Problem #\'s: 1,2,4,11,13 only For each of the following systems and inputs: Che

Question

Problem #'s: 1,2,4,11,13 only

For each of the following systems and inputs: Check whether the system is stable. If the system is stable, use frequency response to determine the steady state response? For a stable system, the time to reach steady state can be estimated as four times the time constant of the slowest pole. When a system is stable, all poles are in the left half plane (LHP). The slowest pole is the one with the largest (least negative) real part. For each stable system, approximately how long will it take for the steady state condition to be achieved. The time constant is the reciprocal of the absolute value of the real part of the pole location.

Explanation / Answer

1) for the first question the poles are s=-1,-1 and zeroes are complex
Repeated poles and in the left half of the s-plane so marginally stable.
2) the pole is s=-10
in the left half of the s-plane so stable.
4)zeroes are s=0,poles are s=-4
in the left half of the s-plane so stable.

11) poles are s=10 by equation denominator to zero
it lies in the right half of the s plane so it is unstable

14)zeroes =+-2i,poles =-1,-10
imaginary zeroes so marginally stable

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