Parallel-Computing Concepts and Methods in Large Scale Floquet Analysis of Helicopter Trim and Stability

Abstract

Rotorcraft stability investigation involves a nonlinear trim analysis for the control inputs and periodic responses, and, as a follow-up, a linearized stability analysis for the Floquet transition matrix (FTM), and its eigenvalues and eigenvectors. The trim analysis is based on a shooting method with damped Newton iteration, which gives the FTM as a byproduct, and the eigenanalysis on the QR method; the corresponding trim and stability analyses are collectively referred to as the Floquet analysis. A rotor with Q blades that are identical and equally spaced has Q planes of symmetry. Exploiting this symmetry, the fast-Floquet analysis, in principle, reduces the run time and frequency indeterminacy of the conventional Floquet analysis by a factor of Q. It is implemented on serial computers and on all three types of mainstream parallel computing hardware: SIMD and MIMD computers, and a distributed computing system of networked workstations; large models with hundreds of states are treated. A comprehensive database is presented on computational reliability such as the eigenvalue condition number and on parallel performance such as the speedup and efficiency, which show, respectively, how fast a job can be completed with a set of processors and how well their idle times are minimized. Despite the Q-fold reduction, the serial run time is excessive and grows between quadratically and cubically with the number of states. By contrast, the parallel run time can be reduced dramatically and its growth can be controlled by a judicious combination of speedup and efficiency. Moreover, the parallel implementation on a distributed computing system is as routine as the serial implementation on a workstation.

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Document Details

Document Type
Technical Report
Publication Date
Mar 03, 1998
Accession Number
ADA344155

Entities

People

  • G. H. Gaonkar
  • S. Subramanian
  • S. Venkataratnam

Organizations

  • Florida Atlantic University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computer Programming
  • Computers
  • Differential Equations
  • Distributed Computing
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Equations Of Motion
  • Frequency
  • Helicopters
  • Network Computing
  • Parallel Computing
  • Periodic Variations
  • Reliability
  • Rotary Wing Aircraft

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Parallel and Distributed Computing.

Technology Areas

  • Space