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 2019 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College