Use of FT-IR/ATR sensors for online process control: Approximate solutions to the fed-batch fermentation control problem and the calibration/prediction problem with errors in the independent variables

The FT-IR/ATR sensing system has several characteristics that are ideal for use in fermentation process control. However, the performance and reliability of the sensor during automatic data acquisition has not been studied despite the fact that the sources of error are commonly known and frequently discussed in the literature.; The feasibility of the FT-IR/ATR sensor was the subject of my M.S. thesis. A laboratory grade spectrometer and four available statistical analysis programs were used to analyze real fed-batch fermentation broths. The FT-IR/ATR sensor was determined to be useful for estimating substrate and product concentrations in dilute, multiple component, and multiple phase aqueous systems. It was noted that biochemical systems have measurement requirements that push the FT-IR/ATR sensor to its detection limit in many applications.; The Ph.D. work was divided into two problems: the fed-batch fermentation control problem and the calibration/prediction problem with errors in variables.; Closed loop control design studies were completed and effective control of the non-linear and non-stationary yeast fermentation process was demonstrated using a non-adaptive constant gain and constant reset proportional and integral (PI) controller. These preliminary, relatively simple and successful results suggested that the bulk of the research could be devoted to the calibration/prediction problem with errors in variables.; Two research questions were posed. How much dead time and process measurement variance are acceptable for a process control sensor? Can current FT-IR/ATR technology perform within these time and variance constraints? In order to develop the mathematical statistics needed for concentration prediction variance estimation, two theorems were developed and/or extended involving generalized inverses. The first theorem applies to all high signal-to-noise ratio multivariate sensors. A step in the proof of this theorem also motivates an approximate solution to the calibration/prediction problem with errors in variables, based on the fact that PCR concentration (dependent variable) predictions are projections onto the true concentration space when absorbances (independent variables) are measured without error. Two statistics were developed and/or extended in order to make several statistical inferences for PCR models. Results are presented to qualitatively demonstrate the properties of this approximate theory. Quantitative decisions about the maximum amount of variance in the independent variables, however, will require further work as will the final answer concerning limits for dead time and process measurement variance (requiring the combination of these two approximate solutions).