Root Locus: Consider the following system
Root Locus: Consider the following system
(a) What are the poles of the open loop system (locations of the open loop poles)? What are zeros of the open loop system (locations of the zeros)?
(b) What is the origin of the asymptotes?
(c) What are the angles of asymptotes?
(d) Find the break-away and break-in points.
(e) Find the angles of departure for all the poles.
(f) Draw the root locus plot of G(s).
(g) For what values of K is the closed loop system stable?
Homework Answers
Theroot-locus design method (d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angle...
Theroot-locus design method
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angles. the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, respectively, and the range of k for closed-loop stability 5 10ん k(s+21
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to K. [ Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, imaginary axis crossing points, respectively (if any).
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is...
Lectures 15-18: Root-locus method 5.1 Sketch the root locus for a unity feedback system with the ...
help on #5.2
L(s) is loop transfer function
1+L(s) = 0
lecture notes:
Lectures 15-18: Root-locus method 5.1 Sketch the root locus for a unity feedback system with the loop transfer function (8+5(+10) .2 +10+20 where K, T, and a are nonnegative parameters. For each case summarize your results in a table similar to the one provided below. Root locus parameters Open loop poles Open loop zeros Number of zeros at infinity Number of branches Number of asymptotes Center of...
Sketch the root locus of the given system above with respect to k
Sketch the root locus of the given system above with respect to k [Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros imaginary axis crossing points, respectively (if any).]
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus us...
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus using the below procedures. (1) find poles and zeros and locate on complex domain (2) find number of branches (3) find asymptotes including centroid and angles of asymptotes (4) intersection at imaginary axis (5) find the angle of departure (6) draw the root migration (b) Find the range of K for which the feedback system is asymptotically stable.
Problem 3:...
Problem 3 (25 points): Consider the following closed-loop control system K(s +9) (s4s + 11) A....
Problem 3 (25 points): Consider the following closed-loop control system K(s +9) (s4s + 11) A. Plot the open-loop poles and zeros on a graph. B. Compute and draw an C. Compute any break-away and break-in points. D. Compute any jo crossings. E. Draw a qualitatively-correct root locus diagram. y asymptote real intercepts and angles. Locate the closed-loop poles on the root locus plot such that the don closed-loop poles have a-damping-ratio equal to.0.5,and-determine corresponding value of the gainK.-
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc...
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc (s) K (s-1) (s+2) (s+3) (a) Determine the open-loop system (i.e., G (s)) poles and zeros. (b) Determine the number of asymptotes and the angles of asymptotes. (c) Determine the break-in/break-out points (if any) (d) Sketch the root locus (e) Determine the value of K (if any) for which the system is marginally stable
Consider the following root locus form
Consider the following root locus form (a) With hand calculations, sketch the root locus plot. Please calculate the asymptotes, centrode, break in/break-away point(s), and locus departure angles and identify where on the real axis the locus exists Investigate whether the locus intersects the imaginary axis, and if it does, calculate the K value and the location on the imaginary axis where this inersection occurs. (b) Obtain the root locus in Matlab and show how your calculations in (a) are validated.
Q3. Consider the feedback system in Figure 3. In the case when 2L G(s) Figure 3:...
Q3. Consider the feedback system in Figure 3. In the case when 2L G(s) Figure 3: Block diagranm G(s) and when k is positive: (a) Sketch the root locus of the closed loop system (10) To assist in this (to indicate on root locus diagram) ) Compute the open loop poles and zeros (i) ealeulate the portion of the locus lying on the real axis; (iii) calculate the angles of asymptotes make with the real axis arad also the value...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a)...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a) Locate open-loop zeros and open-loop poles. b) Construct the root-locus diagram as 0 <K <oo. Mark the portions of the real axis that belong to the root locus - Mark with K =0 the point where the root locus bra O the point where the root locus branches start and with K = oo the point where the branches end. - Find break-away and/or...
Theroot-locus design method
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angles. the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, respectively, and the range of k for closed-loop stability 5 10ん k(s+21
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to K. [ Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, imaginary axis crossing points, respectively (if any).
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is...
help on #5.2
L(s) is loop transfer function
1+L(s) = 0
lecture notes:
Lectures 15-18: Root-locus method 5.1 Sketch the root locus for a unity feedback system with the loop transfer function (8+5(+10) .2 +10+20 where K, T, and a are nonnegative parameters. For each case summarize your results in a table similar to the one provided below. Root locus parameters Open loop poles Open loop zeros Number of zeros at infinity Number of branches Number of asymptotes Center of...
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus using the below procedures. (1) find poles and zeros and locate on complex domain (2) find number of branches (3) find asymptotes including centroid and angles of asymptotes (4) intersection at imaginary axis (5) find the angle of departure (6) draw the root migration (b) Find the range of K for which the feedback system is asymptotically stable.
Problem 3:...
Problem 3 (25 points): Consider the following closed-loop control system K(s +9) (s4s + 11) A. Plot the open-loop poles and zeros on a graph. B. Compute and draw an C. Compute any break-away and break-in points. D. Compute any jo crossings. E. Draw a qualitatively-correct root locus diagram. y asymptote real intercepts and angles. Locate the closed-loop poles on the root locus plot such that the don closed-loop poles have a-damping-ratio equal to.0.5,and-determine corresponding value of the gainK.-
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc (s) K (s-1) (s+2) (s+3) (a) Determine the open-loop system (i.e., G (s)) poles and zeros. (b) Determine the number of asymptotes and the angles of asymptotes. (c) Determine the break-in/break-out points (if any) (d) Sketch the root locus (e) Determine the value of K (if any) for which the system is marginally stable
Q3. Consider the feedback system in Figure 3. In the case when 2L G(s) Figure 3: Block diagranm G(s) and when k is positive: (a) Sketch the root locus of the closed loop system (10) To assist in this (to indicate on root locus diagram) ) Compute the open loop poles and zeros (i) ealeulate the portion of the locus lying on the real axis; (iii) calculate the angles of asymptotes make with the real axis arad also the value...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a) Locate open-loop zeros and open-loop poles. b) Construct the root-locus diagram as 0 <K <oo. Mark the portions of the real axis that belong to the root locus - Mark with K =0 the point where the root locus bra O the point where the root locus branches start and with K = oo the point where the branches end. - Find break-away and/or...
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