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# Automatic Control 4

### definitions 4

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