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In general, auto-tuning implementation of PID controllers relies on dual controllers, exciting/identification experiments or some prior knowledge on the process and hence the considerable cost on auto-tuning implementation occurs. To deal with such a problem, a new auto-tuning scheme of the FPID controller is developed for minimum variance tasks under routine operating conditions in which the closed-loop system is running without any external excitation other than natural disturbances. This paper reveals that the stochastic disturbance model can be uniquely determined from the first several terms of the impulse response coefficients of the closed-loop system when the precondition on the time delay and the order of the disturbance model is satisfied.

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