Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session

Course Description

This course introduces the design of feedback control systems as applied to a variety of air and spacecraft systems. Topics include the properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, the Root locus method, Nyquist criterion, frequency-domain design, and state space methods.


The textbook for the class, available at the COOP or on Amazon, is:

Franklin, Gene, J. David Powell, and Abbas Emami-Naeini. Feedback Control of Dynamic Systems. 6th ed. Prentice Hall, 2009. ISBN: 9780136019695.

The previous edition is very similar, but the problems are numbered differently, and have some changes, so you should use the 6th edition.

Other texts which might be helpful (on reserve in the Aero/Astro Library):

Van de Vegte, John. Feedback Control Systems. 3rd ed. Prentice Hall, 1994. ISBN: 9780002085069.

Ogata, Katsuhiko. Modern Control Engineering. 4th ed. Prentice Hall, 2002.

Kuo, Benjamin. Automatic Control Systems. 8th ed. John Wiley & Sons, 2003. ISBN: 9780471381488.

Ogata, Katsuhiko. Solving Control Engineering Problems with MATLAB. Prentice Hall, 1993. ISBN: 9780130459077.

Use of MATLAB®

The use of a software package like MATLAB is very helpful in the study of Feedback Systems. The software can best be used initially to check work that is first done traditionally with pencil and paper. This is particularly helpful when verifying polar plots (Nyquist plots), Bode diagrams and root loci when first attempting to sketch these functions. In addition, step responses in the time domain can be examined in order to build an intuitive sense of the relations between time and frequency domain behavior. We also will use MATLAB to check the validity of simplifying approximations that are often made when carrying out preliminary designs. Finally we can study more complex problems with a computer-aided design package without the enormous burden of doing extensive computations. We suggest that everyone become familiar with the use of MATLAB on Athena or learn to use the Student Edition of MATLAB (Prentice Hall, Englewood Cliffs, NJ) which is available for both Microsoft and Macintosh computers. Where necessary in the homework, we will indicate Macros (M-files) available on Athena which can be used to aid in studying the problem. Remember that we want you to come away with an understanding of feedback theory in some depth. The computer is to aid in achieving this understanding and should be used intelligently as an engineering tool.


There will be two evening quizzes during the term after lecture 16 and lecture 29.

Final Exam

A three-hour examination will be scheduled during the final exam period.

Problem Sets

Problem sets will be issued during the third lecture of every week and will be due the following week at the beginning of the third lecture. Late problem sets will not be accepted. (See Grading Policies)


Grades will be based on performance in the following required assignments:

Quiz 1 20
Quiz 2 20
Final Exam 30
Weekly homework assignments and labs (about one assignment per week) 25
Participation and assessment of staff 5

Note that attendance in lectures and recitations is mandatory and failure to attend on a regular basis will affect your grade.

Grades in 16.06 are based on the official MIT grading policy.

Collaboration and Academic Honesty

In this course, you may collaborate with others on the solution of problem sets, unless the instructions on a problem set indicate otherwise. Working in small groups can be beneficial, especially if the group is used as a learning resource, not just a source of answers. If you do collaborate, you should acknowledge (by name) others with whom you have worked, including a brief description of the amount and nature of help received from others. Modifying someone else's work to make it appear that it is your own is unacceptable. In case of doubt, consult the course instructor or the graduate TA. By submitting a homework, you affirm that the final work is your own.

You may not use sources such as the solutions from prior offerings of 16.06, whether the solutions were the official solutions from the course staff or the solutions of students, no matter the source (OCW, "bibles," etc.)

It is dishonest and counterproductive to copy the work of others and submit it as if it were your own. The goal of doing problems is to learn the material; the goal is not to turn in the right answer, or surprisingly, even to get a good grade. If you are unable to do the problem sets on your own, it is very unlikely that you will do well on the quizzes. Plagiarism and other forms of cheating are a severe breach of the codes of the Institute and the engineering profession and will be dealt with as such. Violations of these guidelines will be dealt with as per section 10.2 of the MIT Policies and Procedures. A useful discussion of these issues may be found here.

Late Assignments and Missed Quizzes

Generally, we do not accept late homework assignments, since solutions are posted immediately after the due date, and the grading of late homeworks imposes a significant burden on the teaching staff. Likewise, students cannot make up a missed exam, except under specific circumstances. You will be given a makeup exam only under one of the following conditions:

  1. You need to participate in a significant scholastic event (including varsity sports). Allowing makeups for scholastic events is at the discretion of Prof. Hall. In order for your request to be considered, you must make a request to Prof. Hall one week before you need to make travel plans.
  2. You have an illness serious enough that you are unable to take the exam. In this case, you must inform Prof. Hall before the exam, and you may be asked to have Student Support Services verify your illness.
  3. If you miss the final, you automatically receive a grade of "O," unless a failing grade is inevitable. If your absence is subsequently approved by Student Support Services, the grade will be changed to "OX," which allows you to arrange for a makeup final.