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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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5.4. PID Controller Algorithms

Here we continue to work in deviation variable form. Recall that a proportional-only controller could lead to offset between the desired setpoint and the actual output. This happened because the controller output (process input) and process output came to new equilibrium values before the error went to zero. The next step is to add a term where the controller output is proportional to the integral of the error, in addition to the term that is proportional to the error. This is known as proportional-integral (PI) control. As long as there continues to be an error signal to the controller, the controller output (process input) will continue to change. Therefore, the integral of the error forces the error signal to ...

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