# Nonlinear power flow feedback control for improved stability and performance of airfoil sections

## Abstract

A computer-implemented method of determining the pitch stability of an airfoil system, comprising using a computer to numerically integrate a differential equation of motion that includes terms describing PID controller action. In one model, the differential equation characterizes the time-dependent response of the airfoil's pitch angle, .alpha.. The computer model calculates limit-cycles of the model, which represent the stability boundaries of the airfoil system. Once the stability boundary is known, feedback control can be implemented, by using, for example, a PID controller to control a feedback actuator. The method allows the PID controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be optimized. This permits operation closer to the stability boundaries, while preventing the physical apparatus from unintentionally crossing the stability boundaries. Operating closer to the stability boundaries permits greater power efficiencies to be extracted from the airfoil system.

- Inventors:

- Issue Date:

- Research Org.:
- SNL (Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States))

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1092897

- Patent Number(s):
- 8,527,247

- Application Number:
- 12/633,045

- Assignee:
- Sandia Corporation (Albuquerque, NM)

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Patent

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Wilson, David G., and Robinett, III, Rush D.
```*Nonlinear power flow feedback control for improved stability and performance of airfoil sections*. United States: N. p., 2013.
Web.

```
Wilson, David G., & Robinett, III, Rush D.
```*Nonlinear power flow feedback control for improved stability and performance of airfoil sections*. United States.

```
Wilson, David G., and Robinett, III, Rush D. Tue .
"Nonlinear power flow feedback control for improved stability and performance of airfoil sections". United States. https://www.osti.gov/servlets/purl/1092897.
```

```
@article{osti_1092897,
```

title = {Nonlinear power flow feedback control for improved stability and performance of airfoil sections},

author = {Wilson, David G. and Robinett, III, Rush D.},

abstractNote = {A computer-implemented method of determining the pitch stability of an airfoil system, comprising using a computer to numerically integrate a differential equation of motion that includes terms describing PID controller action. In one model, the differential equation characterizes the time-dependent response of the airfoil's pitch angle, .alpha.. The computer model calculates limit-cycles of the model, which represent the stability boundaries of the airfoil system. Once the stability boundary is known, feedback control can be implemented, by using, for example, a PID controller to control a feedback actuator. The method allows the PID controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be optimized. This permits operation closer to the stability boundaries, while preventing the physical apparatus from unintentionally crossing the stability boundaries. Operating closer to the stability boundaries permits greater power efficiencies to be extracted from the airfoil system.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2013},

month = {9}

}