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 n^th 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	PZ ↔ TF; TF ↔ SS; SS ↔ SFG	Pole Zero to/from Signal Flow Graph (note: PZ↔TF is same as TF↔PZ)

References

Erik Cheever Department of Engineering Swarthmore College

References

Erik Cheever Department of Engineering Swarthmore College