Zero-Pole Cancellation in Transfer Functions

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When the transfer function of a system has poles in the right half-plane of the complex numbers, the system is unstable. While it is theoretically possible to design a proportional-derivative (PD) compensator to cancel the poles, in practice is it is difficult to create perfect pole-zero cancellation due to imprecision in the model.


This Demonstration shows the locus root of a unity (negative) feedback system for three scenarios:

1. The plant (i.e. the instability) is not compensated, and the closed-loop system is unstable for some values of the gain.

2. The plant is compensated with a zero placed precisely at the unstable pole. Thus, the closed-loop system is stable for any value of gain.

3. There is a mismatch between the position of the zero and the unstable pole, causing the closed-loop system to be unstable.

Poles are marked by a cross "×" and zeros by a dot "·".


Contributed by: Hugo Tadashi (March 2011)
Open content licensed under CC BY-NC-SA



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