CAREER: Control Design using Data-Driven Models: Exploiting Model Structure

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

ABSTRACT PI: Robert S. Parker Institution: University of Pittsburgh Proposal Number: 0134129 Industry is demanding higher and higher levels of performance from their processes and little capital investment is available for retrofitting or additional sensors. Thus processes must operate in highly nonlinear regimes, likely under linear control algorithms. This CAREER award addresses the integration of research and education with the goal of developing tools and students capable of solving problems in nonlinear model identification and control. Specifically, the research will focus on the use of control-relevant process models in nonlinear model-based optimal controller design. The modeling studies use third-order Volterra and Volterra-Laguerre representations, a subclass of nonlinear polynomial moving-average models. The selection of these model structures is motivated by (i) the ability to tailor input sequences to excite (or cancel) particular model dynamics; (ii) the opportunity to reduce the coefficient space and noise corruption with little to no decrease in model accuracy; (iii) the wide class of systems these model structures can approximate (e.g. polymerizers, distillation columns, bioreactors); and (iv) the utility of these structures in controller synthesis. Based on a polymerization reactor case study, third-order Volterra models will be identified using tailored input sequences, design to excite the linear, nonliear diagonal, or nonlinear off-diagonal terms. The resulting model will then be projected onto the orthonormal Laguerre basis to reduce coefficient dimension and noise effects on the output estimate. These models will then be used to synthesize a nonlinear model predictive control algorithm. The culmination of the project will be the integration of the identification and control results into a single algorithm for simultaneous identification and control. The educational component has two primary aims. The first is to help the student retain material from class to class, and to be able to employ material from a given class on an application example. Consistent with ABET 2000 criteria, these cross-curriculum problems will probe the students' mathematical skills. The type of problems examined serve to vertically integrate the curriculum with a recurring case study which draws on earlier courses, and therefore reinforces retention of material across classes. The integration of research and education is accomplished through the use of research results in the development of two new units for the Process Control Modules, case studies that examine data-driven model identification and nonlinear model predictive control at a level accessible to the undergraduate.