Process Control Terms

Reference data and engineering information about process control terms for miscellaneous applications.

processcontrolterms

Overview

Engineering reference data for Process Control Terms in miscellaneous.

$y = x \cdot k$

Multiply by conversion factor.

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Dead Time: The delay between a control action and the initial response in the process variable. Also known as transport delay.
Lag Time: The time required for a process variable to move 63.3% of its final value after a step change, following the dead time. This is often associated with the process time constant.
Process Gain: The sensitivity of a process, defined as the ratio of change in process variable ( $\Delta PV$ ) to change in controller output ( $\Delta CO$ ). High process gain indicates a large response to input changes.
Gain Margin: A stability metric representing the factor by which the controller gain can be increased before the system reaches the verge of instability, typically measured in decibels.
Overshoot: The extent to which the process variable exceeds the set point during a transient response to a disturbance or set point change.
Dominant Lag Process: A process where the lag time is significantly larger than the dead time, common in temperature, level, flow, and pressure loops.
Hysteresis: The dead band or signal change required before a final control element (e.g., valve) begins to move, often due to mechanical friction.
Cascade Control: A control strategy using two or more controllers, where the output of the master controller sets the set point for the slave controller.

The following formulas are fundamental for PID control and process analysis:

Controller Gain from Proportional Band: $G_c = \frac{100}{PB}$ where $G_c$ is the controller gain (dimensionless) and $PB$ is the proportional band (in percent).
Control Error: $e(t) = SP(t) - PV(t)$ where $e(t)$ is the instantaneous error, $SP(t)$ is the set point, and $PV(t)$ is the process variable.
Process Gain: $K_p = \frac{\Delta PV}{\Delta CO}$ where $K_p$ is the process gain, $\Delta PV$ is the change in process variable, and $\Delta CO$ is the change in controller output.
Lag Time Constant ( $\tau$ ): In a first-order plus dead time (FOPDT) model, the time constant $\tau$ is the lag time, representing the time for the process variable to reach 63.3% of its final step response after the dead time. It is often derived from the lag time definition.