How do I reduce the outer loop in the first question with 3 inputs?

[John54321]

Homework Statement

I have got 2 questions like this and I'm struggling any help would be much appreciated please. Thanks

Homework Equations

The Attempt at a Solution

 

[Hesch]

Just reduce loop by loop, inside out.

Use Masons rule. Rightmost inner "loop" is just an addition: G3 + G4.

 

[John54321]

Thanks for the quick response, I will try and understand what you've written and look at masons rule.

 

[Hesch]

Use Masons rule.

Masons rule says, that if you have a loop with a forward feeding block, G, and a negative back-feeding block, H, the transfer function of the reduced block will be:

G / ( 1 + G * H )

Now the leftmost inner block has positive feed back, so the transfer function for this loop will be:

( G1 * G2 ) / ( 1 - G1 * G2 * H1 )

 

[John54321]

Thanks very much for explaining this, now I've got to draw this out step by step. Much appreciated.

Thanks

John

 

[John54321]

Hi

So will the inner right loop be (G3 + G4) ?

Thanks

 

[Hesch]

Yes: input*G3 + input*G4 = input*(G3+G4) = output.

Transfer function = output/input = (G3+G4).

 

[John54321]

Hi

So this is how it should look with the two transformations ?

Thanks for help

 

[Hesch]

So this is how it should look with the two transformations ?

It's not a transformation, it's a reduction of the Laplace transformed.

The reduced transfer function (leftmost inner loop) must be drawn as one block wherein there is a fraction: Numerator = (G1*G2), denominator = (1 - G1*G2*H1).

Otherwise your drawn transfer function will be read as: ( G1*G2 ) * ( 1 - G1*G2*H1 ).

 

[John54321]

Hi

Ok thanks very much for your help now the next question looks more involved.

 

[John54321]

Hi which I'm put would I start with as there are 3 ? Please thanks for your help

 

[Hesch]

Did you reduce the outer loop in the first question?

which I'm put would I start with as there are 3 ? Please thanks for your help

I don't quite understand your question ( maybe because I'm not american or english ): 3 of what? Inputs? Please reword your question.

Furthermore I don't understand what is meant by the question in 2): Describe the relationship . . . ?

You can "move" θ_d1 and θ_d2 backwards in the loop, dividing them with the transfer function they are passing by this movement. Doing this you will have one (parallel) input:

θ_i + ( θ_d1/G1 ) + ( θ_d2/(H2*G2*G1) ).

Having removed the inputs from the loop, you can reduce the loop, and multiply its transfer function by its 3 inputs in parallel.

( My best guess ).