Analysis and control of nonlinear singularly perturbed systems under sampling

Abstract

This chapter discusses that the problem of modeling a process is of utmost importance in control theory. For the same process, different models depending on the specific control task are designed because unmodeled high frequency dynamics occur as unknown disturbances and parametric uncertainties. The control system must possess sufficient robustness and insensitivity properties. For these reasons, singular perturbations legitimize simplifications of a dynamics model. One of these simplifications is the omission of this high-frequency dynamics that increases the dynamics order of the system. However, a digital control design based on a reduced system may be unsatisfactory or even unstable. The chapter presents a digital control scheme that is robust with respect to stable unmodeled high-frequency dynamics. The basic idea of this scheme is to introduce a delay between the input and data measurements. This is done based on the reduced sampled system deduced from a slow sampling. It also introduces some of the basic concepts of nonlinear systems with slow and fast dynamics by a sampled scheme with slow and fast sampling to take into account the time scale property. The improvements with the delayed zero-order hold have been explained in the chapter by way of examples.