# Determine the required value of feedback (H) to control the heater output

Homework Statement:
Determine the required value of feedback (H) to stabilize this heater output
Relevant Equations:
θo= θD*P*He / -θD+T*H
Just need a bit of guidance to make sure that I am heading the right way.

Question is:
Fig 3 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.

I have attached the block diagram to this post

So far I have

θo= θD*P*He / -θD+T*H

θD = Distubance
P = Power Supply = 2
He= Heater = 0.4
T = Transducer = 0.05
H = Proportional control = ???

But does θD then cancel out as there is a positive and negative on both sides?

This would then give:

θo= P*He / T*H

Is this the correct way to be going as the next step for this equation would be to make H the subject to equal a value?

Thanks In Advance

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## Answers and Replies

collinsmark
Homework Helper
Gold Member
Problem Statement: Determine the required value of feedback (H) to stabilize this heater output
Relevant Equations: θo= θD*P*He / -θD+T*H

Just need a bit of guidance to make sure that I am heading the right way.

Question is:
Fig 3 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.

I have attached the block diagram to this post

So far I have

θo= θD*P*He / -θD+T*H

θD = Distubance
P = Power Supply = 2
He= Heater = 0.4
T = Transducer = 0.05
H = Proportional control = ???

But does θD then cancel out as there is a positive and negative on both sides?

This would then give:

θo= P*He / T*H

Is this the correct way to be going as the next step for this equation would be to make H the subject to equal a value?

Thanks In Advance
I don't think that's quite right.

Put units on your figures. For example, don't just say that
"P = Power Supply = 2."
Instead, say,
"P = Power Supply = 2 amps/volt"

Now consider the open-loop gain. In other words, forget about the feedback path for now. Don't worry, we'll come back to it later. Calculate the open-loop gain. Don't forget the units.

Now let's focus on the feedback path. If the open-loop gain converts volts to degrees C, then the feedback path must convert degrees C to volts (in a way, working backwards, from output toward the input). And it must do so in such a way that the total closed loop gain = -1 (unit-less). What value of H causes the overall closed loop gain to be equal to -1? [Edit: by the way, the negative sign is inherent in the subtraction operation of the feedback path from the input. I.e., there's no need to represent the negative sign in H.]

Once you think you have an answer, test it out. Suppose, for example, the temperature disturbance is -3 deg C (i.e, 3 degrees too cold). Work your way through the feedback path to determine the correction voltage. Now work your way through the open-loop path, starting with that voltage [Edit: well, technically the negative of that voltage, since it's subtracted]. If all works out, you should get +3 deg C change in temperature.

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