PID Control Basics

PID Control Basics

Proportional-Integral-Derivative, PID, control is a control loop feedback mechanism in which the controller continuously calculates an error value as the difference between a measured process value (PV) and a desired set value (SV).

The PID controller attempts to minimize the error over time by adjusting a control variable to a new value.

• In this control:
  • P accounts for the present values of the error.
  • I accounts for the past value of the error.
  • D accounts for the predicted future values of the error based on the current rate of change.

PID2 Notice

• CICON version 4.01 supports PID control for all types of CIMON PLCs.
• PID2 functions are available with the following PLC type and firmware:

PID Availability
CPU	XP	CP	BP	PLC-S
Version	v4.27	v4.26	-	v1.37

v4.26 CP CPU Compatibility

The self-learning function is not supported on the CP3U and CP4U CPUs.

PID Basics

Direct/Forward Action & Reverse Action

• Direct/Forward Action:
  • The manipulation value (MV) will increase when the process value (PV) is greater than the set value (SV).
  • Works with heating systems.
• Reverse Action:
  • The manipulation value (MV) will decrease when the process value (PV) is greater than the set value (SV).
  • Works with cooling systems.

Change of MV according to PV

Control Graph by Forward and Reverse Action

Proportional (P) Control Action

• Proportional (P) control generates the manipulation value (MV) in proportion to the error (E).

  • E:
    • Difference between the set value (SV) and process value (PV).

• The manipulation value (MV) is calculated as follows:

  • MV = K_p + E
    • K_p: proportional gain
      • If the K_p value is too large, the control process is getting fast but the system will be in danger for oscillation.
      • If the K_p value is too small, the control process is getting slow to make it stable.

• Under proportional (P) control, the offset, or residual error, will remain until the bias on the controller's output is manually changed to remove the offset.

Integral (I) Control Action

• Integral (I) control will generate the manipulation value (MV) in proportion to the time-integral of the error (E).

• Integral action eliminates the offset.

• If the integral time is set too long, the controller will be sluggish.

• If the integral time is set too short, the control loop will oscillate and become unstable.

• The integral (I) action is used with the PI control or PID control.

  • It is not used by itself.

Derivative (D) Control Action

• Derivative (D) control will generate the manipulation value (MV) in proportion to the rate of change in the error (E).

• By adding the D control, quick corrective action can be obtained at the beginning of the upset condition.

• If the derivative time is set too long, oscillations will occur and the control loop will run unstable.

• If the derivative time is set to 0, the derivative control does NOT function.

• The derivative (D) control is used with PI and PID control.

  • It is not used by itself.

PID Control Formula

• The direct/forward action, reverse action, and filtered present value are calculated in the following:

Direct/Forward Action

• MV_n = MV_n-1 + K_p{(E_n - E_n-1) + (T_s / K_i) × E_n + (K_d / T_s) × (2PV_nf-1 - PV_nf - PV_nf-2)}
• E_n = SV - PV_nf

Reverse Action

• MV_n = MV_n-1 + K_p{(E_n - E_n-1) + (T_s / K_i) × E_n - (K_d / T_s) × (2PV_nf-1 - PV_nf - PV_nf-2)}
• E_n = PV_nf - SV

Filtered Present Value

• PV_nf = PV_n + α(PV_nf-1 - PV_n)

Variables

• E_n: Currently sampling deviation
• E_n-1: Deviation at an interval before
• K_p: Proportional integer
• K_i: Integral integer
• K_d: Differential integer
• T_s: Sampling interval
• α: Filter coefficient
• MV_n: Present manipulation value
• SV: Set value
• PV_n: Process value of the present sampling cycle
• PV_nf: Process value of the present sampling cycle after filtering
• PV_nf-1: Process value of the preceding sampling cycle after filtering
• PV_nf-2: Process value of the sampling cycle two cycles before after filtering