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.)

SES # | TOPICS | NOTES |
---|---|---|

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 |

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) |