G(s) = 2e-Ts / s + 1 Note: Do not attempt to approximate e-Ts. Assume the time d
ID: 1860303 • Letter: G
Question
G(s) = 2e-Ts / s + 1 Note: Do not attempt to approximate e-Ts. Assume the time delay T = 0 sec. Draw the Nyquist plot of G(s) and use Nyquist criterion to determine the stability of the closed-loop system. If it is stable, find the gain margin and phase margin using the Bode plots of G(s). Assume the time delay T = 1 sec. Draw the Nyquist plot of G(s) and use Nyquist criterion to determine the stability of the closed-loop system. If it is stable, find the gain margin and phase margin using the Bode plots of G(s). Assume the time delay T = 2 sec. Draw the Nyquist plot of G(s) and use Nyquist criterion to determine the stability of the closed-loop system. If it is stable, find the gain margin and phase margin using the Bode plots of G(s). Comment on the effect of the time delay on the stability. Hint: F(j omega) = G(j omega) = where theta = tan-1 omega.Explanation / Answer
Nyquist Plots are a way of showing frequency responses of linear systems. There are several ways of displaying frequency response data, including Bode' plots and Nyquist plots.
Bode' plots use frequency as the horizontal axis and use two separate plots to display amplitude and phase of the frequency response.
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Nyquist plots display both amplitude and phase angle on a single plot, using frequency as a parameter in the plot.
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Nyquist plots have properties that allow you to see whether a system is stable or unstable. It will take some mathematical development to see that, but it's the most useful property of Nyquist plots.
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Undersea telephone cables needed to be reliable, and to have a constant gain that did not change as the amplifier aged. In those days, electronic amplifiers were constructed with tubes, and tubes had gains that could change dramatically as they aged.
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A Nyquist plot is a polar plot of the frequency response function of a linear system.
That means a Nyquist plot is a plot of the transfer function, G(s) with s = jw. That means you want to plot G(jw).
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G(jw) is a complex number for any angular frequency, w, so the plot is a plot of complex numbers.
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The complex number, G(jw), depends upon frequency, so frequency will be a parameter if you plot the imaginary part of G(jw) against the real part of G(jw).
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