Cybernetic Model Predictive Control
 

Timothy J. Crowley¹, Francis J. Doyle III¹, and Jeffrey D. Varner²

¹University of Delaware
Department of Chemical Engineering
150 Academy Street
Newark, DE 19716

²Department of Chemical Engineering and Materials Science
University of Minnesota
421 Washington Ave SE
Minneapolis, MN 5545

crowley@che.udel.edu
(302) 831-0466

Model predictive control (MPC) is considered by many to be one of the most significant developments in process control. This is mainly due to its ability, given an adequate process model, to compute optimal control actions for multi-variable processes and due
to explicit handling of process constraints.  Today, MPC is widely used in the petroleum and chemical industries, particularly to control continuous, multi-variable processes whose local operating behavior can be described adequately by linear models. 

Migration of MPC to bioprocesses has been slow.  One reason is that cell physiology manifests highly complex, nonlinear dynamic behavior. Developing a high fidelity model of cell behavior for model predictive control is extremely difficult.  Furthermore, most bioreactors are operated in some variant of batch or fed-batch mode rather than in continuous operation.  Application of MPC to batch systems is more difficult than to continuous systems because process dynamics can change dramatically over time in a batch process.  Finally, measurements of key process variables, such as biomass concentration, are often unavailable on-line due to lack of sensor technology and/or the need to strictly maintain aseptic conditions. 

To overcome some of these limiting factors in bioprocess control, we have proposed the cybernetic model predictive control (CMPC) approach. Central to this approach is the use of a cybernetic model of cell metabolic regulation.  The cybernetic framework is an abstract surrogate for a mechanistic model of metabolic regulation.  Mathematically, enzyme synthesis rates and activities are controlled by cybernetic variables, which are expressed in terms of reaction rates in convergent and divergent pathways.  The expressions for cybernetic variables are derived by postulating that the cell allocates its limited resources to maximize synthesis rates of end-products in convergent pathways, and the product of end-products in divergent pathways. These expressions are equivalent to the optimality condition in economics which stipulates that the optimal allocation policy occurs where the fractional return on investment equals the fractional allocation of resources.

A cybernetic model of PHB synthesis in Alcaligenes eutrophus is used to study the potential of CMPC. The model is incorporated into a multi-rate model predictive controller.  The multi-rate feature of this controller addresses shortcomings in available on-line measurements by combining infrequent laboratory measurements of key process variables with frequent on-line measurements, to estimate bioreactor states and compute control actions based on these state estimates.  Control performance is studied in both continuous and fed-batch operation, with significant process/model mismatch.