Homework 2-merged

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Georgia Institute Of Technology *

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3531

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Mechanical Engineering

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Feb 20, 2024

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ae 3531 homework 2 problem 4 num1 = [0.5 1]; den1 = [1]; sys1 = tf(num1,den1) sys1 = 0.5 s + 1 Continuous-time transfer function. Model Properties num2 = [10]; den2 = [1 2 0]; sys2 = tf(num2,den2) sys2 = 10 --------- s^2 + 2 s Continuous-time transfer function. Model Properties sysg = series(sys1,sys2) sysg = 5 s + 10 --------- s^2 + 2 s Continuous-time transfer function. Model Properties sys = feedback(sysg, [1]) sys = 5 s + 10 -------------- s^2 + 7 s + 10 Continuous-time transfer function. Model Properties problem 6 s = tf( 's' ) s = 1

s Continuous-time transfer function. Model Properties sys1 = 12.8*0.1/(s^2 + 2.8*s + 1.6 +0.64*0.1); sys2 = 12.8*1/(s^2 + 2.8*s + 1.6 +0.64*1); sys3 = 12.8*10/(s^2 + 2.8*s + 1.6 +0.64*5); sys4 = 12.8*10/(s^2 + 2.8*s + 1.6 +0.64*10); sys5 = 12.8*25/(s^2 + 2.8*s + 1.6 +0.64*25); p1 = pole(sys1); p2 = pole(sys2); p3 = pole(sys3); p4 = pole(sys4); p5 = pole(sys5); h = pzplot(sys1,sys2,sys3,sys4,sys5) h = resppack.mpzplot grid on step(sys1) 2

step(sys2) 3

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step(sys3) step(sys4) 4

step(sys5) 5

problem 7 s = tf( 's' ) s = s Continuous-time transfer function. Model Properties sys1 = 25/(s^2 + 12*s + 25); sys2 = 25/(s^2 + 10*s + 25); sys3 = 25/(s^2 + 8*s + 25); sys4 = 25/(s^2 + 6*s + 25); sys5 = 25/(s^2 + 4*s + 25); sys6 = 25/(s^2 + 2*s + 25); sys7 = 25/(s^2 + 25); sys8 = 100/(s^2 + 10*s + 25); sys9 = 100/(s^2 + 8*s + 100); hold on step(sys1) step(sys2) step(sys3) step(sys4) step(sys5) step(sys6) step(sys7) step(sys8) step(sys9) legend( 'sys1' , 'sys2' , 'sys3' , 'sys4' , 'sys5' , 'sys6' , 'sys7' , 'sys8' , 'sys9' ) xlim([0 10]) hold off 6

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tfvec = [sys1 sys2 sys3 sys4 sys5 sys6 sys7 sys8 sys9] tfvec = From input 1 to output: 25 --------------- s^2 + 12 s + 25 From input 2 to output: 25 --------------- s^2 + 10 s + 25 From input 3 to output: 25 -------------- s^2 + 8 s + 25 From input 4 to output: 25 -------------- s^2 + 6 s + 25 From input 5 to output: 25 -------------- s^2 + 4 s + 25 From input 6 to output: 25 -------------- s^2 + 2 s + 25 7

From input 7 to output: 25 -------- s^2 + 25 From input 8 to output: 100 --------------- s^2 + 10 s + 25 From input 9 to output: 100 --------------- s^2 + 8 s + 100 Continuous-time transfer function. Model Properties for i = 1:1:9 p = pole(tfvec(i)) temp = stepinfo(tfvec(i)) end p = 2×1 -9.3166 -2.6834 temp = struct with fields: RiseTime: 0.8743 TransientTime: 1.5845 SettlingTime: 1.5845 SettlingMin: 0.9011 SettlingMax: 0.9985 Overshoot: 0 Undershoot: 0 Peak: 0.9985 PeakTime: 2.5605 p = 2×1 -5 -5 temp = struct with fields: RiseTime: 0.6717 TransientTime: 1.1668 SettlingTime: 1.1668 SettlingMin: 0.9008 SettlingMax: 0.9999 Overshoot: 0 Undershoot: 0 Peak: 0.9999 PeakTime: 2.3900 p = 2×1 complex -4.0000 + 3.0000i -4.0000 - 3.0000i temp = struct with fields: RiseTime: 0.4936 TransientTime: 0.7512 SettlingTime: 0.7512 SettlingMin: 0.9018 SettlingMax: 1.0152 Overshoot: 1.5165 Undershoot: 0 Peak: 1.0152 PeakTime: 1.0477 8

p = 2×1 complex -3.0000 + 4.0000i -3.0000 - 4.0000i temp = struct with fields: RiseTime: 0.3711 TransientTime: 1.1887 SettlingTime: 1.1887 SettlingMin: 0.9083 SettlingMax: 1.0948 Overshoot: 9.4773 Undershoot: 0 Peak: 1.0948 PeakTime: 0.7829 p = 2×1 complex -2.0000 + 4.5826i -2.0000 - 4.5826i temp = struct with fields: RiseTime: 0.2930 TransientTime: 1.6819 SettlingTime: 1.6819 SettlingMin: 0.9065 SettlingMax: 1.2537 Overshoot: 25.3741 Undershoot: 0 Peak: 1.2537 PeakTime: 0.6908 p = 2×1 complex -1.0000 + 4.8990i -1.0000 - 4.8990i temp = struct with fields: RiseTime: 0.2411 TransientTime: 3.9192 SettlingTime: 3.9192 SettlingMin: 0.7228 SettlingMax: 1.5265 Overshoot: 52.6542 Undershoot: 0 Peak: 1.5265 PeakTime: 0.6447 p = 2×1 complex 0.0000 + 5.0000i 0.0000 - 5.0000i temp = struct with fields: RiseTime: NaN TransientTime: NaN SettlingTime: NaN SettlingMin: NaN SettlingMax: NaN Overshoot: NaN Undershoot: NaN Peak: Inf PeakTime: Inf p = 2×1 -5 -5 temp = struct with fields: RiseTime: 0.6717 TransientTime: 1.1668 SettlingTime: 1.1668 SettlingMin: 3.6033 SettlingMax: 3.9997 Overshoot: 0 Undershoot: 0 9

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Peak: 3.9997 PeakTime: 2.3900 p = 2×1 complex -4.0000 + 9.1652i -4.0000 - 9.1652i temp = struct with fields: RiseTime: 0.1465 TransientTime: 0.8409 SettlingTime: 0.8409 SettlingMin: 0.9065 SettlingMax: 1.2537 Overshoot: 25.3741 Undershoot: 0 Peak: 1.2537 PeakTime: 0.3454 problem 9 s = tf( 's' ) s = s Continuous-time transfer function. Model Properties sys = 17/(s^2+2*s+17) sys = 17 -------------- s^2 + 2 s + 17 Continuous-time transfer function. Model Properties stepinfo(sys) ans = struct with fields: RiseTime: 0.3054 TransientTime: 3.4340 SettlingTime: 3.4340 SettlingMin: 0.7922 SettlingMax: 1.4559 Overshoot: 45.5913 Undershoot: 0 Peak: 1.4559 PeakTime: 0.7829 sysa = 17/((s^2+2*s+17)*(s+0.01)); sysb = 17/((s^2+2*s+17)*(s+0.1)); sysc = 17/((s^2+2*s+17)*(s+1)); sysd = 17/((s^2+2*s+17)*(s+10)); syse = 17/((s^2+2*s+17)*(s+100)); subplot(2,1,1) hold on 10

step(sys) step(sysa) step(sysb) step(sysc) step(sysd) step(syse) xlim([0 20]) hold off sysf = (17*(s+0.01))/(s^2+2*s+17); sysg = (17*(s+0.1))/(s^2+2*s+17); sysh = (17*(s+1))/(s^2+2*s+17); sysi = (17*(s+10))/(s^2+2*s+17); sysj = (17*(s+100))/(s^2+2*s+17); subplot(2,1,2) hold on step(sys) step(sysf) step(sysg) step(sysh) step(sysi) step(sysj) hold off 11

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