Envelopes for Flight Through Stochastic Gusts

probability, that a steady ight state can be maintained when stochastic wind gusts act upon an airplane. First we linearize the airplane dynamic equations and present them as a linear time invariant system with the airplane’s velocity and angular velocity as the state and gust velocity as the input. We then treat the gust velocity as a stationary random process and append the dynamics of a coloring lter to the linearized airplane equations so that the input is Gaussian white noise. We analyze the eect of the noise on the airplane’s dynamics, using the resulting equations to quantify the eects of stochastic wind gusts on an airplane’s steady ight envelope. During the analysis we introduce the notion of stationary ight and a stationary ight envelope to guarantee, within a specied probability, steady ight under such conditions. We also present a numerical example of a general aviation aircraft in steady level ight through moderate turbulence. In the example, the airplane’s cruise speed uctuates with a variance of 1.2 m 2 /s 2 and we show examples of stationary ight envelopes for this case.

[1]  R. McClean.  The optimization of an autopilot for an airplane subjected to random atmospheric turbulence , 1960 .

[2]  Frederic M. Hoblit.  Basic PSD Concepts and Application to Gust Loads , 1988 .

[3]  Carsten W. Scherer,et al.  Robust control against disturbance model uncertainty: a convex solution , 2007, 2007 46th IEEE Conference on Decision and Control.

[4]  W. G. Price,et al.  Hydroelasticity of Ships , 1980 .

[5]  Johnhenri R. Richardson,et al.  Scaling of Airplane Dynamic Response to Stochastic Gusts , 2014 .

[6]  Semyon M. Meerkov,et al.  Robustness with respect to disturbance model uncertainty: Theoryand application to autopilot performance analysis , 2000 .

[7]  Christine M. Belcastro,et al.  Aircraft Loss-of-Control Accident Analysis , 2010 .

[8]  G. L. Teper,et al.  Aircraft stability and control data , 1969 .

[9]  E. G. Rynaski.  Gust alleviation - Criteria and control laws , 1979 .

[10]  J. D. Robson,et al.  The description of road surface roughness , 1973 .

[11]  David A. Hinton.  Forward-look wind-shear detection for microburst recovery , 1992 .

[12]  R. Syski.  Passage Times for Markov Chains , 1992 .

[13]  M. Pachter,et al.  Full Envelope Flight Control System Design Using Qualitative Feedback Theory , 1996 .

[14]  T. Teichmann,et al.  Dynamics of Flight: Stability and Control , 1959 .

[15]  Isaac Horowitz,et al.  Quantitative feedback design theory : QFT , 1993 .

[16]  Robert F. Stengel,et al.  Optimal Recovery from Microburst Wind Shear , 1993 .

[17]  Wei Wei,et al.  QFT-based robust/fault-tolerant flight control design for a remote pilotless vehicle , 2000 .

[18]  Masayuki Sato,et al.  Disturbance suppression via robust MPC using prior disturbance data: Low computational complexity method , 2009, 2009 IEEE International Conference on Control and Automation.

[19]  Frederic M. Hoblit,et al.  Gust Loads on Aircraft: Concepts and Applications , 1988 .

[20]  Antonio Filippone.  Aircraft Flight and Performance , 2005 .

[21]  Robert C. Nelson,et al.  Flight Stability and Automatic Control 2nd Edition , 1998 .

[22]  Bernard Etkin,et al.  Turbulent Wind and Its Effect on Flight , 1981 .

[23]  N. Harris McClamroch,et al.  Steady Aircraft Flight and Performance , 2011 .

[24]  D. Andrisani,et al.  Gust alleviation using direct turbulence measurements , 1979 .

[25]  William H Phillips,et al.  Theoretical study of some methods for increasing the smoothness of flight through rough air , 1951 .