Global analysis, control, and Bayesian estimation of nonlinear dynamic systems using cell-to-cell mapping.

摘要

The analysis of long term behavior of nonlinear dynamic systems and obtaining meaningful data from noisy measurements are two important tasks of process systems engineering. This thesis is focused on global analysis and Bayesian data estimation of nonlinear chemical processes using a cell-to-cell mapping method.; The nature of nonlinear systems is that multiple attractors, including equilibrium state, periodic motions and chaotic motions, can coexist. Thus, different initial conditions can lead to different attractors and each attractor will have a domain of attraction (DOA).; Presently, cell mapping is the only viable method to delineate DOAs. In this thesis, various cell mapping methods have been reviewed and compared. Then, a new tool for global analysis, Generalized Interpolated Cell Mapping (GICM), is proposed. The accuracy and computational efficiency are demonstrated. Then, GICM is used to analyze non-isothermal CSTRs with steady state multiplicity and periodic motions. Effect of parameter on attractors and DOAs are investigated. In addition, GICM is used to quantify the measures of controllability, time optimality and robustness of a PID and simplified n-P controlled CSTR.; This dissertation also discusses data estimation methods. Most existing methods cannot handle nonlinear systems with non-Gaussian errors and/or constraints. Using cell mapping to create a finite state Markov chain, a new Bayesian data rectification method, "Cell Filter" is developed. It works on the discrete probability density function directly. It is capable of handling nonlinear dynamic systems with non-Gaussian errors. A strategy to handle equality and inequality constraints are also proposed. Kalman filter, extend Kalman filter, moving horizon estimator, probability grid filter, and Monte Carlo particle filter are implemented. Simulation examples demonstrate that the proposed cell filter is more accurate, robust and computationally efficient than most other existing methods at least for low dimensional systems.; At last, the application of cell mapping to optimal control has been discussed. Promising result is shown with a CSTR example.