ME 451-Control Systems, Spring 2007

Announcements from the instructor

- (April 25) Good luck with your final!
- (April 20) Please read Lecture 40 before the Monday lecture.
- (April 16) Please review my class notes, hws and midterm exams for the final exam. If you need more examples, you may find many ME 451 systems and controls problems in http://www.egr.msu.edu/me/graduate/exams. Please feel free to work on those exam problems with classmates. The final exam will be easiler than those since it is closed book and you can only bring 3 pages of cheat sheets.

- (April 11) Please read the Frequency Response part in the text book. Use Lecture 35, for Lag Compensator design.
- (April 9) hw10 is posted.
- Fellowship FLY http://www.studentpipeline.org/

- (April 6) hw10 will be posted on Monday. Have a great weekend with no hw!
- (March 30) hw9 is posted.
- (March 23) Updated hw solution 7 and hw solution 8 are posted.
- (March 23) The
**root locus**is the locus of the poles of the closed loop system (recall the usual setup) as the system gain*k*is varied on some interval.

- (March 20) An illustrative example for utilizing the auxiliary polynomial in Routh-Hurwitz stabiltiy criterion test.
- (March 16) Hw 8 is posted. The 2nd midterm exam will be on Wednesday, March 28. The scope contains materials in until Friday 3/23/07, (from hw5 to hw8).

- (March 12) Extra office hours: Monady 2:00pm-3:00pm are added to the exsisting office hours Wed 10:00pm-11:00am, and Wed 5:00pm-6:30pm.
- (March
2) Hw7 due by 3/17/07 is posted. We have covered stability today. For those of you who are traveling
so did not come today, please read my lecture note Lecture 22.

- (February 23), Hw6 and Hw5 solution are posted.
- (February 23), If you redo the hw problems that were originally marked off, please bring the original hws and the new answers with you in my office hours, then I will try to see if you finally understand those problems. If you show your understandings, I give you some credits back to you proportionally to the number of such marked off problems.
- (February 19), Play with Position and velocity feedback for the 2nd order system in Simulink.
- (February 16), hw5 is posed.
- (February 12), The midterm solution is posted.
- (February 9), A linearization handout, hw4 solution and the reveiw note are posted.
- (February 9), I remind you of the fact that anyone in ME451 can consult any of TAs in the control lab about hw problems. See the TA schedule.
- (February 6), A complete presentation on "time response" is posted here. pdf file. Please preview this material. This gives you a good visualization of effects of poles in the first and second order systems.
- (February 2), New office hours: 2459 Engineering Building, Wed 10:00pm-11:00am, and Wed 5:00pm-6:30pm.
- (February 2), Solution for hw3 is posted. hw4 is posted.
- (February 2), The first midterm exam will be in the class 2/12/07 Monday. The scope contains materials covered in the lectures until Wed 2/7/07, i.e., from hw1 to hw4. If you can solve hws well, you will do fine in the exam.
- In the exam, I will allow you to bring a letter sized paper (one side for mid terms and two sides for the final exam) where you can write important formulas and equations. It has to be only with your hand-written formulas.
- (February 2), You can find some examples with solutions in Professor Feeny's class web site.
- ME132 is the lower version of our class taught by Professor Packard in ME, UC Berkeley. You may visit his class web site.
- More examples can be found in other references (most of them can be checked out from the engineering library)
- Modern Control Engineering by Katsuhiko Ogata
- Control Systems Engineering by Norman S. Nise
- Modern Control Systems by Richard C. Dorf and Robert H. Bishop
- Feedback Control of Dynamic Systems by Gene F. Franklin and J. David Powell

- (January 26), HW3 is posted and HW2 solution is posted. See the animation about vibration systems.
- (January 26), For the final exam date and schedule, please check the registrar's office website.
- (January 19), Check "impedance" in wiki.
- (January 12), Please hand in your homework at the beginning of the class.
- (January 10), Wikipedia, http://en.wikipedia.org/wiki/Main_Page is a great place to get references. For example, search for "causal system" or "frequency response"!
- I recommend that you start
taking notes from the class. It will be useful for the following reasons.
- It will remind you of
what you have learned in the class. You can also mark points where you
did not fully understand so that you can get them back to me in the office hours.
- In the mid and final exams, I will allow you to bring a letter sized paper (one side for mid terms and two sides for the final exam) where you can write important formulas and equations. It has to be with your hand-written formulas. Your notes will be very useful to make this summary sheet in a short time.

Instructor: Jongeun Choi, Assisntant Professor

2459 Engineering Building

East Lansing, MI 48824, Phone: (517)-432-3164

Website: http://www.egr.msu.edu/~jchoi/

Lecturer: MWF: 12:40-1:30pm, room 2205 EB

Office hours: 2459 Engineering Building, Wed 10:00-11:00am, and 5:00-6:30pm. Extra hours can be arranged by groups only (via email)

Laboratory Instructor: Professor C. J. Radcliffe

2445 Engineering Building

East Lansing, MI 48824, Phone: (517)-355-5198

Website: http://www.egr.msu.edu/classes/me451/radcliff/lab

TA for Homework: Andrew White

Email: whitea23@msu.edu

TA will grade homework and will also be available during his laboratory sessions to help students with homework.

Course Description

Mathematical modeling of dynamic systems. Standard feedback control formulation. Transient and sinusoidal steady-state analysis. Time and frequency domain controller synthesis.

Required Text

*Feedback Control Systems, *C. L. Phillips and R. D. Harbor, Prentice Hall, 4th edition, 2000, ISBN 0-13-949090-6

Handouts and Notes

- Lecture 1, January 8, Introduction to feedack control, linear system, impulse response, output of linear systems.
- Lecture 2, January 10, Impulse response, causal linear time invariant (LTI) system, complex numbers, why Laplace trasform is needed?.
- Lecture 3, January 12, Why do we use Laplace transform?, frequency response, transfer function, Laplace transform.
- Lecture 4, impulse, repeated-roots, complex-roots, January 17, Diac delta function, partial fraction expansions,
- Lecture 5, notes, January 19, electrical circuits, electrical impedance, lowpass filter, highpass filter.
- Lecture 6, January 22, electrical circuits, block diagram algebra, feedback connection.
- Lecture 7, January 24, Blcok diagram algebra, mechanical systems.
- Lecture 8, prob0, mechanical systems, quarter car model.
- Lecture 9, quarter car model, hw prob3.
- Lecture 10, hw3 prob3, electromechanical system.
- Lecture 11, how to get the spring force?, linearization.
- Lecture 12, poles and zeros of a transfer function, initial and final value theorems, time response, first order system.
- Lecture 13, hw_hints, first order systems.
- Lecture 14, review, additional linearization note
- midterm 1 solution
- Lecture 15, PD controller that stabilizes the linearized inverted pendulum, slides 2nd order system.
- Lecture 16, 2nd order system response, Polar vs. Cartesian reporesentations, overdamped, critically damped, uncerdamped, undamped responses.
- Lecture 17, 2nd order system response, time response spcifications.
- Lecture 18, time specifications, frequency response.
- Lecture 19, frequency response.
- Lecture 20, control system, steady state error.
- Lecture 21, steady state error for the closed loop system (note are the same as Lectuer 20)
- Lecture 22, steady state error of the rigid body (car model) with PD controller, stability (BIBO, asymptotic stable, marginally stable, unstable LTI systems)
- Lecture 23, stability, Routh-Hurwitz test.
- Lecture 24, Routh-Hurwitz test.
- Lecture 25, Routh-Hurwitz Stability Criterion and Root Locus.
- Lecture 26, Root locus, steps 1, 2
- Lecture 27, Root locus, step 3, An illustrative example for utilizing the auxiliary polynomial in Routh-Hurwitz stabiltiy criterion test.
- Lecture 28, Root locus, steps 4, 5, sisotool and matlab files for examples,
- Lecture 29, Root locus, step 6, review.
- midterm 2 solution
- Lecture 30, midterm 2.
- Lecture 31, Root locus example.
- Lecture 32, Controller design via Root Locus, PD, Phase Lead Compensator.
- Lecture 33, hw problems
- Lecture 34, simplified PLC synthesis procedure, An example for Phase Lead Compensator, Phase Lag Compensator.
- Lecture 35, Lag Compensator, use this note for designing a lag compensator.
- Lecture 36, PID Controller, Frequency Response.
- Lecture 37, Bode Plot.
- Lecture 38, Bode Plot (real poles and zeros).
- Lecture 39, Bode Plot.
- Lecture 40, 2nd order system with complex poles, gain margin and phase margin.
- Lecture 41, Final Exam Review.

Readings

- Week 1, January 8, 10, 12: Phillips, Chapter 1, Appendix A, B
- Week 2, January 17, 19: Chapter 2.1, 2.2, 2.3, 2.5, 2.6
- Week 3, January 22, 24, 26: Chapter 4.1, 4.2, 4.3, 4.4, 4.7
- Week 4-8, : Chapter 5.1, 5.2, 5.4, 5.5
- Week 9 Feb 26: Chpater 6.
- Week12, March 16: Chapter 7.1
- Week13, March 19: Chapter 7.1-7.4
- Week14, March 26: Chapter 7.1-7.10
- Week15, April 2: Chapter 8
- Read Chapter 8.1, 8.2, 8.6.

Homework

- HW1 due date: 1/19/07 and its solution.
- HW2 due date: 1/26/07 and its solution or solution Feel free to take any of two solutions!
- HW3 due date: 2/02/07 and its solution. A grading criterion for the ill-posed problem 1 is also given in the solution.
- HW4 due date: 2/09/07 and its solution.
- HW5 due date: 2/23/07 and its solution.
- HW6 due date: 3/02/07 and its solution.
- HW7 due date: 3/17/07 and its updated solution.
- HW8 due date: 3/23/07 and its solution.
- HW9 due date: 4/06/07 and its solution.
- HW10 due date: 4/16/07 and its solution.
- HW11 due date: 4/25/07 and its solution.

Grading

Note

Homework
15%

Exam 1 15%

Exam 2 15%

Final Exam(comprehensive) 30%

Laboratory work 25%

Total 100%

Exam 1 15%

Exam 2 15%

Final Exam(comprehensive) 30%

Laboratory work 25%

Total 100%

Note

- Homework will be done in one week from the day it is assigned.
- 100% laboratory attendance and 75% marks in the laboratory reports will be required to pass the course.
- Laboratory groups for all sections will be posted on the door of 1532 EB.