4-830 4-cr-Du RoC (I-AB-D 鍋(1) 7(1) = ex₁+ fxx+ JV (1) [a b] [8] acond LT 14 THE USE OF CELL PHONES OR ANY COMMUNICATION DEVICE IS NOT ALLOWED DURING THE EXAM AND WILL RESULT IN YOUR EXAM TO BE TERMINATED. C(S) 1-For the flow graph shown below find the transfer function: G(S) = Mason's gain formula R(S) using (20 PTS) G₁(s) G₂($) G3(S) G4(s) G5(s) R(s) C(s) H₁(s) G8(s) G7(s) Ha(s) H2(s) G6(s) [ 2-8 - 7(1) - ex₁+fxx+Ju(1) [h] [8] ach B. ง A-6-1x2 AB-[ch obyci] 1-4-4-4 stend state in [fs-cles] Tes) fat fuck of stand 5' 1 CA) · Lica (Ex S12= -EWWE Shift -ō L oper chuit i KWA 25+ uninatural freq Eidemping ratio √ C(1)=1-ci (TEL) = 1-2 [ over shoe will 1133 TT- never shed tri rise time te: fall time Ep-11 Brisetting (20 PTS) 2- Use Routh-Hurwitz method to examine the stability of the feedback system that is given by the block diagram shown below: (Hint: Routh-Hurwitz method is applied on a transfer function of a system). X(S) + Σ 40 G(s)= 1 S3+15S+85S+225S2 +274S -30 H(S)=1 Y(S) S' A-B-1x2 -YOU 7(1) = ex₁ + fx₂+ JU (1) A.B. [btch "oby.ci] [a b] [5] ach 51-24 SO-A-B DC 5-0 sted state li[l)-cs] Tes)= 151,2=-EW₁ =jWn√T-E² L 0 Shortō cret LE ofer creuit ī vs. Li/A+ v(5) Kwa Jess Eidamping ratio $25+ Wainatural freq = √1-2 C(t)=1-C [Cos(w√ E "pover sheet tr: rise ti ツイー ה … … … 37t 3. Sketch the Bode magnitude and the phase plots as functions of o for the linear system described by the following transfer function: 1010 (S+10)² G(S)= (S+100)(S+1000)3 (20 PTS) 4. A step input is applied to a unity feedback system that has the following open loop transfer function:G(S) = Find the following: 9 S²+3s+9 a. the natural frequency (20 PTS) b. the damping ratio and type c. the output of the system as a time domain function y(t) d. sketch the output of the system as a time domain function e. the overshoot value of the output response. 5. For the feedback control system shown below, sketch the Root-Locus 0<k<oo on the S-Plane. for (20 PTS) Y(S) X(S) + Σ K H(S)=1 (S+2)(S+6) where: G(s) = (S+1)(S+5)(S+7)(S+9)(S+11) Is the system stable for all values of k? Explain. G(S)