Nyquist Criterion with an Unstable Pole

The Nyquist Criterion determines closed-loop stability from the open-loop frequency response. For a system with an open-loop pole in the right-half plane, the closed-loop system is stable only if the Nyquist plot encircles the critical point -1 counterclockwise an equal number of times.

Exploring the effect of Gain K

You can use the interactive module to see how the gain affects the Nyquist plot and stability.

1. Open the Nyquist Criterion with an Unstable Pole interactive module.
2. Set Gain K to 2. Observe the Nyquist plot encircling the critical point -1 counterclockwise once. The system status is Stable.
3. Change Gain K to 0.5. The radius of the Nyquist plot decreases and it no longer encircles -1. The winding becomes 0, and the status changes to Unstable.
4. Change Frequency to -1 with K = 2. Observe the selected point moving to Loop real -1.0 and Loop imaginary 1.0.