Procedure of the Synthesis of Control Device by the Method of Analytical Design of the Optimal Regulator for the Problem of Aircraft Guidance Along a Hyperbola

Abstract

The purpose of the article is to describe the methodology for obtaining the structure of the optimal controller, which provides the guidance of the aircraft to the target point on the plane, using the method of time difference of arrivals (TDoA) for two navigation positions. The main feature of the system is that one measurement of time difference of arrivals between the aircraft and two navigation positions does not allow to describe the position of the aircraft on the plane fully. It describes only the line of position (LOP) in the form of a hyperbola. The aiming problem is solved by choosing a hyperbola passing through the target point, bringing the aircraft to a given hyperbola, followed by its movement along this hyperbola. In this case, the choice of the target hyperbola is a trivial task, in contrast to the task of determining the structure of the control system implementing the right and effective guidance law. The regulator obtained on the basis of the method of analytical design of the optimal regulator, according to the results of the computer simulation, showed its operability.