Understanding Control Actions: Integral, Derivative, Proportional
Integral Action
Moves the valve at a rate proportional to the integral area obtained between the variation of the variable and the set point over time.
Time Integral Action
The interval of time during which, when a step input signal is applied, the output signal due to the integral action equals that due to the proportional action.
Reset Windup
This is the phenomenon that occurs when the error decreases while the area under the integral action continues to increase. This may lead to saturation of the integral action.
Solutions to exceeding the limit:
- Switch to manual control.
- Use an anti-reset windup mechanism that stops integration when a limit is reached.
Derivative Action
In this control mode, a response appears as soon as the error signal starts to change, providing a rapid response to error signals. When the error is in a steady state, derivative control does not respond, since a permanent error (velocity error) does not change over time. Therefore, it is not used alone but is combined with proportional control.
In linear control regulation, a linear relationship exists between the rate of change of the controlled variable and the position of the final control element. The element moves proportionally to the derivative or slope of the variable. It does not eliminate the offset (although it reduces it), and is often combined with integral action (PID). The characteristic of derivative action is a rapid response with a slow start and end.
Proportional Control
These processes are fast but have the disadvantage of offset. The Proportional Band (PB) usually falls between 1.0 and 500. The smaller the proportional band, the greater the sensitivity of the controller. It is used when an offset is not important. It is estimated to be used in around 20% of cases compared to other control types.
Proportional Control of Time Variable
This is a variant of an on/off controller. The ratio of connection time to disconnection time of the final control element is proportional to the value of the controlled variable. The length of a complete cycle (connect + disconnect) is constant, but the ratio between the connection and disconnection time of each cycle varies as the controlled variable deviates from the set point. This type of controller is used only in electrical systems. An example is the temperature regulation in an electric furnace where the final element is a resistance.
Action Proportional
The change in controller output is proportional to the error relative to the set point, so there is a linear relationship between the value of the controlled variable and the position of the final control element (within the proportional band). That is, the valve moves the same value per unit deviation. The corrective action is a simple, fixed multiple of the measured error, acting like a multiplier.
Frequent terms when discussing a proportional controller are:
Controller Gain (Kp)
The relationship between the variation in the output and the error that produces the variation in the input signal.
Proportional Band (PB)
Its relationship is the inverse of the gain: PB (%) = 100/Kp. It is the percentage change in the controlled variable necessary to elicit a full range of the final control element.
Offset
An undesirable characteristic inherent in proportional control. It consists of the stabilization of the variable at a value that does not match the set point after a disturbance is introduced into the system. The offset can be reduced by reducing the PB, but this may cause instability in the process. It is used when it does not matter if the controlled variable does not exactly reach the set point. It can be eliminated by readjusting the set point.
Advantages: Simplicity, stability, fast response, and relatively stable, accelerating the response.
Disadvantages: Offset, and overshoot caused by a significant oscillation time.