Achieving state estimation equivalence for misassigned disturbances in offset‐free model predictive control

Abstract

in Wiley InterScience (www.interscience.wiley.com).Integrated white noise disturbance models are included in advanced control strategies, such as Model Predictive Control, to remove offset when there are unmodeled disturbances or plant/model mismatch. These integrating disturbances are usually modeled to enter either through the plant inputs or the plant outputs or partially through both. There is currently a lack of consensus in the literature on the best choice for the structure of this disturbance model to obtain good feedback control. We show that the choice of the disturbance model does not affect the closed-loop performance if appropriate covariances are used in specifying the state estimator. We also present a data based autocovariance technique to estimate the appropriate covariances regardless of the plant's true unknown disturbance source. The covariances estimated using the autocovariance technique and the resulting estimator gain are shown to compensate for an incorrect choice of the source of the disturbance in the disturbance model. Any correlated disturbance that enters the plant and is not included in the model results in biased predicted states. It is customary to assume that the disturbance enters through the inputs or the outputs. The bias can be removed by using the predicted and measured outputs to estimate the disturbance. In the target calculator formulation, the state is augmented with integrating disturbances. The target calculator then ensures offset free control in presence of unmodeled disturbances 4 by shifting the steady state target for the regulator depending on the estimate of the bias (under the assumption that the bias remains constant in the future). The integrating disturbance can be added either to the input, 5,6 the output, 7,8 or a combination of both. 9-11 Most industrial MPC implementations add the bias term to the output. 1,12 In Refs. 10 and 11, rank conditions that should be satisfied for the disturbance models to ensure offset-free control were independently derived, and the lack of consensus in the literature on the choice of the disturbance model was also pointed out. The examples in these references show significant difference in the closed-loop behavior of the controller depending on the choice of the disturbance model. Recently, 13 a method for a combined design of a disturbance model and its observer by solving an appropriate H 1 control problem was presented. The results presented in Ref. 13 differ considerably from the autocorrelation-based technique to be discussed in this article. The autocorrelation-based technique uses steady state operating data to specify the estimator gain as opposed to designing the disturbance models for a specified disturbance.The main contribution of this article is to show that for linear models, the choice of the disturbance model does not affect the performance of the closed-loop when the estimator gain is found from appropriately identified noise covariances. The equivalence in the estimator gains is shown by appealing to realiz...

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