(183m) Constrained Least Square Parameter Identification Algorithms for Dual-Rate Systems with Inter-Sample Output Estimation

Multi-rate systems, where inputs and/or outputs have different sampling rates, are encountered in many chemical and biological engineering applications. Typically, this occurs in systems where multiple variables are measured. Process variables such as temperature, pressure and pH are measured more frequently, at times nearly continuously, while other variables, such as species concentrations in a reaction mixture, are measured less frequently. The simplest way to handle multi-rate systems is to neglect excess data from fast sampling signals and synchronize the signals with the slowest sampling rate. With this method, great amount of data will be discarded, the data that may contain crucial information regarding system dynamics. Therefore, some effort has been devoted to modeling, analysis and identification of multi-rate systems to take advantage of the rich information available in the experimental databases. In all the techniques proposed, multi-rate systems are generally simplified to multiple dual rate systems where the slower sampling rate is a positive integer () multiple of the faster sampling rate. Polynomial transformation technique is used to derive a dual rate model from a single rate model. 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 here 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 frequency of faster sampled inputs with inter-sample output estimation, a beneficial feature. The MLCS algorithm is guaranteed to be stable, enables more accurate parameter identification with better convergence rate, and results in better prediction vis-a-vis two conventional dual rate models, identification algorithms for which are unstable. The beneficial features of the MLCS algorithm are illustrated with two examples, 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. Faster prediction of the slower sampled output is achieved using a single rate-ARX prediction model, the parameters in the model being related to parameters identified for the dual rate model for the output. The more frequent output prediction vis-a-vis output sampling will be of substantial utility in optimization and control of processes. For mammalian cell culture, glucose and glutamine feed rates are considered as inputs. The data required for parameter estimation are generated from simulated fed-batch experiments using a well-tested first principles model. The predictions of the less frequently sampled concentrations of glucose, glutamine, and monoclonal antibody track very well the data for these, with the errors for reasonable prediction horizons considered being limited to 10% or less. The prediction accuracy can be increased further if data from prior experiments with dynamic similarities are available. The models can be used reliably for model predictive control.