Offset problem and k-incremental predictors in self-tuning control

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Abstract
Regulation against offsets such as those induced by load disturbances is a principal requirement in process control, and is commonly achieved by the integral term in the classical PID algorithm. It is important, therefore, that self-tuning controllers attain the same objective along with their useful adaptive property. In an important class of self-tuners based on predictive control theory two problems arise: the well known ‘λ offset’ originating from the weighting placed on control activity and the hitherto little recognised ‘prediction offset’ which stems from possible bias in the prediction of the auxiliary output variable. This bias stems from the estimation of the predictor model in positional form. Various ad hoc solutions have been proposed in the literature, such as inserting a forward-path integrator; the weaknesses in these ideas are explored in the paper. A novel k-incremental predictor is derived which solves the offset problem whilst retaining the other attributes of the self-tuning controller such as its model following performance. A by-product of the predictor is that the estimation becomes better conditioned numerically as it works on zero mean data. Moreover, the design is robust in the sense that the freezing of estimation does not detract from its offset elimination property.

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