Question8.Problem 9. For a similar PD controlled positioning system given in the previous problem, where1Ge(s) = K(s+ 4) and Gp(s)s(s+2)(s²+10s+41)sketch the root-locus of the system for K = 1 by means of the computations requested below. A tyipicalcascaded control system is presented in the figure below.(a) When sketching the root locus, if necessary, make use of the asymptotes finding oa and O, that are theintersecting point and angles with the real axis, respectively with the following formula,E finite poles-E finite zeros#finite poles-#finite pzeros(2k+1)aand ea =, where k = 0,±1,±2, ..#finite poles-#finite pzeros(b) If the root locus intersects the jo-axis, find the values of poles at crossing points, the value of gain K atthe crossings points and write the range of gain K making the system stable.(c) If there are complex poles find the angle of departure.(d) Find the breakaway and break-in points if they exist.(e) Plot the root-locus of the system for the positive values of gain in MATLAB.(f) Repeat the same steps for a PID controlled positioning system that has the following transfer functions.K(s+4)(s+0.5)1Ge(s) =and Gp(s) =(s+2)(s²+10s+41)R(s)C(s)Ge(s)| Gp(s)Solution 9.

Answered: Image /qna-images/answer/a6ca7f83-905f-496b-93a6-84e3178cc426.jpg

Question8. Problem 9. For a similar PD controlled positioning system given in the previous problem, where Gc(s) = K(s+ 4) and Gp(s) %3D s(s+2)(s²+10s+41) sketch the root-locus of the system for K = 1 by means of the computations requested below. A tyipical cascaded control system is presented in the figure below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding oa and O, that are the intersecting point and angles with the real axis, respectively with the following formula, (2k+1)# #finite poles-#finite pzeros' (b) If the root locus intersects the jw-axis, find the values of poles at crossing points, the value of gain K at Σinite poles- Σ δnite zeros Og = #finite poles-#finite pzeros and 0a = where k = 0,±1,±2, .. the crossings points and write the range of gain K making the system stable. (c) If there are complex poles find the angle of departure. (d) Find the breakaway and break-in points if they exist. (e) the root-locus of the system for the positive values of gain in MATLAB. (f) Repeat the same steps for a PID controlled positioning system that has the following transfer functions. K(s+4)(s+0.5) Gc(s) = and Gp(s) : %3D (s+2)(s²+10s+41) R(s) (s) Gę(s) Gp(s) Solution 9.

Question8. Problem 9. For a similar PD controlled positioning system given in the previous problem, where Gc(s) = K(s+ 4) and Gp(s) %3D s(s+2)(s²+10s+41) sketch the root-locus of the system for K = 1 by means of the computations requested below. A tyipical cascaded control system is presented in the figure below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding oa and O, that are the intersecting point and angles with the real axis, respectively with the following formula, (2k+1)# #finite poles-#finite pzeros' (b) If the root locus intersects the jw-axis, find the values of poles at crossing points, the value of gain K at Σinite poles- Σ δnite zeros Og = #finite poles-#finite pzeros and 0a = where k = 0,±1,±2, .. the crossings points and write the range of gain K making the system stable. (c) If there are complex poles find the angle of departure. (d) Find the breakaway and break-in points if they exist. (e) the root-locus of the system for the positive values of gain in MATLAB. (f) Repeat the same steps for a PID controlled positioning system that has the following transfer functions. K(s+4)(s+0.5) Gc(s) = and Gp(s) : %3D (s+2)(s²+10s+41) R(s) (s) Gę(s) Gp(s) Solution 9.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.4P

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