Using the Nyquist criterion, find the range of K for

Step 1 of 8

Part A.

We first observe the frequency response at unity gain, then apply scaling to determine the range of stability for the given system.

It is convenient to sketch the Nyquist diagram of the unity gain system as a visual aid.

Step  2 of 8

We then determine the negative real axis crossing. This occurs when .

We choose the positive frequency  based on the Nyquist plot, then compute the real-axis crossing value.

Step 3 of 8

The open loop poles are , and . With this, we know that .

Figure 1 shows that there are no encirclements around -1, so .

For the system to remain stable, . This implies that until  is outside the contour , the gain can be increased.

Hence, the maximum gain possible is

Finally, the range of