Compensation of measurable disturbances for two-time-scale nonlinear systems

This paper deals with a class of two-time-scale nonlinear systems with time-varying disturbances, modeled within the framework of singular perturbations. Systems in both standard and nonstandard form are considered. For these systems, we synthesize well-conditioned control laws that utilize feedback of the full state vector and feedforward compensation of disturbances to exponentially stabilize the fast dynamics and enforce a pre-specified input/output behavior independently of the disturbances in the closed-loop slow subsystem. Singular perturbation methods are employed to establish that the discrepancy between the output of the closed-loop full-order system and the output of the closed-loop slow subsystem is proportional to the value of the singular perturbation parameter. The stability of the closed-loop system is analyzed using Lyapunov's direct method and precise conditions that guarantee boundedness of the trajectories, for sufficiently small values of the singular perturbation parameter, are derived. The application of the developed methodology is illustrated through a catalytic continuous stirred tank reactor example, modeled as a singularly perturbed system in nonstandard form.