Statistical robust control

Robust control provides an effective means towards an ultimate objective of guaranteed stability and product quality during process operations. These primary objectives can be achieved through the design of model-based control systems which are robust to uncertainties. Traditional approaches to robust control use deterministic (norm-bounded perturbation) methods to characterize uncertainties. Although statistical information is often available about plant behavior, these deterministic approaches to robust control are not general enough to utilize this information efficiently. As a consequence, this a priori process knowledge is neglected. The result is incomplete controller analysis methods for stability and performance that can lead to decreased process productivity.;In this research, the conceptual and theoretical groundwork is laid for a new approach to robust control. The proposed methodology is developed for a general statistical characterization of model uncertainty and process behavior. A comprehensive statistical treatment of robust control methods is developed from problem formulation to controller design. The results achieved so far demonstrate that the innovative use of a statistical characterization of model uncertainty yields controllers with reduced conservativeness obtained through improved statistical analysis methodologies and novel design strategies that previously were unavailable by use of traditional approaches. The most important issues necessary to achieve a statistical formulation of robust control are addressed in this research through the development of the following methodologies: (1) Characterization of a priori process knowledge by a statistical representation. (2) Formulation of a probabilistic setting to rigorously characterize model uncertainty. (3) Derivation of an entropy measure to quantify stochastic model uncertainty. (4) Employment of statistical functions to characterize closed-loop performance behavior. (5) Coordination of robust performance and stability concepts within a statistical framework. (6) Development of statistically-based approaches to robust control design. All developments are conducted in a new framework that uses a general statistical representation of model uncertainty. This framework is shown to incorporate current uncertainty descriptions as a special case.