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# automatic control 6

### review 2

Question | Answer |
---|---|

Continuation locus | part 1) imagine plotting a root locus for an initial range of K, perhaps for 0<K<K1. |

Continuation locus | part 2) If we let K=K1+K2, we can then plot a new locus with parameter K2, a locus which is the continuation of the original locus and whole starting poles are the roots of the original system at K=K1. |

What are the extensions of the root-locus method (p. 284)? | Method can be extended to consider negative values of the parameter, a sequential consideration of more than one parameter and systems with time delay |

What is the definition of a negative root locus? | The angle of L(s) is 0+360(l-1) for s on the negative locus |

What is the effect of time delay on stability? | Time delays always reduce the stability of a system |

What is Pade approximant (p. 290)? | Common means for finding an approximation that will be good for small s |

What are the advantages (and disadvantage) of the frequency-response design method (pp. 314-315)? | part 1) Provides good designs in the face of uncertainty in the plant model, ease with which experimental information can be used for design purposes, the easiest method to use for designing compensation, |

What are the advantages (and disadvantage) of the frequency-response design method (pp. 314-315)? | part 2) the underlying theory is somewhat challenging and requires a rather broad knowledge of complex variables. |

What is frequency response?; | Linear system’s response to sinusoidal inputs |

magnitude and phase?; | Magnitude M is given by |G(jw)| and the phase phi is given by <[G(jw)] |

Composite plot from individual terms | phases of the individual terms are added directly to obtain the phase of the composite expression, G(jw) |

Bode Plot | two curves; the logarithm of magnitude versus log w and the phase versus log w |

Decibel | standard way to measure the power gain |

Advantages of bode plots (1) | part1)1. dynamic compensator design can be based entirely on body plots, 2. bode plots can be determined experimentally, |

Advantages of bode plots (2) | part2) 3. bode plots of systems in series simply add, which is quiet convenient, 4. the use of a log scale permits a much wider range of frequencies to be displayed on a single plot than is possible with linear scales |

Composite curve | when the system has several poles and several zeros, plotting the frequency response requires that the components be combined into a composite curve |

nonminimum-phase systems (p. 335); | a system with a zero in the right half-place undergoes a net change in phase when evaluated for frequency inputs between zero and infinity, which is greater than if all poles and zeros were in the left half-plane |

steady-state errors (page 336); | steady state error of a feedback system decreases as the gain of the open loop transfer function increases |

Describe the neutral stability analysis method (p. 338). | Can determine the stability of a system by simply inspecting the denominator in factored form to observe whether the real parts are positive or negative. |

What are gain margin?; | The factor by which the gain can be raised before instability results |

Created by:
delafuente