PID adaptive control of incremental and arclength continuation in nonlinear applications
| Autor: | Andrea M. P. Valli, Graham F. Carey, Renato N. Elias, Alvaro L. G. A. Coutinho |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Adaptive control
business.industry Applied Mathematics Mechanical Engineering Computational Mechanics PID controller Computational fluid dynamics Finite element method Computer Science Applications Nonlinear system Continuation Flow (mathematics) Mechanics of Materials Control theory Fluid dynamics business Mathematics |
| Zdroj: | International Journal for Numerical Methods in Fluids. 61:1181-1200 |
| ISSN: | 1097-0363 0271-2091 |
| DOI: | 10.1002/fld.1998 |
| Popis: | SUMMARY A proportional-integral-derivative (PID) control approach is developed, implemented and investigated numerically in conjunction with continuation techniques for nonlinear problems. The associated algorithm uses PID control to adapt parameter stepsize for branch—following strategies such as those applicable to turning point and bifurcation problems. As representative continuation strategies, incremental Newton, Euler‐Newton and pseudo-arclength continuation techniques are considered. Supporting numerical experiments are conducted for finite element simulation of the ‘driven cavity’ Navier‐Stokes benchmark over a range in Reynolds number, the classical Bratu turning point problem over a reaction parameter range, and for coupled fluid flow and heat transfer over a range in Rayleigh number. Computational performance using PID stepsize control in conjunction with inexact Newton‐Krylov solution for coupled flow and heat transfer is also examined for a 3D test case. Copyright q 2009 John Wiley & Sons, Ltd. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Plný text