Abstract
Mathematical models are very important for system modeling. This chapter presents the derivation of several mathematical models for different systems. They can be constructed from knowledge of the physical characteristics of the system. Mathematical models that represent the dynamic behavior of physical systems are constructed using differential equations. Mechanical systems are usually considered to comprise the linear lumped parameter elements of stiffness, damping, and mass. In case of electrical systems, the basic passive elements of electrical systems are resistance, inductance, and capacitance. It is convenient to consider thermal systems as being analogous to electrical systems so that they contain both resistive and capacitive elements. Like thermal systems, it is convenient to consider fluid systems as being analogous to electrical systems. There is one important difference however, and this is that the relationship between pressure and flow-rate for a liquid under turbulent flow conditions is nonlinear.
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