ABSTRACT
This chapter discusses the process of obtaining mathematical description of a dynamic system that is a system whose behavior changes over time. It describes models of continuous-time systems in terms of linear or nonlinear differential equations. Physical systems of interest to engineers include electrical, mechanical, electromechanical, thermal, and fluid systems, among others. Using the lumped parameter assumption, their behavior is mathematically described by ordinary differential equation (ODE) models. The mathematical modeling of a physical system is enabled by the choice of variables associated with the physical characteristics of its components. These variables naturally divide into flow and across variables. Modeling of a physical system involves two kinds of variables: flow variables and across variables. An industrial process model, in its simplified form, can be represented by a first-order ODE accompanied by a dead time. State variable models are time-domain models that express system behavior as time derivatives of a set of state variables.
