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# Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments

By
R. Russell Rhinehart
R. Russell Rhinehart
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ISBN:
9781118597965
No. of Pages:
400
Publisher:
ASME-Wiley
Publication date:
2016
Although many power law like models can be easily solved with classic gradient based optimizers, it is not hard (in my experience) to encounter ones that generate problems. Here is a simple one that arose from a desire (in model-based control) to calculate the valve stem position required to produce a desired air flow rate. The model is derived from first principle pressure losses in the pipe and valve, with the valve characteristic (modified equal percentage) modeled as a power law relation:
$u=a(F2783.2−kF2)b$
where u is the controller output (nominally the valve position) and F is the flow rate. The three model coefficients are a, b, and k.
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