PI auto-tuning during a single transient

A certain adaptive PI tuner operates by injecting variable-frequency sinewaves at the PI's set-point. Its initialisation requires: (a) a stable preliminary controller, (b) reasonable values (correct within a factor of about 3) of the first probing frequency ω0 and of the plant's gain |Gp(jω0)|, and (c) an effective choice of the adaptive gain Ka for rapid tuning. The challenge is to prime the parameters of both the PI and the adaptive algorithm during an open-loop starting transient, using data obtained before the output attains its set-point, and then to complete the tuning for a short period while under closed-loop control. A relevant parameter is Tm, the time for the plant's impulse response to attain its maximum (or equivalently the time for a maximum slope of the step-response s(t)), and a simple estimator of Tm is described. One of three generic plant models is adopted according to the relative position of Tm within the primary experimental time [T1...T2], and it is shown how initialisation depends on the chosen model. The described approach is shown to be effective for a range of plants.

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