Analysis and Control of Parametrically Excited Dynamical Systems

Abstract

The primary objective of this research is to develop new tools of analysis and control strategies for mechanical systems which can be modeled as a set of differential equations with time-periodic coefficients. These systems include helicopter rotor blades (in forward flight), asymmetric rotor bearing systems high speed reciprocating engines, etc. Analysis is essential for basic understanding of such systems and it is the first step before one can attempt to design or develop an active control technology. In this research techniques have been developed to construct dynamically equivalent time invariant forms of time periodic systems, utilizing the Lyapunov-Floquet (L-F) transformation. These time-invariant forms permit one to employ classical control methods readily available for time-invariant systems. An efficient symbolic technique to compute stability boundaries explicitly in terms of system parameters has been developed. Unlike the traditional averaging and perturbation methods, this approach does not require the time varying parameters to be small. Further, it has been shown that transient response of periodic linear systems with either deterministic or stochastic external excitation can also be efficiently computed using the L-F transformation technique. Control of several rotating time-periodic systems has been studied, utilizing the time-invariant forms constructed via the L-F transformation. For the time-invariant systems classical state-feedback and observer based controllers can be designed and the time-varying controller can be obtain by back transformation. Control of lumped model systems as well as elastic beam models and systems with periodic discontinuities have been considered.

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Document Details

Document Type
Technical Report
Publication Date
Sep 10, 1998
Accession Number
ADA358020

Entities

People

  • Subhash Sinha

Organizations

  • Auburn University

Tags

Communities of Interest

  • Air Platforms
  • Autonomy

DTIC Thesaurus Topics

  • Boundaries
  • Chebyshev Polynomials
  • Computational Science
  • Computations
  • Differential Equations
  • Engineering
  • Equations
  • Excitation
  • Feedback
  • Helicopter Rotors
  • Linear Differential Equations
  • Linear Systems
  • Mechanical Engineering
  • Nonlinear Systems
  • Observers
  • Perturbations
  • Polynomials

Fields of Study

  • Physics

Readers

  • Control Systems Engineering.