Identified Parameters are Closer to the Physical Coefficients
Most physical phenomena are more transparent in a continuous-time setting, as the models of a physical system obtained from the application of physical laws are naturally in a continuous-time form, such as differential equations. A continuous-time model is preferred to its discrete-time counterpart in the situation where one seeks a model that represents an underlying CT physical system and wishes to estimate parameter values that have a physical meaning, such as time constants, natural frequencies, reaction times, elasticities, mass values, etc.
While these parameters are directly linked to the CT model, the parameters of discrete-time models are a function of the sampling interval and do not normally have any direct physical interpretation.
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Illustration with a Simple Mechanical System
For example, consider a mechanical system represented by the following second-order continuous-time transfer function model:
1
G(s)= --------------
ms^2 + bs + kwhere s denotes the Laplace transform variable while the parameters represent the mass, elasticity and friction coefficients that have a direct physical meaning.
Now, a discrete-time model of the same process will take the following form:
b0z + b1
G(z)= ----------------
z^2 + a1z + a2where z denotes the Z-transform variable. The parameters of the corresponding discrete-time model are a function of the sampling period and do not have any direct physical meaning.
Continuous-time Models are Preferred in Most Scientific Areas
In many areas such as, for example, astrophysics, economics, mechanics, environmental science and biophysics, one is interested in the analysis of the physical parameters of the considered system. In these areas, the direct identification of continuous-time models has definite advantages.
Additional Information
For more information on identification of continuous-time dynamic models visit the CONTSID Toolbox web page.