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SYSSIMHW6(1)

# SYSSIMHW6(1) - Problem1 a Splanepoles lambda= 0.0611...

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Problem 1: a) S-plane poles lambda = -0.0611 + 0.9356i -0.0611 - 0.9356i -0.1476 + 0.3876i -0.1476 - 0.3876i b) Frequency Response: Using bode plot for this:

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-120 -100 -80 -60 -40 -20 0 Magnitude (dB) 10 -2 10 -1 10 0 10 1 -360 -270 -180 -90 0 Phase (deg) Bode Diagram Frequency (rad/sec) C) AB-3 Stability Region:
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 AB3 Stability region real(LT) Imaginary(LT) The regions from this plot are 1) Absolutely unstable. 2) relatively stable. 3) relatively unstable. D) i)Absolutely unstable. T=1.7

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-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 LambdaT plot for absolutely unstable T real axis Imaginary axis ii)Relatively stable. T=0.2
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 LambdaT plot for Relatively stable T real axis Imaginary axis iii)Relatively unstable. T=0.71 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 LambdaT plot for Relatively Unstable T real axis Imaginary axis E) Plotting all Z-plane poles:

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Absolutely unstable. T=1.7 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -3 -2 -1 0 1 2 3 Z-plane poles of the system real axis Imaginary axis Relatively stable. T=0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Z-plane poles of the system real axis Imaginary axis   Relatively unstable. T=0.71
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