Passivity Analysis for Non-Linear, Non-Stationary Entry Capsules: Rotational Motion

Abstract

To analyze the passivity of non-linear, time-varying systems we study an entry capsule that enters the atmosphere in a lift-down configuration (i.e., a bank angle larger than 90o) to avoid skipping flight, and which is controlled by a Reaction Control System only. Deriving the passivity conditions for rotational motion, and evaluating these conditions along the trajectory shows that the (non-linear) entry capsule is Almost Strictly Passive, and the sufficient conditions to apply Simple Adaptive Control are met. Further, the preliminary design of an attitude-control system using the theory of Simple Adaptive Control is discussed and analyzed. The two designs for both a low and a high dynamic pressure operating condition show an excellent performance. Each design uses its own controller parameters (i.e., weighting matrices, zero integral gain and integral-gain filter parameter), which necessitates the use of an interpolation scheme once a trajectory with changing operating conditions is flown. The nominal mission (entry at 220 km altitude with a velocity of 11 km/s, and final conditions at Mach = 1) can be own without any difficulty. The angle-of-attack command is provided by a trim law, and although some deviations are observed when the capsule becomes less aerodynamically stable, this deviation does not diverge in spite of the pitch-thruster saturation. Responses due to errors in the initial attitude and angular rates show smooth curves in both attitude motion and thruster controls. A Monte-Carlo analysis that includes errors in the initial attitude, angular rate and inertia properties shows similar results, and it can be concluded that the performance of the controller given the current dispersions is satisfying.