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2. Control-system elements in a modern piloted aircraft. Mathematical Description Of The Aircraft Body-Fixed Axis System. Referring to Fig. 1, one sees an xyz axis system consisting of three mutually perpendicular (orthogonal) axes with origin at the aircraft’s center of gravity. These so-called body-fixed axes are important in the development of the mathematical model of the aircraft. As the name implies, the bodyfixed axes are fixed in the aircraft body or airframe. The axis system has its origin at the aircraft center of mass, with the xz axes lying in the aircraft’s plane of symmetry.

That is, the eigenvectors determine how each state variable contributes to the vehicle response for each possible mode of motion. Like eigenvalues, open-loop and closed-loop eigenvectors can be defined. As a control-system design technique, eigenstructure assignment allows the creation of controllers that meet mode-based performance specifications. Examples of mode-based specifications are minimum damping, minimum settling time, and decoupled responses. The last refers to allowing specified system inputs to affect only certain system outputs.

Defined as a weighted sum of mean squared system errors and control inputs (sometime referred to as an L2 norm). For example, one such index might be Here the system error is defined as the deviation of the state vector x(t) from an equilibrium point. The solution to the LQR problem typically involves the solution of the matrix Riccati equation. As Eq. (35) indicates, implementation of such control laws requires measurement of the entire state vector. This requirement can be 26 AIRCRAFT DYNAMICS AND CONTROL obviated through introduction of a state estimator that provides continuous estimates of the state vector based upon measurement of a subset or combination of the system state variables.

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