problems and examples in your textbook in chapter 7.
You could use software tools for your homework – wherever it says Matlab you could use any software you like (scilab, matlab, mathematica, etc).
However, make sure you can plot the Bode plot by hand and be able to discuss it and correctly find the stability information from the plot.
There is a semilog paper in PDF on the class web page and attached to this email as well.
When you discuss system stability using Bode plot, go ahead and analyze system stability using one of the other techniques you know to verify and re-enforce the concepts.
Utilize computer tools to plot system response and try to understand the effect of parameter changes on the system response ie location of eigenvalues,
Also as discussed in class, investigate and ask questions on how the plot will change if a certain controller is included, or a lead or a lag controller or how is the low frequency plot for a type 0, 1, 2, etc system look like or how is the high frequency of a relative order 0, 1, 2, 3 etc system look like?
You are to solve and turn in the following problems from your textbook on chapter 7:
**B-7: 2, 4, 5 (evaluated at w=wn), 20, 23, 26, 27, 30**
**Assigned reading: Sections 7-10, 11,12 (design of lead and lag compensators using frequency response techniques)**
Homework # 6 - Chapter 7 - Due Wednesday, August 4, 2010 (beginning of class)
Use computer tools but make sure you understand the procedures and steps and the reasons for them.
Study and redo the solved problems A-7 in your textbook that relate to the material covered in class up to lead compensator design.
Also, as mentioned in class, change the additional phase added and observe its effects on the design requirements and the system response.
Use the tools shown in class to experiment and understand the effects of parameter changes to the overall Root Locus, Bode Plot and Response characteristics.
**HW Problems:**
B-7-23, 24, 32, 33, 34
**Assigned reading:**
Sections 7-10, 11, 12, 13 (design of lead, lag and lag-lead compensators using frequency response techniques)
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PREVIOUS YEARS and/or SEMESTERS
Homework 5 - Chapter 8 (Due July 20, 20 at beginning of class)
Homework 6 - Chapter 9 (Due July 27, 20 at beginning of class)
Homework 7 - Chapter 12
Notes on Final and Demos
**Homework # - Chapter 3 - Due June ****(beginning of class) **
The problems are designated as **B-3: 1, 2, 3, 7, 8, 11, 28, 29**
**Problem B-3-4**:
You do not have to turn this in but I will strongly encourage you to try to solve it using Matlab or Scilab. (Back to top)
**Homework # 2 - Chapter 5 - Due , (beginning of class) **
Go over the solved problems in your textbook indicated as A_ and make sure you understand them and also spend some time with a software tools such as Scilab or Matlab and become familiar with it if you are not. Your textbook has a lot of computer code (in Matlab) to analyze control problems.
The problems to work out and turn in are the following (they all are B_5_xx)
**9, 10, 11, 15, 16, **
**In addition, you must perform the analysis for the velocity feedback and PD controllers and compare their effect on the closed loop transfer function as discussed in class.**
Note some of them are very basic where others require a little more analysis.
If the problem statement says Matlab, you could use any software package you desire.
If you want to solve additional problems for practice, go ahead and if you have difficulty, let me know. (Back to top)
**Homework # 3 - Chapter 5 - Due Monday June 29, (beginning of class) **
Go over the solved problems in your textbook indicated as A_ and make sure you understand them and also spend some time with a software tools such as Scilab or Matlab and become familiar with it if you are not. Your textbook has a lot of computer code (in Matlab) to analyze control problems.
The problems to work out and turn in are the following (they all are B_5_xx)
** 23, 24, 25, 26, 27, 28, 30, 31, 32**
Note some of them are very basic where others require a little more analysis.
If the problem statement says Matlab, you could use any software package you desire.
**B - 5: 7, 8, 12, 14, 18, 21 (Strongly encourage you to work these problems as practice problems – DONOT turn them in) **(Back to top)
Homework # 4 - Chapter 6 - Due Monday July 6, (beginning of class)
The problems to work out and turn in are the following (they all are B_6_xx)
**2, 3, 4, 5, 9, 10, 11, 12 (use any software tool: matlab/scilab/octave), 14, 15**
If you like, verify your work with software tools – use help command to get more info on their usage:
matlab command - **rlocus**,
scilab command - **evans**,
octave command - **rlocus**.
I strongly advice to study the solved problems in chapter 6 (i.e. A-6- problems) and experiment with the problems on using software tools, especially section 6.4 in your textbook.
Note: Octave is another freeware numerical analysis software well suited for simulation and analysis of dynamic systems, *http://www.octave.org*.
There is a graphical front end called QtOctave which can be found at
*https://forja.rediris.es/projects/csl-qtoctave/ *
I strongly advice to study the solved problems in chapter 6 (i.e. A-6- problems).
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Homework # 5 - Chapter 8 - Due Monday July 20, (beginning of class)
**Reading Assignment** 8.1, 8.2, 8.3
**We will cover** Phase and Gain Margin, Cutoff frequency and use Bode Plot to discuss stability and design
** Work solved examples** 8.1, 8.2, 8.3, 8.5, 8.6, A 8.4
**HW Due Monday July 20, 2009**
Chapter 8: 1, 2, 3a, 4a, 5, 6, 8 (Bode not Polar), 23 (Bode not Nyquist)
Remember that one of the problems is a Bode plot of a Lead and a Lag compensator (individually).
**Notes on software tool usage**
You are required to draw by hand and then verify with software tools.
(matlab: bode; scilab: bode; octave:octave) issue the help command to find out how to use the command in each software.
Experiment with software tools – input a different constant and observe the changes.
When using software tools, plot each normalized factor individually before the total plot.
This approach will show you how the addition takes place as you encounter a new break frequency going from low to high frequencies.
For example [this assumes using matlab] (a indicates a factor with break frequency 1)
We have 4 of these factors a1, a2, a3, a4
a12 = conv(a1,a2)
a123 = conv(a12, a3)
a1234 = conv(a123,a4)
Bode(a1, a2, a3, a4, a12, a123, a1234)
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Homework # 6 - Chapter 9 - Due Monday July 27, at beginning of class
Make sure you study the theory and work the solved problems in the book indicated with A 9.
The more you practice properly, the better you become.
Use computer tools for this homework set, experiment and make sure you understand the steps to be followed. You could use Matlab, Scilab or Octave - they all have similar commands - use help bode in each to get help and see auxiliary commands for finding Phase and Gain Margins and Crossover Frequencies.
**HW B-9 **
2, 3, 4, 5, 6, 9 (this a lead-lag, follow the procedure in the book section 9.4 and example 9.3 to design it)
**Note on GTA Office Hours in CAD Lab:** On Friday July 24, the TA will hold office hours in the CAD lab to provide help to whoever might need it especially using computer tools. She is familiar with MATLAB and not Octave/Scilab.
I requested the small computer room so that you will not be disturbed by other students from 10:00 -12:00 noon.
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Homework # - Chapter 8 - Due (beginning of class)
For those using Matlab, you could experiment with the RLTOOL command.
I donot know if there is an equivalent SCILAB command – if anyone finds something similar let me know and I will inform the rest of the class.
Note that you could use computer tools where appropriate and encourage you to do so considering you could analyze simple problems by hand and identify the required information.
Also, where appropriate, extend the problem statement to find wcg, wcp, GM, PM, discuss stability, limits on stability and also plot step responses (various K-values) of closed loop system (again using computer tools).
** B-8: 26, 27, 28, 29, 30, 31, 32, 33, 34**
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Homework # - Chapter 11 - Due (beginning of class)
Use computer tools as you see fit and to verify hand calculations.
Make sure your simulation results are reasonable.
Make sure you could perform hand calculations if needed.
**Chapter 11:
B-11: 2, 4, 5, 14, 1****6**
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Homework # - Chapter 12 - Due (beginning of class)
Use computer tools as you see fit and to verify hand calculations.
Make sure your simulation results are reasonable.
Make sure you could perform hand calculations if needed.
**Chapter 12:
B-12: 3, 6, 8, 9, 10, 12**
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NOTES TO ALL STUDENTS:
- I would like to get feedback from everyone reference to a course evaluation and especially comments on how to improve the course and my teaching methods.
Your input/comments constructive criticism will be appreciated and it could be anonymous if you so prefer but if you put your name down it will not influence my decision on your grades at all.
- Lab demo sessions to be announced later.
- The review session will be the last day of the semester.
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