PID controller

A proportional-integral-derivative controller (PID controller) is a generic control loop feedback mechanism widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly.

The PID controller calculation (algorithm) involves three separate parameters; the Proportional, the Integral and Derivative values. The Proportional value determines the reaction to the current error, the Integral determines the reaction based on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element.

By "tuning" the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system.
Some applications may require using only one or two modes to provide the appropriate system control. This is achieved by setting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are particularly common, since derivative action is very sensitive to measurement noise, and the absence of an integral value prevents the system from reaching its target value due to the control action.

A block diagram of a PID controller
Note: Due to the diversity of the field of control theory and application, many naming conventions for the relevant variables are in common use.
Contents[hide]
1 Control loop basics
2 PID controller theory
2.1 Proportional term
2.2 Integral term
2.3 Derivative term
2.4 Summary
3 Loop tuning
3.1 Ziegler-Nichols method
3.2 PID tuning software
4 Modifications to the PID algorithm
5 Limitations of PID control
6 Physical implementation of PID control
7 Alternative Nomenclature and PID forms
7.1 Pseudocode
7.2 Ideal vs Standard PID form
7.3 Series / interacting form
8 See also
9 External links
9.1 PID tutorials
9.2 Simulations
9.3 Special topics and PID control applications
10 References
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