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lecture_6 - 16.333: Lecture # 6 Aircraft Longitudinal...

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Unformatted text preview: 16.333: Lecture # 6 Aircraft Longitudinal Dynamics Typical aircraft open-loop motions Longitudinal modes Impact of actuators Linear Algebra in Action! Fall 2004 16.333 51 Longitudinal Dynamics Recall: X denotes the force in the X-direction, and similarly for Y and Z , then (as on 413) X , . . . X u u Longitudinal equations (see 413) can be rewritten as: mu = X u u + X w w mg cos + X c m ( w qU ) = Z u u + Z w w + Z w w + Z q q mg sin + Z c I yy q = M u u + M w w + M w w + M q q + M c There is no roll/yaw motion, so q = . Control commands X c , Z c , and M c have not yet been specified. Fall 2004 16.333 52 Rewrite in state space form as mu X u X w mg cos u X c Z c ( m Z w ) w Z u Z w Z q + mU mg sin M u M w M q w q + = M c M w w + I yy q 1 m u w q m Z w M w I yy 1 X u X w mg cos u X c Z c Z u Z w Z q + mU mg sin M u M w M q w q + = M c 1 E = A X + descriptor state space form c X = E 1 ( A X + c ) = A X + c X Fall 2004 16.333 53 Write out in state space form: X u X w g cos m m Z q + mU mg sin Z u Z w m Z w m Z w m Z w m Z w I 1 [ M u + Z u ] I 1 [ M w + Z w ] I 1 [ M q + ( Z q + mU )] yy mg sin I 1 yy yy yy 1 A = M w = m Z w Note: slight savings if we defined symbols to embed the mass/inertia X u = X u /m , Z u = Z u /m , and M q = M q /I yy then A matrix collapses to: g cos X u X w A = Z u Z w g sin Z q + U 1 Z w 1 Z w 1 Z w 1 Z w M u + Z u M w + Z w M q + ( Z q + U ) g sin 1 M w = 1 Z w Check the notation that is being used very carefully To figure out the c vector, we have to say a little more about how the control inputs are applied to the system. Fall 2004 16.333 54 Longitudinal Actuators Primary actuators in longitudinal direction are the elevators and thrust....
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This note was uploaded on 11/07/2011 for the course AERO 16.333 taught by Professor Alexandremegretski during the Fall '04 term at MIT.

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lecture_6 - 16.333: Lecture # 6 Aircraft Longitudinal...

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