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Research Papers

# On Nonlinear Dynamics and an Optimal Control Design to a Longitudinal Flight

[+] Author and Article Information
Danilo Carlos Pereira

Department of Mechanical Design (DPM), FEM-UNICAMP, 13083-970 Campinas, Sao Paulo, Brasildanilocp@pop.com.br

José Manoel Balthazar

Department of Mechanical Design (DPM), FEM-UNICAMP, 13083-970 Campinas, Sao Paulo, Brasiljmbaltha@rc.unesp.br

Fábio Roberto Chavarette

UNESP-Rio Claro, P.O. Box 178, 13230-560 Rio Claro, Sao Paulo, Brasilfabioch@rc.unesp.br

Marat Rafikov

University of Ijuí (UNIJUI), P.O. Box 560, 98700-000 Ijuí, Rio Grande do Sul Brazilmarat9119@yahoo.com.br

J. Comput. Nonlinear Dynam 3(1), 011012 (Dec 12, 2007) (6 pages) doi:10.1115/1.2802111 History: Received November 17, 2006; Revised July 29, 2007; Published December 12, 2007

## Abstract

In this work, we analyzed a bifurcational behavior of a longitudinal flight nonlinear dynamics, taking as an example the F-8 aircraft “Crusader.” We deal with an analysis of high angles of attack in order to stabilize the oscillations; those were close to the critical angle of the aircraft, in the flight conditions, established. We proposed a linear optimal control design applied to the considered nonlinear aircraft model below angle of stall, taking into account regions of Hopf and saddled noddle bifurcations.

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## Figures

Figure 2

(a) Equilibrium and periodic solutions for the system (1), m=m0 in the variable q, with com θ<0 and θ>0 and (b) equilibrium and periodic solutions for the system (1), m=m0 in the variable q, with com θ<0 and θ>0

Figure 3

Evolution of the point limits in relation to the increase of the mass m0 of the system

Figure 4

Evolution of the point limits in relation to the increase of the mass=4.35m0

Figure 1

(a) Dynamic model of aircraft (5) and (b) peculiar angles of the aircraft

Figure 5

Evolution of the point limits in relation to the increase of the mass=4.38m0

Figure 6

Evolution of the point limits in relation to the increase of the mass=4.47m0

Figure 7

Evolution of the point limits in relation to the increase of the mass=4.58m0

Figure 8

Evolution of the point limits in relation to the increase of the mass=4.61m0

Figure 9

Balance and periodic solutions for the system with m=5m0

Figure 10

0.37rad→21deg, below angle of stall, first case

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