Nonlinear modeling and identification for process control

Citation

Rhodes, Carl (1998) Nonlinear modeling and identification for process control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/96TN-SN45. https://resolver.caltech.edu/CaltechETD:etd-02042008-082018

Abstract

Ideally, processes to be controlled would behave in a linear manner so that well-developed methods of linear control could be applied directly. However, environmental regulations and increased competition are forcing these processes to operate in regions where the assumptions of linearity tend to break down. There has been a great deal of recent academic interest in the control of nonlinear systems, but there are relatively few applications of these methods in industry. One major reason may be the lack of tools for developing models suitable for nonlinear control schemes. A number of tools that can be used in the modeling of nonlinear systems for process control are presented in this thesis. In the first section, the problem of determining the proper regression vector size for black-box modeling is examined. The false nearest neighbors algorithm (FNN) is suggested as a solution for this problem. Extensions, analysis, and numerous applications of the FNN algorithm are given and the algorithm is seen to be a useful tool in the identification of nonlinear models. In the second section of the thesis, the problem of nonlinear model reduction for systems exhibiting large time-scale separations is examined. A method of determining the reduced order manifold of slow dynamics is outlined and it is proved that this algorithm identifies the proper manifold. Some thoughts on how the results of the algorithm can be used for developing reduced models are presented. In the third section, the concept of data-based control is introduced. This method of control attempts to utilize process data directly through local modeling techniques. Some preliminary work in this area is given for trajectory tracking and computing controllable sets and data-based control is successfully applied to an experimental electrical circuit. Finally, some thoughts on possible future work in this field are presented.

Thesis Files