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