Control de bioreactores

Discrete Linear Control of Continuous Stirred Tank Bioreactors
Héctor Hernández-Escoto, Salvador Hernández-Castro, Ernesto Aguilar-Carrillo Chemical Engineering Department, Guanajuato University, Guanajuato, México, (e-mail: hhee@quijote.ugto.mx) Abstract: These work addresses the design of a control system for the class of continuous stirred tank bioreactors where a single biomass/singlesubstrate process takes place. Exploiting the linear behavior of the reactor around the steady state, a discrete PI-controller and a discrete high-gain linear estimator are used; systematically the estimator is constructed, and the both control and estimator are tuned by a conventional pole-assignement procedure. The controller and estimator are of practical implementation since they are linear, andmanage discrete-delayed measurements, typical in an industrial framework. The performance of the control system is shown and discussed via simulation, regulating substrate concentration of a reactor to produce ethanol at large scale, and of a self-oscillating reactor. Keywords: Bioreactor, discrete control, discrete estimation, discrete-delayed measurements, linear control, linear estimation. 1.INTRODUCTION Since several decades, bioreactors have motivated numerous works in the control field, because of their commercial importance, and complex dynamics response: i.e., food, pharmaceutical, cosmetics products, and fuels are manufactured through them; and the processes behaves in a nonlinear form whose operation is carried out with measurement techniques or instruments that imply time delay,or give secondary measurements intended to infer the key variables of the process. This work focuses on continuous stirred tank bioreactors (CSTBR), which play an important role on large production of cell mass or product. For this class of processes, most control systems are designed following the linearizing feedback approach (i. e., Harmand et al., 2006); but PI controllers have shown theircapability for regulating them € (Zhao and Skogestad, 1997). Considering the “actual” € industrial automation platforms, and that the key variable measurement is discrete-delayed, or inferred from secondary € continuous measurements, the resulting control elements are € not implementable because either they seem complex, or they are designed in a framework of continuous signals. The above mentionedhas motivated a research line of automatic control systems of reactors that: (i) are based on deterministic models, (ii) manage discrete-delayed measurements, common on industrial frameworks, and (iii) are of technical feasibility, and non-expensive implementation. Methodologically speaking, first it must be considered that, as above mentioned, PI controller are capable to control the CSTBR, andthey have the easier implementable form, but it is hindered by the discretedelayed nature of the measurement; and following this line, it is necessary to settle on the implementable scheme of a control system with linear control elements. Then, in this work the discrete counterpart of a linear control system is designed on the basis of the reactor model, in a systematic way that considers the effectof the sampling period in which discrete-delayed measurements are obtained. 2. THE CONTIONUOUS STIRRED TANK BIOREACTOR AND ITS CONTROL PROBLEM The class of CSTBR where simple microbial growth process takes place is considered. It is assumed that the volume and temperature are constant. From material balance, and a formation rate of cell mass (or biomass) argument, the bioreactor model takes thefollowing form:
˙ C = rg (C,S,P) + D ⋅ (Ci − C ) := fC (⋅) ˙ S = −YS /C (S) ⋅ rg (C,S,P) + D ⋅ ( Si − S ) := f S (⋅) ˙ P = YP /C ⋅ rg (C,S,P) + D ⋅ ( Pi − P ) := f P (⋅)

(1a) (1b) (1c) (1d)

y S (t i ) = S(t i−1 ) , t i+1 = t i + δ

where C, S, and P are the concentrations of cell mass, substrate, and product, respectively; Ci, Si, and Pi are the concentrations of cell mass, substrate, and...