# Determine the gain of proportional controller

1. Jan 30, 2015

### ilovescience85

1. The problem statement, all variables and given/known data

FIGURE 9 shows the block diagram of the control of an electric heating

system. The heater is driven from a voltage-controlled power supply, the

voltage V1 being derived from a potientiometer. The output temperature,

θO, is subject to disturbances, θD, because of changes in the ambient

temperature. It is proposed to apply 'disturbance feedback control' to the

system by the inclusion of a transducer that measures the external

temperature and feeds a signal back to the input via a proportional

controller of gain H.

Determine the required value of H to eliminate the effect of the disturbance.

2. Relevant equations
Unsure

3. The attempt at a solution
Unsure where to start.

#### Attached Files:

• ###### Fig9.JPG
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2. Jan 30, 2015

### milesyoung

You could start by finding the transfer function from $\theta_D$ to $\theta_O$. I'd suggest you replace everything in the boxes with symbols, so you get a general result without numbers and units mucking up your algebra - it's a useful habit.

Also, this is feed-forward control - there's no feedback path in that diagram.

3. Jan 30, 2015

### ilovescience85

Would the following equation be used to help calculate the gain of the Proportional controller? I've attached the equation as a jpeg.

#### Attached Files:

• ###### Equation.JPG
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4. Jan 30, 2015

### milesyoung

I don't know what those symbols mean, and the image itself is frustratingly small

I can't really help you if you don't show me what it is you're doing.

5. Jan 30, 2015

### ilovescience85

I'm a bit lost as we've never had anything like this question within the learning material. I've attached a larger image hopefully.

#### Attached Files:

• ###### Equation.JPG
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6. Jan 30, 2015

### milesyoung

I still don't know what the symbols in that equation represent. You'll have to tell me, and preferably also how you arrived at the equation.

7. Jan 30, 2015

### ilovescience85

I've attached the extracts from the learning material.

#### Attached Files:

• ###### ICP-3-7.pdf
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8. Jan 30, 2015

### milesyoung

That's for a specific kind of feedback system. I think you'd be much better off if you tried to work out the algebra in this problem.

If we call the transducer $T$, the power supply $S$, and the heater $A$, can you find an expression for $\theta_O$?

One method is to just follow the signal pathway around as you write down the operations you encounter, e.g. you could start with $\theta_O = \theta_D + \dots$, where you add the rest by following $\theta_D$ as it goes through the transducer etc. and back to the summing junction.