M. Remy

An approach to the selection of optimal sensor locations in distributed parameter systems

Abstract This paper presents an approach to the selection of optimal sensor locations in distributed parameter systems, which distinguishes the purposes of state estimation from the purposes of parameter estimation. In the first case, the optimality criterion is based on a measure of independence between the sensor responses, while in the second case, it is based on a measure of independence between the parameter sensitivity functions. The procedure, which is general and can be applied to models with any degree of complexity, is illustrated with the optimal placement of temperature sensors in a catalytic fixed-bed reactor. Some numerical results for the on-line estimation of temperature and concentration profiles as well as for the estimation of unknown model parameters are discussed.

Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design

Abstract Parameter estimation in nonlinear distributed-parameter systems is usually accomplished by minimizing an output least-square criterion, which is defined implicitly through the solution of the model equations. This paper addresses itself to two important practical issues of the parameter-estimation procedure, i.e., the numerical procedure used to compute the gradient of the criterion with respect to the unknown parameters, and the selection of experimental conditions, i.e., sensor locations and input signals. An experiment design procedure based on the sensitivity matrix is presented. The methods for gradient computation and experiment design have been successfully applied to several process models, and are illustrated in this paper with a simple heat-conduction problem and a more complex model of a catalytic fixed-bed reactor.

Modeling and control of cement grinding processes

In this study, a nonlinear dynamic model of a cement grinding process, including a ball mill and an air separator in closed loop, is developed. This gray-box model consists of a set of algebraic and partial differential equations containing a set of unknown parameters. The selection of a model parametrization, the design of experiments, the estimation of unknown parameters from experimental data, and the model validation are discussed. Based on the resulting model, a dynamic simulator can be developed, which appears as a useful tool to analyze the process behavior and to understand the origin of instabilities observed in real-life operations. As a result, a cascaded control structure for regulating the mill flow rate, and a proportional integral controller for regulating the cement fineness are designed. Experimental data demonstrate the effectiveness of this control scheme. Alternatively, if on line measurements of the recirculated flow rate are available, a feedforward control of the feed flow rate is described, which ensures a better decoupling of mass flow rate and fineness regulation.

On the use of simultaneous perturbation stochastic approximation for neural network training

Learning, i.e., estimation of weights and biases in neural networks, involves the minimization of a quadratic error criterion, a problem which is usually solved using backpropagation algorithms. This study, which is essentially experimental, aims at assessing the potential of first- and second-order simultaneous perturbation stochastic approximation (SPSA) algorithms to handle this minimization problem. To this end, several application examples in identification and control of nonlinear dynamic systems are presented. Test results, corresponding to training of neural networks possessing different structures and sizes, are discussed in terms of efficiency, accuracy, ease of use (parameter tuning), and implementation.

Neural modeling and control of a heat exchanger based on SPSA techniques

The aim of the paper is twofold: first, we consider a variation of the first-order simultaneous perturbation stochastic approximation (SPSA) algorithm developed by Spall (1992, 1998) which makes use of several numerical artifices, including adaptive gain sequences, gradient smoothing and a step rejection procedure, to enhance convergence and stability. Second, we present numerical studies on a non-trivial test-example, i.e., the water cooling of sulfuric acid in a two-tank system. This numerical evaluation includes the development of a neural model as well as the design of a model-based predictive neural PID controller.

Stoichiometric identification with maximum likelihood principal component analysis

This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.

Continuous-discrete confidence interval observer - Application to vehicle positioning

In vehicle positioning applications, the confidence level in the position and velocity estimates can be even more significant than accuracy. In this study, a probabilistic interval method is proposed, which combines, through union and intersection operations, the information from a possibly uncertain predictor (the vehicle model) and measurement sensors. The proposed method is compared to Kalman filtering and to guaranteed interval estimation in the context of railway vehicles where security is the key objective.

Application of stochastic approximation techniques in neural modelling and control

Learning, i.e. estimation of weights and biases in neural networks, involves the minimization of an output error criterion, a problem which is usually solved using back-propagation algorithms. This paper aims to assess the potential of simultaneous perturbation stochastic approximation (SPSA) algorithms to handle this minimization problem. In particular, a variation of the first-order SPSA algorithm that makes use of several numerical artifices including adaptive gain sequences, gradient smoothing and a step rejection procedure is developed. For illustration purposes, several application examples in the identification and control of nonlinear dynamic systems are presented. This numerical evaluation includes the development of neural network models as well as the design of a model-based predictive neural PID controller.

MODELING AND PREDICTIVE CONTROL OF CEMENT GRINDING CIRCUITS

Abstract The purpose of this paper is to show that a distributed-parameter model of a continuous ball mill can be developed by discretizing the particle size continuum into a few size intervals only. Despite this coarse discretization of the particle size distribution, the ball mill model provides a good representation of the real process, which can be combined with a classifier model to build a complete simulator of a closed-loop grinding circuit. This simplified process representation is compared with a detailed first-principle model previously developed and validated by the authors. The main advantage of the simplified model is that it can be easily incorporated in an on-line control scheme. For illustrative purposes, a NMPC scheme is implemented to regulate the product fineness when variations in the grindability of the raw material occur as a measurable disturbance. The control objective, based on a size interval content, is compatible with traditional fineness measurements.

Some observations on modeling and control of cement grinding circuits

Based on system analysis and experimental data, a dynamic model of a closed-loop cement grinding circuit, which consists of a mixed set of algebraic and partial differential equations, is developed and validated. The model equations are solved numerically using the method of lines and the resulting simulation program is used to gain some insight into the process dynamics and to design and compare control loops to achieve product specifications. The influence of the model nonlinearities, which are related to the dependency of the rates of breakage on the mill hold-up, is highlighted. In particular, this nonlinearity introduces a strong coupling between PI control loops using the fresh feed flow rate and the louver position of the classifier as manipulated variables. Several variations of this basic control scheme are thoroughly analyzed, and the necessity of an efficient mill flow rate control for the stability of the fineness control loop is demonstrated.