What is the role of P, I, D parameters in PID control

There are three parameters P, I and D in PID control. Only by understanding the meaning and function of these three parameters can the PID parameter tuning of the controller be completed and the controller achieve the best control effect. In this article, we will introduce the functions of P, I, and D parameters in PID control.

There are three parameters P, I and D in PID control. Only by understanding the meaning and function of these three parameters can the PID parameter tuning of the controller be completed and the controller achieve the best control effect. In this article, we will introduce the functions of P, I, and D parameters in PID control.

proportional action

The proportional controller is actually an amplifier with adjustable magnification, that is, △P=Kp×e, where Kp is the proportional gain, that is, Kp can be greater than 1 or less than 1; e is the input of the controller, that is, the measurement The difference between the value and the given value, also known as the deviation.

It should be noted that, for most analog controllers, the proportional gain Kp is not used as the scale, but the proportionality is used to scale, that is, δ=1/Kc×100%. That is to say, the proportionality is proportional to the reciprocal of the magnification of the controller; the smaller the proportionality of the controller, the greater its magnification and the greater its ability to amplify the deviation, and vice versa.

After understanding the above relationship, it can be known that the larger the proportionality (that is, the proportional band), the smaller the magnification of the controller, and the smoother the curve of the controlled parameter; the smaller the proportionality, the greater the magnification of the controller, and the controlled parameter the more volatile the curve.

Proportional control has a disadvantage, that is, a residual error will be generated, and the integral action must be introduced to overcome the residual error.

Integral action

The integral action of the controller is set to eliminate the residual error of the automatic control system. The so-called integral means accumulation over time, that is, when there is a deviation input e, the integral controller will continuously accumulate the deviation over time, that is, the speed of integral accumulation is proportional to the size of the deviation e and the integral speed. As long as there is a deviation e, the output of the integral controller will change, that is to say, the integral always works, and the integral will stop only when the deviation does not exist.

For a constant deviation, the essence of adjusting the integral action is to change the rate of change of the controller output, which is measured by the time required for the output of the integral action to equal the output of the proportional action. When the integral time is small, it means that the integral speed is large, and the integral effect is strong; on the contrary, the integral time is large, and the integral effect is weak. If the integral time is infinite, it means that there is no integral action, and the controller becomes a pure proportional controller.

In fact, the integral action is rarely used alone, and is usually used together with the proportional action, so that it not only has the proportional action of amplifying (or narrowing) the deviation, but also has the integral action of accumulating the deviation over time, and its action direction is consistent. At this time, the output of the controller is: △P=Ke+△Pi, where △P is the change of the output value of the controller; Ke is the output caused by the proportional action; △Pi is the output caused by the integral action.

Differential action

The differential action is mainly used to overcome the lag of the controlled object, and is often used in temperature control systems. In addition to using differential action, pay attention to the hysteresis of measurement transmission when using the control system, such as the selection and installation position of temperature measurement elements.

In a conventional PID controller, the output change of the differential action is proportional to the differential time and the speed of the deviation change, and has nothing to do with the magnitude of the deviation. The greater the speed of the deviation change and the longer the differential time, the greater the output change of the differential action . However, if the differential action is too strong, it may cause oscillations by itself due to the rapid change, resulting in obvious “spikes” or “jumps” in the output of the controller. In order to avoid this disturbance, the differential-first PID operation rule can be used in the PID regulator and DCS, that is, only the measured value PV is differentiated. When the given value SP of the controller is manually changed, it will not cause a sudden change in the output of the controller. , which avoids the disturbance to the control system at the moment of changing SP. Such as TDC-3000, a soft switch is added to the conventional PID algorithm, and the user can choose whether the controller differentiates the deviation or the measured value during configuration.

When a step signal is input, the ratio of the maximum change value output by the differentiator at the beginning to the output change after the differential action disappears is the differential amplification factor Kd, that is, the differential gain. The unit of the differential gain is time. Set the differential time (or differential gain) ) to zero cancels the function of differentiation.

In order to remember the three functions of proportion, integration and differentiation, three jingles are specially copied for your reference.

Proportional action
slip

Proportional governor, like an amplifier;

When a deviation comes, enlarge it and send it out;

How much to zoom in, look carefully at the knob;

The larger the scale, the lower the magnification.

Integral action jingle

Resetting the regulator, accumulating skills;

As long as the deviation exists, the accumulation will not stop;

Accumulate fast and slow, look carefully at the knob;

The integration time is long and the accumulation speed is low.

Differential action jingle

Speaking of differentiators, it is not mysterious at all;

Step input comes, output jumps up;

Decline fast and slow, look carefully at the knob;

The longer the differentiation time is, the slower the descent will be.

A note on resetting the regulator: Resetting means re-setting, because the integral action in the controller is to complete the re-setting work. Proportional-integral controllers were previously called resetting regulators.

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