# PID Tuning Fundamentals: Calculating Model Parameters

PostedThursday, November 29,2018 at 12:18 PM Tuning PID control loops involves the collection and analysis of test data as well as the modeling of the associated process dynamics. My last post covered best practices for capturing good data through an effective bump test. Before tuning parameters can be generated, however, it’s necessary to calculate the underlying model parameters. Those parameters are: Process Gain, Process Time Constant, and Process Dead-Time.

The three model parameters can be calculated easily using a trend of your bump test data. The graphic shows how to perform those calculations. It’s worth noting that there are important nuances to the different model parameters that you should keep in mind:

• Process Gain: Process Gain (KP) is the sensitivity or “how far” variable. It determines the distance that the Process Variable (PV) travels in response to a change in Controller Output (CO).  The sign – whether positive or negative – is a critical detail as it determines the direction and denotes the type of controller (i.e. direct acting vs. reverse acting). For more about calculating Process Gain, click here.
• Process Time Constant: Process Time Constant (τP) is the “how fast” variable. It describes the speed with which the measured PV responds to changes in CO. More specifically it represents the time needed for the PV to reach 63.2% of its total and final change. For more about calculating Process Time Constant, click here.
• Process Dead-Time: Process Dead-Time (θP) is the “how much delay” variable and it’s by far the easiest to calculate. It represents the amount of delay or lag between a change in CO and the initial response of the PV. It’s often referred to as the killer of control as the larger the Dead-Time the more difficult a process is to control. For more about calculating Process Dead-Time, click here.

Once values for each model parameter are determined they can then be converted into tuning parameters and uploaded to your PID controller. If that procedure is of interest, then be sure to read the next PID Tuning Fundamentals post. Alternatively, sign up for one of our many Practical Process Control workshops to learn a simple, repeatable, and proven technique for tuning PID controllers for optimal performance.