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# Automatic Control 4

### definitions 4

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

Describe estimator design (p. 497 | Contruction of a state estimate is a key part of state-space control design |

full-order estimators; | feed back the output error to correct the state estimate equation |

reduced-order estimators | reduces the order of the estimator by the number of sensed outputs |

estimator pole selection | If the estimator poles are slower than the controller poles, the disturbances are dominated by dynamic characteristics of the estimator |

Regulator | combines control-law design, estimator design and control law with estimated state variables to get a regulator that can reject disturbances but has no reference input |

conditionally stable compensator | a system that is unstable as the gain is reduced from its nominal value |

a nonminimum-phase compensator | the RHP portion of the locus will not cause difficulties because the gain has to be selected to keep all closed-loop poles in LHP |

command following (p. 524); | good command following is done by properly introducing the reference input into the system equations |

a general structure for the reference input; | given r(t), the most linear way to introduce r into the system equations is to add terms proportional to it in the controller equations |

Truxal's formula | 1/Kv = sum(1/zi) – sum(1/pi) |

Describe integral control and robust tracking (pp. 536-540 | We need to use integral control to obtain robust tracking |

Robust Tracking Control: The Error-Space Approach (section 7.10.2); | A more analytical approach to giving a control system the ability to track nondecaying input and to reject a nondecaying disturbance |

Discuss loop transfer recovery (LTR; page 554-). | It is possible to modify the estimator design so as to try to “recover” the LQR stability robustness properties to some extent. LTR is effective for minimum-phase systems |

Diophantine equation | a(s)d(s) +b(s)cy(s) = alphac(s)alphae(s) |

dimension of the controller. | 2m+1 unknowns in d(s) and cy(s) and n+m equations from the coefficients of powers of s |

What are the rules for plotting a positive root locus? | Rule 1- n branches of the locus start at the poles of L(s) and m of these branches end on the zeros of L(s) Rule 2- loci are on the real axis to the left of an odd number of poles and zeros Rule 3- for large s and K, n-m of the loci are asymptotic to lin |

Angle of the asymptotes | phi = [180 + 360(l-1)]/[n-m], l=1,2,…,n-m |

Rule for departure angles | q(phi)=sum omega – sum phi – 180 – 360(l-1) |

Rule for arrival angles | q(omega)=sum phi – sum omega + 180 + 360(l-1) |

Summarize the rules for plotting a root locus (pp. 248-249). | Rule 1- n branches of the locus start at the poles of L(s) and m branches end on the zeros of L(s) Rule 2- loci are on the real axis to the left of an odd number of poles and zeros Rule 3- For large s and K, n-m of the loci are asymptotic to lines at an |

Summarize the rules for plotting a root locus 2 | Summarize the rules for plotting a root locus Rule 5 – locus crosses the jw axis at points where the Routh criterion shows a transition from roots in the left half-plane to roots in the right half-plane |

Summarize the rules for plotting a root locus 3 | Rule 6- the locus will have multiple roots at points on the locus where the derivative is zero |

Created by:
delafuente