On One Approach to the Synthesis of Robust Control of the Stabilization of the Hypothetical Aircraft Longitudinal Motion

For a linearized model of the fourth order of longitudinal motion of an airplane-type aircraft with three controls, analytical expressions of control laws are obtained that ensure robustness according to one of the coefficients of the model of the control object having the smallest range of values. As such a coefficient, the increment of the lifting force from the increment of the angle of attack and the angle of inclination of the trajectory is considered. The work is based on the original decomposition of the control object model and the modal synthesis method developed on its basis. The search for robust control is based on the parametrization of a set of solutions and the assignment of eigenvalues of a closed system. The idea of this approach is as follows. If, for a given control object, we find in an analytical form the entire set of feedback control laws that provide a given set of eigenvalues, then with the appropriate parametrization of this set, we can distinguish a subset of robust control laws with respect to a particular factor. The basis for obtaining a parameterized solution to the synthesis problem is the similarity transformation for the matrix of eigenvalues of the zero level of the decomposition of the control object. The results of numerical simulation of the control of the longitudinal motion of the aircraft using synthesized analytical laws are presented. Based on its results, the influence of the coefficient of the model is estimated, at which, for a non-robust analytical control law, the aircraft loses stability in longitudinal motion. It is noted that the robust control law has no restrictions with respect to the error of setting the considered coefficient of the model, which characterizes the increment of the lifting force of the aircraft from the increment of the angle of attack and the angle of inclination of the trajectory.

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