2.004 | Fall 2007 | Undergraduate

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.)

1 Introduction; mechanical elements (PDF)
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)
6 Poles and zeros; 1st order systems (PDF)
7 2nd order systems (PDF)
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  
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
Chapter 2, pp. 1-9 and 23-25
Chapter 3, pp. 1-9, 17-20, and 32-39

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  
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  
35 Stability and steady-state error in state space; controllability and observability  
36 Optimal control; the minimum time problem  
37 Review: modeling and transfer functions (PDF)
38 Review: root locus, feedback design (PDF)
39 Review: frequency domain and design (PDF)

Course Info

Learning Resource Types
Problem Sets with Solutions
Lecture Notes