contolshw5

# contolshw5 - >> pzmap(sys1>>...

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Problem 1 (a) >> num = [1 1.2 3.1]; >> den = [1 11 13 30]; >> [r,p,k] = residue(num,den) r = 0.9796 0.0102 - 0.0018i 0.0102 + 0.0018i p = -10.0000 -0.5000 + 1.6583i -0.5000 - 1.6583i >> sys1 = tf(num,den) Transfer function: s^2 + 1.2 s + 3.1 ------------------------ s^3 + 11 s^2 + 13 s + 30 >> pzmap(sys1) The dominant pole is –10, -0.5 + 1.6583i and –0.5 – 1.6583i cancels.

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Problem 1 (b) >> num = [1 2.1]; >> den = [1 10 41 76 52]; >> [r,p,k] = residue(num,den) r = -0.0960 + 0.0530i -0.0960 - 0.0530i 0.1920 0.0200 p = -3.0000 + 2.0000i -3.0000 - 2.0000i -2.0000 -2.0000 The dominant pole is –2, –3.0 + 2.0i and -3.0 – 2.0i.
Problem 1 ( c ) >> num = [1 -1.2]; >> den = [1 11 8 -20]; >> [r,p,k] = residue(num,den) r = -0.1273 0.1333 -0.0061 p = -10.0000 -2.0000 1.0000 The dominant pole is -2.0 and 1.0 is cancelled.

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Problem 2 >> num = [1 6.2 37.7]; >> den = [1 24 247 1518 5486 10944 8840]; >> sys1=tf(num,den) Transfer function: s^2 + 6.2 s + 37.7 -------------------------------------------------------- s^6 + 24 s^5 + 247 s^4 + 1518 s^3 + 5486 s^2 + 10944 s + 8840

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Unformatted text preview: >> pzmap(sys1) >> sgrid >> [r,p,k]=residue(num,den) r =-0.0024 0.0003 - 0.0002i 0.0003 + 0.0002i-0.0132 + 0.0117i-0.0132 - 0.0117i 0.0282 p =-10.0000 -3.0000 + 5.0000i-3.0000 - 5.0000i-3.0000 + 2.0000i-3.0000 - 2.0000i-2.0000 Step Response of 6 th order vs. 4 th order system Step Response of 6 th order vs. 3 rd order system Step Response of 6 th order vs. 4 th order system >> sys0=tf(num0,den0) MATLAB CODE Transfer function: s^2 + 6.2 s + 37.7-------------------------------------------------------------s^6 + 24 s^5 + 247 s^4 + 1518 s^3 + 5486 s^2 + 10944 s + 8840 >> step(sys0) >> hold off >> step(sys0) >> hold on >> num2 = [0.0043]; >> den2 = [1 8 25 26]; >> sys2 = tf(num2,den2) Transfer function: 0.0043-----------------------s^3 + 8 s^2 + 25 s + 26 >> step(sys2) >> hold off >> num3=[0.0043]; >> den3=[1 18 105 276 260]; >> sys3=tf(num3,den3) Transfer function: 0.0043------------------------------------s^4 + 18 s^3 + 105 s^2 + 276 s + 260 >> step(sys0) >> hold on >> step(sys3)...
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contolshw5 - >> pzmap(sys1>>...

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