test2-soln - EET309 Test2-Soln 1. From block diagram in...

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Unformatted text preview: EET309 Test2-Soln 1. From block diagram in Figure 1 below. Figure 1 (a) Write down the open loop transfer function G(s)H(s) for the system in Figure 1. (2 Marks) O.L.T.F, ( 29 ( 29 ( 29( 29 3 1 + + = s s s K s H s G (b) Sketch root locus as K is varied from 0 to ∞ . (10 Marks) Angle of asymptotes, θ a = ±60º, ±180º Point of intersect, 33 . 1 3 3 1- =-- = a σ Breakaway point, ( 29 s s s K 3 4 3 3 + +- = ( 29 3 8 3 2 = + +- = s s ds dK 2 111 . 3 67 . 2 1 3 8 2 ±- = = + +- s s s s=-2.21 and -0.45 Therefore breakaway is -0.45 Crossing at j ϖ axis : ( 29 732 . 1 3 3 1 ....... .......... 3 4 3 4 3 2 3 3 3 ± = = → = = + +-- = = + + + ± ϖ ϖ ϖ ϖ ϖ ϖ ϖ K j j j s K s s s ( 29 1 1 + s s R(s) ( 29 3 + s K C(s) E(s) EET309 Test2-Soln -10-8-6-4-2 2 4-6-4-2 2 4 6 Root Locus Real Axis Imaginary Axis (c) What is the value of K when the system is marginally (critically) stable....
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test2-soln - EET309 Test2-Soln 1. From block diagram in...

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