# System Analysis and Control

ME 4555

Northeastern University
**Instructor:** Laurent Lessard

This is an undergraduate-level course in classical control theory. The course covers modeling of physical systems, analysis and performance of linear systems, and basic feedback controls. This course presents material that is fundamental and foundational for the study and practice of control systems. Concepts includes the s-domain, PID control, root locus, frequency-domain, and Bode plots. This is not an official course website, but rather a public online space where I will post course-related materials as I develop them. These notes are still under development (use at your own risk!) and will continue to be improved every time I teach the course.

**IMPORTANT:** The notes below are from Spring 2022-23, which was the last time Prof. Lessard taught this course. More recent offerings of the course might use different notes/materials.

## Part I: System modeling

## Part II: System analysis

## Part III: Feedback control

## Part IV: Bonus material

**Discrete-time control.** Most plants have continuous-time dynamics (described by ODEs), whereas most sensors provide measurements at evenly spaced points in time (discrete time). Moreover, most controllers nowadays are implemented in software or on microcontrollers, which means the implementations must be digital (all time is discretized). So how does one carry out controller design for these sorts of hybrid systems that have a mixture of discrete and continuous parts?

**Balancing a stick, and the limits of human performance.** This demonstration is inspired by

John Doyle. See for example this

series of papers or one of John’s many

talks on YouTube. I adapted the demo to include connections to the course material, for example root locus plots and Bode plots. Here are my notes:

## Textbook:

There is no required textbook for the class. However, I can recommend several excellent books as reference texts:

- Dorf, R.C. and Bishop, R.H.,
*Modern Control Systems*, Prentice Hall.
- Ogata, K.,
*Modern Control Engineering*, Prentice Hall.
- Kluever, C.A.,
*Dynamic Systems, Modeling, Simulation, and Control*, Wiley.
- Nise, N.S.,
*Control Systems Engineering*, Wiley.
- Astrom, Murray,
*Feedback Systems: An Introduction for Scientists and Engineers* (free online)

You will not need these books. I’m only listing them in case you want to consult additional references.

## Online references:

There are many excellent online references for classical control. My top recommendations are: