The state space approach to modeling, also known as the time domain approach, is a helpful way of representing systems even with non-zero initial conditions.
General State-Space Representation
Assumptions:
- Time is greater than or equal to the initial time (
) - Initial conditions
Where:
Steps for Finding the State Space Representation given an Electrical Network
- Assign a label to all branch currents.
- Determine the state variables using the derivative equations drawn from energy storing elements.
- Take advantage of Kirchhoff’s laws to compute for the required currents and voltages. Replace the currents of non-energy storing elements using Ohm’s law.
- Use the resulting equations from step 3 and substitute it to the equations found in step 2.
- Use the previous values and substitute them into the
, the system matrix , the state vector , the input matrix , and the input vector . - Write the output equations.