# The result of a disturbance on an output

• David J
In summary, the conversation discusses a proportional control system with an input of 10 units and an uncontrolled input of 50 units. The output response to a step change in the uncontrolled input is shown in a graph. The question asks for the change in offset in the output and the inclusion of additional control actions to minimize the offset and disturbance. The answer is calculated using a formula and a Laplace transform method is also mentioned. The solution involves drawing a modified block diagram with a PID controller. Further clarification is provided in a separate thread.
David J
Gold Member

## Homework Statement

[/B]
The proportional control system of figure 3(a) (attachment 235263) has an input, ##\theta_{1}##, of 10 units. The uncontrolled input, ##\theta_{2}##, has a value of 50 units, prior to a step change down to 40 units. The result of this disturbance upon the output, ##\theta_{o}## is shown in figure 3(b) (attachment 235264)

(a) Calculate the change in offset in the output produced by the step change

(b) Draw a modified block diagram to show how the offset could be minimised by the inclusion of another control action. Also, show by means of a sketch how the modification might be expected to affect the output response.

(c) Show, by drawing a modified block diagram, how the magnitude of the disturbance could be minimised by the inclusion of a third type of control action

2. Homework Equations

##\theta_{0}=\frac{\theta_{2} +G\theta_{1}}{1+G}##

## The Attempt at a Solution

(a)
[/B]
Prior to the step change

##\theta_{0}## = ##\frac{50 + (9*10)}{1+G}##

so ##\theta_{0}## = ##\frac{140}{10}##=## 14 m^{3 h-1}##

After the step change

##\theta_{0}## = ##\frac{40 + (9*10)}{1+G}##

so ##\theta_{0}## = ##\frac{130}{10}##=## 13 m^{3 h-1}##

So in the first instance would I be correct in saying that the change in offset in the output as a result of the step change will be ## 1 m^{3 h-1}## ?

I attached some notes, (pages 16 and 17) which I think are in relation to this question

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My approach may be too simple-minded, but the output plot looks like the initial output response is a decrease of 5 units. I don't know what m and h are.

Hello, the method you see above is the method I was given in my notes but I discovered another way of doing this using laplace transform. The answer from that method was very similar to this which makes me think my answers are close.

The m is for cubic meters but I have just realized that the question does not actually suggest and units so I may be wrong in using ##m^{3h-1}##

h is the feedback error I think.

I will post the laplace method in this thread during the next couple of days

The output response to the ##\theta_2## input is the same as the closed loop response of a negative feedback loop with ##G^{\prime} = 1## and ## H^{\prime} = 0.1 * 9 = 0.9## feedback gain.

I submitted this and it was marked as correct as per my working out in the first post. The answers to b and c just required a block diagram showing the addition of the integral action and the derivative action resulting in a block diagram of a PID controller. I will mark this as solved now but if anyone needs any help with this again I can advise.

thanks

David J said:
I submitted this and it was marked as correct as per my working out in the first post. The answers to b and c just required a block diagram showing the addition of the integral action and the derivative action resulting in a block diagram of a PID controller. I will mark this as solved now but if anyone needs any help with this again I can advise.

thanks

Hi DavidJ again,

Looking at this I don't see how you can't take the H figure into account? I work the formula to have the bottom of the fraction as 1+G*H ?

## What is a disturbance on an output?

A disturbance on an output refers to any external factor or event that causes a change or disruption in the output of a system or experiment. This can include both physical and non-physical disturbances, such as changes in temperature, pressure, or the introduction of new variables.

## How do disturbances affect the output of a system?

Disturbances can have a wide range of effects on the output of a system, depending on the type and severity of the disturbance. In some cases, a disturbance may cause a slight change in the output, while in others it may lead to significant variations or even a complete change in the output.

## Can disturbances be controlled or eliminated?

In most cases, it is difficult to completely control or eliminate disturbances on an output. However, scientists and engineers can often minimize the impact of disturbances by designing systems with built-in mechanisms to counteract or compensate for them.

## What are some common sources of disturbances on an output?

Disturbances can come from a variety of sources, both internal and external. Some common sources include environmental factors, such as changes in temperature or humidity, as well as human error or equipment malfunctions.

## How do scientists account for disturbances when analyzing data?

When analyzing data, scientists typically take into account any known or potential disturbances and try to control or mitigate their effects. This can involve using statistical methods to identify and remove outliers or adjusting data to account for known disturbances.

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