【Control Version】One Question per Day 20180417

PID is an abbreviation for Proportional, Integral, and Derivative. The proportional control mechanism responds in proportion to the system’s deviation; as soon as a deviation occurs, proportional control takes action to reduce that deviation. A large proportional gain can speed up regulation and reduce errors, but an excessively high proportional gain reduces the stability of the system, and may even lead to its instability. Integral control function: It enables the system to eliminate steady-state error and improve accuracy. Due to errors, integral regulation is carried out until no error remains, at which point it stops; the output of integral regulation becomes a constant value. The strength of the integration effect depends on the time constant Ti during integration; the smaller Ti is, the stronger the integration effect. Conversely, a larger Ti value results in a weaker integrating effect; the addition of integral control can reduce system stability and slow down the dynamic response. The integral action is often combined with the other two control laws to form a PI controller or a PID controller. Differential control action: The differential effect reflects the rate of change of the system’s error signal; it has predictive capabilities, allowing it to anticipate the trend in error changes. As a result, it enables proactive control, eliminating the error before it even develops.

Proportional element: It responds proportionally to the error signal e(t) of the control system; as soon as an error occurs, the controller takes action to reduce it. The larger the proportionality coefficient kP, the faster the system’s response speed; however, if it is too large, the system will experience overshoot and may even become unstable. Integration stage: Used to eliminate static error and improve the error-free performance of the system. The strength of the integrating effect depends on the integration time constant Ti; the larger Ti is, the weaker the integrating effect, and vice versa. However, it has a lagging effect that slows down the system’s response speed, increases overshoot, and may cause oscillations. Differential element: It monitors the trend (rate of change) of the deviation signal, generates a differential output to adjust the error. When there is a sudden change in the error, it enables timely control; moreover, it introduces an effective early correction signal into the system before the deviation signal changes too significantly, thereby accelerating the system’s response time and reducing the adjustment period. However, it leads to sensitivity to disturbances and poor interference resistance.

1. The function of the proportional parameter KP is to accelerate the system’s response speed and improve its regulation accuracy. 2. One of the main functions of the integral action parameter Ti is to eliminate the steady-state error of the system. 3. The function of the differential action parameter Td is to improve the dynamic performance of the system; its main role is to suppress changes in the deviation in any direction during the response process, and to predict such deviations in advance.

KP, the proportional control coefficient, which accelerates the system’s response speed and improves its control accuracy； KI, integral control coefficient, for eliminating residuals ； KD, the differential adjustment coefficient, improves the dynamic performance of the system.

Proportional control: It responds proportionally to the system’s deviation; as soon as a deviation occurs, proportional control takes action to reduce that deviation. A large proportional gain enables faster regulation and reduces errors, but an excessive proportional gain reduces the stability of the system, and may even lead to its instability. Integral control function: It enables the system to eliminate steady-state error and improve accuracy. Due to errors, integral regulation is carried out until no error remains, at which point the integral regulation stops and an constant value is output by it. The strength of the integration effect depends on the integration time constant Ti; the smaller Ti is, the stronger the integration effect. Conversely, a larger Ti value results in a weaker integrating effect; the addition of integral control can reduce system stability and slow down the dynamic response. The integral action is often combined with the other two control laws to form a PI controller or a PID controller. Differential control action: The differential effect reflects the rate of change of the system’s error signal; it has predictive capabilities, allowing it to anticipate the trend in error changes. As a result, it enables proactive control, eliminating the error before it even arises. Therefore, the dynamic performance of the system can be improved.

Proportional element: It responds proportionally to the error signal e(t) of the control system; as soon as an error occurs, the controller takes action to reduce it. The larger the proportionality coefficient kP, the faster the system’s response speed; however, if it is too large, the system will experience overshoot and may even become unstable. Integration stage: Used to eliminate static error and improve the error-free performance of the system. The strength of the integrating effect depends on the integration time constant Ti; the larger Ti is, the weaker the integrating effect, and vice versa. However, it has a lagging effect that slows down the system’s response speed, increases overshoot, and may cause oscillations. Differential element: It monitors the trend (rate of change) of the deviation signal, generates a differential output to adjust the error. When there is a sudden change in the error, it enables timely control; moreover, it introduces an effective early correction signal into the system before the deviation signal changes too significantly, thereby accelerating the system’s response time and reducing the adjustment period. However, it leads to sensitivity to disturbances and poor interference resistance.

The role of the proportional parameter is to accelerate the system’s response time and improve its regulation accuracy. The larger the proportional parameter, the faster the system responds and the higher its regulation accuracy; however, this can lead to overshoot and even instability in the system. If the proportional parameter is too small, it will reduce the regulation accuracy and slow down the response time, thereby prolonging the adjustment period and deteriorating the system’s static and dynamic characteristics. The function of the integral parameter is to eliminate the system’s steady-state error. The larger the integral parameter, the faster the steady-state error is eliminated; but if it is too large, integral saturation may occur at the beginning of the response process, resulting in significant overshoot. If the integral parameter is too small, it will make it difficult to eliminate the steady-state error, affecting the system’s regulation accuracy. When the system deviation is large, the integral action should be reduced or even eliminated, while when the deviation is small, it should be enhanced (through methods such as integral separation, triangular integration, variable-speed integration, and anti-integral saturation). An overly large integral coefficient can cause overshoot or even integral saturation, whereas a too small coefficient prevents the steady-state error from being eliminated. The role of the derivative parameter is to improve the system’s dynamic characteristics; it mainly functions by suppressing changes in deviation in any direction during the response process and by predicting such changes in advance. However, if the derivative parameter is too large, it will cause premature braking of the response process, thus prolonging the adjustment time and reducing the system’s resistance to disturbances. The introduction of derivative signals can easily introduce high-frequency interference, and the limitations of the derivative term become particularly evident when there are sudden errors or disturbances.

The function of the proportional parameter is to accelerate the system’s response speed and improve its control accuracy. The larger the proportional parameter, the faster the system’s response speed and the higher its tuning accuracy. However, this can lead to overshoot, and may even cause the system to become unstable. If the proportional parameter is set too low, it will reduce the tuning accuracy, slow down the response speed, thereby increasing the adjustment time and deteriorating the system’s static and dynamic characteristics. The role of the integral parameter is to eliminate the steady-state error of the system. The larger the integral parameter, the faster the static error of the system is eliminated. However, if it is too large, integral saturation occurs at the beginning of the response process, resulting in significant overshoot. If the integral parameter is too small, it becomes difficult to eliminate the system’s static error, affecting the system’s regulation accuracy. When the system deviation is large, the integral effect should be reduced or even eliminated, while it should be enhanced when the deviation is small (integral separation, trapezoidal integration, variable-speed integration, anti-integral saturation). If the integral coefficient is set too high, overshoot will occur, and even integral saturation might happen; if it is set too low, the steady-state error will not be eliminated for a long time. The role of the differential parameter is to improve the dynamic characteristics of the system; it primarily functions by suppressing changes in deviation in any direction during the response process, and by predicting such deviations in advance. However, an excessively large differential parameter will cause premature braking of the response process, thereby prolonging the adjustment time and reducing the system’s resistance to interference. The introduction of differential signals can easily introduce high-frequency interference, and the shortcomings of the differential term become particularly evident when there are sudden errors or disturbances.

PID is an abbreviation for Proportional, Integral, and Derivative. The proportional control mechanism responds in proportion to the system’s deviation; as soon as a deviation occurs, proportional control takes action to reduce that deviation. A large proportional gain can speed up regulation and reduce errors, but an excessively high proportional gain reduces the stability of the system, and may even lead to its instability. Integral control function: It enables the system to eliminate steady-state error and improve accuracy. Due to errors, integral regulation is carried out until no error remains, at which point it stops; the output of integral regulation becomes a constant value. The strength of the integration effect depends on the integration time constant Ti; the smaller Ti is, the stronger the integration effect. Conversely, a larger Ti value results in a weaker integrating effect; the addition of integral control can reduce system stability and slow down the dynamic response. The integral action is often combined with the other two control laws to form a PI controller or a PID controller. Differential control action: The differential effect reflects the rate of change of the system’s error signal; it has predictive capabilities, allowing it to anticipate the trend in error changes. As a result, it enables proactive control, eliminating the error before it even arises. Therefore, the dynamic performance of the system can be improved. By selecting an appropriate differential time, overshoot can be reduced, as well as the settling time. Differential action amplifies noise interference; therefore, excessive differential adjustment is detrimental to the system’s resistance to interference. Furthermore, a differential reaction is the rate of change, and when there is no change in the input, the differential output is zero. Differential action cannot be used alone; it needs to be combined with the other two control mechanisms to form PD or PID controllers.

In PID control, there are three parameters: P, I, and D. The functions of these P, I, and D parameters in PID control. Proportional action: A proportional controller is essentially an amplifier with an adjustable gain factor, namely △P=Kp×e, where 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. A drawback of proportional control is that it generates error; to overcome 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 refers to the accumulation over time; that is, when a deviation input e is present, the integral controller accumulates this deviation over time. The rate of this integration is proportional to the magnitude of the deviation e as well as the integration rate itself. As long as a deviation e exists, the output of the integral controller must change; in other words, integration is always active, and it only stops when there is no deviation. 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 means 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. 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 conventional PID controllers, the output change resulting from the differential action is proportional to the rate of change of the error as well as the differential time; it is independent of the magnitude of the error. The greater the rate of change of the error and the longer the differential time, the larger the output change due to the differential action. However, if the differential action is too strong, it may cause oscillations on its own due to the rapid changes, resulting in significant \"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. In systems like the TDC-3000, a soft switch is added to the conventional PID algorithm; during configuration, the user can choose whether the controller should differentiate the error or the measured value.