In PID control, there are three parameters: P, I, and D. What are their functions?

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In PID control, there are three parameters: P, I, and D. Only by understanding the meaning and function of these three parameters can one adjust the PID parameters of the controller to achieve the best control performance. The ability to skillfully tune PID parameters and put automatic control systems into automatic mode reflects the automation skills of engineering technicians; however, many people do not truly master PID control and PID parameter tuning. This article explains the roles of the P, I, and D parameters in PID control. Proportional action: A proportional controller is essentially an amplifier with an adjustable gain, i.e., △P = Kp × e. Here, Kp represents the proportional gain; this value can be either greater than 1 or less than 1 ； e is the input to the controller, that is, the difference between the measured value and the set value, also known as the error. It should be noted that for most analog controllers, the proportional gain Kp is not used as a scale; instead, the proportional band is used for scaling, i.e., δ = 1/Kc × 100%. In other words, the proportionality is proportional to the reciprocal of the controller’s gain ； The smaller the proportionality of the controller, the greater its amplification factor and its ability to amplify errors; vice versa. Understanding the above relationships, we can see that: the larger the proportional band, the smaller the amplification factor of the controller, and the smoother the curve of the controlled parameter ； The smaller the proportionality, the greater the amplification factor of the controller, and the more volatile the curve of the controlled parameter becomes. The drawback of proportional control is that it produces a steady-state error; to eliminate this error, integral action must be introduced. Integral action: The integral action of a controller is designed to eliminate the residual error in an automatic control system. The so-called integration means accumulation over time; that is, when there is a deviation input e present, the integral controller continuously accumulates this deviation over time. In other words, the rate at which the integral accumulates is directly proportional to both the magnitude of the deviation e and the integration speed. As long as there is a deviation e, the output of the integral controller must change; in other words, integration is always active. Only when there is no deviation does integration cease. For a constant deviation, the essence of adjusting the integral action is to change the rate of change of the controller’s output; this rate is measured by the time required for the output from the integral action to equal the output from the proportional action. A small integration time indicates a high integration speed, and thus a stronger integrating effect ； Conversely, the larger the integration time, the weaker the integrating effect. If the integration time is infinite, it means there is no integration effect, and the controller becomes a pure proportional controller. In practice, the integral action is rarely used alone; it is usually combined with proportional action. This combination gives rise to both the proportional action, which amplifies (or attenuates) the deviation, and the integral action, which accumulates the deviation over time—with both actions acting in the same direction. At this point, the output of the controller is: △P = Ke + △Pi, where △P represents the change in the controller’s output value ； Ke is the output caused by proportional action ； △Pi is the output caused by the integration action. Differential action is primarily used to overcome the lag of the controlled object, and it is commonly applied in temperature control systems. In addition to using differential action, when employing control systems, attention must be paid to the lag in measurements during transmission, such as the selection of temperature sensing elements and their installation location. In a conventional PID controller, the output change due to the differential action is proportional to the derivative time and the rate of change of the error; it is independent of the magnitude of the error. The greater the rate of change of the error and the longer the derivative time, the larger the output change resulting from the differential action. However, if the differentiation effect is too strong, it may itself induce oscillations due to excessively rapid changes, resulting in noticeable “spikes” or “jumps” in the controller’s output. To avoid this disturbance, a differential-leading PID control law can be used in PID regulators and DCS systems; that is, only the measured value PV is differentiated. When the setpoint SP of the controller is manually changed, it does not cause a sudden change in the controller’s output, thereby preventing the disturbance that would occur in the control system at the moment SP is changed. For example, in the TDC-3000, a soft switch is added to the conventional PID algorithm; during configuration, users can choose whether the controller should differentiate the deviation or the measured value. When a step signal is applied, the ratio of the maximum output change at the beginning to the output change after the differential effect disappears is the differential amplification factor Kd, that is, the differential gain. The unit of the differential gain is time; setting the differential time (or differential gain) to zero eliminates the differential function. To help remember the three functions of ratio, integration, and differentiation, three mnemonic phrases are provided for your reference. Mnemonic for proportional action: The proportional valve acts like an amplifier ； A deviation occurs, and it’s amplified and sent out ； What’s the magnification? Look at the knob carefully ； The proportional band is increased, while the amplification factor remains low. Mnemonic for integral action: Reset the regulator; accumulation brings capability ； As long as there is a deviation, the accumulation does not stop ； The speed of accumulation, fast or slow – pay close attention to the knob ； The integration time is long, resulting in a low accumulation rate. A mnemonic for differentiation: When it comes to differentiators, there’s nothing mysterious about them ； When a step input comes in, the output jumps up ； Check the knob carefully to see if the descent is fast or slow ； When the differentiation time is long, the decline is slower. Explanation regarding reset of the regulator: “Reset” means to re-set; in controllers, the integral action is responsible for performing this reset function. Previously, the proportional-integral controller was called a reset regulator.