A Graphical Method for the Determination of Gain Scheduling for Booster Vehicles

摘要

A graphical technique is presented for the scheduling of ballistic missile autopilot forward-loop gain during the boost phase of flight. The procedure discussed provides an exact method for determining the 'best' piecewise constant gain scheduling for the cases of one and two gain changes. The 'best' piecewise constant gain scheduling is taken to be that scheduling which maximizes the minimum gain margin incurred during the times offlight considered. The existence and uniqueness of 'best' gain schedules for the case of more than two gain changes is also discussed. Methods for extending the technique of this paper to situations where there exists uncertainty in the knowledge of critical gain boundries and where the upper and lower gain margins are to differ in magnitude are presented. Although this presentation has been made rather long by the desire to justify the graphical constructions employed, the actual constructions themselves require only a very short time to execute. It is hoped that the results of this paper will prove useful to the controls engineer involved in autopilot synthesis. (Author)