Let's verify our results by zooming in on the Nyquist plot for different gains using the zoom command.

K = 0.79

nyquist(0.79*[1 10 24], [1 -8 15])

Note that the Nyquist diagram does not loop around the -1 point.

We will now look at our step response. Remember that we must look at the closed-loop step response.

k =0.79;
num = [1 10 24];
den = [1 -8 15];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is unstable.

K = 0.80

nyquist(0.80*[1 10 24], [1 -8 15])

Note that the Nyquist diagram goes right through the -1 point.

We will now look at our step response. Remember that we must look at the closed-loop step response.

k =0.80;
num = [1 10 24];
den = [1 -8 15];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is marginally stable.

K = 0.81

nyquist(0.81*[1 10 24], [1 -8 15])

Note that the Nyquist diagram encircles the -1 point.

We will now look at our step response. Remember that we must look at the closed-loop step response.

k =0.81;
num = [1 10 24];
den = [1 -8 15];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is stable.

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8/27/96 LJO