(370i) Constrained Parameter Identification Algorithms for Dual-Rate Systems with Inter-Sample Output Prediction

Conventional identification algorithms for multiple input single output (MISO) dual rate systems are unconstrained, unstable, and slow to converge. Recursive data driven models are developed for dual rate systems in this article by using a modified constrained least square (MCLS) algorithm for parameter identification. Appropriate parameter constraints are imposed in parameter estimation algorithms and stability of these is examined. The MCLS algorithm-based models - dual rate for parameter identification and single rate for output prediction - allow for output prediction at the frequency of faster sampled inputs with inter-sample output estimation, a beneficial feature. The MCLS algorithm is guaranteed to be stable, enables more accurate parameter identification with better convergence rate, and results in better prediction vis-à-vis two conventional dual rate models, identification algorithms for which are unstable. Faster prediction of the slower sampled output is achieved using a single rate-ARX prediction model, the parameters in the model being related to the parameters identified for the dual rate model for the output. Three examples are provided to illustrate model formulation, with numerical illustrations being provided for two of these, with one being a simple discrete time process with a single slower sampled output and another being a fed-batch mammalian cell culture with three slower sampled outputs, concentrations of glucose, glutamine and monoclonal antibody. The numerical illustrations demonstrate the advantage of the proposed method in parameter estimation, inter-sample estimation of less frequently measured output variables, and predictive ability and stability of the proposed method and impact of increased disparity in sampling rates of inputs and output. For mammalian cell culture, glucose and glutamine feed rates are considered as inputs. The predictions of the less frequently sampled outputs track very well the data for these. The prediction accuracy can be increased further if data from prior experiments with dynamic similarities are available. The more frequent output prediction vis-a-vis output sampling will be of substantial utility in process optimization and model predictive control.