## Process Model Structure Specification

This topic describes how to specify the model structure in the estimation procedures Estimate Process Models Using the App and Estimate Process Models at the Command Line.

In the System Identification app, specify the model structure by selecting the number of real or complex poles, and whether to include a zero, delay, and integrator. The resulting transfer function is displayed in the Process Models dialog box.

At the command line, specify the model structure using an acronym that includes the following letters and numbers:

• (Required) `P` for a process model

• (Required) `0`, `1`, `2` or `3` for the number of poles

• (Optional) `D` to include a time-delay term ${e}^{-s{T}_{d}}$

• (Optional) `Z` to include a process zero (numerator term)

• (Optional) `U` to indicate possible complex-valued (underdamped) poles

• (Optional) `I` to indicate enforced integration

Typically, you specify the model-structure acronym as an argument in the estimation command `procest`:

• `procest(data,'P1D')` to estimate the following structure:

`$G\left(s\right)=\frac{{K}_{p}}{1+s{T}_{p1}}{e}^{-s{T}_{d}}$`
• `procest(data,'P2ZU')` to estimate the following structure:

`$G\left(s\right)=\frac{{K}_{p}\left(1+s{T}_{z}\right)}{1+2s\zeta {T}_{w}+{s}^{2}{T}_{w}^{2}}$`
• `procest(data,'P0ID')` to estimate the following structure:

`$G\left(s\right)=\frac{{K}_{p}}{s}{e}^{-s{T}_{d}}$`
• `procest(data,'P3Z')` to estimate the following structure:

`$G\left(s\right)=\frac{{K}_{p}\left(1+s{T}_{z}\right)}{\left(1+s{T}_{p1}\right)\left(1+s{T}_{p2}\right)\left(1+s{T}_{p3}\right)}$`