MCEN4043: System Dynamics


Instructor: Prof. Shalom D. Ruben
Office: ECME 128
Office Hours: Mon 2-3pm, Wed 10-11am
Lecture: Tu,Th 2:00-3:15pm

TA: Nikhar Abbas (OH: Tu 12:30-1:30pm, Th 9:45-10:45am)
TA: Michael Marx (OH: Wed 5-7pm)
TA: Roy Powell (Lab only)
TA: Matt Ballinger (Lab only)

Lab 011: Mon 11am-1pm
Lab 012: Fri 2-4pm

Covers linear dynamic systems and mathematical tools for understanding them, input-output relationships, modeling templates, complex variables, Laplace transform, time-harmonic forcing and response, Fourier series and discrete Fourier transform, and coupled systems. (ECEN 3010, MCEN 3022 and 3043. Restricted to senior MCEN majors.)


We will not have a required textbook this semester! All the material for this course will be covered during lectures completely. But, if you are like me and would like a book for reference/addition resource than I would suggest any of the books in the picture above (find the cheapest edition that you can find). You will notice that the left column of books are all System Dynamics books and on the right (and center) are either Signal Processing or Control books.

If you think you are interested in Robotics/Control than any of the control books will work:

  1. Modern Control Systems by Dorf

  2. Feedback control of Dyanmic Systems by Franklin

  3. Control Systems Engineering by Nise

If you would like a book that is primarily a System Dynamics book, than Ogata’s book is probably my favorite but any will work:

  1. System Dynamics by Ogata

  2. System Dynamics by Palm

  3. System Dynamics of Physical Systems by Cannon

  4. System Dynamics by Karnopp

If you are interested in signal processing and want to know more about digital/discrete (along with continous) time systems get one of these:

  1. Engineering Signals and Systems by Ulaby

  2. Signal Processing First by McClellan

Topics Covered

(not restricted to this order but will following closely)

  1. Modelling

    1. Laplace Transform

    2. Solving Differential Equations Using Laplace

    3. Mechanical (Translation) Systems

    4. Convolution

    5. Electrical Systems

    6. Mechanical (Rotation) Systems

    7. Block Diagrams

    8. Op Amps

    9. Transducers

    10. Fluid/Thermal Systems

  2. Analysis

    1. First/Second/Higher-Order System Response

    2. Performance Measures

    3. Stability

    4. Frequency Response Function

    5. Bode Plots

    6. Fourier Series

  3. Control

    1. Intro to Feedback Control

    2. Root Locus Analysis

    3. Steady-State Error to an input

    4. Steady-State Error to a disturbance

    5. PID Control

Grading Breakdowns

  1. Individual Work (70%)

    1. Midterm Exams (20% each)

      1. Feb. 22 from 7-9pm

      2. Apr. 3 from 7-9pm

    2. Final Exam (30%)

  2. Group Work (30%)

    1. Labs (20%)

    2. Homework/Workshops(10%)

Desire 2 Learn (D2L)

To access the following material, you must log in to D2L:

  1. Lab Handouts

  2. Homework Assignments

  3. Homework Solutions

  4. Exam Solutions



  1. Typed Reports are mandatory (Word and Equation Editor)

    1. Introduction

    2. Lab Body with Results (including graphs and images)

    3. Appendix with Matlab Code

  2. Describe enough to fully demonstrate your understating.

  3. DUE DATE: Eeach Lab is due at the START of the next week’s lab.


  1. Assignments must be neat, organized and legible. In plain English: If we cannot read your assignment, you will not get credit for it. Typed assignments are welcome.

  2. At the start of each problem, write out a brief description of the problem including given information and what is to be found. Put a box around all final answers.

  3. Show your work enough to fully demonstrate your understating and your arrival at your answer.

  4. Write on only one side of the paper. Pages must stapled be in order (i.e. following the order in which the problems were assigned).


  1. You only have TWO WEEKS to question grading from the time the homework\exam\project is returned.

    1. Specificially for exam grade questions, students must write up a detailed document (using Word or other word processing tool, not hand-written) describing the question, staple it to the original exam, and give it to the professor.

  2. This will be the final grading scale used for the course. There is no curve. You are not competing against classmates, so help them out if you can! I reserve the right to lower the scale (i.e., make it easier), but I will not raise it.

A: 90+
B : 83-84
C : 74-76
D : 63-67
F : 59 or below

In-Class Expectations

The following expectations will assist us with the creation of a learning community and a high quality of educational experience. The University of Colorado Classroom Behavior Policy will compliment these expectations:

  1. Turn off your cell phones/ don’t text

  2. No laptops during lectures (unless approved for taking notes)

  3. Refrain from having disruptive conversations

Academic Integrity

You will be asked to complete group homework assignments in this course, but it is also expected that you will abide by The University of Colorado Honor Code at all times.

Late Work

No late work will be accepted