The PID control algorithm is easily the most common type of feedback controller used in the process (and in most other) industries. A PID controller contains three different type of control model: a Proportional part (P); an integral part (I) and a derivative part (D). One form of the PID algorithm is:
where
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controller output (to be sent to the manipulated variable) |
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controller gain (an adjustable constant - one of the controller 'tuning' parameters) |
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error - this is either (measurement-setpoint) or (setpoint -measurement) depending on the desired direction of control action (measurement - setpoint gives a direct acting controller) |
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Integral time constant (also known as the reset time). This is an adjustable constant used to 'tune' the controller |
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Derivative time constant. This is an adjustable constant used to 'tune' the controller |
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The bias is the nominal controller output - setting this value correctly ensures that the system starts at (nearly!) steady-state. |
The proportional part of the algorithm generates a control action which is proportional to the size of the error:
Large errors give rise to large movements in the control action. Proportional action also takes effect immediately an error enters the system and adjusts the behaviour most in the earlier stages of a controlled response. The relative effect of proportional action can be adjusted by changing the controller gain.
The integral part of the algorithm generates a control action which is proportional to the integral of the error with time:
This means that integral action increases with time if an error persists. The effect of integral action in the early stages of a controlled response may be relatively small, but the effect will increase with time and will continue until the error is eliminated. The relative effect of integral action can be adjusted by changing the integral time constant.
The derivative part of the algorithm generates a control action which is proportional to the derivative of the error with time:
Since derivative action is unaffected by the absolute value of the error it is completely useless on its own and must be used along with one or both of the other control modes. The relative strength of derivative action can be adjusted by changing the derivative time constant.
In theory, any of the modes of the PID controller can be switched-on on their own, or in combination with any of the other modes. In the process industries the control modes commonly used (most common first) are: PI (Proportional-Integral), P, PID and I. Derivative control can never be used on its own and ID control serves no useful purpose. PD control is sometimes used in mechanical systems which include integrating elements (e.g. direction control systems), but is rarely (if ever) used in the process industries.