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Journal Article•DOI•

Bifurcation Analysis of Nonlinear Aircraft Dynamics

01 Sep 1982-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 5, Iss: 5, pp 529-536
TL;DR: In this article, a new approach for analyzing nonlinear and high-a dynamic behavior and stability of aircraft is presented, which involves the application of bifurcation analysis and catastrophe theory methodology to specific phenomena such as stall, departure, spin entry, flat and steep spin, nose slice, and wing rock.
Abstract: A new approach is presented for analyzing nonlinear and high-a dynamic behavior and stability of aircraft. This approach involves the application of bifurcation analysis and catastrophe theory methodology to specific phenomena such as stall, departure, spin entry, flat and steep spin, nose slice, and wing rock. Quantitative results of a global nature are presented, using numerical techniques based on parametric continuation. It is shown how our methodology provides a complete representation of the aircraft equilibrium and bifurcation surfaces in the state-control space, using a rigid body model with aerodynamic controls. Also presented is a particularly useful extension of continuation methods to the detection and stability analysis of stable attracting orbits (limit cycles). The use of this methodology for understanding high-a phenomena, especially spin-related behavior, is discussed. RENDS in fighter aircraft design over the past few decades have resulted in configuration s noted for their high speed and performance capability. The cost of achieving this capability has been a drastic, often fatal loss of positive control of the aircraft as the pilot operates at or near the extremes of the flight envelope. This is especially true for aircraft motion at high angles of attack (a), where large deviations both in the state and control variables limits the application of the usual linearized analysis techniques. There is a conspicuous lack of techniques for analyzing global stability and large maneuver response of aircraft. While certain phenomena (e.g., roll coupling) have been analyzed in an isolated manner, there exists a clear need for a unified approach to analyze systematically global aircraft behavior at high a.
Citations
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Journal Article•DOI•
TL;DR: Bifurcation theory has been used to study the nonlinear dynamics of the F-14, and a simple feedback control system was designed to eliminate the wing rock and spiral divergence as mentioned in this paper.
Abstract: Bifurcation theory has been used to study Ihe nonlinear dynamics of the F-14. An 8 degree-of-freedom model that does not include the control system present in operational F-14's has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearlties as functions of the angles of attack and sideslip, the rotation rate about the velocity vector, and the elevator deflection. A continuation method has been used to calculate the steady states of the F -14 as continuous functions of the elevator deflection. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena that cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

147 citations

Journal Article•DOI•
TL;DR: In this paper, applications of global stability and bifurcational analysis methods are presented for different nonlinear flight dynamics problems, such as roll-coupling, stall, spin, etc.

145 citations

Journal Article•DOI•
01 Dec 2003
TL;DR: A hybrid method for adaptive model-based control of nonlinear dynamic systems using neural networks, fuzzy logic and fractal theory and the new neuro-fuzzy-fractal method for the domain of non linear dynamic system control is described.
Abstract: We describe in this paper a hybrid method for adaptive model-based control of nonlinear dynamic systems using neural networks, fuzzy logic and fractal theory. The new neuro-fuzzy-fractal method combines soft computing techniques with the concept of the fractal dimension for the domain of nonlinear dynamic system control. The new method for adaptive model-based control has been implemented as a computer program to show that the neuro-fuzzy-fractal approach is a good alternative for controlling nonlinear dynamic systems. It is well known that chaotic and unstable behavior may occur for nonlinear systems. Normally, we will need to control this type of behavior to avoid structural problems with the system. We illustrate in this paper our new methodology with the case of controlling aircraft dynamic systems. For this case, we use mathematical models for the simulation of aircraft dynamics during flight. The goal of constructing these models is to capture the dynamics of the aircraft, so as to have a way of controlling this dynamics to avoid dangerous behavior of the aircraft dynamic system.

88 citations

Journal Article•DOI•
TL;DR: In this article, the authors examined how these nonlinearities affect the ability to control the aircraft and how they may contribute to loss of control and how damage to control effectors impacts the capability to remain within an acceptable envelope and to maneuver within it.
Abstract: Loss of control is a major factor in fatal aircraft accidents. Although definitions of loss of control remain vague in analytical terms, it is generally associated with flight outside of the normal flight envelope, with nonlinear influences, and with a significantly diminished capability of the pilot to control the aircraft. Primary sources of nonlinearity are the intrinsic nonlinear dynamics of the aircraft and the state and control constraints within which the aircraft must operate. This paper examines how these nonlinearities affect the ability to control the aircraft and how they may contribute to loss of control. Specifically, the ability to regulate an aircraft around stall points is considered, as is the question of how damage to control effectors impacts the capability to remain within an acceptable envelope and to maneuver within it. It is shown that, even when a sufficient set of steady motions exist, the ability to regulate around them or transition between them can be difficult and nonintuitiv...

78 citations

Journal Article•DOI•
TL;DR: In this article, a systematic way of computing the set of all attainable steady states for a general class of helical trajectories is presented, and the proposed reconstruction of attainable equilibrium states and their local stability maps provides a comprehensive and consistent representation of the aircraft flight and maneuvering envelopes.
Abstract: An aircraft's performance and maneuvering capabilities in steady flight conditions are usually analyzed considering the steady states of the rigid-body equations of motion. A systematic way of computation of the set of all attainable steady states for a general class of helical trajectories is presented. The proposed reconstruction of attainable equilibrium states and their local stability maps provides a comprehensive and consistent representation of the aircraft flight and maneuvering envelopes. The numerical procedure is outlined and computational examples of attainable equilibrium sets in the form of two-dimensional cross sections of steady-state maneuver parameters are presented for three different aircraft models.

71 citations

References
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Book•
01 Jan 1967
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.
Abstract: Introduction Foreward by Tudor Ratiu and Richard Cushman Preliminaries Differential Theory Calculus on Manifolds Analytical Dynamics Hamiltonian and Lagrangian Systems Hamiltonian Systems with Symmetry Hamiltonian-Jacobi Theory and Mathematical Physics An Outline of Qualitative Dynamics Topological Dynamics Differentiable Dynamics Hamiltonian Dynamics Celestial Mechanics The Two-Body Problem The Three-Body Problem.

3,561 citations

Book•
12 May 1974
TL;DR: In this article, the structure theory of linear operators on finite-dimensional vector spaces has been studied and a self-contained treatment of that subject is given, along with a discussion of the relations between dynamical systems and certain fields outside pure mathematics.
Abstract: This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

2,891 citations

Book•
01 Jan 1981
TL;DR: The Hopf Bifurcation Theorum has been used in many applications, such as Differential Difference and Integro-differential Equations (by hand).
Abstract: 1. The Hopf Bifurcation Theorum 2. Applications: Ordinary Differential Equations (by hand) 3. Numerical Evaluation of Hopf Bifurcation Formulae 4. Applications: Differential-Difference and Integro-differential Equations (by hand) 5. Applications: Partial Differential Equations (by hand).

2,090 citations

Book•
01 Jan 1975

1,804 citations