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Gain scheduling and process linearity

Can we really have a linear process nonlinearity? Sure!

January 31, 2011

Dear Control Engineering: I was reading the article on gain scheduling and was trying to relate that to process linearity, or a lack of linearity. How do those all interact?

The example that Vance VanDoren used in his article is a spherical tank, and how the amount of liquid required to change the level by one inch changes a great deal if you compare the top or bottom of the tank with the middle. Manipulating the level is subject to the non-linearity that is intrinsic to that kind of tank. That’s why you need something like gain scheduling.

Some months ago we considered the notion of process linearity and what that means. There are elements of a process that tend to be more linear than others. Some of those elements are unavoidable and part of the nature of how chemicals interact, or they’re determined by the characteristics of the equipment, like the spherical tank. Some of those nonlinear elements have linearizable nonlinearities. That is not a contradiction in terms. In the case of the spherical tank, you can predict exactly how the fill rates behave at each end and your gain scheduling scheme can take that into consideration. If you can characterize it properly, it ceases to be a nonlinearity.

Others nonlinearities are due to bad design, like a poorly sized pump or valve that is always working at one end of its adjustability range or another saturated element. They are harder to control because they are more erratic in every respect. They can also destabilize other parts of the process. Those things can usually be fixed if you want to make the effort, but it’s more a hardware issue in most cases.

Peter Welander,