User prompt 1 of 1 - 4/8/2025, 3:30:53 PM: in pid systems, what is proportional on error vs on measurement

GPT-4o mini: In PID (Proportional-Integral-Derivative) control systems, the terms "proportional on error" and "proportional on measurement" refer to how the proportional control action is applied based on the system's error or the measurement of the process variable.

1. *Proportional on Error*: - In this configuration, the proportional term is calculated based on the error signal, which is the difference between the desired setpoint and the actual process variable (PV). - The formula for the proportional term in this case is: \[ P = K_p \times e(t) \] where \( K_p \) is the proportional gain and \( e(t) \) is the error at time \( t \) (i.e., \( e(t) = \text{Setpoint} - \text{PV} \)). - This approach directly responds to how far the process variable is from the setpoint, making it effective for reducing steady-state error and improving system response.

2. *Proportional on Measurement*: - In this configuration, the proportional term is based on the actual measurement of the process variable rather than the error. - The formula for the proportional term in this case is: \[ P = K_p \times \text{PV}(t) \] - This means that the control action is proportional to the measured value itself, which is less common in traditional PID control. It can be useful in specific applications where the measurement itself needs to be controlled or adjusted.

### Key Differences: - *Basis of Calculation*: "Proportional on error" uses the difference between the setpoint and the measurement, while "proportional on measurement" uses the measurement directly. - *Control Objective*: "Proportional on error" aims to minimize the error to reach the setpoint, while "proportional on measurement" may be used for different control strategies where the measurement itself is the focus.

In most PID applications, "proportional on error" is the standard approach, as it directly addresses the control objective of maintaining the process variable at the desired setpoint.

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