Selection of Decentralized Control Configuration for Uncertain Systems

Abstract: Industrial processes nowadays involve hundreds or more of variables to be maintained within predefined ranges to achieve the production demands. However, the lack of accurate models and practical tools to design controllers for such large processes motivate the engineers/practitioners to break the processes down into smaller subsystems and applying decentralized controllers.In contrast to the centralized controller, the decentralized controller is favourable in large-scale systems due to its robustness against loop failures and model uncertainties as well as being easier to tune and update. Yet, two steps are required prior to synthesizing these single-input single-output (SISO) controllers that comprise the decentralized controller. In the first step, a set of manipulated and the controlled variables need to be selected while the second step deals with pairing these variables to close the SISO control loops in a manner that limits the interaction between the loops. The latter step, called "input-output pairing", is usually performed by means of interaction measures (IM) tools using a nominal system model. Taking model uncertainties into consideration when deciding the pairing selection of the decentralized controller is necessary since adopting the pairing based on the nominal system model might be misleading and resulting in poor system performance or instability. It is therefore essential to have tools indicating the extent to which the pairing based on the nominal model persists against gain variations due to uncertainties.The work in this thesis presents a methodology that determines whether the effect of gain uncertainty would invalidate the selected pairing. This has been done following the definition of the most established IM tool used in the industry, the relative gain array (RGA), and some of its variants. Further, a procedure has been developed to automatically obtain the optimal input-output pairing by formulating the pairing rules of relative interaction array (RIA) method as an \textit{assignment problem} (AP), and thus, simplifying the pairing selection for large-scale systems. Thereafter, uncertainty bounds of the RIA elements are employed to validate the pairing selection under the effect of given variations of the system gain. Moreover, following the RIA pairing rules, a method is proposed to calculate a minimum amount of uncertainty that renders a perturbed system for which the pairing, obtained from the nominal system model, becomes invalid.In the aforementioned methodologies, a parametric system model is assumed to be known. To relax this constraint, an approach is therefore proposed and evaluated which identifies the pairing of the decentralized controller directly from the input-output data. This approach has the advantage of exempting the user from deriving a complete parametric model of the plant to decide the input-output pairing, and hence saves the efforts by finding the parameters of the most significant subsystems in a multivariable system. The frequency response of the system and its covariance, and subsequently the dynamic RGA (DRGA) and corresponding uncertainty bounds, are estimated from the input-output data by employing a nonparametric system identification approach. In short, the work presented in this thesis provides beneficial methodologies for researchers in academia as well as engineers in industry to predict the influence of the system gain uncertainty on the pairing selection of decentralized controllers.