Systems, Modeling, and Control II
Lecture Notes
Lecture 2 refers to the following MATLAB® files for solving ODEs: (ZIP) (The ZIP file contains: shaft_w_coulomb_viscous.m, shaftcv_kernel.m, and shaftcv_solve.m files.)
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SES # |
TOPICS |
NOTES |
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1 |
Introduction; mechanical elements |
(PDF) |
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2 |
Solving ODEs; cruise control |
(PDF) |
|
3 |
Laplace transforms; transfer functions; translational and rotational mechanical transfer functions |
(PDF) |
|
4 |
Electrical and electro-mechanical system transfer functions |
(PDF) |
|
5 |
DC motor transfer function |
(PDF) |
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6 |
Poles and zeros; 1st order systems |
(PDF) |
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7 |
2nd order systems |
(PDF) |
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8 |
2nd order systems (cont.) |
(PDF) |
|
9 |
More than 2 poles; zeros; nonlinearities and linearization |
(PDF) |
|
10 |
Examples of modeling & transfer functions |
(PDF) |
|
11 |
Block diagrams; feedback |
(PDF) |
|
12 |
Analysis of feedback systems |
(PDF) |
|
13 |
Quiz 1 |
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|
14 |
Stability; Routh-Hurwitz criterion |
(PDF) |
|
15 |
Stability analysis |
Please see the following selections from MathWorks, Inc. "Control System Toolbox Getting Started Guide." (PDF - 1.8 MB) Chapter 1, all |
|
16 |
Steady state error analysis |
(PDF) |
|
17 |
Root locus introduction |
(PDF) |
|
18 |
Root locus example |
(PDF) |
|
19 |
Design of transient response using root locus |
(PDF) |
|
20 |
Positive feedback |
(PDF) |
|
21 |
Examples of design via root locus |
(PDF) |
|
22 |
Steady-state error compensation |
(PDF) |
|
23 |
Transient response compensation; transient and steady-state error compensation |
(PDF) |
|
24 |
Compensation examples |
(PDF) |
|
25 |
Feedback compensation and its physical realization |
(PDF) |
|
26 |
Feedback design examples |
(PDF) |
|
27 |
Quiz 2 |
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|
28 |
Frequency response; bode plots |
(PDF) |
|
29 |
Bode plot examples |
(PDF) |
|
30 |
Gain margin and phase margin |
(PDF) |
|
31 |
Design using the frequency response; lead, lag, lead-lag compensators |
(PDF) |
|
32 |
The state-space representation |
(PDF) |
|
33 |
Solving the state equations in the time and space domains |
(PDF) |
|
34 |
State equation examples |
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|
35 |
Stability and steady-state error in state space; controllability and observability |
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|
36 |
Optimal control; the minimum time problem |
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|
37 |
Review: modeling and transfer functions |
(PDF) |
|
38 |
Review: root locus, feedback design |
(PDF) |
|
39 |
Review: frequency domain and design |
(PDF) |
Labs
A brief description of the 2.004 lab facilities and rules is provided for reference: (PDF)
The first six labs deal with a physical plant consisting of a rotational flywheel and motor, detailed in this handout: (PDF) (Courtesy Prof. Emanuel Sachs. Used with permission.)
The motor specification sheet may be found here (PDF)
Lab 1: Coulomb and Viscous Friction (PDF)
Lab 2: Characterization of Lab System Components (PDF)
Lab 3: Construction of a Proportional Velocity Controller (PDF)
Lab 4: Closed-loop Performance of a Proportional Velocity Controller (PDF)
Lab 5: Elimination of Steady-state Error Using Integral Control Action (PDF)
Lab 6: Closed-loop Position Control, and the Effect of Derivative Control Action (PDF)
The final set of lab projects involves the design of an active damping system for a skyscraper, including a set of MATLAB® files for simulating the tower and its vibrations.
Project Introduction (PDF)
Lab: Active Damping of Tall Building Vibrations (PDF 1) (PDF 2)
Tower Data (ZIP) (The ZIP file contains: 13 .m files.)
Assignments
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ASSIGNMENTS |
SOLUTIONS |
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Problem set 1 (PDF) |
(PDF) |
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Problem set 2 (PDF) |
(PDF) |
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Problem set 3 (PDF) |
(PDF) |
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Problem set 4 (PDF) |
(PDF) |
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Problem set 5 (PDF) |
(PDF) |
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Problem set 6 (PDF) |
(PDF) |
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Problem set 7 (PDF) |
(PDF) |
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Problem set 8 (PDF) |
(PDF) |
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Problem set 9 (PDF) |
(PDF) |
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Problem set 10 (PDF) |
(PDF) |
Exams
This page contains the two quizzes, together with their solutions, for the semester.
Quiz 1 (PDF)
Quiz 2 (PDF)