Process Engineering Division – Instrumentation and Automation Section – Daily Topics – Topic No. 2021-01-07

Static deviations are eliminated through integration, while dynamic deviations are reduced through differentiation

If the dynamic deviation is large, then D needs to be adjusted; if the static deviation is large, then P and I need to be adjusted.

Adjust D for large dynamic deviations, and adjust P and I for large static deviations.

The output of a PID controller consists of three components: the P-component output, the I-component output, and the D-component output. The P-component output is proportional to the magnitude of the error; the strength of the P-action is proportional to Kp (and inversely proportional to the gain δ)； The output of part I is proportional to the amplitude of the deviation and the duration of the deviation; the intensity of the effect of I is inversely proportional to the integration time Ti (and proportionally to the integration rate Ki) ； The output of section D is proportional to the rate of change of the deviation, and the strength of the effect of D is proportional to the differentiation time TD (proportional to the differentiation rate KD). The sensitivity of the P-action response control system to deviations is higher the stronger the P-action. The D-action reaction control system is sensitive to changes in deviation; the more severe the deviation change, the larger its output component, effectively overcoming dynamic deviations in the system.

In automatic control, the PID controller relies on the proportional action to prevent excessive oscillations, and on the derivative action to reduce dynamic errors. So what is the difference between these two actions? Answer: Proportional control (P) is a type of continuous control and represents the most fundamental control law. The proportional control law states that the relationship between the controller’s output P and its input error e is proportional. The adjustment action is rapid, with no lag ； After the regulation process is complete, a certain residual error remains, which is a drawback of proportional control ； The value of Kc must be appropriate; otherwise, it may cause oscillations in the system or an increase in the residual error. Suitable for applications where a certain degree of deviation is acceptable and the requirements for adjustment quality are not stringent. It is suitable for applications without lag, that is, for situations where fast adjustment is required. The proportional-integral control (PI) law refers to the dual proportional and integral relationship between the regulator’s output p and the input error e: when the input error e changes suddenly, the proportional element acts promptly to suppress the effect of the disturbance – this is the coarse adjustment; subsequently, the integral control effect gradually builds up and intensifies, thereby eliminating any remaining error – this is the fine adjustment. It is mainly used in situations where high control accuracy is required and no offset is allowed. The proportional-differential control (PD) law refers to the relationship between the regulator’s output signal and the error signal, which includes both proportional and differential components: when the input error e changes abruptly, the output immediately jumps to KD times the proportional value, and then gradually decreases to the proportional value. Due to its leading effect, it enables early control and helps to overcome the common phenomenon of capacity lag. Suitable for applications with significant capacity lag. In practical applications, pure proportional-differential control is used less frequently; instead, a combination of proportional, integral, and differential control is employed the most, that is, PID control. Proportional-integral-derivative control (PID) refers to the relationship between the output of a controller and its input, which involves proportional, integral, and derivative actions. Therefore, proportional-integral-derivative control is denoted as PID. In PID control, the proportional element serves as the foundation, performing the basic regulation function by preventing the amplification of disturbances. The integral element helps to eliminate residual errors, thereby improving the quality of regulation. The derivative element provides lead action, which can be used to overcome capacity delays and achieve better transition process performance metrics. Therefore, the combined use of the three can achieve a more comprehensive regulator function, making the operation of the automatic control system more stable and reliable. Scenarios suitable for Proportional-Integral-Derivative control: situations where high control quality is required ； The controlled parameters exhibit lagging behavior, especially in cases where the capacity lag is relatively large.

In factory PID control, PI control is generally used; it is sufficient to overcome static and dynamic deviations. D control is employed in situations with control lag, such as in furnace temperature regulation, where differential action is used in advance to address the issue of lag.

Proportional action relies on the magnitude of the deviation for regulation; the greater the deviation, the larger the output, which allows for rapid suppression of deviations and thus prevents excessive oscillations； Differential action is regulated based on the rate of change of the deviation; the faster the frequency of deviation changes, the greater the output. When the deviation remains constant, the differential action is zero, thereby suppressing dynamic deviations.

Adjust D for large dynamic deviations, and adjust P and I for large static deviations.

In factory PID control, PI control is generally used; it is sufficient to overcome static and dynamic deviations. D control is employed in situations with control lag, such as in furnace temperature regulation, where differential action is used in advance to address the issue of lag.

If the dynamic deviation is large, then D needs to be adjusted; if the static deviation is large, then P and I need to be adjusted.