ABSTRACT
This chapter develops different techniques of obtaining and expressing such mathematical descriptions for various physical systems, which include mechanical, electrical, electromechanical, thermal, chemical, and hydraulic systems. It concentrates on dynamic systems, that is, systems whose variables are time-dependent. A dynamic system model is defined as the mathematical representation of the behavior of a dynamic system. The chapter discusses four general forms of dynamic system models. They are: State-variable matrix form; Input-output differential equation form; Transfer function form; and Block diagram form. The system model must incorporate both the element laws and the interconnection laws. The element laws involve displacements, velocities, and accelerations. Thus, a controller designed for a linear system model to satisfy performance specifications may perform poorly when applied to the actual system. The trade-off here is between mathematical tractability of the linearized model and greater validity of a nonlinear model.
