Transformation: Differential Equation ↔ State Space

Given a system differential equation it is possible to derive a state space model directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the state space model.

Example: Diff Eq → State Space

Find a state space model for the system described by the differential equation:

 

Step 1: Find the transfer function using the methods described here (1DE ↔ TF)

Step 2: Find a state space representation using the methods described here (TF ↔ SS).  In this case we are using a CCF form).

Example: State Space → Diff Eq

Repeat the previous example, but reverse the order (i.e., do step 2 (SS → TF) then step 1 (TF → SS)).

References

© Copyright 2005 to 2022 Erik Cheever    This page may be freely used for educational purposes, but the url must be referenced.

Comments?       Questions?       Suggestions?       Corrections?
Erik Cheever        Department of Engineering          Swarthmore College