Modeling of Uncertain Systems

Abstract

As discussed in Chap. 1 it is well understood that uncertainties are unavoidable in a real control system. The uncertainty can be classified into two categories: disturbance signals and dynamic perturbations. The former includes input and output disturbance (such as a gust on an aircraft), sensor noise and actuator noise, etc. The latter represents the discrepancy between the mathematical model and the actual dynamics of the system in operation. A mathematical model of any real system is always just an approximation of the true, physical reality of the system dynamics. Typical sources of the discrepancy include unmodeled (usually high-frequency) dynamics, neglected nonlinearities in the modeling, effects of deliberate reduced-order models, and system-parameter variations due to environmental changes and torn-and-worn factors. These modeling errors may adversely affect the stability and performance of a control system. In this chapter, we will discuss in detail how dynamic perturbations are usually described so that they can be well considered in system robustness analysis and design.