Minimization of Control Signals at Stabilizing Spatial Motion of a Maneuverable Aircraft

Abstract

This study deals with the problem of stabilizing spatial motion of a maneuverable aircraft with three controls and nine state parameters. In the task it is required to provide specified dynamic properties of the controlled plant at minimal control actions. For numeric matrices describing one of flight modes of a typical maneuverable aircraft the parameterized set of controllers by state vector is synthesized basing on the generalized Bass – Gura formula. This formula allows analytically calculating modal control for multi-input objects and simplifies parameterization of this control. The task of row-by-row minimization of gain matrix quadratic norm at fixed poles values is solved analytically by choosing the values of supplementary parameters which do not change the closed-loop control system spectrum. A technique for parameterization of two rows of three is proposed. In parameterized rows the minima are obtained at the condition of forced zeroing the coefficients corresponding to linear velocity. Based on simulation results the poles are chosen at which along with optimal supplementary parameters one may synthesize a controller allowing for specified range of initial conditions to obtain the most rapid transient with required dynamics and minimal control actions.