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ECE486

ECE486 (Control Systems) is a 4-credit-hour course that satisfies the 1-of-6 Electrical Engineering Foundations Course requirement for CEs and counts as a lab course. It is offered in the fall and spring.

Content Covered

  • Models for Dynamic Physical Systems
  • Small-signal Linearization of Systems
  • Block Diagrams
  • BIBO Stability
  • Steady State Error, Disturbance Rejection
  • PID Controllers
  • Feedback Control
  • Laplace Domain Design Methodology (Root Locus)
  • Frequency Response Design Methodology (Bode and Nyquist plots)
  • State Space Design Methodology

Note: Control Systems, in this course, refer to obtaining useful properties of systems, such as disturbance rejection and stability, using mathematics. This is different from using a microcontroller and software. The latter is not covered in this course.

The first part of ECE486 is a brief survey on what a control system is, why it is important, and the parameters that a control system designer is looking for. The next part of the course covers the Laplace Transform and how to design a control system using the Laplace domain. The course continues by talking about how to design control systems using the frequency domain (which has various benefits and drawbacks compared to the Laplace domain). Finally, the course wraps up by giving a brief survey of designing control systems using state-space method (which is the most powerful, albeit the most difficult). The course places great emphasis on design and experimentation.

This course has a required lab component. In the lab, students apply the various methods learned in lecture to design control systems, usually for a DC motor. For the final lab project, students are tasked with balanacing an inverted pendulum. This is a nontrivial task, but very fulfilling when it works.

The course only deals with linear and time-invariant (LTI) systems.

Prerequisites

ECE210 is the only official prerequisite to the course. However, the course teaches students everything about systems, BIBO stability, Linearity, and the Laplace Transform, so it is not necessary to remember any of these from ECE210. A more pertinent prerequisite is MATH257, since the state-space method relies heavily on linear algebra methods and theorems, such as finding eigenvalues.

When to Take it

Take this course if you have any sort of passing interest in controls. Control systems are also important in fields such as power systems and robotics. Be warned that the course does require a decent time commitment due to the amount of content and work required. If you do wish to take this course as soon as possible, take ECE210 as soon as possible.

Course Structure

This course has somewhat weekly homeworks, somewhat weekly prelabs, labs, and lab reports, two midterms, and one final. Homeworks, prelabs, and lab reports often depend on the use of Matlab.

The homeworks start weekly and tend to lighten up as the semester goes on. They never collide with exam weeks. Homework sets are generally not too difficult and will contain both calculations and derivations of expressions. Some homeworks will take under an hour, while others require more calculation and can be generally annoying. Students who pay attention and stay engaged in lecture will find these homeworks to be conceptually simple.

There are a total of 8 labs (7 normal ones and a final lab project), each of which have a prelab and a lab report. Labs are performed in pairs. Each lab has certain checkpoints that need to be demonstrated to lab TAs. With the exception of the final lab project, students should have no trouble completing the lab in the allotted time. The prelab is submitted individually, while the lab report is done in pairs. Prelabs and lab reports can get tedious and sometimes difficult since they require some obscure technique or software. Therefore, start these early and go to lab office hours. Labs start light and easy, but quickly ramp up as students are expected to get more familiar with the lab and all the equipment.

The exams are usually pretty reasonable, as this is a 400-level course, with averages in the 80s or 90s. Very few practice exams are given out, but students should be extremely comfortable with the material after working through the homeworks and the labs. Cheatsheet policies may vary depending on the semester and the lead instructor. For the Spring 2023 semester, students were allowed to bring one double-sided 8.5x11 cheatsheet to the first exam, two double-sided 8.5x11 cheatsheets to the second exam, and so on. Students were highly recommended to reuse cheatsheets from prior exams, although this was not enforced.

Overall, the course requires about 10 hours a week and is often stated to be on par, or slightly harder than, ECE385 in terms of time commitment.

Instructors

Faculty in the area of controls and power generally rotate as far as teaching this course. Professor Alejandro Garcia-Dominguez taught this course in the Spring 2023 semester.

Course Tips

The course content can often get tedious, as each technique often carries many steps that are mathematically long. Make sure you understand why each step is the way it is and when to use each technique.

Ask questions in lecture! Controls is a confusing and nuanced topic and it is easy to get lost. Believe me, you are not the only one who gets lost every lecture. Ask questions!

Start the prelabs and lab reports early. They will get very annoying as the semester progresses.

Life After

This is the only ECE class on controls at the undergraduate level. Related classes include ECE310 - Digital Signal Processing I (more on linear systems) and ECE470 - Introduction to Robotics. For those interested in continuing control systems, ECE515 - Control System Theory and Design is usually the next course to take. ECE486 also briefly touches on optimization techniques while covering state-space method. For those interested in that type of content, ECE490 - Introduction to Optimization would be a great course to take.

Infamous Topics

  • Root locus method: The method is long and tedious. Write each step down, practice applying it on your own in homeworks, and put it on your cheatsheet for the exam. If you fully understand what each step is useful for, then the method will become intuitive and easier to remember.

Resources