Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic : Models for Control System

Difficulty : High

Marks : 10M

I)

II) Shifting of take off point after a block

III) Blocks in series

IV) Eliminate feedback loop.

V) Shifitng take of point after a block

VI) Blocks in series

VII) Eliminate feedback loop.

Now simplify,

$$\frac{C(s)}{K(s)} = \frac{\frac{G2.G3.G4}{1+ G3.G4.H2}}{1+ [(\frac{G2.G3.G4}{1+G3.G4.H2})*(\frac{H1}{G4})]}$$

$$\frac{C(s)}{K(s)} = \frac{G2.G3.G4}{1+G3.G4.H2+G2.G3.H1}$$

=> VII) Becomes,

VIII) Blocks in series:

IX) Eliminate feedback loop and simplify,

$$ \frac{C(s)}{K(s)} = \frac{\frac{G1.G2.G3.G4}{1+G3.G4.H2+G2.G3.H1}}{1+ [\frac{G1.G2.G3.G4}{1+G3.G4.H2+G2.G3.H1}][\frac{H3+G3.G4.H2.H3}{G3.G4}]}$$

$$ \frac{C(s)}{K(s)} = \frac{G1.G2.G3.G4}{1+G3.G4.H2+G2.G3.H1 + (G1.G2)(H3+G3.G4.H2.H3)}$$

$$ \frac{C(s)}{K(s)} = \frac{G1.G2.G3.G4}{1+G3.G4.H2+G2.G3.H1 + G1.G2.H3 + G1.G2.G3.G4.H2.H3)}$$

$$ \therefore \frac{C(s)}{K(s)} = \frac{G1.G2.G3.G4}{1+G3.G4.H2+G2.G3.H1+G2.G3.H3+G1.G2.G3.G4.H2H}$$