Dynamic Analogies

Introduction:

A system may possess various physical characteristics incorporating, for example, mechanical, electrical, thermal, and fluid components.

DynamicAnalogies

The procedure of model development will be facilitated if we understand the similarities of the characteristics of different types of components.

This issue is addressed in the present section. Analogies exist among mechanical, electrical, hydraulic, and thermal systems.

 The basic system elements can be divided into two groups: energy-storage elements and energy dissipation elements gives the linear relationships, which describe the behavior of translator-mechanical, electrical, thermal, and fluid elements.

These relationships are known as constitutive relations.

 In particular, Newton’s second law is considered the constitutive relation for a mass element. The analogy between mechanical and electrical elements is known as the force-current analogy.

This analogy appears more logical than a force-voltage analogy, this follows from the fact that both force and current are through variables, which are analogous to fluid flow through a pipe, and furthermore, both velocity and voltage are across variables, which vary across the flow direction, as in the case of fluid pressure along a pipe.

The correspondence between the only two elements—capacitance and resistance—can be identified. In this case constitutive relations exist between temperature difference and heat transfer rate. Proper selection of system variables is crucial in developing an analytical model for a dynamic system.

A general approach that may be adopted is to use across variables of the A-type (or, across-type) energy storage elements and the through variables of the T-type (or, through-type) energy storage element as system variables

Note that if any two elements are not independent (e.g., if two spring elements are directly connected in series or parallel) then only a single state variable should be used to represent both elements.

Independent variables are not needed for D-type (dissipative) elements because their response can be represented in terms of the state variables of the energy storage elements (A-type and T-type).

 State-space models and associated variables will be discussed in more detail in a later section.