Control System: Find the Transfer Function From Block Diagram

[jaus tail]

Homework Statement

Homework Equations

To find Ca / Rb we take Ra = 0 --- is this right?
I used mason's formula
P1 = -G2 G1 H1
Loop = G1, G2, -H1, -H2
Using Mason's Gain we get:
Delta1 = 1
Delta = 1 - G1G2H1H2
Using Mason's Gain
TF = -G1G2H1 Divided by ( 1 - G1G2H1H2)
But substituting the values I don't get the answer that matches any options.

The Attempt at a Solution

Substituting I get:

This gives answer in cube as second term of numerator will go in cube for s. None of options have s cube.


Second Question:

I think the options are wrong.
For left TF we get C(s)/R(s) = 10/11
For Right we get C(s)/R(s) = 5/3.5
Multiplying them doesn't give the answer

 

[scottdave]

It's been awhile since I've done these, but I got the same result as you, for the second one: C/R = 100/77. I haven't worked through the first one, yet.

 

[donpacino]

To find Ca / Rb we take Ra = 0 --- is this right?

yes
I got the same thing as you for the second problem.

In problem number one you can dive both the top and bottom side by s...

 

[jaus tail]

Not sure if that helps.
I'm getting: Ca/Rb = -G2 H1 G1 divided by (1 + ( -G2 H1 G1 H2 ) )
And that's not reducing to any of the options.

 

[scottdave]

Not sure if that helps.
I'm getting: Ca/Rb = -G2 H1 G1 divided by (1 + ( -G2 H1 G1 H2 ) )
And that's not reducing to any of the options.

Sounds like the problem might be "hosed"

 

[jaus tail]

Could be. Even I think the question has some typo.