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III.1.a. w=tf(20,[1 0]) Transfer function: 20 s >> ltiview({'step','impulse','bode','nyquist'},w) 0 0.2 0.4 0.6 0.8 1 0 10 20 30 0 0.2 0.4 0.6 0.8 1 19 19.5 20 20.5 21 0 20 40 Magnitude (dB) 10 0 10 1 -91 -90 -89 Phase (deg) -1 -0.5 0 0.5 -10 -5 0 5 10 III.1.b. >> w=tf([20 0],[0.1 1]) Transfer function: 20 s 0.1 s + 1 >> ltiview({'step','impulse','bode','nyquist'},w) 0 0.2 0.4 0.6 0 50 100 150 200 0 0.2 0.4 0.6 -2000 -1500 -1000 -500 0 -50 0 50 Magnitude (dB) 10 0 10 2 0 45 90 Phase (deg) -50 0 50 100 150 200 -100 -50 0 50 100 III.1.c TH1 w=tf(20,[50 1]) Transfer function: 20 50 s + 1 >> ltiview({'step','impulse','bode','nyquist'},w) 0 100 200 300 0 5 10 15 20 0 100 200 300 0 0.1 0.2 0.3 0.4 -50 0 50 Magnitude (dB) 10 -3 10 -2 10 -1 10 0 -90 -45 0 Phase (deg) -5 0 5 10 15 20 -10 -5 0 5 10 TH2 w=tf(20,[100 1]) Transfer function: 20 100 s + 1 >> ltiview({'step','impulse','bode','nyquist'},w) 0 200 400 600 0 5 10 15 20 0 200 400 600 0 0.05 0.1 0.15 0.2 -50 0 50 Magnitude (dB) 10 -4 10 -2 10 0 -90 -45 0 Phase (deg) -5 0 5 10 15 20 -10 -5 0 5 10 III.2. >> G1=tf([1 1],conv([1 3],[1 5])) Transfer function: s + 1 s^2 + 8 s + 15 >> G2=tf([1 0],[1 2 8]) Transfer function: s s^2 + 2 s + 8 >> G3=tf(1,[1 0]) Transfer function: 1 - s >> H1=tf(1,[1 2]) Transfer function: 1 s + 2 >> G13=G1+G3 Transfer function: 2 s^2 + 9 s + 15 s^3 + 8 s^2 + 15 s >> G21=feedback(G2,H1) Transfer function: s^2 + 2 s s^3 + 4 s^2 + 13 s + 16 >> G=G13*G21 Transfer function: 2 s^4 + 13 s^3 + 33 s^2 + 30 s s^6 + 12 s^5 + 60 s^4 + 180 s^3 + 323 s^2 + 240 s >> Gk=feedback(G,1) Transfer function: 2 s^4 + 13 s^3 + 33 s^2 + 30 s s^6 + 12 s^5 + 62 s^4 + 193 s^3 + 356 s^2 + 270 s >> ltiview({'step','impulse'},Gk) 0 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0 1 2 3 4 5 6 7 8 9 -0.1 0 0.1 0.2 0.3 >> Gh=G*1 Transfer function: 2 s^4 + 13 s^3 + 33 s^2 + 30 s s^6 + 12 s^5 + 60 s^4 + 180 s^3 + 323 s^2 + 240 s >> ltiview({'bode','nyquist'},Gk)\ -100 -50 0 Magnitude (dB) 10 -1 10 0 10 1 10 2 -180 -90 0 Phase (deg) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -0.2 0 0.2 III.3.a. >> G1=tf(8,[1 2]) Transfer function: 8 s + 2 >> G2=tf(1,conv([0.5 1],[1 1])) Transfer function: 1 0.5 s^2 + 1.5 s + 1 >> H=tf(1,[0.005 1]) Transfer function: 1 0.005 s + 1 >> G=feedback(G1*G2,H) Transfer function: 0.04 s + 8 0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 10 >> Gk=feedback(G,1) Transfer function: 0.04 s + 8 0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.05 s + 18 >> ltiview({'step','impulse'},Gk) 0 10 20 30 40 50 60 70 80 90 100 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 90 100 -1 0 1 2 >> Gh=G*1 Transfer function: 0.04 s + 8 0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 10 >> ltiview({'bode','nyquist'},Gh) -200 0 200 Magnitude (dB) 10 -1 10 0 10 1 10 2 10 3 -360 -180 0 Phase (deg) -1.5 -1 -0.5 0 0.5 1 -4 -2 0 2 4 [...]... >> w=tf(20, [10 0 10 1] ) Transfer function: 20 -10 0 s^2 + 10 s + 1 Bode Diagram 200 Transfer function: 20 -10 0 s^2 + 15 s + 1 >> bode(w) >> w=tf(20, [10 0 20 1] ) Transfer function: 20 -10 0 s^2 + 20 s + 1 100 50 0 -50 0 -90 Phase (deg) >> bode(w) >> w=tf(20, [10 0 15 1] ) Magnitude (dB) 15 0 -18 0 -270 -360 -3 >> bode(w) >> hold off 10 -2 10 -1 10 Frequency (rad/sec) 0 10 1 10 ... 4 .11 s + 42 >> ltiview({'step','impulse'},Gk) 5 0 -5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 20 10 0 -10 -20 >> Gh=G *1 Transfer function: 0 .1 s + 20 -0.0025 s^4 + 0. 512 5 s^3 + 2.52 s^2 + 4. 01 s + 22 Phase (deg) Magnitude (dB) >> ltiview({'bode','nyquist'},Gh) 200 0 -200 -18 0 -270 -360 -450 -1 10 0 1 10 2 10 10 10 3 20 10 0 -10 -20 -4 -2 0 2 4 6 8 10 12 14 ... 0. 512 5 s^3 + 2.52 s^2 + 4.098 s + 37 .13 >> ltiview({'step','impulse'},Gk) 4 2 0 -2 -4 0 1 2 3 4 5 6 0 1 2 3 4 5 6 20 10 0 -10 -20 >> Gh=G *1 Transfer function: 0.08782 s + 17 .56 0.0025 s^4 + 0. 512 5 s^3 + 2.52 s^2 + 4. 01 s + 19 .56 Phase (deg) Magnitude (dB) >> ltiview({'bode','nyquist'},Gh) 200 0 -200 -18 0 -270 -360 -450 -1 10 0 1 10 2 10 10 10 8 2 x 10 1 0 -1 -2 -2 -1 0 1 2... III.3.c >> G1=tf (17 .564 411 , [1 2]) Transfer function: 17 .56 s+2 >> G2=tf (1, conv([0.5 1] , [1 1])) Transfer function: 1 0.5 s^2 + 1. 5 s + 1 >> H=tf (1, [0.005 1] ) Transfer function: 1 0.005 s + 1 >> G=feedback(G1*G2,H) Transfer function: 0.08782 s + 17 .56 0.0025 s^4 + 0. 512 5 s^3 + 2.52 s^2 + 4. 01 s + 19 .56 >> Gk=feedback(G ,1) Transfer function: 0.08782 s + 17 .56 ... s^2 + 15 s + 1 1 0 -0.5 -1 -1. 5 -2 0 50 10 0 15 0 Time (sec) >> impulse(w) >> hold off 200 250 >> w=tf(20, [10 0 0 1] ) Transfer function: 20 10 0 s^2 + 1 >> nyquist(w) >> hold on >> w=tf(20, [10 0 5 1] ) Transfer function: 20 10 0 s^2 + 5 s + 1 >> nyquist(w) >> w=tf(20, [10 0 10 1] ) Transfer function: 20 -10 0 s^2 + 10 s + 1 Nyquist Diagram 50 >> nyquist(w) 40 >> w=tf(20, [10 0 15 1] ) >> nyquist(w)... s^2 + 5 s + 1 >> step(w) >> w=tf(20, [10 0 10 1] ) Transfer function: 20 -10 0 s^2 + 10 s + 1 Step Response >> step(w) 40 >> w=tf(20, [10 0 15 1] ) 35 Transfer function: 20 -10 0 s^2 + 15 s + 1 30 Amplitude >> step(w) 25 20 >> w=tf(20, [10 0 20 1] ) 15 Transfer function: 20 -10 0 s^2 + 20 s + 1 10 5 0 >> step(w) >> hold off 0 50 10 0 15 0 Time (sec) 200 250 >> w=tf(20, [10 0 0 1] ) Transfer... 10 0 s^2 + 1 >> impulse(w) >> hold on >> w=tf(20, [10 0 5 1] ) Transfer function: 20 10 0 s^2 + 5 s + 1 >> impulse(w) >> w=tf(20, [10 0 10 1] ) Transfer function: 20 -10 0 s^2 + 10 s + 1 Impulse Response 2 >> impulse(w) 1. 5 >> w=tf(20, [10 0 15 1] ) >> impulse(w) >> w=tf(20, [10 0 20 1] ) Transfer function: 20 -10 0 s^2 + 20 s + 1 0.5 Amplitude Transfer function: 20 -10 0 s^2 + 15 ... Diagram 1 0.8 0.6 Imaginary Axis 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.8 -0.6 -0.4 -0.2 0 Real Axis 0.2 0.4 0.6 0.8 >> bode(A,B,C,D) Bode Diagram Magnitude (dB) 0 -50 -10 0 Phase (deg) -15 0 0 -90 -18 0 -270 -1 10 0 10 1 10 Frequency (rad/sec) 2 10 3 10 III .1. d >> w=tf(20, [10 0 0 1] ) Transfer function: 20 10 0 s^2 + 1 >> step(w) >> hold on >> w=tf(20, [10 0 5 1] ) Transfer function: 20 10 0 s^2... >> w=tf(20, [10 0 20 1] ) Transfer function: 20 -10 0 s^2 + 20 s + 1 >> nyquist(w) >> hold off 20 Imaginary Axis Transfer function: 20 -10 0 s^2 + 15 s + 1 30 10 0 -10 -20 -30 -40 -50 -7 -6 -5 -4 -3 Real Axis -2 -1 0 1 8 x 10 >> w=tf(20, [10 0 0 1] ) Transfer function: 20 10 0 s^2 + 1 >> bode(w) >> hold on >> w=tf(20, [10 0 5 1] ) Transfer function: 20 10 0 s^2 + 5 s + 1 >> bode(w)... G1=tf(20, [1 2]) Transfer function: 20 s+2 >> G2=tf (1, conv([0.5 1] , [1 1])) Transfer function: 1 0.5 s^2 + 1. 5 s + 1 >> H=tf (1, [0.005 1] ) Transfer function: 1 0.005 s + 1 >> G=feedback(G1*G2,H) Transfer function: 0 .1 s + 20 -0.0025 s^4 + 0. 512 5 s^3 + 2.52 s^2 + 4. 01 s + 22 >> Gk=feedback(G ,1) Transfer function: 0 .1 s + 20 -0.0025 s^4 + 0. 512 5 . ltiview({'bode','nyquist'},Gh) -200 0 200 Magnitude (dB) 10 -1 10 0 10 1 10 2 10 3 -450 -360 -270 -18 0 Phase (deg) -4 -2 0 2 4 6 8 10 12 14 -20 -10 0 10 20 III.3.c >> G1=tf (17 .564 411 , [1 2]) Transfer function: 17 .56 s + 2 >>. (dB) 10 -1 10 0 10 1 10 2 10 3 -360 -18 0 0 Phase (deg) -1. 5 -1 -0.5 0 0.5 1 -4 -2 0 2 4 III.3.b. >> G1=tf(20, [1 2]) Transfer function: 20 s + 2 >> G2=tf (1, conv([0.5 1] , [1 1])) . 0.8 1 19 19 .5 20 20.5 21 0 20 40 Magnitude (dB) 10 0 10 1 - 91 -90 -89 Phase (deg) -1 -0.5 0 0.5 -10 -5 0 5 10 III .1. b. >> w=tf([20 0],[0 .1 1]) Transfer function: 20 s 0 .1 s + 1 >>

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