Abstract
To derive linear aircraft flight dynamics plant for use in automatic flight control system design. To decouple aircraft dynamics into longitudinal and lateral-directional plants, and to briefly study the stability and control derivatives. To consider modeling of servo actuators for aircraft’s engine and control surfaces. To present single- and multi-variable automatic flight control systems (stability augmentation systems and autopilots) for both longitudinal and lateral-directional dynamics. To design and analyze aircraft control systems using both transfer function and state-space methods
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Notes
- 1.
Since aircraft are almost always powered by airbreathing engines that produce thrust by aerodynamic means, the aerodynamic and propulsive forces are always clubbed together.
- 2.
Early fighter aircraft of World War-I era – like the British Sopwith Camel – were quite small and light-weight in construction, but had relatively big rotary engines. Hence, such aircraft encountered a significant coupling between the pitching motion (rotation about j), and the yawing motion (rotation about k) caused by the constant angular momentum of the engine. Thus, a pitching moment applied by the pilot invariably produced an unintended yaw (and roll), making the aircraft very difficult to control. It is believed that many crashes during fighting (extreme maneuvering) were caused by this inertial coupling. However, engine angular momentum is negligible for a conventional modern aircraft.
- 3.
Generally, C mwf0 < 0 due to a positively cambered wing airfoil that is necessary for producing C Lwf > 0 when the wing–fuselage angle-of-attack is zero. In contrast, the tail airfoil is symmetrical to produce both positive and negative tail lift for stability and control.
- 4.
Often, \(\bar{{x}}_{n}\) is called the stick fixed neutral point referring to a cockpit control lever named stick, manipulated by the pilot for longitudinal control.
- 5.
Since neither the thrust nor the drag is much affected by a small pitch rate, by differentiating the first of (4.27) with q and putting α = 0, we have C xq = 0.
- 6.
The long-period mode is also called the phugoid mode in standard aeronautical terminology.
- 7.
Some special airplanes can have a thrust vectoring engine for better maneuverability, or for a shorter runway length requirement.
- 8.
In such a case, the engine servo is part of the aircraft plant.
- 9.
A further approximation, called Lanchester’s model, can be obtained in the incompressible flow limit:
$${Z}_{u} \simeq -\rho US{C}_{\mathrm{Le}} = -\frac{2mg} {U},$$and Z q < < mU, resulting in
$${\omega }_{\mathrm{p}} \simeq\frac{g\sqrt{2}} {U} ; \qquad {\zeta }_{\mathrm{p}} \simeq - \frac{{X}_{u}U} {2\sqrt{2}mg}.$$ - 10.
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1.
Note that the equilibrium flight direction, Ψ e, need not be zero.
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2.
We are using ϕ and ψ for roll and yaw angle perturbations in this section. This should not cause confusion with the usage of ϕ for the flight path angle and ψ for the heading (azimuth) angle elsewhere in the book (such as in Chap. 2).
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1.
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© 2011 Springer Science+Business Media, LLC
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Tewari, A. (2011). Automatic Control of Aircraft. In: Automatic Control of Atmospheric and Space Flight Vehicles. Control Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4864-0_4
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DOI: https://doi.org/10.1007/978-0-8176-4864-0_4
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