State-space Model Of Electrical Systems
State-space model of Electrical systems
Remember that the impedance approach is valid only if the initial conditions involved are all zeros. Since the transfer function requires zero initial conditions, the impedance approach can be applied to obtain the transfer function of the electrical circuit. This approach greatly simplifies the derivation of transfer functions of electrical circuits. Consider the circuit shown in Figure 2 (b).Assume that the voltages ei and eo are the input and output of the circuit, respectively. Then the transfer function of this circuit is
For the system shown in Figure 1,
This is same to that of the transfer equation obtained from LCR circuit.
State-space representation:
A state-space model of the system shown in Figure 1 may be obtained as follows:
First, note that the differential equation for the system can be obtained from Equation of the transfer function of the LCR circuit as
