Computational Mathematics and Modeling

, Volume 24, Issue 3, pp 418–431

# Mathematical Modeling of Controlled Longitudinal Motion of a Paraglider

• A. M. Formal’skii
• P. V. Zaitsev
Article

A paraglider consists of a harness and a wing. Both bodies are assumed perfectly rigid. They are connected by suspension lines, which are regarded as perfectly rigid weightless rods. These rods are rigidly attached to the harness and to the wing. The paraglider model is thus a single rigid body with three degrees of freedom. A propeller motor is rigidly attached to the harness. The thrust developed by the propeller is applied to the harness. The thrust vector maintains constant orientation relative to the harness. We develop a mathematical model of a paraglider moving in the longitudinal plane. Stationary motion regimes are identified assuming constant thrust. A thrust control is proposed that stabilizes the paraglider flight at a given altitude. Regions of asymptotic stability of paraglider motion at a constant altitude are constructed in the plane of feedback coefficients (allowing for delay). Regions ensuring a given stability margin are also constructed in this plane. Simulation results are presented for paraglider flight.

## Keywords

Pitch Angle Stability Margin Longitudinal Motion Thrust Vector Constant Altitude
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
V. M. Lokhin, S. V. Man’ko, M. P. Romanov, I. B. Garnev, D. V. Evstigneev, and K. S. Kolyadin, “Promising systems and aggregates based on aircraft,” Perspektivnye Sistemy i Zadachi Upravleniya. Tematicheskii Vypusk, Izv. TRTU, No. 3, Izd. TRTU, Taganrog (2006).Google Scholar
2. 2.
G. V. Abramenko, D. V. Vasil’kov, and O. V. Voron’ko, Design of Complex Science-Based Technical Systems [in Russian], RFFI, Moscow (2006).Google Scholar
3. 3.
A. A. Lebedev and L. S. Chernobrovkin, Flight Dynamics of Pilotless Aircraft [in Russian], Mashinostroenie, Moscow (1973).Google Scholar
4. 4.
S. M. Gorlin, Experimental Aeromechanics [in Russian], Vysshaya Shkola, Moscow (1970).Google Scholar
5. 5.
N. V. Butenin, Ya. L. Luntz, and D. R. Merkin, A Course in Theoretical Mechanics. Dynamics [in Russian], Vol. 2, Nauka, Moscow (1979).Google Scholar
6. 6.
Ya. N. Roitenberg, Automatic Control [in Russian], Nauka, Moscow (1992).Google Scholar