4. Place of roots or Evans place

The root locus (or pole locus) method can be applied to pulsed (or sampled) servo systems.

However, we must not forget that, on the one hand, the poles and possibly the zeros of F *(p ) are infinite in number and, on the other hand, the locus recurs periodically with period Ω.

It is, in fact, simpler to consider an Evans locus in the plane of z, where the number of poles and zeros is limited.

The difference between using the p-plane and the z-plane lies in the interpretation of the locus: instability, for example, occurs in the z-plane when the locus crosses the unit circle. This intersection defines a limit value for the gain. The speed of a periodic response depends on the distance separating the real poles from 1; responses are less damped the closer the conjugate poles are to the unit circle. Figure