A Volterra series approach to nonlinear process control and control-relevant identification

This dissertation is on the topic of nonlinear process identification and control using Volterra series as the process model. The issues addressed cover the analysis of feedback Volterra series systems, input-output (I/O) linearization control design, robustness analysis, control-relevant identification, model parameter number reduction and multi-input multi-output (MIMO) Volterra series. To analyze the properties of a feedback Volterra series system as well as robustness with respect to modeling error, a local form of the small gain theorem is developed. The local gain is defined on a subset of the input signal and hence its approximation for a finite Volterra series can be obtained. The local small gain theorem is then used to analyze the properties of a feedback Volterra series and, in particular, an inverse Volterra series. An uncertainty description is proposed to account for the modeling errors arising from truncating high order terms and the corresponding robustness issue is addressed for a nonlinear Internal Model Control structure. To overcome some difficulties in inverting Volterra series, which is an essential part in control synthesis, an I/O linearization operator is constructed using a discrete-time formulation. This operator removes the causality requirement in an inverse Volterra series, and has a better tuning feature for the admissible signal range. Based on the closed-loop control requirement, a control-relevant Volterra model identification criterion is established, which puts the control design and the model identification in an interactive framework. Examples have displayed a larger stability range and better response performance in the resulting control system than using conventional model identification. To reduce the parameter number in a Volterra series, a so-called Volterra-Laguerre model and its orthogonal regression analysis are developed. Conditions under which a nonlinear process can be approximated by the Volterra-Laguerre model are derived. To make the Volterra series approach more applicable, a MIMO Volterra series is formulated and some results obtained for a SISO Volterra series are extended. Two case studies of a reversible exothermic CSTR and a Model IV FCCU are given to demonstrate the application of the proposed techniques to chemical process control problems. Some future research directions, such as the experiment design for nonlinear model identification, are also proposed.