Kinetic State Tracking for a Class of Singularly Perturbed Systems

The trajectory-following control problem for a general class of nonlinear multi-input, multi-output two-time scale system is revisited. While most earlier works used singular perturbation theory and assumed that an isolated real root exists for the nonlinear set of algebraic equations that constitute the slow subsystem, here two-time scale systems are analyzed in the context of integral manifolds. This accounts for the existence of multiple roots. It is shown that the slow subsystem has a center manifold, and for small values of the slow state, an approximate solution of the nonlinear set of transcendental equations can be computed. Geometric singular perturbation theory is used as the model reduction technique, and dynamic inversion is used to formulate stabilizing control laws for slow state tracking. The control laws are independent of the scalar perturbation parameter, and an upper bound for it is determined such that boundedness of all the closed-loop signals is guaranteed. The methodology is validated through numerical simulation of a generic two- degree of freedom kinetic model and a nonlinear, coupled, six degree-of-freedom model of the F/A-18A Hornet. Results presented in the paper show that this methodology permits close tracking of the reference trajectory while maintaining all the control signals well within their specified bounds. Copyright 2010 by Anshu Siddarth and John Valasek.

Kinetic State Tracking for a Class of Singularly Perturbed Systems Conference Paper