Physical system modeling

Automatic control is interested in mathematical models describing the evolution in time of system variables as a response to excitation. Such mathematical models are also known as dynamical models and systems represented by these models are called dynamical systems. The dynamical models, which are useful for classical control techniques consist of differential equations, in particular, ordinary differential equations where the independent variable is time. Partial differential equations arise when several independent variables exist, for instance, a flexible body where vibration has to be described with respect to both position in the body and time. However, this class of problem is outside the scope of classical control; hence, partial differential equations are not used to model physical systems in this book.