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# automatic control 5

### definitions 5 & review

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

What are the rules for plotting a negative (0 degree) root locus? (Part1) | Rule 1- The n branches of the locus leave the poles and m approach the zeros and n-m approach asymptotes to infinity Rule 2- The locus is on the real axis to the left od an even number of real poles plus zeros Rule 3- The asymptotes are described by |

What are the rules for plotting a negative (0 degree) root locus? (part2) | R.4-Departure angles from poles & arrival angles to zeros are found by searching in the near neighborhood of the pole or zero where the phase of L(s) is 0, so that q(phi)=sum omega – sum phi – 180 – 360(l-1) & q(omega)=sum phi – sum omega + 180 + 360(1-1) |

What are the rules for plotting a negative (0 degree) root locus? | Rule 5- The locus crosses the imaginary axis where either letting s=jw or applying Routh’s criterion shows a change between stability and instability Rule 6- The equation has multiple roots at points on the locus where b(da/ds)-a(db/ds)=0 |

Give a summary of Bode plot rules (pp. 329-330). (part 1) | 1.Manipulate the transfer function into the bode form 2. determine the value of n for the K0(jw)^n term 3. Complete the composite magnitude asymptotes 4. Sketch in the approximate magnitude curve |

Give a summary of Bode plot rules (pp. 329-330). (part 2) | 5. plot the low-frequency asymptote of the phase curve 6. sketch in the approximate phase curve 7. locate the asymptotes for each individual phase curve 8. graphically add each phase curve |

What is root locus? | Rules for plotting the paths of the roots |

Who developed this method? | W. R. Evans |

What are the applications? (pp. 230-231) | Used to study the effect of loop gain variations. Used to plot the roots of any polynomial with respect to any one real parameter |

Describe Evan's method for root-locus (p. 232) | Suggested that we plot the locus of all possible roots of 1+KL(s)=0 as K varies from zero to infinity and then use the resulting plot to aid us in selecting the best value of K. |

What is the "root locus"? | The graph of all possible roots of 1+KL(s)=0 relative to parameter K |

the root-locus forms? | 1+KL(s)=0, 1+K[b(s)/a(s)]=0, a(s)+Kb(s)=0, |

What is breakaway point (p. 235)?; | where roots move away from the real axis |

breakin point (p. 236)? | the point of multiple roots where two or more roots come into the real axis |

State the formal definitions of a root locus (p. 237). | Set of values of s for which 1+KL(s)=0 is satisfied as the real parameter K varies from 0 to infinity |

positive or 180 degree locus?; | when K is real and positive |

negative or 0 degree locus? | when K is real and negative |

Lead compensation | approximates the function of PD control and acts mainly to speed up a response |

Lag compensation | approximates the function of PI control an is usually used to improve the steady-state accuracy of the system |

Zero and pole of a lead | zero is placed in the neighborhood of the closed-loop w and the pole is located at a distance 5 to 20 times the value of the zero location |

analog and digital implementations. | Lead compensation can be implemented using analog electronics, but digital computers are preferred |

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delafuente