Optimization of Stabilization of the Lateral Motion of an Aircraft Using the Decomposition Method of Modal Synthesis

Abstract

For the fourth-order model of the lateral motion of an aircraft with two controls, analytical expressions for the laws of stabilization control are obtained, which ensure the optimal placement of the poles. The synthesis is based on a two-level decomposition of the control object and the method of modal control of MIMO systems developed earlier by the authors with the optimal placement of the poles of a closed control system. The method is based on the features of quadratic control obtained by solving the nonlinear Lurie-Riccati matrix equation. In this case, for the optimal controller, it is necessary that the closed control object be asymptotically stable, and the matrix obtained by the product of the matrix of feedback coefficients by the control matrix of the dynamic plant must be positive-definite symmetric. Using this approach, final analytical expressions for the matrix of feedback coefficients are obtained and, accordingly, they can be used for any aircraft that has the same structure of its own dynamics and control matrices. The results of modeling the stabilization of the lateral motion of an aircraft using the obtained analytical control laws that ensure the optimal placement of the poles and, accordingly, the control laws using the decomposition method of synthesis with the same dynamic properties in the form of the value of the poles of a closed control system are presented. These properties correspond, as in the first case, to the optimal values of the placed poles. A comparison of transient processes by components of the maximum deviation of the controls shows that with optimal control, the maximum deviation of the rudder is 1.5 times less than with control using the standard decomposition method. All other parameters of the transient process, both in terms of the components of the state vector and the control vector, are approximately the same.