Investigation of Adaptive SDRE Control Reconfiguration Subject to Control Surface Failures

Abstract

This paper investigates the state of the art adaptive G&C design called State Dependent Riccati Equation (SDRE) based Dual-Loop Servo for a reusable launch vehicle (RLV) during reentry flight conditions. The paper captures the basic state dependent equations needed for the dual-loop servo structure: SDRE Outer Loop Servo Serving as the Guidance Loop Function and SDRE Inner Loop Servo Serving as the Control Loop Function. Control performance allocation via six control surface deflections (i.e., 2 elevons, 2 rudders, and 2 body flaps) will be accomplished via the real-time dynamic (adaptive) gain calculation using the SDRE algorithm. The ability to adjust its G&C gain subject to loss of one control surface or a combination of multiple control surfaces is explored to achieve adaptive optimal control allocation subject to the HamiltonJacobi-Bellman (HJB) optimization principle. Since The SDRE design methodology employs nonlinear fully coupled dynamics equations updated in real-time via state dependent (SD) quantities supplied by vehicle’s sensors and actuators measurements (i.e., RLV’s health state vector) and computes its G&C actions based on HJB principle, thus its solution is at least suboptimal in this respect. As a result, it is expected to outperform most of other state of the art design principles (e.g., dynamic inversion, SDRE, gain scheduling, etc). The paper examines the RLV’s G&C design using the SDRE dual loop structure to accommodate four different flight conditions during which two control surfaces per flight condition become disabled. The proposed SDRE based control laws, via simulation, have demonstrated its attractive features in maintaining rate stabilization while the baseline traditional control law like Dynamic Inversion (DI) based technique fails to stabilize the RLV.