| In this thesis, we study fault tolerant control (FTC) for the decentralized robust servomechanism problem (DRSP) of a colocated large flexible space structure (LFSS) under sensor and actuator failures (SAF). The control objective is to devise a decentralized con- troller that maintains the stability of the LFSS, tracks a constant reference for healthy outputs, regulates against an unknown constant disturbance for healthy outputs, and is robust against parametric uncertainties, so that "spillover effects" do not occur. Two FTC frameworks are considered: An active FTC framework that assumes SAF are known, and a passive FTC framework for which SAF are unknown. The active FTC framework ex- tends existing work on DRSP of a nominal LFSS, and applies a PID controller that has fault-dependent adjustments. Necessary and sufficient conditions for a solution to exist are determined, notably an easy-to-test rank condition. For the passive FTC framework, a PD controller that stabilizes an LFSS under unknown SAF is found. Although perfect tracking and regulation are not attained under the PD controller, by applying high gains, the errors for healthy outputs can be reduced to any desired level. However, outputs with failed sensors and healthy actuators can reach undesirably high magnitude under high gains. To improve performance under low gains, insights on steady-state outputs are applied to develop a feed-forward control that has good performance in tracking, but not regulation. Further analysis on the PD controller reveals a method to diagnose SAF using steady-state outputs. As a result, the PD controller and PID controller are found to have complementary advantages, leading to an 3-stage integrated FTC procedure. First, the PD controller can stabilize the LFSS under unknown SAF (passive FTC). Next, fault diagnosis is performed while the LFSS is stabilized. Finally, a reconfigured PID con- troller applying diagnosed SAF enables healthy outputs to meet control objectives (active FTC). Three examples, including a benchmark space platform with 200 states obtained by finite-element analysis, are used to illustrate the results throughout this thesis. |
