Fixed-structure adaptive -improvement control: Performance enhancing, indirect adaptive control for stable plants.

Abstract

Achievable performance in vibration control for Large Spacecraft Structures (LSS) is limited by the modelling errors due to unpredictable changes in structural dynamics. Adaptive algorithms can recover the performance traded for robust stability guarantees necessary for fixed-gain LSS control designs. We consider adaptive regulation of stable, LTI, non-minimum phase, SISO plant models with compact parametric uncertainty subjected to a broadband, bounded disturbance and sensor noise. The sign of the high-frequency gain and a bound on the plant order are assumed known. We propose the BIBO stable Fixed-Structure Adaptive-Improvement (FSAI) algorithm and analyze its properties. FSAI provides a switched system framework for online control optimization of a baseline stabilizing controller and quantitative bounds on the output for all time. FSAI is aimed not at adaptive stabilization but at adaptive performance enhancement. It achieves BIBO stability through enforcing output constraint set membership and the use of a computed upper bound on settling times derived from a new bound, the Hybrid set-bound, of the matrix exponential on a set of matrices. The Hybrid Set-Bound is compared to other bounds in the literature in terms of both conservatism and computational effort. It is of the same computational complexity as the well-known Schur bound and improves on it in the examples considered. Integral cost functions are derived for the Hybrid set-bound and the extensions to set-bounds of common bounds in the literature. Based on the output admissible sets of Gilbert and Tan, the concept of Output Bound Satisfaction (OBS) is introduced and shown to be distinct from BIBO stability over finite time scales. Finally, FSAI control is implemented on the ground on flight-traceable hardware as part of the MACE II project. The hardware reflects the limitations of many flight processors (33 MHz with 0.8 MB for control tasks) As part of the implementation, an online Nyquist criterion is developed. FSAI searched through 34,000 controllers, implementing some destabilizing controllers (as is allowed by OBS), but maintained acceptable output levels and improved the performance of a 13th order controller applied to an 80th order plant by 40%.