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Parallel-computing concepts and methods toward large-scale floquet analysis of helicopter trim and stability

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Date Issued:
1994
Summary:
The rotorcraft trim solution involves a search for control inputs for required flight conditions as well as for corresponding initial conditions for periodic response or orbit. The control inputs are specified indirectly to satisfy flight conditions of prescribed thrust levels, rolling and pitching moments etc. In addition to the nonlinearity of the equations of motion and control inputs, the control inputs appear not only in damping and stiffness matrices but also in the forcing-function or input matrix; they must be found concomitantly with the periodic response from external constraints on the flight conditions. The Floquet Transition Matrix (FTM) is generated for perturbations about that periodic response; usually, a byproduct of the trim analysis. The damping levels or stability margins are computed from an eigenanalysis of the FTM. The Floquet analysis comprises the trim analysis and eigenanalysis and is routinely used for small order systems (order N < 100). However, it is practical for neither design applications nor comprehensive analysis models that lead to large systems (N > 100); the execution time on a sequential computer is prohibitive. The trim analysis takes the bulk of this execution time. Accordingly, this thesis develops concepts and methods of parallelism toward Floquet analysis of large systems with computational reliability comparable to that of sequential computations. A parallel shooting scheme with damped Newton iteration is developed for the trim analysis. The scheme uses parallel algorithms of Runge-Kutta integration and linear equations solution. A parallel QR algorithm is used for the eigenanalysis of the FTM. Additional parallelism in each iteration cycle is achieved by concurrent operations such as perturbations of initial conditions and control inputs, follow-up integrations and formations of the columns of the Jacobian matrix. These parallel shooting and eigenanalysis schemes are applied to the nonlinear flap-lag stability with a three-dimensional dynamic wake (N ~ 150). The stability also is investigated by widely used sequential schemes of shooting with damped Newton iteration and QR eigenanalysis. The computational reliability is quantified by the maximum condition number of the Jacobian matrices in the Newton iteration, the eigenvalue condition numbers and the residual errors of the eigenpairs. The saving in computer time is quantified by the speedup, which is the ratio of the execution times of Floquet analysis by sequential and parallel schemes. The work is carried out on massively parallel MasPar MP-1, a distributed-memory, single-instruction multiple-data or SIMD computer. A major finding is that with increasing system order, while the parallel execution time remains nearly constant, the sequential execution time increases nearly cubically with N. Thus, parallelism promises to make large-scale Floquet analysis practical.
Title: Parallel-computing concepts and methods toward large-scale floquet analysis of helicopter trim and stability.
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Name(s): Nakadi, Rajesh Mohan.
Florida Atlantic University, Degree grantor
Gaonkar, Gopal H., Thesis advisor
College of Engineering and Computer Science
Department of Ocean and Mechanical Engineering
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1994
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 90 p.
Language(s): English
Summary: The rotorcraft trim solution involves a search for control inputs for required flight conditions as well as for corresponding initial conditions for periodic response or orbit. The control inputs are specified indirectly to satisfy flight conditions of prescribed thrust levels, rolling and pitching moments etc. In addition to the nonlinearity of the equations of motion and control inputs, the control inputs appear not only in damping and stiffness matrices but also in the forcing-function or input matrix; they must be found concomitantly with the periodic response from external constraints on the flight conditions. The Floquet Transition Matrix (FTM) is generated for perturbations about that periodic response; usually, a byproduct of the trim analysis. The damping levels or stability margins are computed from an eigenanalysis of the FTM. The Floquet analysis comprises the trim analysis and eigenanalysis and is routinely used for small order systems (order N < 100). However, it is practical for neither design applications nor comprehensive analysis models that lead to large systems (N > 100); the execution time on a sequential computer is prohibitive. The trim analysis takes the bulk of this execution time. Accordingly, this thesis develops concepts and methods of parallelism toward Floquet analysis of large systems with computational reliability comparable to that of sequential computations. A parallel shooting scheme with damped Newton iteration is developed for the trim analysis. The scheme uses parallel algorithms of Runge-Kutta integration and linear equations solution. A parallel QR algorithm is used for the eigenanalysis of the FTM. Additional parallelism in each iteration cycle is achieved by concurrent operations such as perturbations of initial conditions and control inputs, follow-up integrations and formations of the columns of the Jacobian matrix. These parallel shooting and eigenanalysis schemes are applied to the nonlinear flap-lag stability with a three-dimensional dynamic wake (N ~ 150). The stability also is investigated by widely used sequential schemes of shooting with damped Newton iteration and QR eigenanalysis. The computational reliability is quantified by the maximum condition number of the Jacobian matrices in the Newton iteration, the eigenvalue condition numbers and the residual errors of the eigenpairs. The saving in computer time is quantified by the speedup, which is the ratio of the execution times of Floquet analysis by sequential and parallel schemes. The work is carried out on massively parallel MasPar MP-1, a distributed-memory, single-instruction multiple-data or SIMD computer. A major finding is that with increasing system order, while the parallel execution time remains nearly constant, the sequential execution time increases nearly cubically with N. Thus, parallelism promises to make large-scale Floquet analysis practical.
Identifier: 15085 (digitool), FADT15085 (IID), fau:11863 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (M.S.E.)--Florida Atlantic University, 1994.
Subject(s): Floquet theory
Helicopters--Control systems
Rotors (Helicopters)
Parallel processing (Electronic computers)
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/15085
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.