# System equivalence

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System equivalence

In the systems sciences the term system equivalence is the notion that a parameter or component of a system behaves in a similar way as a parameter or component of a different system. Similarity means that mathematically the parameters/components will be indistinguishable from each other. Equivalence can be very useful in understanding how complex systems work.

Overview

Examples of equivalent systems are first- and second-order mechanical, electrical, torsional, fluidic, and caloric systems.

Equivalent systems are mostly used to change large and expensive mechanical, thermal, and fluid systems into a simple, cheaper electrical system. Then the electrical system can be analyzed to validate that the system dynamics will work as designed. This is a preliminary inexpensive way for engineers to test that their complex system performs the way they are expecting.

This testing is necessary when designing new complex systems that have many components. Businesses do not want to spend millions of dollars on a system that does not perform the way that they were expecting. Using the equivalent system technique, engineers can verify and prove to the business that the system will work. This lowers the risk factor that the business is taking on the project.

Chart of equivalent variables for the different types of systems

:

Flow variable: moves through the system

Effort variable: puts the system into action

Compliance: stores energy as potential

Inductance: stores energy as kinetic

Resistance: dissipates or uses energy

For example:

Mechanical systems

:Force "F" = −"kx" = "C dx/dt" = "M d"2"x/dt"2

Electrical systems

:Voltage "V" = "Q/C" = "R dQ/dt" = "L d"2"Q"/dt"2

All the fundamental variables of these systems have the same functional form.

References

* Panos J. Antsaklis, Anthony N. Michel (2006), "Linear Systems", 670 pp.
* M.A. Kaashoek & J.H. Van Schuppen (1990), "Realization and Modelling in System Theory".
* Katsuhiko Ogata (2003), "System dynamics", Prentice Hall; 4 edition (July 30, 2003), 784 pp.

* [http://vam.anest.ufl.edu/demos/firstordersystem.html A simulation using a hydraulic analog as a mental model for the dynamics of a first order system]

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