Variable Structure Models in Process Observation and Control

Abstract

A method is proposed for the modeling, observation, and control of processes characterized by sequential transformation steps. Using the method, such processes are described by a battery of alternative submodels, each of which qualitatively represents one of the process steps. The submodels cannot themselves track transitions from step to step. This is handled by switching to an alternative submodel with a significantly better predictive performance than that presently in use. The main advantage of the proposed approach is that each submodel is significantly simpler than the full model of the system. Example applications demonstrate that these submodels, when combined with the switching strategy, are also convenient for parameter estimation, state observation, and regulatory control.

Multimodel Approach for Modelling of Biotechnological Processes

“…(iii) Aggregation of local models through a suitable switching strategy: For the deployment of these local models in closed loop operation, the local model predictions need to be aggregated to yield a representative prediction in the region of operation. Several model/controller scheduling techniques have been proposed [3,4,5,6,7,8,9,18,36,42] in recent times for use within the multiple-model based framework, i.e. based on the scheduling algorithm to weigh local models towards control of chemical reactors [32], using local model performance indices to select local controllers [25], a supervisor based hierarchical technique for local controller selection based on virtual control loop feedback error [22], based on fuzzy decomposition of the steady state map [40], decision trees, discrete logic, expert systems, hybrid systems, and variable structure systems [3].…”

“…After this step an adaptive algorithm is used to identify unknown evolution of the system. A residual identification approach, without a priori data requirement, and efficient filter (local dynamical-model or variable-structure observer) [5,6] allows to assess the quality of the basic models and to use more easily dynamic models. Very important problem for multimodel base design is the dimensionality problem or models number reduction.…”

Modelling of E.coli fermentations: comparison of multicompartment and variable structure models

“…The phases we identify are identical to these noted earlier for the multicompartment model but the corresponding submodels will predict growth and production only and will not attempt to portray intracellular processes and predict the transition between them. The formal criterion for switching between submodels could be performance of the submodel currently in use, i.e., the transition to an alternative submodel occurs when its predictive performance is significantly better than that of the submodel presently in use (Dainson et al 1995).…”

“…The multi-compartment model can be further simplified and the number of parameters reduced by the application of a Variable Structure Model (Dainson et al 1995). In this approach a multi-compartment model of a fermentation process can be reduced into a battery of alternative submodels, each of which qualitatively represents one of the process metabolic phases.…”

“…To overcome this difficulty, correction of the states of an inactive submodel according to the estimates of a leading one is performed. The algorithm for such a correction is given elsewhere (Dainson et al 1995).…”