Stochastic Grey-Box Modelling as a Tool for Improving the Quality of First Engineering Principles Models

Niels Rode Kristensen, Henrik Madsen, Sten Bay Jørgensen
2004 IFAC Proceedings Volumes  
A systematic framework for improving the quality of first engineering principles models using experimental data is presented. The framework is based on stochastic grey-box modelling and incorporates statistical tests and nonparametric regression in a manner that permits systematic iterative model improvement. More specifically, the proposed framework provides features that allow model deficiencies to be pinpointed and their structural origin to be uncovered through estimation of unknown
more » ... al relations. The performance of the proposed framework is illustrated through a case study involving a model of a fed-batch bioreactor, where it is shown how an incorrectly modelled biomass growth rate can be uncovered and a more appropriate functional relation inferred. Abstract: This paper studies identification of a general single-input and single-output (SISO) multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant lifted system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and a real-time implementation. Abstract: In this paper, we provide a novel iterative identification algorithm for multi-rate sampled data systems. The procedure involves, as a first step, identifying a simple initial model from multi-rate data. Based on this model, the "missing" data points in the slow sampled measurements are estimated following the expectation maximization approach. Using the estimated missing data points and the original data set, a new model is obtained and this procedure is repeated until the models converge. An attractive feature of the proposed method lies in its applicability to irregularly sampled data. An application of the proposed method to an industrial data set is also included. Abstract: Identification based PID tuning is studied. The proposed approach consists of the identification of linear or nonlinear process model and model based control design. The identification test can be performed in both open loop and closed-loop. The so-called ASYM method is used to solve the identification problem. The method identifies a low order process model with a quantification of model errors (uncertainty). The PID tuning is based on internal model control (IMC) tuning rules. Two case studies will be performed to demonstrate the methodology. The first one is the adaptive control of the dissolved oxygen of a bioreactor; the second one is the nonlinear PID control of a pH process.
doi:10.1016/s1474-6670(17)38722-0 fatcat:3n2uqgrghbd2xdp4tqoyvnvwgu