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Case Studies

## Excerpt

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.

21.1Valve Characterization
21.2CO2 Orifice Calibration
21.3Enrollment Trend
21.4Algae Response to Sunlight Intensity
21.5Batch Reaction Kinetics
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