(186c) Constant - Yield Control of Continuous Bioreactors

Continuous stirred microbial bioreactors, often called chemostats, cover a wide range of applications in the biotechnological processes. One important class of applications is related to anaerobic digestion, which is a key process in wastewater treatment, sludge management, energy from biomass, etc. Anaerobic digestion’s primary product is biogas, which is a valuable energy product.

 The dynamics of a chemostat is often adequately represented by a two-state dynamic model involving the microbial biomass and the limiting organic substrate, whereas the manipulated input is the dilution rate. The problem of controlling a chemostat is quite challenging when cell growth follows Haldane (or Andrews) kinetics, involving substrate inhibition. In this case, the chemostat exhibits steady state multiplicity, and the design steady state (which is stable) can be very close to an unstable steady state. Thus, the goal of control is stabilization, in the sense of enlargement of the stability region. In the particular case of anaerobic digesters, a successful empirical stabilization approach is the so-called constant - yield control [1], which is based on the intuitive idea that the controller must keep the ratio of production rate divided by the organic feed rate constant.

 Earlier work by one of the authors ([2]) has studied the chemostat stabilization problem in the case of negligible cell mortality and negligible endogenous metabolism. Using a control - Lyapunov function approach, it was shown in [2] that the chemostat can be stabilized globally, over the entire first quadrant. Moreover, it was shown that the resulting control law is a proportional feedback of the biomass growth rate, and can be interpreted as a constant-yield control policy.

 In this work, we study the more general stabilization problem, including the effects of cell mortality and endogenous metabolism. The intuitive idea of constant - yield control will be used, and this will give rise to proportional feedback of the biomass growth rate. However, the resulting closed loop system’s stability basin will no longer be the entire first quadrant. Lyapunov stability analysis will be applied to obtain an estimate of the stability region of the closed loop system, which depends upon the values of the cell mortality rate constant and cell maintenance rate constant. It will be seen that the constant - yield control law guarantees a very large stability region, corresponding to almost global stabilization for all practical purposes.

References

[1] P. Pullammanappallil, S. A. Svoronos, D. P. Chynoweth and G. Lyberatos, Expert system for control of anaerobic digesters, Biotechnology and Bioengineering, Vol.58, 1998, pp. 13-22.

 [2] I. Karafyllis, C. Kravaris, L. Syrou and G. Lyberatos, A vector Lyapunov function characterization of Input-to-State stability with application to robust global stabilization of the chemostat, European Journal of Control, Vol. 14, 2008, pp. 47-61.