Realization

Realization or realisation may refer to:

Music

Other

Realisation (metrology)

The realisation of a unit of measure is the conversion of its definition into reality. The International vocabulary of metrology identifies three distinct ways in which this is done - the first being the realisation of a measurement unit from its definition, the second the reproduction of measurement standards and the third the process of actually adopting a particular artefact as a standard.

In the case of the International System of Units, realisation techniques for the base units base are maintained by the International Bureau of Weights and Measures

Overview

The Oxford English Dictionary defines the word "realise" (also spelt "realize") as "to convert (something imagined, planned, etc.) into real existence or fact." The International vocabulary of metrology identifies three distinct ways in which this is done - the first being the realisation of a measurement unit from its definition, the second the reproduction of measurement standards and the third the process of actually adopting a particular artefact as a standard.

Realization (systems)

Realization, in the system theory context refers to a state space model implementing a given input-output behavior. That is, given an input-output relationship, a realization is a quadruple of (time-varying) matrices such that

with describing the input and output of the system at time .

LTI System

For a linear time-invariant system specified by a transfer matrix, , a realization is any quadruple of matrices such that .

Canonical realizations

Any given transfer function which is strictly proper can easily be transferred into state-space by the following approach (this example is for a 4-dimensional, single-input, single-output system)):

Given a transfer function, expand it to reveal all coefficients in both the numerator and denominator. This should result in the following form:

The coefficients can now be inserted directly into the state-space model by the following approach:

This state-space realization is called controllable canonical form (also known as phase variable canonical form) because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state).