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Unformatted text preview: C ( s ) 1 ( s + 6)( s 24 s + 8) (a) Let us use proportional control, i.e., C ( s ) = K . Sketch the root locus plot. (No need to ﬁnd the departure angles.) Can we stabilize this system with proportional control? (b) Let us now try proportional derivative control, i.e., C ( s ) = K (1 + K d s ). Find the range of K d such that for each K d in that range we can ﬁnd some K > 0 to stabilize the system. (c) Let C ( s ) be a PD controller with K d = 1. Sketch the root locus plot. Find the value of K for which system displays sustaining oscillations. Determine the frequency of oscillations. Q4. Consider the below system. Take m = 1kg and b = 1Ns/m. Sketch the root locus plot as the spring gets stiﬀer, i.e., k : 0 → ∞ N/m. What can we say about the relation between the settling time and the stiﬀness of the spring? k x f m f x b...
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 Spring '10
 erkmen
 TS, Root Locus Plot

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