Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments
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21 Case Studies
"Case Studies." Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments. Ed. R. Russell Rhinehart. ASME-Wiley, 2016.
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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:
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.