Proportional-Integral-Derivative (PID) Function Block
The controller block frequently shown in control system block is generally thought of as the Laplase transfer functions that act as the control compensating elements.
The industrial controller block usually includes the summing junction as well as the compensating equation. The entire controller functions are shown in the dotted block below:
The PID function block combines all the necessary logic to perform; analog input channel processing, proportional-integral-derivative (PID) control with the option for nonlinear control (including error-squared and notched gain), and, analog output channel processing. This block can run in the DeltaV controller or execute in a Fieldbus device.
The PID function block supports mode control, signal scaling and limiting, feedforward control, override tracking, alarm limit detection, and signal status propagation. To support testing, you can enable simulation. (Reference: DeltaV Help)
The actual implementation of this block contains more functions than just the compensating algorithm. The user needs to be able to run the control in manual, provide anti-reset windup, output limits, bumpless manual to automatic transfers as well as implement cascade and feed forward control.
Block Execution - PID Function Block
The PID function block provides proportional (P) + integral (I) + derivative (D) control. Two PID equation forms are supported in the block, both forms supporting external reset and feedforward:
The standard form is a discrete implementation of:
The series form is a discrete implementation of:
Where:
E(s) is error (SP-PV)
± is + for reverse acting and – for direct acting (Direct_Acting in CONTROL_OPTS)
KNL is nonlinear gain applied to P + I terms but not to D term. Nonlinear action is activated in FRSIPID_OPTS by selecting Use_Nonlinear_Gain_Modification.
P(s) is the variable to which proportional action is applied. P(s) is determined by parameters STRUCTURE and BETA (which sets the weighting factor for proportional action applied to SP change).
D(s) is the variable to which derivative action is applied. D(s) is determined by parameters STRUCTURE and GAMMA (which sets the weighting factor derivative action on SP change).
L(s) is the external reset input which is either from BKCAL_IN or OUT.
Tr is reset time (parameter RESET) in seconds.
Td is derivative time (parameter RATE) in seconds
GAINa is normalized gain after scaling the parameter GAIN from PV to OUT (Delta V works in engineering units so it is necessary that the parameter GAIN be scaled to maintain the meaning of the normalized entry).
F(s) is the feedforward contribution.
The operator interfaces with the controller through a “faceplate” DeltaV controller faceplate is: