PID Loop Simulator: Modelling the Process

Description| How it works| Derivative on PV| Process Model| Robustness| PID Tuning| PID Equations

To use the simulator, we need a model of the process. Obtaining the process parameters is known as System Identification.

Most chemical processes fall into one of 2 categories - first order process with dead time (FOPDT) and integrating processes with dead time. This app works with the former. (A simulation of a PI controller on a delay free integrating process is also available on this site, see PI Control of Integrating Process).

An FOPDT process is characterised by 3 parameters:

1. Process Gain - the ratio of the change in process variable to the ratio of the change in manipulated variable

2. Time constant - which measures the speed of response

3. Dead time - time between moving the manipulated variable and start of the process response

One of the most common ways of obtaining these parameters is by doing a step test. To do this, wait for the process to be steady and then step the Manipulated Variable (MV). The process variable (PV) will move as shown below.

First Order Process Model

Calculate the parameters as follows:

Dimensionless Gain = (Change in PV/PV range)/(Change in MV/MV Range)

Time constant = Time taken for the PV to change by 63.2% of the final change

Dead time = Time for the PV to start moving after the change in the MV

For the step response shown in the figure above, Dimensionless Gain = (10/200)/(5/100), where PV range = 200 units and MV range = 100 units

Time constant = 30 sec

Dead time = 60 sec

Key in these parameters into the simulator and study the effects of changing the tuning parameters on the response of the system.

Why 63.2% ?

The response of a delay free first order system is described by:

Change in PV = Process gain x (1 - exp(-Time/Time Constant))x Change in MV

Since the final change in PV = Process gain x Change in MV, this equation can be written as

Change in PV = Final Change in PV x (1 - exp(-Time/Time Constant))

At time = time constant,

Change in PV = (1 - exp(-1)) x Final Change in PV = 0.632 x Final Change in PV or 63.2% of the final change in the PV

I would like to thank Hannu Lehmuskuja to correcting an error in these equations.

System Idenfitication Tool

A powerful but easy to use tool for system identfication is available at the business site

System Identification