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# Automatic Control 1

### definitions 1

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