System Analysis and Control

ME 4555
Northeastern University

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 control. 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 up-to-date course-related materials.

IMPORTANT: The notes below are from Spring 2026, which was the last time Prof. Lessard taught this course. More recent offerings of the course (or different instructors) might use different notes/materials.

Course material

Old materials

Resources

The notes for this course are assembled in this online textbook.
Relevant sections of the book are linked below for each lecture.

Part I: Modeling

	Lecture	Notes
1.	Introduction	Introduction & Intro to modeling Linear mechanical systems
2.	Rotational mechanics	Rotational systems Kinematic constraints
3.	Linear systems and linearization	Linear systems Linearization
4.	Laplace-domain modeling	Laplace transforms Transfer functions
5.	Circuit modeling	RLC circuits Impedance method
6.	Operational amplifiers	Operational amplifiers Op amp circuit analysis
7.	Electromechanical systems	DC motors Electromechanical systems
8.	Block diagrams	Block diagrams Simulink demo

Part II: Analysis

	Lecture	Notes
9.	Impulse response	Impulse response MATLAB demo
10.	Laplace inversion tools	Partial fraction expansion Inverse Laplace transforms
11.	First-order systems	First-order systems First-order case studies
12.	Second-order systems	Second-order systems Second-order performance
13.	Feedback and stability	Feedback and P-control Stability criteria
14.	Higher-order systems and zeros	Higher-order systems The effect of zeros

Part III: Control

	Lecture	Notes
15.	PI and PID control	PI control PID control
16.	Root locus	Root locus More root locus
17.	Root locus design	Root locus design Control System Designer demo
18.	Frequency response and Bode plots	Frequency response Bode plots
19.	Bode sketching	1st/2nd order Bode plots Sketching Bode plots
20.	Stability margins and delays	Stability margins Delay and delay margin
21.	Frequency-domain design	Frequency-domain design Lead/lag compensation

These are older handwritten notes and handouts that I used prior to 2026. Keeping them here for reference.

Part I: System modeling

	Lecture notes	Dates	Supplementary material
1.	Introduction		Math prerequisites
2.	Linear mechanical systems
3.	Rotational mechanical systems
4.	Systems with kinematic constraints
5.	RLC circuits		Extra circuit problems + solutions
6.	Op amps
7.	DC motors
8.	Hydraulic systems

Part II: System analysis

	Lecture notes	Dates	Supplementary material
9.	Intro to Simulink
10.	Linear systems		Extra circuit problems + solutions
11.	The Laplace transform		Linearity and linearization
12.	More Laplace transforms
13.	Impedance analysis of circuits
14.	The impulse response
15.	Simulating LTI systems in Matlab
16.	Inverse Laplace transforms
17.	More inverse Laplace transforms
18.	First-order systems
19.	Second-order systems		DEMO: Second-order step response
20.	More second-order systems

Part III: Feedback control

	Lecture notes	Dates	Supplementary material
21.	Feedback and proportional control		Stability criteria
22.	Final Value Theorem		10-min video on PID control
23.	PID control		DEMO: Inverted pendulum PID control
24.	Root locus plots		Root locus cheat sheet
25.	RL dominant poles, effect of zeros		DEMO: Dominant poles
26.	RL design, pendulum on a cart		Dominant poles
27.	RL design, PID for a DC motor
28.	Frequency response
29.	Bode plot for 1st order systems		DEMO: 1st order forced response
30.	Bode plot for 2nd order or higher		DEMO: 2nd order forced response
31.	Bode design, stability margins
32.	Bode design with SISOtool

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?

Discrete-time analysis and control

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:

Mathematical derivations
Diagrams and figures

Textbook:

The provided online notes are all you will need for the class. That being said, I can recommend several excellent books in case you would like to consult additional references:

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

Online references:

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

Brian Douglas’s Classical Control Theory Course. Controls course designed for online learning. All videos are short (~10min) and exceptionally clear.
Richard Pates’s Course on Basic Controls. Medium-length videos (15-20min) that cover introductory controls topics. Very clear presentation that also goes into detail explaining and proving relevant mathematical results.
Christopher Lum’s Control Theory Playlist. This series of videos covers all of classical controls in a more traditional lecture-based format. There are also detailed MATLAB demos and worked examples.