- On-Off Control
- Proportional Only Control
- Proportional-Integral Control

- The level in the tank is measured.
- It is then compared to the setpoint level.
- If the actual level is below the setpoint level by a specified amount then the outlet control valve is shut.
- If the actual level is above the setpoint level by a specified amount then the outlet control valve is opened.

The specified amount in question is known as the deadzone and in the experiment is defined as a percentage of the total height of the tank.

The graphs below show that if the deadzone is small then the level is
close to its setpoint but the valve is being opened and closed
continuously which is unsatisfactory *(why?)*.

On the other hand if the deadzone is large then there is not as much opening and closing of the valve but the level is not very close to the setpoint, which is also unsatisfactory.

The optimal solution depends on the application of the loop and is a compromise between the two solutions shown below.

In proportional only control the algorithm which describes the action of the controller is

- The level in the tank is measured.
- It is then compared to the setpoint.
- The resulting compensatory action of the controller is proportional to the error between the above two values.

The variable which determines the proportionality is known as the proportional band. The relationship between the adjustment and error is

Thus

- If the PB is small the adjustment will be sensitive to changes in the error and the response will be oscillatory.
- If the PB is large the adjustment is not so sensitive and the response is smoother.

Note that the value at no error always stays constant. If there are changes to the conditions, either a setpoint change or other disturbance, then there must be a corresponding change in the adjustment. However, for any adjustment there must be an error. This leads to one of the disadvantages of using proportional control. At the new steady state there has to be an error or offset.

Therefore the two graphs below show that

- For a small PB the response shows a small offset but there are a lot of oscillation.
- For a large PB the response is smooth but there is a large offset.

Again the optimal solution depends on the application of the loop and is a compromise between the two solutions shown.

The third and final controller action used in this experiment is proportional-integral control. This is an extension of the proportional controller shown above. It works by summing the current controller error and the integral of all previous errors. i.e.:

It could simply be thought of as a way of continuously adjusting the
*value at no error* so as to eliminate the offset.

The new variable introduced to define the amount of integral action is known as the integral reset time of the controller.

- The smaller this number the less sensitive the adjustment is to changes in the error and so is more accurate.
- The larger the number the more sensitive the adjustment is to changes and so is less accurate.

Thus the advantage of using integral action with proportional action is that it can eliminate the offset. The disadvantages of proportional-integral control are that it gives rise to a higher maximum deviation, a longer reponse time and a longer period of oscillation than with proportional action alone. This type of control action is therefore used where the above can be tolerated and offset is indesirable.

The two graphs below show the effect of changing the integral reset time. Note that the proportional band is constant at a value between the two extremes used for the graphs in the previous section.

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