Sliding mode observer for biomass estimation in a biohydrogen production process

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Abstract

This work deals with the problem of estimation of biomass concentration and specific growth rate in a biohydrogen production process. A photo-fermentation process with the photosynthetic bacteria Rhodobacter capsulatus is considered. The reaction dynamics is represented with a Monod law while the hydrogen production rate is modeled with a Luedeking-Piret expression. A sliding mode observer is proposed and designed, which gives an estimate of both biomass concentration and specific growth rate from measurements of the produced hydrogen volume. The proposed observer is completely robust against the growth kinetic model, and it presents a first-order reduced dynamics. Numerical simulation results are presented for a batch biohydrogen production process.

Highlights

► We consider a biohydrogen production process with a purple non-sulfur bacteria. ► We develop a sliding mode observer using measurement of the produced hydrogen volume. ► An estimation of biomass concentration and specific growth rate is achieved. ► The observer exhibits asymptotic convergence. ► It is independent of the growth kinetics with first-order reduced dynamics.

Introduction

Hydrogen is considered a promising energy carrier as an alternative to fossil fuels. Besides being renewable, its combustion generates no pollution and provides an amount of energy per unit weight higher than the energy obtained from hydrocarbon fuels.

In the last years there has been an increasing interest in obtaining hydrogen from biological processes (biohydrogen), as these processes are environment friendly. Biological hydrogen production is basically based on either biophotolysis, photo-fermentation or dark fermentation [1].

Diverse experiments have been carried out, using pure and mixed cultures of microorganism, for a large variety of substrates and under different operating conditions. Both the hydrogen yield and the specific production rate have been shown to be strongly dependent on the carbon source and the physiological conditions [2]. Although the utilization of organic wastes as substrate could help to waste minimization and cost reduction, biohydrogen production has not yet entered bulk markets mainly because of its comparatively high costs and low production rates.

In this work we consider a photo-fermentation process, which has been found to be the most promising bioproduction process due to its high substrate to product conversion yield [3]. In such a process, a photoheterothrophic bacteria reduces organic acids into H2 and CO2 mainly through nitrogenase enzyme. In addition to hydrogen generation, the photo-fermentation provides the possibility of organic waste treatment at industrial scale by using mixed culture of microorganisms [4].

On the other hand, photo-fermentation processes are affected by physicochemical conditions in which microorganism grows such as: C/N ratio, light intensity, temperature, pH and operating mode [3]. Another important constraint is that during the photo-fermentation process, only a few measurements are available online.

In order to make progress towards an economically viable biohydrogen production process, it is essential to apply advanced control strategies which can optimize the process and significantly improve the production rates. Since any control strategy which can be applied will require as much information as possible, the implementation of state observers (or software sensors) for the estimation of those variables which are not accesible becomes a crucial task.

In this direction, one of the earliest contributions to state estimation in bioprocesses was proposed in [5], where a specific growth rate estimation was performed assuming that it is a bounded time-varying parameter. More recently [6], proposed a high-gain state observer, while [7] proposed a hybrid observer which combines high-gain with asymptotic estimation properties. A special class of nonlinear observers is that one which operates under sliding mode (SM) regime. Particularly [8], proposed an SM observer for specific growth rate estimation from biomass measurements. Regarding biohydrogen generation, there are just a few works published dealing with state estimation. Among them [9], presents a model predictive control strategy using an asymptotic observer, whereas [10] proposes a moving horizon state estimator to be applied to biohydrogen process control.

This work deals with the problem of estimation of biomass concentration and specific growth rate in a biohydrogen production process. The photo-fermentation process with purple non-sulfur bacteria Rhodobacter capsulatus is considered. The reaction dynamics is represented with a Monod law, while hydrogen production rate is modeled with a Luedeking-Piret expression. An SM observer is designed which provides an estimation of microorganisms (biomass) concentration and specific growth rate from measurements of the produced hydrogen volume. Some distinctive features of this observer are that it presents a reduced-order dynamics and it is independent of the growth kinetics (provided it is bounded).

The work is organized as follows. Section 2 introduces the photo-fermentation bioprocess model and some necessary assumptions. The SM observer for biomass concentration and specific growth rate is described in Section 3. Section 4 presents numerical results, which are discussed in Section 5. Finally, conclusions are given in Section 6.

Section snippets

Process model and problem statement

The following model represents the photo-fermentation process for biohydrogen production with R. capsulatus in a batch culture, under anaerobic condition and nitrogen-limiting substrate [11]. Variation of biomass and substrate concentration is expressed as:Xt=μ(S)XSt=1YXSμ(S)X,where X is biomass concentration (g L−1) and S substrate concentration (g L−1). μ(S) is the specific growth rate (h−1) and YXS substrate on biomass yield (g g−1).

Specific growth rate is represented with a Monod lawμ(S

SM estimation in a class of nonlinear system

Consider a class of nonlinear system that can be represented by the following model:x1t=ε(x,t)x1x2t=k10x1+k20x2+k11x1ty=x2where x1, x2 R+, ε(x,t) is a scalar bounded function, and kT = [k10 k20] a constant vector. Then, in order to obtain estimates of x1 and ε(x,t) using measurement of y = x2, the following observer is proposed:x^1t=ε^(y,x^)x^1x^2t=k10x^1+k20x^2+k11ε^(y,x^)x^1y^=x^2ε^(y,x^)=Msign(yx^2)where x^1 and x^2 are the state estimates, ε^(y,x^) an estimation of ε(x,t), sign(.

Numerical results

Numerical simulation results for a batch biohydrogen production process are presented in this section to illustrate the proposed observer performance. The initial conditions are X(0) = 0.13 g L−1, S(0) = 4.19 g L−1 and P(0) = 0 mL [10], the batch run is 52 h. The model parameters are presented in Table 1.

Fig. 1 shows the state evolution for the photo-fermentation process. The initial substrate concentration is consumed by biomass for biomass growth and product formation. Hydrogen is produced

Discussion

As was verified in the previous section, the sliding mode regime enforces the observer to operate on the surface P˜=0. Because of the SM reduced-order dynamics, the error X˜ tends to zero with a first-order dynamics, and then an estimation of biomass concentration is achieved.

It is worthy to remark that the development of the observer does not require any model (Monod, Haldane, etc.) for specific growth rate μ(t). Indeed, an upper bound μ¯max is only required. This allows the utilization of the

Conclusions

An SM observer of biomass concentration and specific growth rate was designed for a biohydrogen production process. The convergence of the observer was verified by numerical simulation in a photo-fermentation process with the bacteria R. capsulatus. The proposed observer assumes no particular model for μ(), only requiring the growth rate to be bounded.

This algorithm could be employed both for online monitoring of the biohydrogen production process and for the application of advanced control

Acknowledgments

This work was funded by ANPCyT (PICT 2007-00535), CONICET (PIP 1052 2009/2011) and UNLP (11/I127) of Argentina.

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