Abstract:
Robust high precision control of spacecraft formation flying is one of the most
important techniques required for high-resolution interferometry missions in the
complex deep-space environment. The thesis is focussed on the design of an
invariant stringent performance controller for the Sun-Earth L2 point formation
flying system over a wide range of conditions while maintaining system robust
stability in the presence of parametric uncertainties.
A Quasi-Linear Parameter-Varying (QLPV) model, generated without approximation
from the exact nonlinear model, is developed in this study. With
this QLPV form, the model preserves the transparency of linear controller design
while reflecting the nonlinearity of the system dynamics.
The Polynomial Eigenstructure Assignment (PEA) approach used for Linear
Time-Invariant (LTI) and Linear Parameter-Varying (LPV ) models is extended
to use the QLPV model to perform a form of dynamic inversion for a broader
class of nonlinear systems which guarantees specific system performance. The
resulting approach is applied to the formation flying QLPV model to design a
PEA controller which ensures that the closed-loop performance is independent of
the operating point.
Due to variation in system parameters, the performance of most closed-loop
systems are subject to model uncertainties. This leads naturally to the need
to assess the robust stability of nonlinear and uncertain systems. This thesis
presents two approaches to this problem, in the first approach, a polynomial
matrix method to analyse the robustness of Multiple-Input and Multiple-Output
(MIMO) systems for an intersectingD-region,which can copewith time-invariant
uncertain systems is developed. In the second approach, an affine parameterdependent
Lyapunov function based Linear Matrix Inequality (LMI) condition is
developed to check the robust D-stability of QLPV uncertain systems.