Modern University for Modern Sciences and Arts

Faculty of Engineering

Automatic Control System

ESE 346/ESE416

Sheet – 4

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Problem 1:

Obtain the transfer function for the system shown using Mason’s Rule.

Problem 2:

A signal flow graph is shown below. Use Mason’s formula to find the transfer

function Y(s)/R(s).

Problem 3: (assignment)

A signal flow graph is shown below. Use Mason’s formula to find the transfer

function Y(s)/R(s) using Mason's Gain Formula.

-H2

-H1

G1 G2 G3 G4 1 Y(s)

1

-1

-H1

-H3

1 G1 G2 G6 G3

G5

Y(s) R(s) G4

-H2

-H2

-H3

1 G1 G2 G6 G3

G7

G5

Y(s) R(s) G4

G8

-H4

-H1

Problem 4:

Determine the zeros-poles of the following open loop transfer function

GH(S) = 10 (S+1) / (S+2)(S+3)

Problem 5:

Sketch the root-locus diagram for the following open loop transfer functions

G(s)H(s)= K / [S(S+2)(S2+2S+2)]

G(s)H(s)= K (S+1)(S+4)(S+7) / [S(S+3)(S2+2S+2)]