Nonlinear system modeling based on constrained Volterra series estimates

A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least squares algorithm with $q\geq 1$. If the system $m\left( \cdot \right)$ is a continuous and bounded map with a finite memory no longer than some known $\tau$, then (for a $D$ parameter model and for a number of measurements $N$) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order $\sqrt{N^{-1}\ln D}$, even for $D\geq N$. The performance of models obtained for $q=1,1.5$ and $2$ is tested on the Wiener-Hammerstein benchmark system. The results suggest that the models obtained for $q>1$ are better suited to characterize the nature of the system, while the sparse solutions obtained for $q=1$ yield smaller error values in terms of input-output behavior

Identification and Control of a Batch Crystallization Process

Crystallization is a slow chemical process evolving in a reactor called crystallizer. A solution initialized in a high temperature is cooled down such that the dissolved solute is transferred from the solution into pure crystalline phase. The evolution of the process characterizes the properties of the crystals in the end-product. The transient nature of the process together with the stochasticity that governs the chemical kinetic phenomena motivate the development of efficient methods for identification and control. The kinetics of the process are modeled with nonlinear equations which contain a number of parameters to be identified from the measured data. An appropriate model is required such that model-based control techniques can be implemented. Under these conditions, experiment design for open loop control of the crystallization is studied in this thesis where a nonlinear model of the crystallization is used as a model structure in the prediction error identification framework. A temperature cooling profile constitutes the input to the system which must be designed in such a way that the crystals formed at the end of the process admit the desired performance criteria. The first part of the thesis deals with the derivation of the optimal cooling profile using the D-optimality criterion in order to obtain the most informative data about the kinetic parameters. Sequentially, an optimization method is used as an open loop control law for the crystallization process. The selection of the optimal input profile is achieved by minimization of the performance degradation, occurring in the controlled process, from the use of the identified model instead of the true unknown system.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin

Batch-to-batch model improvement for cooling crystallization

Two batch-to-batch model update strategies for model-based control of batch cooling crystallization are presented. In Iterative Learning Control, a nominal process model is adjusted by a non-parametric, additive correction term which depends on the difference between the measured output and the model prediction in the previous batch. In Iterative Identification Control, the uncertain model parameters are iteratively estimated using the measured batch data. Due to the different nature of the model update, the two algorithms have complementary advantages and disadvantages which are investigated in a simulation study and through experiments performed on a pilot-scale crystallizer