Bjarne A. Foss

Constructing NARMAX models using ARMAX models

This paper outlines how it is possible to decompose a complex non-linear modelling problem into a set of simpler linear modelling problems. Local ARMAX models valid within certain operating regimes are interpolated to construct a global NARMAX (non-linear NARMAX) model. Knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models, hence it should not be considered as a pure black-box approach, but as an approach that utilizes a limited amount of a priori system knowledge. It is shown that a large class of non-linear systems can be modelled in this way, and indicated how to decompose the systems range of operation into operating regimes. Standard system identification algorithms can be used to identify the NARMAX model, and several aspects of the system identification problem are discussed and illustrated by a simulation example.

State and Output Feedback Nonlinear Model Predictive Control: An Overview

The purpose of this paper is twofold. In the first part, we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implementational aspects of this control strategy. Most of the theoretical developments in the area of NMPC are based on the assumption that the full state is available for measurement, an assumption that does not hold in the typical practical case. Thus, in the second part of this paper the focus on the output feedback problem in NMPC. After a brief overview on existing output feedback NMPC approaches we derive conditions that guarantee stability of the closed-loop if an NMPC state feedback controller is used together with a full state observer for the recovery of the system state.

Identification of non-linear system structure and parameters using regime decomposition

Abstract An off-line algorithm for empirical modeling and identification of non-linear dynamic systems is presented. The minimal input to the algorithm is a sequence of empirical data and the model order. Using this information, the algorithm searches for an optimal model structure and parameters within a rich non-linear model set. The model representation is based on the interpolation of a number of simple local models, where each local model has a limited range of validity, but the local models yield a complete global model when interpolated. The method is illustrated using simulated data.

Operating regime based process modeling and identification

Abstract This paper presents a non-linear modeling framework that supports model development in between empirical and mechanistic modeling. A model is composed of a number of local models valid in different operating regimes. The local models are combined by smooth interpolation into a complete global model. It is illustrated how different kinds of empirical and mechanistic knowledge and models can be combined with process data within this framework. Furthermore, we describe a flexible computer aided modeling tool that supports modeling within this framework. Simple but illustrative examples from chemical engineering are used to highlight the flexibility and power of the framework.

Nonlinear predictive control using local models — applied to a batch fermentation process

Abstract The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local state-space model structures are developed for each regime. These are combined into a global model structure using an interpolation method. Unknown local model parameters are identified using empirical data. The control problem is solved using a model predictive controller based on this model representation. As an example, a simulated batch fermentation reactor is studied. The model-based controllers performance is compared to the performance with an exact process model, and a linear model. It is experienced that a non-linear model with good prediction capabilities can be constructed using elementary and qualitative process knowledge combined with a sufficiently large amount of process data.

Constrained nonlinear state estimation based on the UKF approach

In this paper we investigate the use of an alternative to the extended Kalman filter (EKF), the unscented Kalman filter (UKF). First we give a broad overview of different UKF algorithms, then present an extension to the ensemble of UKF algorithms, and finally address the issue of how to add constraints using the UKF approach. The performance of the constrained approach is compared with EKF and a selection of UKF algorithms on nonlinear process systems with multimodal probability density functions. The conclusion is that with an algebraic reformulation of the correction part, the reformulated UKF shows strong performance on our selection of nonlinear constrained process systems.

A field study of the industrial modeling process

Abstract This paper analyzes the modeling process by means of a field study in the chemical industries. A diversified set of experienced modelers from two different countries have been interviewed using a case study approach. The interviews focussed on the modeling process. Other issues like life-cycle perspectives and the use of modeling in the process industries were treated as well. The information has been summarized and presented in a structured manner imposing the least possible bias from the authors. Based on the interview information the modeling process is discussed in detail. Further, fundamental research issues are identified, and a research agenda is proposed.

Oil production optimization—A piecewise linear model, solved with two decomposition strategies

This paper presents a new method for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Lagrange relaxation and the Dantzig–Wolfe methods, which allows us to efficiently decompose a real-time optimization problem. Furthermore, all nonlinearities are modeled by piecewise linear models, resulting in a mixed integer linear program, with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that both the Lagrange relaxation and in particular the Dantzig–Wolfe approach offers an interesting option for complex production systems. Moreover, the method compares favorably with the non-decomposed method.

Robust control and analysis of a wind-diesel hybrid power plant

The aim of this paper is twofold: first to present multivariable frequency domain techniques as a tool for controller design and dynamic analysis of an autonomous wind-diesel power system; and secondly to study how robust model based controllers can be designed for such systems. Dynamic system analyses using multivariable frequency domain techniques are verified against detailed nonlinear simulation studies. The results are encouraging in the sense that the main conclusions in terms of robust stability and performance agree very well with the simulation results. It is also shown that improved performance of the system can be achieved using simple model based controllers. >

Joint optimization of oil well placement and controls

Well placement and control optimization in oil field development are commonly performed in a sequential manner. In this work, we propose a joint approach that embeds well control optimization within the search for optimum well placement configurations. We solve for well placement using derivative-free methods based on pattern search. Control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Joint optimization yields a significant increase, of up to 20% in net present value, when compared to reasonable sequential approaches. The joint approach does, however, require about an order of magnitude increase in the number of objective function evaluations compared to sequential procedures. This increase is somewhat mitigated by the parallel implementation of some of the pattern-search algorithms used in this work. Two pattern-search algorithms using eight and 20 computing cores yield speedup factors of 4.1 and 6.4, respectively. A third pattern-search procedure based on a serial evaluation of the objective function is less efficient in terms of clock time, but the optimized cost function value obtained with this scheme is marginally better.