Detailed relationship between proportional band and proportional control (P) output

Proportional control

TITLE: Proportional control action

Proportional control (P) is one of the simplest ways to control. The output of its controller is proportional to the input error signal. Depending on the equipment, the proportional band is generally 2 to 10% (temperature control). However, only the P control will produce the off set (steady state error) mentioned below, so the integral control (I) is generally added to eliminate the steady state error. The relationship between the proportional band and the proportional control (P) output is shown in the figure. Example of setting with the MVp expression:

figure 1

Figure 2: Relationship between proportional band and output

Steady state error (Off set)

In proportional control, when the error stabilizes at a certain value after a certain period of time, the error at this time is called an offset. When only proportional control is used, different steady-state errors occur depending on the load variation and the inherent characteristics of the device. The inconsistency between the intersection of the load characteristic and the control characteristic curve and the set value is the cause of the steady state error. The proportional band hour will not be generated. To eliminate the steady-state error, we set the manual reset value --manual reset value (MR) to eliminate the control error.

Figure 3: Off set produced by proportional control

Manual reset

Equation 1: MR: manual reset value

As mentioned earlier, steady state error cannot be eliminated by only proportional control. For this reason, if the MR (manual reset value) is set to be variable, the output of the regulator can be freely adjusted (ie, adjusted). As long as the manual operation output is equivalent to the amount of offset, it can be consistent with the target value. This is called a manual reset, which is usually available on a proportional regulator. In the actual automatic control, it is not practical to manually reset each time an offset occurs. The integral control function described later can automatically eliminate the steady-state error.

Figure 4

Integral control

Integral control action

The so-called integral control (I) is to automatically change the output when the steady-state error occurs, so that it is the same as the output of the manual reset action, and achieve the purpose of eliminating the steady-state error. When there is an error in the system, the integral control is performed. According to the integral time, the output of the regulator will change at a certain speed. As long as the error still exists, the output will be continuously performed.

Figure 5

Definition of integration time:

When the integral term and the proportional term contribute the same to the output of the controller, that is, the time taken for the integral action to repeat the proportional action is the integration time.

Differential control

Differential control action (D) (Differential control action)

The function of the differential control (D) is to predict the future trend of the error signal by the rate of change of the error. By providing advanced control, differential control can stabilize the controlled process. Therefore, it is often used to counteract the unstable trend caused by integral control.

Figure 6

Definition of differential time:

When the input quantity continues to change at a certain rate, the differential term and the proportional term contribute the same to the output of the controller, that is, the time taken by the differential action to repeat the proportional action is the derivative time.Control Valve, Flow Control Valve, Hydraulic Control Valve, Proportional Directional Control Valve