Homework 2 Questions pt.1 - P EE 3151 Homework 2 Fall 2019 Total 80 points Due Due Monday 1 For the block diagram shown below(1 draw the equivalent

# Homework 2 Questions pt.1 - P EE 3151 Homework 2 Fall 2019...

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Unformatted text preview: P EE 3151 Homework # 2 Fall 2019 Total: 80 points; Due: September 30, 2019 Due Monday 1. For the block diagram shown below, (1) draw the equivalent signal flow graph of the system, (2) find E(s)/R(s), and (3) find C(s)/R(s). (15 points) GA G1 G G3 H2 2. For the two feedback systems shown below, (a) Find the closed-loop transfer functions T1 and T2 for each system, (b) Show that T1 = T2 = 100 when Ki = K2 = 100, and (c) Compare the sensitivities of the two systems with respect to the parameter K1 for the nominal values of K1 = K2 = 100. (20 points) T. = Ville R(S) K C (s) 1- 009 9 4, MZ (1) 0.0099 -.09 R(S) K1 K2 c(s ) 1 +. 094, + , 09 *2 + , 60814 , 42 L. =09 k. 0.09 ( 100 ) ( 100) 0.09 LZ =- 09 k z 1 +. 09 ( 160 ) (2) 4 = 1 -(-,0941 - 0942 ) +.008 *. 1/2 3. For a unity feedback control system with controller Gc(s) = K and plant Gp(s) = 1/[s(s+K1)], (a) calculate the sensitivity of the closed-loop transfer function to changes in K1, and (b) how would you select a value for K to minimize the effects of K1 variation. (10 points) 4. Construct the signal flow graph for the following set of simultaneous equations: X2 = A21 X1 + A23 X3, X3 = A31 X1 + A32 X2 + A33 X3, X4 = A42X2 + A43X3. Identify the (a) input node, (b) output node, (c) forward paths, (d) feedback paths, and (e) self-loop. (15 points)...
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