Question

Objective: is to test your understanding of the root locus sketch, and to see how MATLAB can help you Plot the root-locus for the following unity-feedback systems. You should apply the 10 Rules we dis- cussed in class; you should find breakaway/break-in points, angle of departures, asymptotes, jw-axis crossings, and range of K such that the system is stable. You should also verify your solutions via MATLAB 5. Draw the Root-Locus given that this is the characteristic polynomial of the closed-loop system: (1 +K)s2 + (2 – 2K)s +2K = 0. Hint: for Problem 5, you should write the polynomial as 1 +KG(s) = 0, and then follow the typical steps to draw the root-locus.

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Abdul-Rahim Taysir

Answer 1

rivers that (1+1) s? + (2-26) Stak=0 s² tis? +28 - 2kstakao s²+28 tk (8² 28+2)=0 8²+28 s²_28+2 To fiand break point- dklas=0 (5328+2)(23+2) -(83+287(23-2) ds 8²-28+2) 28² +4 ~ 288-287 us=0 48? +45+4=0 r $?_ S-1=0 (-1) ± Je-lo?_4010(-1) 8o de 2 283 - S = 2 S = 1t55 l^6187 - 0-618

at kal 282 +2=0 so root Is=ts locus is jo 153.430 82153 0-618 >> Pets o P-153.400 - ***