Let's zoom in on the Nyquist diagrams corresponding to different gains using the zoom command.

K = 4.5

nyquist(4.5*50, [1 9 30 40])

Note that the Nyquist diagram does not encircle the -1 point.

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

k =4.5;
num = 50;
den = [1 9 30 40];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is stable.

K = 4.6

nyquist(4.6*50, [1 9 30 40])

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 =4.5;
num = 50;
den = [1 9 30 40];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is marginally stable (Note the time axis).

K= 4.7

nyquist(4.7*50, [1 9 30 40])

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 =4.7;
num = 50;
den = [1 9 30 40];
[num1, den1] = cloop (k*num,den);
step(num1,den1)

The system is unstable.

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8/27/96 LJO