First‐Order Systems
Joseph L. Hellerstein, Yixin Diao, Sujay S. Parekh, Dawn M. Tilbury · 2004
This chapter presents techniques for analyzing first-order systems. First-order systems are of interest for several reasons: (a) many real world systems (e.g., the IBM Lotus Domino Server and the Apache HTTP Server) can be modeled as first-order systems; (b) several approximations used in control design are based on first-order systems; and (c) first-order systems are simple and hence have pedagogical value. The chapter addresses both the statics and dynamics of first-order systems, with particular emphasis on dynamics. The properties studied are stability, steady-state output, settling time, and maximum overshoot. Where possible, simple formulas are used to communicate the underlying theory, and various examples are used to demonstrate the application of the theory to computing systems.