(1) Please answer the following questions: (a) Root loci are usually plotted for variations in the gain. Sometimes we ar

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1 Please Answer The Following Questions A Root Loci Are Usually Plotted For Variations In The Gain Sometimes We Ar 1 (43.51 KiB) Viewed 22 times

(1) Please answer the following questions: (a) Root loci are usually plotted for variations in the gain. Sometimes we are interested in the variation of the closed-loop poles as other parameters are changed. Consider a unity feedback system with the following forward transfer function d) +8) 1015** Stadt G(s)=- 10(s+a) s(3+1)(8+8) SIS Before drawing the root locus, the characteristic equation should be converted into a proper form. Please write the correct form. (5 points) Answer: (b) Find all the breakaway and/or re-entry points, if any, for the system with the open- loop transfer function G(s)H(s)=- K(s+1) (5 points) s(s+10) Answer (c) Consider the open-loop transfer function G(s)H(s)-- K (8+1(8+2)(8 +48+8) On the root-locus diagram, find the angle of departure at the designated pole -2+j2 (5 points) Answer: (d) Find the jo-axis crossing points with co> 0 and the corresponding gain K of the root loci of the open-loop transfer function given by G(s)H(s)-- K (6 points) 3(8+3)(8+6) Answer: 0- K- (e) Which of the polar plots shown below is the correct plot for G(jo)-1/[(jo)(1+jost)? (5 points) Answer € OC