Control Valve Linearization
November 26, 2011
A control valve’s flow characteristic is an X-Y curve that maps the percentage of flow you’ll get for any given valve opening (Figure 1). The design characteristic (also called inherent flow characteristic) of a valve assumes a constant pressure differential across the valve. More relevant to us is the installed characteristic, which is the way the valve operates in the real process. The installed characteristic of a valve can be determined by plotting the measured flow rate at different valve openings. You can do tests on the live process to get this data, or you can get it from the process historian (make sure you use steady-state data).
Figure 1 – A Nonlinear Flow Characteristic
The installed flow characteristic of a control valve directly affects the process gain. It is essential that the installed characteristic is linear (the above plot is a straight line) so that the process gain is constant, regardless of the controller output. If the gradient of the curve varies by more than a factor of two, control loop performance will be noticeably affected. If nothing is done to linearize the valve the controller will have to be detuned to accommodate the maximum process gain. This leads to sluggish control loop response over much of the valve’s operating range.
A nonlinear flow characteristic should be linearized to obtain good control performance throughout the valve’s operating range. This is done with a linearizer (also called a characterizer). The linearizer is a control block, function generator, f(x) curve, or a lookup table, placed between the controller and the valve (Figure 2). Although the linearization can be done in a digital positioner, the DCS/PLC is the best location for it. This allows replacement of the positioner without having to reprogram the linearization curve in the new positioner.
Figure 2 – Linearizing a Nonlinear Valve Characteristic
Linearization is done with an X-Y curve or function generator that is configured to represent the reciprocal (inverse) of the control element’s flow curve (Figure 3).
Figure 3 – How a Linearizer Works
To design the linearizer, you have to first determine the flow characteristic curve of the valve operating in the actual process. For this you should take readings of the flow or process variable (PV) and controller output (CO) under steady-state conditions at various controller output levels. You need a minimum of three (PV, CO) data pairs for this, but four or five would be better for characterizing a nonlinear relationship.
Make sure you span the entire operating range of the controller output, and try to obtain readings spaced equally across the controller output span. You can do process tests to obtain these values, or examine data from your process historian. Then convert the process variable data from engineering units to a percentage of full scale of the measurement.
Sort the data pairs in ascending order, and enter them into a function generator. The PV readings in percent become the X values (input side) and the CO readings become the Y values (output side). Include a (0, 0) point if you don’t already have one in your dataset and be sure to estimate a (100, Y) point also if you don’t have one. Also, if your valve opens as the CO decreases, your Y column will obviously have to reflect this.
For example, you get the following (PV, CO) pairs form historical data: (120, 22); (280, 39); (530, 63). The PV is ranged 0 to 1000 kg/hr. You plot the data and estimate that 1000 kg/hr will occur at about 85%. The characterizer will look like this:
| Flow measurement in percent of full scale | Controller output readings (in %) |
| These values go on the input-side of the linearizer | These values go on the output-side of the linearizer |
| 0 (you must have a zero point) | 0 |
| 12 | 22 |
| 28 | 39 |
| 53 | 63 |
| 100 (you must have a full-scale point) | 85 (this can be an estimation) |
After implementing a linearizer in the DCS or PLC, you can test its accuracy by checking whether the controller output and flow measurement are roughly at the same percentage of full scale. For example: 20% and 50% controller output should result in roughly 20% and 50% flow rate. You should retune the controller after implementing the linearizer because it likely had changed the process gain.
Although this discussion mentioned only control valves, the same applies to other final control elements, like vanes, dampers, feeders, etc.
Stay tuned!
Jacques Smuts
Author of the book Process Control for Practitioners
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