Time Block Diagram and State Equation

Shunt DC motor

1

Solving field voltage equation and armature voltage equation:

Permanent Magnet DC Motor

2

3Solving for dr /dt :

State equation in matrix (vector matrix) :

For Shunt DC motor

4System Equation :

x = state vectoru = input vector

for Permanent Magnet DC Motor

Chapter 3

Reference frames

But

then

----------- 1

----------- 2

----------- 3

----------- 4

Sub equation 3 in to equation 1

From equation 2 we have

The desired transformation obtained by substituting the appropriate transformation in to , Hence

Transformation between two reference frames portrayed by trigonometric relationships.

BY T.K