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3. Note that the order of the rotations , , is essential to the definition of the Euler angles. Equations Expressed in Body-Fixed Coordinates. The vectors F, vc , G, and h can be conveniently expressed as components in the body-fixed xyz axes of Fig. 1 as follows: where i,j,k represent unit vectors parallel to the x, y, and z body-fixed axes and where X, Y, and Z represent the components of the aerodynamic and propulsive forces alone, with the contribution of the gravitational forces now included in such terms as −mg sin .
In Fig. 12, the elements Gi (z) are defined as By writing the Gi (z) in Eq. (33) in terms of inverse powers of z, linear difference equations can be formed between the input and output of each Gi (z). These difference equations can then be programmed in the flight control computer. 25 s. AIRCRAFT DYNAMICS AND CONTROL 23 Performance Assessment via Simulation. Part of the design cycle of any flight control system involves computer simulation of the completed design with the control law implemented digitally.
These caveats are not meant to imply that sequential loop closure, per se, is not a useful approach to control system design. When taken as a part of more powerful design techniques, such as the quantitative feedback theory (QFT) approach to be discussed, sequential loop closure can be a powerful tool (16). Fortunately, advances in the theory of feedback control provide many synthesis tools that allow the flight control designer to attack the challenging problems just enumerated. An excellent and thorough summary of such techniques can be found in Ref.