From Basic to Advanced PI Controllers: A Complexity vs. Performance Comparison

The history of PIDs dates back to the beginning of the twentieth century when preliminary works of [Sperry (1922)] and [Minorski (1922)] provided mathematical results for the control of the ship motion and of automatically steered bodies in general. In particular, Minorski was the first to introduce three-term controllers with Proportional-Integral-Derivative (PID) actions. The success of PID was fast and solid, as nowadays they still represent the most popular choice in most industrial process control applications. The main reasons for their success are:

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