Description of Course Goals and CurriculumMAE 433 is an introduction to feedback control. The course teaches the theory and practice behind controlling dynamical systems (everything from circuits to cars to satellites). In general, the course places a large emphasis on the general principles of feedback: that feedback can reduce the sensitivity of a system to disturbances and change the dynamics of a system. Understanding how each section of material relates to these principles is key to succeeding. Most of the first half of the course is focused on frequency-domain control design. This discussion includes PID control, frequency-domain tools for analyzing controllers, and frequency-domain design methodologies. This section is not too mathematically intense, and does not require substantial knowledge from previous courses. The second half of the course is focused on time-domain control design. This discussion includes state feedback, time-domain design methodologies, controllability, observability, and observer-based feedback. This section leans heavily on linear algebra, so reviewing linear algebra topics is key to succeeding. Course material is well organized and builds up over the course of the semester, so it’s important to not miss any components. Though it may initially seem like the material from the first half of the semester is not relevant to that covered in the second half, it becomes apparent that the frequency-domain analysis tools learned in the first part of the semester are key to analyzing the state-space controllers designed in the second half of the semester.
Learning From Classroom InstructionMAE 433 consists of two hour-and-a-half lectures and one three-hour lab per week. Lecture follows the course textbook (which is just bound notes put together by Professor Rowley), and consists of both theory and examples, including demonstrations in Matlab. Because the course moves quickly and builds on itself, coming to lecture is key to keeping up with the material. Professor Rowley is a very interactive lecturer, and does a good job of asking and answering questions. He also incorporates collaborative pop quizzes and note card-based response questions in lecture. These quizzes tend to be among the most helpful parts of lecture, as they are an opportunity to really nail down concepts. Since they are given without warning, coming to lecture is a must, or else you could suffer a grade penalty. Labs follow material presented in lecture, but are self-contained activities: there are no pre-labs, lab reports, or other lab-related assignments. Labs are mostly graded on completion, so they are very low-stress. Paying attention to labs and finding connections to course material will help you in the rest of the course, but labs are not a major focus. All assigned readings are from the course textbook, which is extremely concise but covers all the material required for the course. A good strategy is to skim the relevant textbook section before each lecture, then read it thoroughly before starting that week’s problem set. Since the textbook is fully comprehensive, knowing the material in the textbook is key to doing well in the course.
Learning For and From AssignmentsWeekly problem sets tend to be fairly long and difficult, and will be more in-depth than the examples in the textbook or lecture. Collaboration is encouraged, and finding a good group to do psets with is very valuable. Pset problems tend to fall into three categories: proofs, application problems, and in-depth design problems. Proofs tend to be short and simple, but can be difficult to get started on, so office hours are helpful. Many psets have one or two proofs, but exams do not tend to have these sorts of problems. Application problems may involve reading graphs or diagrams, or are short computational problems. Most psets have at least two of these problems, and the exams tend to have many of them. These often build on examples in the textbook, so they are very doable if you consult the textbook. Design problems are longer, many-part problems that require synthesizing many concepts from the course. Half of the final exam is a single one of these design problems, and paying attention to them is key to doing well in the course. Office hours are the best resource to help approach them. Pop quizzes are short, and you may collaborate with your neighbors on them. They are relatively easy, and there will be an opportunity to ask questions before the quiz is given out. Asking questions during this time is extremely important! There are two exams: a midterm and a final. The midterm is a 1.5-hour in-class exam, and consists of several shorter problems, much like those found in the homework. The midterm is open-book, but is not open-computer. Re-doing homework problems and doing the provided practice midterm are the best ways to study, as both of these provide similar problems to the exam. The final is a 4-hour take home, and consists of several short problems and one long design problem. It is very similar to a problem set, though it covers a much broader span of material. It is open-book, and MatLab can be used for the design problem. Just as for the midterm, re-doing homework problems and doing the practice final are exam are key to doing well on the final. Since the final has a design problem that incorporates material from throughout the semester, reviewing the design problems on the later psets is especially important. It’s also important to be very familiar with MatLab, especially with the help function, as you will not be able to use the internet during the exam.
External ResourcesOffice hours are a great resource, both for conceptual questions and for homework questions. In general, Professor Rowley’s office hours are best for conceptual questions, while TA office hours tend to be better for pset-specific questions. The TA’s are also very willing to schedule additional office hours if you feel behind. For studying on your own, the course book is generally the best resource. Because Professor Rowley wrote the course notes to contain exactly what he focuses on, they should generally be the first place to go when confused. However, Feedback Systems: An Introduction for Scientists and Engineers by K.J. Åström and R.M. Murray is also a useful textbook, and is on reserve in the engineering library. It has additional information and examples beyond those in the course notes, but isn’t as focused on relevant material.
What Students Should Know About This Course For Purposes Of Course SelectionMAE 433 teaches principles of control theory, which is valuable for all students in engineering and computer science. Students interested in a career in robotics, manufacturing, process engineering, signal processing, or many other fields will find direct uses for the material covered in this course. All mechanical and aerospace engineers will find this material extremely relevant to design and independent work, and should take this course as early as possible. Even students who will not find a direct use for the material will learn a lot from the mathematics and ways of thinking that Rowley teaches. MAE 433 is taught extremely well, and tends to receive very good reviews. The course is of approximately average difficulty for courses in engineering and the sciences, and an average student might spend 12-15 hours per week on it. Because the material is extremely different from anything taught in most other engineering classes, it is a very interesting and exciting course to take. Students from all engineering and science disciplines should be able to understand this material, as long as you have taken MAT 202 or 204 (linear algebra).
Automatic Control Systems