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# Automatic Control 1

### definitions 1

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

root locus | rules for ploting the paths of the roots |

What are phase conditions | root locus of L(s) is the test of points in the s-plane where the phase of L(s) is 180 degrees |

Magnitude condition | K = -1/L(s) |

Graphical calculation of the desired gain | compute the gain to place the roots at the dot(s=so) by measuring the lengths of these vectors and multiplying the lengths together |

Notch compensation | used to achieve stability for systems with lightly damped flexible modes |

Example of lag compensation | take G(s)=1/[s(s+1)], include the lead compensation KD1(s)=K(s+5.4)/(s+20) that produced the locus and raised the gain until the closed-loop roots correspond to a dampint ration of 0.5. |

Discuss contrasting methods of approximating delay | For low gains and up to the point where the loci cross the imaginary axis, the approximate curves are very close to the exact. The pade curve follows the exact curve much further than does the first-order lag, and its increased accuracy would be useful if |

frequency response plot?; | the output y is a sinusoid with the same frequency as the input u and that the magnitude ratio M and phase phi of the output are independent of the amplitude A of the input are a consequence of G(s) being a linear constant system |

Bandwidth | natural specification for system performance in terms of frequency response |

Resonant peak | maximum value of the frequency-response magnitude |

Bode form of the transfer function | KG(jw)= Ko(jwt1+1)(jwt2+1)/(jwta+1)(jwtb+1) |

Classes of terms of transfer functions | 1. Ko(jw)^n, 2.(jwt+1)^+-1, 3.[(jw/wn)^2 +2squiggly(jw/wn) +1]^+-1 |

Break point | w=1/tau |

Peak amplitude | |G(jw)|=1/2squiggly at w=wn |

What is neutrally stable (p. 339)? | With K defined such that a closed-loop root falls on the imaginary axis |

What is the Nyquist stability criterion (p. 340)? | Relates the open-loop frequency response to the number of closed-loop poles of the system in the RHP |

Describe the argument principle (p. 341); | A contour map of a complex function will encircle the origin Z-P times, |

.application to control design | To apply the principle to control design, we let the C1 contour in the s-plane encircle the entire RHP, |

Created by:
delafuente