Learn more about System Identification Toolbox

What Is a Continuous-Time Process Model?

Continuous-time process models are low-order transfer functions that describe the system dynamics using static gain, a time delay before the system output responds to the input, and characteristic time constants associated with poles and zeros. Such models are popular in the industry and are often used for tuning PID controllers, for example. Process model parameters have physical significance.

You can specify different process model structures by varying the number of poles, adding an integrator, or including a time delay or a zero. The highest process model order you can specify in this toolbox is three, and the poles can be real or complex (underdamped modes).

In general, a linear system is characterized by a transfer function G, which is an operator that takes the input u to the output y:

For a continuous-time system, G relates the Laplace transforms of the input U(s) and the output Y(s), as follows:

In this tutorial, you estimate G using different process-model structures.

For example, the following model structure is a first-order, continuous-time model, where K is the static gain, T_p1 is a time constant, and T_d is the input-to-output delay:

About This Tutorial

Preparing Data for System Identification

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