Electrical System modeling
We here consider the following electrical system, with an input voltage and an output voltage
In order to model the system in a mathematical way, we need to use Kirchhoff’s laws:
In addition, we need to express the mathematical function of each component:
Using the 2 mathematical expressions, we come to the following second order differential
State-space system modeling
The equations for an RLC circuit are the following. They result from
Kirchhoff’s voltage law and Newton’s law.
The R, L and C are the system’s resistance, inductance
We define the capacitor voltage Vc and the inductance current iL as the state variables X1 and X2.
Rearranging these equations
These equations can be put into
matrix form as follows,
output equation is
diagram shows these equations modeled in Xcos.
the output Vc(t) we use CLSS block from Continuous time systems Palette.
Acausal with Modelica