Experiment design for control‐relevant identification of partially known stable multivariable systems

Abstract

Design of experiments for identification of control‐relevant models is at the heart of robust controller design. In a number of prior publications, experiment designs have been developed that generate input/output data for efficient identification of models satisfying the integral controllability (IC) condition. The design of process inputs for such experiments is often, but not always, based on the concept of independent random rotated inputs, with appropriately proportioned amplitudes. However, prior publications do not account for models that may already be partially known before identification. In this work, this issue is addressed by developing a general experiment design framework for efficient identification of partially known models that must satisfy the IC condition. This framework produces optimal designs by solving appropriately formulated optimization problems, based on a number of rigorous theoretical results. Numerical simulations illustrate the proposed approach and potential future extensions are suggested. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2986–3001, 2016

Design of Experiments for Control-Relevant Multivariable Model Identification: An Overview of Some Basic Recent Developments

“…This result connects the achievable robustness of decoupling multivariable controllers that include integral action with the kind and magnitude of associated model uncertainty. Therefore, in order to design a robust model-based decoupling multivariable controller, the model used must satisfy the IC condition in Equation (11). Consequently, model identification experiments must be designed in a way that explicitly incorporates Equation (11).…”

“…Therefore, in order to design a robust model-based decoupling multivariable controller, the model used must satisfy the IC condition in Equation (11). Consequently, model identification experiments must be designed in a way that explicitly incorporates Equation (11). Unfortunately, incorporating Equation (11) directly in DOE is problematic, as the eigenvalue inequalities' "main weakness is that they consist of a coupling between the process model and the true process, which is highly cumbersome" [13].…”

“…i . The ellipsoidal uncertainty set in the above Equation (20) typically arises in least-squares parameter estimation, with 21over Equation (11) in DOE is that Equation (21) involves inputs directly (in M T M or, equivalently, C m , Equation (19)). Therefore, Equation (21) can be combined as either a constraint or objective with whatever additional criterion is used in DOE, to characterize optimal inputs.…”

“…DOE that generates data allowing the efficient identification of multivariable models which satisfy these two crucial properties has been the focus of substantial work in recent years [1][2][3][4][5][6][7][8][9][10][11]. Among these publications, the works in [1,2] and [9][10][11] offer rigorous guidelines for addressing the two multivariable model properties mentioned above. Possibly because of the complexity involved in developing the results generated by that work, it appears that these results have remained largely inaccessible to the control community, despite the relative simplicity of corresponding recipes.…”

“…Finally, there are many more cases of control-relevant DOE (e.g., when individual input and/or output variance constraints are present) for which no rigorous results are available, the only exception being the framework initiated in [9] and further developed in [10,11]. Publications referring in passing to these results include [12,[14][15][16][17][18].…”