# Course syllabus suggestions

If you are planning to use *Feedback Systems* as a textbook for a course, there are several ways of using the material in the textbook, depending on your audience. This page contains some suggestions for how the material in the text can be taught.

## Using AM08 as a text

In developing this book, we have attempted to condense the current knowledge by emphasizing fundamental concepts. We believe that it is important to understand why feedback is useful, to know the language and basic mathematics of control and to grasp the key paradigms that have been developed over the past half century. It is also important to be able to solve simple feedback problems using back-of-the-envelope techniques, to recognize fundamental limitations and difficult control problems and to have a feel for available design methods.

There are a couple of lessons learned based on teaching out of the text:

- The text is organized in a slightly unusual fashion compared to many other books on feedback and control. If you have taught a controls course out of a different textbook in the past, you will probably need to set aside some time to update lectures, homework sets, exercises and notation.
- Chapter 3 can be confusing if students who are new to modeling and control try to read it on their first pass through the book. We recommend covering perhaps one example as motivation, pointing out that some of the features of the examples are beyond what is studied in the text (eg, the hybrid dynamics of the cruise control system).
- The exercises in the text need to be augmented by "standard" problems that build up basic skills. We have elected not to include problems in the printed text which involve doing things that are very similar to what is in the textbook itself, but these are very valuable for students seeing the material for the first time. The solutions manual contains some of these types of exercises (and we are happy to include more if you are willing to send them to us!).
- For many courses you may need to include a review of linear algebra (eigenvalues, eigenvectors, rank, null space) before you get to Chapter 5 - Linear Systems (and perhaps a bit earlier). At Caltech we include a hands-on introduction to MATLAB and SIMULINK in the first week of the course, since many students have not used those programs before.
- Several instructors have commented that the students find the material to be quite difficult. The rapid transition from introductory material to concepts such as asymptotic stability, Lyapunov functions and reachability leaves some students struggling to keep up with the concepts. Some instructors may find it useful to proceed more slowly through these sections, depending on the background of the class.

## Course suggestions

When using *Feedback Systems* to teach a more traditional course in engineering, the same basic syllabus as the one above can be used but the course can be augmented by including the advanced sections in the text and/or including material from the text supplements. The following notes provide guidelines for what additional material can be included:

### 10 week course for engineers

A one quarter (10 week) course for seniors and/or first year graduate students in traditional engineering disciplines can cover the major elements of modeling, state space analysis and design, and frequency domain analysis and design. At the undergraduate level, students struggle with the material on Lyapunov functions in Chapter 4 - Dynamic Behavior and so this material should be de-emphasized unless it is particularly relevant.

Suggested syllabus:

Week | Chapter | Comments |

1 | Chapter 1 - Introduction | 1 lecture on feedback/control + optional MATLAB tutorial and linear algebra review |

2 | Chapter 2 - System Modeling | Include 1-2 examples from Chapter 3 - Examples if desired |

3 | Chapter 4 - Dynamic Behavior | Focus on stability and skip sections on Lyapunov functions |

4 | Chapter 5 - Linear Systems | |

5 | Chapter 6 - State Feedback | |

6 | Chapter 7 - Output Feedback | Can be covered quicky if review for midterm is required |

7 | Chapter 8 - Transfer Functions | Use Laplace transforms if students have this already |

8 | Chapter 9 - Frequency Domain Analysis | |

9 | Chapter 10 - PID Control | |

10 | Chapter 11 - Frequency Domain Synthesis |

### 15 week course for engineers

In a 15 week course, one can cover one chapter per week, with additional time spent on some combination of system modeling (for those students without a strong background in ODEs), Lyapunov functions (in Chapter 4 - Dynamic Behavior), fundamental limits (Chapter 11 - Frequency Domain Synthesis) and robust performance and unmodeled dynamics (Chapter 12 - Robust Performance). Most of Chapter 3 - Examples should still be skipped, with sections assigned as reading as they come up in the course.

### Frequency domain first

If desired, the material in the course can be inverted so that frequency domain concepts are presented first and state space concepts follow. A typical course sequence would then be:

- Chapters 1-3: basic concepts of modeling and stability, plus selected examples
- Chapters 8-12: frequency domain analysis and design
- Chapters 4-7: state space analysis and design

Some care should be taken in the beginning of Chapter 8 to insure that students are comfortable with modeling a system in state space form

since this form is assumed in deriving the transfer function. This is covered briefly in Chapter 2, but some additional lecture material at the start of Chapter 8 would be prudent.

### 10 week graduate course for non-majors (state space)

For a 10 week graduate course, it would be best to focus on either state space for frequency domain modeling. For many disciplines, state space models are the most relevant and so we present that emphasis here. The material that is likely to take time for students to learn is ODEs (if they have had limited exposure) and nonlinear analysis (especially Lyapunov functions). The material on Lyapunov functions can be skipped if nonlinear systems are not as relevant for a given set of students.

Suggested syllabus:

Week | Chapter | Comments |

1 | Chapter 1 - Introduction | 1 lecture on feedback/control + optional MATLAB tutorial and linear algebra review |

2 | Chapter 2 - System Modeling | Include 1-2 relevant examples from Chapter 3 - Examples |

3 | Chapter 4 - Dynamic Behavior | Concepts of stability, linear stability |

4 | Chapter 4 - Dynamic Behavior | Lyapunov functions |

5 | Chapter 5 - Linear Systems | |

6 | Chapter 6 - State Feedback | |

7 | Chapter 7 - Output Feedback | |

8 | Chapter 8 - Transfer Functions | |

9 | Chapter 9 - Frequency Domain Analysis | |

10 | Chapter 10 - PID Control |

### 15 week graduate course for non-majors

In a 15 week graduate course, all of the material in the book can be covered, with 2 weeks spent on modeling, 2 weeks on dynamic behavior (including Lyapunov functions), and 2 weeks on frequency domain synthesis (with particular emphasis on limits of performance). Most of Chapter 3 - Examples should still be skipped, with sections assigned as reading as they come up in the course.

For courses in disciplines where students may not have a working knowledge of linear algebra and differential equations, some instructors have reported it may be beneficial to spend several weeks reviewing these topics before starting on the material in the book.