PID Tuning Tips - How to Linearize Your Process

Linearize Your Process - Get Optimal Response at All Production Rates

by John Gerry, P.E.


Click here to see the complete presentation in more detail as a web-cast.


A non-linear process will have different response across the operating range. It will be sluggish at one end of the range and comparatively faster or even oscillatory at the other.


Setpoint changes in different ranges shows non-linearity.  Stable at the low end, oscillatory towards the high end.


In the graph taken from a flow loop, the setpoint is yellow, the process variable white and controller output green. This loop is stable where the first setpoint change is made. At the second setpoint change, the loop is getting oscillatory at the higher value of the controller output.


Controller in manual.  Equal changes in output, yield unequal changes in PV in the same non-linear process.


This is the same non-linear flow loop. The controller is in manual and colored green. The process variable or flow is white. We changed the controller output by equal intervals. At the lower part of the range the flow changed very little. When the controller outputs gets higher, the flow changes a lot. This is another way to see the non-linearity.


PV plotted against CO.  Same change in CO produces different change in PV.This graph is created by taking the controller output from the previous graph and plotting it against the flow or PV. This is called the process characteristic and is another way to see the non-linearity in the loop.


For example, a change in controller output represented by distance between the green lines, causes a change in PV or flow represented by the distance between the lavender lines.


You can see the non-linearity by looking at the same change in controller output at different parts of the range. At the low end of the controller output range, the controller output change causes a small change in PV. This same change in controller output at the higher end of the range causes a much larger change in flow. The process has a small gain at lower controller outputs and a high gain at higher controller outputs.


 If the maximum gain of the process divided by the minimum gain is larger than 2 or 3 then characterization will help the performance by a factor of 2 or 3.


Linearize the process with a characterizer block at the output of the controller.Add a characterizer block at the controller output as circled in green. Many control systems already have characterizer blocks you can add to the controller output.


What goes in the block is critical of course. The characterizer should re-map the controller output so the net effect is that the controller sees a linear process. In a sense, the characterizer cancels the non-linearity of the process. It does this by using a shape that is opposite that of the process characteristic.


ExperTune PID Tuner finds the code that linearizes your process.


 Using the code on the right in the characterizer block, linearizes our flow loop. The last part of the code, underlined in red, handles where the controller output or CO is large. A red arrow points to this same area on the process characteristic. When the controller output or CO is large, the code multiplies the CO by 0.5627 to find the final output. 0.5627 is circled in green. This small multiplier compensates for the large process gain at larger CO's.

   ExperTune PID Tuner X-Y pair list that linearizes the process.

Many control systems let you enter the characterizer "code" as an X-Y pair list as shown here on the right.


ExperTune's Advanced software includes a characterizer wizard that will build the best characterizer for you based on plant data you collect. It let's you choose the type of characterizer to match your control system and you can graphically customize it by dragging, adding or deleting its design boxes.


ExperTune's software also includes a pH characterizer, but this is a subject for another presentation.


Click here to see the complete presentation in more detail as a web-cast.


This article was written and provided by John Gerry P.E., president of Expertune.  Expertune designs pre-packaged industrial software which maximizes productivity and efficiency and reduces waste in the process industries: chemical, pulp and paper, utilities, refining, and food processing.  For more information on Expertune, please visit their website at:


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