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automatic control 5

definitions 5 & review

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
Created by: delafuente