# Control systems: Simplifying block diagram

1. Mar 26, 2017

### MattH150197

1. The problem statement, all variables and given/known data
How to show a block diagram can be simplified to a standard first order form for the diagram shown in the image attached and the question is shown in 1.a

2. Relevant equations
Standard first order form K/(1+tD) where K gain and t is time constant

3. The attempt at a solution
So i got ((Kb*H-h)*Kp-4)*1/2s = h Is this correct? and how do i show it in standard first order form from here? Thanks

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2. Mar 26, 2017

### Hesch

Figure 1 shows two closed loops: An inner and an outer loop.

Use Mason's rule to calculate the transfer function as for the inner loop.

Insert this inner transfer function in the outer loop and use Mason again to calculate h(s)/H(s) for the outer loop ( the transfer function for the outer loop ).

The characteristic equation for h(s)/H(s) will be in the form:

as + b = 0 → τ = b / a.

3. Mar 26, 2017

### MattH150197

Enlarged image of diagram as requested

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• ###### aaa.jpg
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4. Mar 26, 2017

### MattH150197

Hesch sorry im not quite sure how from what youve said i can show it is a first order system as i need to show it in the form h = K/(1+tD), im just not sure how to get there from what i worked out

5. Mar 26, 2017

### Hesch

You don't need to show in this form.

Using Mason you should get:

h(s)/H(s) = Kp * Kb / ( 2s + 4 + Kp ) →

h(s) = H(s) * Kp * Kb / ( 2s + 4 + Kp )
( if you wish )

6. Mar 26, 2017

### Staff: Mentor

I think it's nearly there; Check what's fed back via the "4" block. That 4 looks mighty lonely in your equation, given that the term its being summed with is bound to have some units associated with it... .

7. Mar 26, 2017

### Hesch

To determine the steady state gain from the above equation, let s → 0, so

h(0) = H(0) * Kp * Kb / ( 4 + Kp )

8. Mar 27, 2017

### MattH150197

Ah yeah i understand what you have done now actually Hesch, thanks for the help guys.