Zero-Pole Cancellation in Transfer Functions

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

[more]

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 "·".

[less]

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


Details


Snapshots



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send