Prediction and control of limit cycling motions in boosting rockets

Abstract

An investigation concerning the prediction and control of observed limit cycling behavior in a boosting rocket is considered. The suspected source of the nonlinear behavior is the presence of Coulomb friction in the nozzle pivot mechanism. A classical sinusoidal describing function analysis is used to accurately recreate and predict the observed oscillato~y characteristic. In so doing, insight is offered into the limit cycling mechanism and confidence is gained in the closed-loop system design. Nonlinear simulation results are further used to support and verify the results obtained from describing function theory. Insight into the limit cycling behavior is, in turn, used to adjust control system parameters in order to passively control the oscillatory tendencies. Tradeoffs with the guidance and control system stabilitylperformance are also noted. Finally, active wntrol of the limit cycling behavior, using a novel feedback algorithm to adjust the inherent nozzle sticking-unsticking characteristics, is considered. Introduction The Ballistic Tactical Target Vehicle (BTTV) is a suborbital rocket whose reentry vehicle serves as a target for advanced air defense and theater defense systems under d e v e l ~ ~ m e n t . ~ ~ Flight telemetry results from the first two missions indicate the presence of low amplitude, low frequency steady oscillations in both the vehicle attitude and actuator piston d i ~ ~ l a c e m e n t . ~ * ~ Fig. 1 illustrates this characteristic in the vehicle pitch attitude response during second stage boost of the first mission. Note that the flight data has been post processed. The impact of the oscillatory motions upon the guidance and control objectives appear to have been minor; however, their presence was unexpected and is of concern, especially with regards concerning the origins of the oscillatory behavior and the physical mechanism by which they occur. The hardware in question is the decommissioned Minuteman I Stage 3 system which is used as the second stage for the BTTV vehicle. After discussions * Flight Dynamics and Control Engineer. Member AIAA. Copyright O 1993 by the American Institute of Aeronautics and Astronautics, Inc. All rights resewed. with individuals intimately familiar with the Minuteman I Stage 3 characteris tics, it became known that this system has a long history of exhibiting small, slow periodic motions during the boost phase. These characteristics are in fact so common that routine preflight analysis is used in estimating the oscillatory motion for the specific flight vehiclelcontrol system in question. The results are then compared with an existing data base to determine whether the oscillatory motions will impact the guidance and control mission objectives. This data base suggests the oscillatory motions are limit cycling behavior due to nonlinearities present in the actuator-nozzle system: a conventional hydraulic actuator driving vectorable nozzles. Coulomb or dry friction present in the nozzle pivot is the primary culprit. Additional nonlinearities are present, but are not considered here.