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Drawing a Polar Plot using Matlab

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A unity feedback system has a process: (see attachment)

Determine the range of K for which the system is stable by drawing a polar plot.

The radius = K/2 for K > 1 there is P = 1 and N = -1.

Z = N + P = -1 + 1 = 0 and the system is stable for K >1.

I believe the best way to show a polar plot is to use a Nyquist plot in Matlab.

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https://brainmass.com/engineering/electrical-engineering/drawing-polar-plot-using-matlab-174822

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A unity feedback system has a process

Determine the range of K for which the system is stable by drawing a polar plot.

The Nyquist plots with several K have been plot by using BM_polar.m.

From analysis, .
The real part is and the imaginary ...

Solution Summary

This solution of 198 words explains the unity feedback system process and includes Nyquist plots in Matlab that explains a polar plot.

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A two part question and solution

PART1
Finding the periodicity in N of the discrete time signal x(n) = Cos(3pi*Ts.n + pi/4) and then plotting the discrete signal. From this the condition on the sampling period is determined

PART2
It is shown also how to determine the z transform of the composite discrete time signal given by

y(n) = y(n-1) -0.5*y(n-2) +x(n) + x(n-1)

From this the output function due to a step input x(n) = u(n) = 1 is determined as

Y(z) = z^2*(z + 1)/{(z - 1)*(z^2 - z + 0.5)}

Further it is shown how to do the partial expansion of Y(z) into its partial fractions.

From this the inverse z transform to find the output in the time domain due to the step input is determined

two part question and solution

PART1
Finding the periodicity in N of the discrete time signal x(n) = Cos(3pi*Ts.n + pi/4) and then plotting the discrete signal. From this the condition on the sampling period is determined

PART2
It is shown also how to determine the z transform of the composite discrete time signal given by

y(n) = y(n-1) -0.5*y(n-2) +x(n) + x(n-1)

From this the output function due to a step input x(n) = u(n) = 1 is determined as

Y(z) = z^2*(z + 1)/{(z - 1)*(z^2 - z + 0.5)}

Further it is shown how to do the partial expansion of Y(z) into its partial fractions.

From this the inverse z transform to find the output in the time domain due to the step input is determined

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