# PID tuning improves process efficiency

**Using modeling**

After the bump test is performed and the type of process involved is determined, the next step involves fitting a model to the data. Modeling is one of the best ways to understand process data. A first order plus dead time (FOPDT) dynamic process model is usually sufficient to describe the process response and allow calculation of good tuning constants.

In this model, the PV is the measured process variable and the CO signal is the manipulated variable. The FOPDT model is simple (low order and linear), thus it only approximates the behavior of the real process. It’s represented by the following equation:

**Lumped parameter process model**

The lumped parameter model is an FOPDT model. This model describes the process response with simple linear equations comprised of three parameters: gain (), time constant (), and dead time ().

For the lumped parameter model, two forms of models are required depending on the nature of the process control loop: the self-regulating process (flow, temperature, etc.) and the integrating process (level).

Because an integrating process is more difficult to control, a different model must be used to describe this type of process, which is described by this equation:

**Tuning correlation**

There are many different tuning correlation methods used to calculate the PID tuning constants.

Ziegler-Nichols and Cohen-Coon are the two most popular techniques for calculating tuning constants. These two techniques emphasize speed of response. Internal model control (IMC), also referred to as the “Lambda rules,” offers a robust alternative that balances speed of response with controller stability or robustness. IMC tuning can be used for linear and nonlinear processes, and it produces a smoother FOPDT response than other techniques.

IMC tuning is based on the concept that ideal control is possible with an exact model of the process. However, a mismatch between the model and the actual process can occur because of external disturbances that affect the process, which can lead to faulty results. As a result, IMC was designed to have methods for compensating for disturbances and modeling error, including filters and compensators in the higher frequency domain where many errors occur in other models.

Like other tuning procedures, a step test must be performed with IMC to determine the process characteristics. After determining the lumped parameter process model, a desired closed loop time constant () for the control loop must be selected.

If the closed-loop time constant is too large, a slow control loop will result. Therefore, a smaller value will create a faster control loop. But if the closed-loop time constant ( is set to be shorter than the FOPDT process time constant (), the advantages of IMC tuning will disappear.

Generally, the value for should be set between one and three times the value of (). In many cases, * = 3 x * is optimal to achieve a very stable control loop. Therefore, after determining the FOPDT process model, the IMC technique has one single tunable parameter: the closed-loop time constant. The controller speed is made more aggressive or more conservative by changing the closed-loop time constant.

IMC has one drawback in that the controller’s integral time is set to equal the process time constant. A process with a very long time constant means the controller will also have a very long integral time—and long integral times lead to very slow recoveries from disturbances.

Properly tuning a PID controller isn’t a simple process, but it’s one of the best methods for improving productivity, quality, and safety in a process. By achieving a stable regulatory control system through improved PID tuning, the SV can be safely moved closer to the constraint while reducing the variability of the PV, thus reducing inefficiencies in the process.

However, collecting data and performing all of the modeling mathematics can be difficult and time consuming. Fortunately, advanced software can simplify PID controller tuning and reduce the possibility of error (see Figure 3).

Whether PID loop tuning is performed manually or with assistance from loop tuning software, the resulting improvements in the performance of each control loop will lead to significant overall performance gains throughout the process plant.

*Dr. Merle Likins, PE, retired, has undergraduate and graduate degrees in chemical engineering from the University of Louisville. He is a licensed professional engineer in five states and has more than 35 years of experience in process automation. Dr. Likins has an extensive background in petroleum and chemical processes. He also has many years of experience in multivariable control, online process models, and online optimization. Prior to retirement, Dr. Likins worked with Yokogawa Corp. of America from 1992-2013.*

This article appears in the Applied Automation supplement for *Control Engineering *and *Plant Engineering. *