# Transmittance and state space representation equations designation

The considered electrical circuit is analyzed as an object which is to be controlled automatically, therefore, its transmittance and state space representation equations will be written down.

Transmittance is given by formula

$$H(s) = \frac{Y(s)}{U(s)}$$

State space representation equations

$$\dot{ \textbf{x} } = A \cdot \textbf{x} + B \cdot \textbf{u}$$ $$\textbf{y} = C \cdot \textbf{x} + D \cdot \textbf{u}$$

An example which is solved step by step for the considered electric circuit can be found here

Transmittance and state space representation

# A dynamic model of a series RLC circuit

An example where a transfer function H(s) and the state space representation equations are defined for a series RLC circuit. As a result the dynamic model of the considered electrical system will be obtained in two forms. The considered electrical circuit is composed of three components: resitor, capacitor and inductor.

http://www.mbstudent.com/control-theory-state-space-representation-RLC-circuit-example-1.html

# State space representation

In control theory and automation engineering dynamic models of system which are often created. It is a lot of cheaper and faster to simulate something than prepare real experiment. To simulate an object behaviour the state space representation is applied. State space representation allows to examine object features when it is under influence of various extortions. Set of examples about mentioned method are placed below.

State space representation for various systems