Lateral Motion Control Invariance Helicopter on the Roll Angle. Analytical Synthesis

Abstract

For the linearized fourth-order model of the isolated lateral motion of a single-rotor helicopter as a MIMO system containing two inputs, the control is analytically synthesized, which ensures the invariance of the roll angle motion in the presence of disturbances in the control channels, as well as the required placement of the poles of the closed-loop system, given any specific values from the area of their stability. The approach to the synthesis of invariant control consists in finding a matrix of feedback coefficients of a linear system that satisfies the invariance conditions, which are a system of power matrix equations of a certain design. The synthesis is based on the application of theor ems based on the use of the regularization condition of the matrix equation and the invariance conditions under disturbances in the control channels, as well as theorems that make it possible to place the poles of the MIMO system using the original decomposition of the control object. Regularization of a matrix equation is understood as a solution to the problem of providing a given set of singular values for an inverted symmetric square matrix. The invariance of the MIMO system is considered with respect to unmeasured disturbances inthe control channels. The use of such an approach to the synthesis of invariant control made it possible to obtain an analytical solution that is versatile and can be applied in various flight modes of single-rotor helicopters with different dynamic properties. The results of the numerical synthesis of the lateral motion of a singlerotor helicopter using the obtained laws of invariant control, which confirm the reliability of the analytical expressions, areshown.