# Transforming between Mathematical Models of Systems

There are many different ways to represent any physical system, differential equations, transfer function, state space... Since they all represent the same physical system, there must be ways to transform from one to another.  This document has links to individual pages describing these transformations.

In many cases when transforming from one representation to another, an easier alternative is to go through an intermediate representation.  For example when changing from a single nth order differential equation to a state space representation (1DE↔SS) it is easier to do from the differential equation to a transfer function representation, then from transfer function to state space (1DE↔TF followed by TF↔SS).

The "Printable" link (above) links to a page that has all of these transformations.

Contents
 Transformation Alternative Description CDE → 1DE Coupled Differential Equation to Single Differential Equation 1DE ↔ TF Single Differential Equation to/from Transfer Function 1DE ↔ SS 1DE ↔ TF; TF ↔ SS Single Differential Equation to/from State Space 1DE ↔ PZ 1DE ↔ TF; TF ↔ PZ Single Differential Equation to/from Pole Zero 1DE ↔ SFG 1DE ↔ TF; TF ↔ SS; SS ↔ SFG Single Differential Equation to/from Signal Flow Graph TF ↔ SS Transfer Function to/from State Space TF ↔ PZ Transfer Function to/from Pole Zero TF ↔ SFG TF ↔ SS; SS ↔ SFG Transfer Function to/from Signal Flow Graph SS ↔ SS State Space to/from State Space SS ↔ PZ SS ↔ TF; TF ↔ PZ State Space to/from Pole Zero (note: SS↔TF is same as TF↔SS) SS ↔ SFG State Space to/from Signal Flow Graph PZ ↔ SFG TF ↔ SS Pole Zero to/from Signal Flow Graph (note: PZ↔TF is same as TF↔PZ)

References

© Copyright 2005 to 2014 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College

References

© Copyright 2005 to 2014 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College