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# 4-6.Proportional integral (PI) control

It is thought that it can be controlled well by proportional control, but in reality, there is a problem when the current value approaches the set value.

That is, the amount of operation becomes too small, and it becomes impossible to control it further finely.
As a result, the current value is very close to the set value and becomes stable.
When this happens, it will be close to the set value, but it will not be perfect for the set value forever.

This slight error is called “Offset”.

Offset means that the small difference between the set value and the current value continues at a constant value.
To put it simply, it’s a gap.

Integral control is used to eliminate this offset.
In other words, the slight difference is accumulated in time, and the operation is performed so that the difference (offset) is eliminated by increasing the operation amount at a certain size.

Control that adds integral action to proportional action in this way is called “PI control.”

As explained in the previous section, proportional control is control that performs heating in proportion to the difference (deviation) between the current value and the set value within the proportional band. It is set 5to10%.

### ● Why does offset appear?

In the proportional control, the heating amount becomes too small in consideration of the stability near the set value, and the control cannot be performed more finely. The result will be stable with the current value very close to the set value. Because it keeps the status quo and does not reach the amount of heat needed to change it.

### ① The heating target is too large or too small.

If a large load is applied compared to the conditions under which the equipment or system was designed, the amount of heat taken off by this load will increase, so that it will stabilize below the set value. Conversely, when a lightly loaded object is inserted, the opposite is true, and it is stable at high places.

### ② When the ambient temperature of the device changes

In winter, the ambient temperature of the device is low and the amount of heat taken increases, so offsets lower than the set value are likely to occur. Conversely, since the ambient temperature is high and the heat radiation is small in summer, etc., it is easy to produce a high offset.

### ③ When the set value is changed

For example, in a heating furnace adjusted to 500℃, a lower offset tends to occur when used at a temperature higher than 500℃, and a higher offset tends to occur when set below 500℃.

### ● What is controller doing inside?

First, it is premised that offset is not theoretically eliminated by proportional control alone. Considering the current situation that is stable even after a long time, it is clear that some output signal is output from the controller. However, at the current output, the power is insufficient and it is stable without reaching the target value.

In order to make this offset zero, it is necessary to output an output signal that has been added to the current output signal to correct the deviation. This is the role of integral control. The integral control is 1. It means that the past deviation is stored and the deviation is eliminated within the range of 2 set times.

Until the integral of the difference between the present value PV becomes zero and the set value SV temperature is reached, the integral control shifts the proportional band from the original SV to a higher temperature and outputs it to eliminate the offset.

If the integration time is too long, the amount of correction per hour will be insufficient, and the offset will not be resolved forever.
If the integration time is short, the correction is strongly required, and a large amount of correction works in a short time, and the deviation can be corrected in a short time.
However, care must be taken if the integration time is set too short, because hunting tends to occur and stable control results are not required.
The default setting is 120 seconds, and the default setting is about 100 to 150 seconds.

### ● Integral control is a correction operation that adjusts the output to make the offset zero within the set time.

Integral control has control ability even by itself. Therefore, only I operation can be controlled. However, control response is significantly worse than PI control.
In the early days of analog control, I-operation-only control was sometimes used because it could be simple and cheap. However, they are rarely used these days.