No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Dynamic behavior of a continuous stirred bioreactor under control input saturation
Journal of Chemical Technology and Biotechnology
Abstract
A continuous stirred bioreactor with open-loop periodic behavior is analyzed under closed-loop conditions, using the dilution rate as control input. In the absence of control input bounds, the limiting substrate concentration converges to set point. When stringent bounds on control input are imposed, it becomes permanently saturated; then a limit cycle is generated, and the substrate concentration oscillates around an equilibrium point induced by saturation (EPIS). Suitable conditions are developed to avoid the presence of this closed-loop limit cycle. When the above conditions are satisfied, numerical simulations show that the substrate concentration in the closed-loop bioreactor has no permanent oscillations, the EPIS disappears and the limiting substrate concentra-tion converges again to set point, in spite of the control input bounds. © 1998 SCI
... The performance degradation caused by input constraints has motivated many studies, where simultaneous approaches are developed to improve the performance of closed-loop systems. For a specific class of chemical processes [Alvarez et al., 1991, 1993, Barron et al., 1997, Barrón and Aguilar, 1998], the bounded control problem has been studied using nonlinear state-feedback, where the fundamental idea is that the controller makes the desired steady state (stable or unstable) a globally and asymptotically stable attractor without saturation. Although the conditions to exclude equilibrium points induced by saturation are established for a class of continuous reactors, it is not straightforward to propose a general extension. ...
This work focuses on the control design for feedback linearizable nonlinear systems with unknown time-varying disturbances and uncertainty such that bounds on inputs and state constraints are not violated. Exploiting the special structure of the systems considered, controllers based on Lyapunov's direct methods are easily synthesized, which enforce asymptotic stability in the presence of bounded inputs. However, these controllers do not account explicitly for state constraints in the presence of disturbances and uncertainty. The solution of this task is addressed in this work by an optimization-based method, the so-called normal vector approach.
... The saturated SF and OF control design problem has been addressed, in the chemical reaction engineering field in general, employing: (i) ad hoc saturation handling schemes for nonlinear geometric (Kendi and Doyle, 1998;Mendez-Acosta et al., 2005), and geometric-MPC (Kurtz and Henson, 1997) SF controllers, (ii) geometric and bifurcationbased approaches (Alvarez et al., 1991;Alonso and Banga, 1998; Barron and Aguilar, 1998), (iii) observer-based antiwindup schemes (Kapoor and Daoutidis, 1999), and (iv) Lyapunov approaches for saturated PI and geometric controllers (Jadot et al., 1999;Rapaport and Harmand, 2002;El-Farra and Christofides, 2003). ...
The problem of designing a saturated Output-Feedback (OF) controller for a three
species continuous fermenter with substrate and product-inhibited kinetics is addressed. The
reactor must be operated at maximum production rate by manipulating the feed rate on the basis
of a (biomass, substrate or reaction rate) measurement. The combination of global dynamics
concepts with State-Feedback (SF) and OF nonlinear control tools yields a linear dynamical
OF saturated control design with: (i) robust stability conditions in terms of the controller gains
and saturation limits, and (ii) simple tuning guidelines. The linear OF saturated controller: (i)
recovers, in a practical stability sense, the behavior of a globally stabilizing nonlinear robust SF
saturated controller, and (ii) becomes a linear PI controller in the absence of saturation. The
proposed approach is illustrated and tested with a representative example through simulations.
... where the input vector consists of cool water flow rate, acid and base flow rate. It is noticeable that in this part as well as in Section 3 the optimization problem can be solved for manipulating substrate feed rate as studied in [9,25,42,43] too. However, it is a bit easier to control bioreactors concerning variables, such as pH and temperature, for optimizing the microbial growth [3]. ...
Bioprocesses, which are involved in producing different antibiotics and other pharmaceutical products, may be conveniently classified according to the mode chosen for the process: either batch, fed-batch or continuous. From the control engineer's viewpoint it is the fed-batch processes, however, which present the greatest challenge to get a pure product with a high concentration. To achieve this goal, control of the following parameters has significant importance dealing with these processes: temperature, pH, dissolved oxygen (DO2). Bioprocesses have complicated dynamics. Hence, their control is a delicate task; Nonlinearity and non-stationarity, which make modeling and parameter estimation particularly difficult perturbs such processes. Moreover, the scarcity of on-line measurements of the component concentrations (essential substrates, biomass and products of interest) makes this task more sophisticated. In this paper, Model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor has been developed. MPC is performed via determining the control signal by minimizing a cost function in each step. The results of this controller to maximize penicillin concentration have been displayed and also compared with the results of auto-tuned PID controller used in previous works.
... These variables are easier to measure and control and have negligible perturbations. However, variables subject to large fluctuations such as substrate concentration, selected in this work, can be just as important for growth optimization (Barron and Aguilar, 1998;Dondo and Marques, 2001). Large levels of substrate can be toxic for the microbial growth while too little can force an early stationary or decay phase. ...
The article investigates the operability of a nonideal unstructured kinetic model of continuous bioreactors. The study of operability (interactions between design and control) can help in identifying control problems that could be overcome during the design stage. The issue of operability has been studied extensively in the literature for chemically reactive systems but has not received the same attention for bioreactive systems. The bioreactor model investigated here allows for general dependence of growth rate and yield coefficient on the substrate. The nonideality of the bioreactor is described by the fraction of reactor total volume that is perfectly mixed and by the fraction of the feed entering the perfectly mixed zone. The static and dynamic analyses of the model enable the delineation of regions of input and output multiplicity, as well as the conditions for the existence of oscillatory behavior in the bioreactor. This allows the determination of boundaries between safe and washout regions and the delineation of regions of undesired oscillations. The general analysis is illustrated through a specific example for substrate-inhibited growth rate and linear dependence of the yield on the substrate. The analysis illustrates how modeling decisions and ultimately the design and operating parameters influence the operating characteristics of the bioreactor.
... where the input vector consists of cool water flow rate, acid and base flow rate. It is noticeable that in this part as well as in Section 3 the optimization problem can be solved for manipulating substrate feed rate as studied in[9,25,42,43]too. However, it is a bit easier to control bioreactors concerning variables, such as pH and temperature, for optimizing the microbial growth[3]. ...
Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).
... These were the ideal variables to control since they often have negligible perturbations. However, variables subject to large fluctuations, such as substrate regulation can be just as important for growth optimization [2,3]. For instance, too much substrate can be toxic while too little can force an early stationary phase or the onset of endogenous decay (i.e., death by starvation). ...
Bioreactor control has become very important in recent years due to the difficulty in controlling the highly non-linear behaviour associated with such systems. Model predictive control (MPC) was used to control a non-linear continuous stirred tank bioreactor to an unstable steady state, which was the desired set point. The effect of varying predictor horizon, an important MPC controller tuning parameter, was studied. As the predictor horizon increased, the trajectory moved away from steady state towards a period attractor. The relationship between the changing manipulated input and the system behaviour for different initial conditions as a result of the non-linearities associated with the bioreactor dynamics was also analyzed. The results indicated that the controlled bioreactor can exhibit non-intuitive non-linear behaviour and even a well-designed control scheme may result in very poor performance.
Substrate toxicity can impose operability challenges in the biological treatment of xenobiotic compounds. These can arise from transients in the feed to conventional continuous processes, as well as in more challenging systems, sequencing batch reactors (SBRs), whose operation is always inherently dynamic. Via the use of the classic Haldane model for microbial toxicity, and unsteady-state material balance equations for SBR operation, we have analysed the behaviour of an SBR reactor operating over multiple cycles and have shown that both high performance and low performance can be obtained depending on the feed substrate concentration and the selected SBR exchange ratio. That is, both the intrinsic microbial kinetics as well as the selection of process operating conditions can lead either to high performance (high removal efficiency) or low performance (low removal efficiency) operation. Using this approach, we have also discussed the performance for the SBR treatment of 2 "real" substrates possessing widely different kinetic parameters, showing the impact of these parameters, as well as process operating conditions, on the operability of SBR biotreatment systems handling xenobiotic compounds. This could be of significant value to practitioners wishing to select high performance operating regimes for the treatment of a specific xenobiotic compound. To our knowledge, this is the first systematic study of the impact of substrate toxicity on SBR operability, and is also a first step in modeling the impact of substrate detoxification, via the use of discontinuous Two-Phase Partitioning Bioreactors, on the dynamic performance of xenobiotic biotreatment processes.
This work focuses on control design for input-output feedback linearizable nonlinear systems with bounded inputs and state constraints in the presence of uncertainty. Controllers based on Lyapunov’s direct method have been synthesized before for this class of nonlinear systems to enforce asymptotic stability in the presence of bounded inputs. However, none of these controllers accounts explicitly for state constraints. In order to address this task, we propose an optimization-based design method for which two properties will be guaranteed simultaneously despite parametric uncertainty, namely, closed-loop stability with bounded inputs and feasibility of the transient in the presence of state constraints.
In this work, the normal vector method for robust design is considered to account for actuator saturation effects when unknown time-varying disturbances are present, and desired dynamic properties have to be guaranteed. The normal vector method ensures that desired dynamic properties hold despite uncertain parameters by maintaining a minimal distance between the operating point and so-called critical manifolds where the process behavior changes qualitatively. In this paper input saturation is considered for the first time in the normal vector framework. In order to solve the resulting optimization problem, first and second order derivatives of the flow of a dynamical system has to be computed efficiently. For this purpose, a new platform for source-level manipulation of mathematical models, currently under development at RWTH Aachen University, is proposed to solve the technical difficulties arising when the event of actuator saturation takes place.
The problem of designing a saturated Output-Feedback (OF) controller for a continuous bioreactor with
Haldane kinetics is addressed. The reactor must be operated at maximum biomass production rate by
manipulating the feed rate on the basis of a (biomass or substrate) measurement. The consideration of the
problem as an interlaced observer-control design leads to a saturated PI controller that recovers (up to
observer convergence) the behavior of a detailed model-based robust nonlinear state-feedback (SF) globally
stabilizing saturated controller. The saturated PI control scheme has: (i) closed-loop stability conditions in
terms of control gains and limits, and (ii) a simple construction-tuning procedure. The proposed approach is
illustrated and tested with a representative case example through numerical simulations.
The problem of designing a saturated output-feedback controller to stabilize a class of continuous threestate
bioreactors with Haldane inhibited kinetics is addressed. The reactor must be maintained about
the (locally stable but possibly structurally unstable) steady-state with maximum production rate by
manipulating the substrate feed rate on the basis of a biomass measurement. The consideration of the
problem in the light of bioreactor (bifurcation and invariant set) dynamical and (passivity and observability)
structural characteristics leads to a saturated linear dynamic OF control design with: (i) PI scheme
with observer-based antiwindup protection, (ii) simple construction and tuning, and (iii) closed-loop
robust stability conditions in terms of control gains and limits. The PI controller recovers (up to observer
convergence and saturation) the behavior of a model-based nonlinear state-feedback passive stabilizing
controller equivalent to an exact nonlinear model-based predictive controller with infinite-time receding
horizon. The proposed approach is illustrated with a representative case example through numerical
simulations.
A novel measurement method of temperature model for bioreactor has been proposed. Temperature is the key parameter in monitoring
the bioreactor operation. However, the system input signal of bioreactor is delayed, and model parameters are uncertain, so
the output of temperature is non-steady-state. Many dynamic measurements are not steady so that it cannot be described by
variables constant in time. In this paper, we adopt the monopulse signal as input so that the output of the bioreactor system
is steady. This method has a powerful ability to steady the output of the bioreactor. In view of the measurement results,
it can be seen that the model dynamic measurement approaches the real process. The analytical expression of the monopulse
response for the temperature model of the bioreactor is obtained. The novel measurement approach is simple and can be easily
adopted by industry.
Keywordsmeasurement method-temperature model-monopulse response-time-variant-bioreactor
In this paper, the problem of rigorously characterizing the existence of limit cycles in a class of two-state bioreactors is addressed. The reactor class is the simplest one which retains the essences of the oscillatory phenomena, and ample enough to include a diversity of monotonic and nonmonotonic kinetics. On the basis of global dynamics framework, analytic conditions for the existence of limit cycles are drawn, and the results are applied to characterize the reactor behavior with a linear P controller. The results are physically interpreted and put in perspective with previous open and closed-loop bioreactor studies. The findings are illustrated with a representative case example though numerical simulations.
The closed-loop dynamic behavior of a chemical reactor with two consecutive and oscillatory exothermic reactions is analyzed. When bounds are imposed on the control input, equilibrium points induced by saturation (EPIS) are generated. In this case, the reactor dynamic trajectories are deviated towards the EPIS and their convergence to the set-point is no longer guaranteed. By means of bifurcation analysis, necessary and sufficient conditions are derived to obtain quasi-optimal regulatory control and to avoid the presence of EPIS. Simulation studies proved the advantages of implementing these conditions, giving smooth responses with no oscillation.
Biotechnology is the use of living organisms to enhance products, our lives and our environment. It is a broad and complex discipline that encompasses many specialized areas. The promise that biotechnology holds for developing countries is well recognized and it is an important tool that can be applied to diverse economic sectors with a focus on the production of food crops, livestock management, human health care, the chemical industry and environmental management. This book covers applications of biotechnology in selected areas such as health care, agriculture, microbial systems, sect;in silico analysis for drug designing and drug discovery and the environment.
Multivariable adaptive control of a continuous stirred tank bioreactor (CSTBR) via the algorithm of weighed moving identification with an adjustable estimation interval is presented. Control of the reactor is carried out by using the dilution rate and the composition of feeding substrate as the manipulated variables. The dynamic behavior of the CSTBR is nonlinear. By using the proposed method, it is possible to operate the system at a steady state within a limit cycle, or across a separatrix.
The dynamic behavior of an isothermal biological CSTR modelled by idealized cell and substrate balance equations has been investigated theoretically in terms of multiplicity and stability of steady states and existence and stability character of limit cycles. Various types of dynamic behavior have been classified in terms of a Damköhler number and two other system parameters. The predicted types of behavior have been illustrated by numerical computation of cell and substrate concentration trajectories.
Changes in the operating parameters of a continuous stirred-tank bioreactor degrading phenol, controlled such that almost all the phenol introduced into the bioreactor was degraded, were studied. In particular, control of the dilution rate and phenol concentration in the feed to prevent washout after the occurrence of a disturbance upstream of the bioreactor was investigated. The highest dilution rate Dm and the highest phenol concentration S0m in the feed which did not cause washout of the biomass from the bioreactor were measured and compared with those predicted by a short-cut method. It was found that the experimental Dm and S0m were larger than the calculated values by 25% and 15% respectively.The introduction into a bioreactor of biomass from another culture to avoid washout was also studied. The minimum biomass concentration Xmin required in the bioreactor for preventing washout after the disturbance has occurred was measured and compared with that calculated from equation developed by Migiro and Sokół in 1992. It was found that, when the first disturbance was a step increase in phenol concentration in the feed, followed by a step decrease in dilution rate, the concentration Xmin predicted from the equation was sufficient to prevent washout. When the first disturbance was a step increase in the dilution rate, followed by a step decrease in phenol concentration in the feed, the value of Xmin required for preventing washout was approximately 10% larger than that calculated from the equation.
An examination is made of three aspects of the problem of continuous oscillations for accepted and relatively simple fermentation models. First, a careful analysis of the conventional growth model with flow terms and a constant yield shows that such a system cannot exhibit sustained oscillations. Second, the empirical observations noted in the earlier study using a variable yield function to generate sustained fermentation oscillations is now developed mathematically. In the third aspect of the problem of predicting oscillatory region in the substrate-cell phase plane within another oscillatory region.
Identification and control of continuous fermentation processes are dif-ficult tasks due to the complexity and high coupling of dynamic behaviour of this kind of system. In this work is implemented an on-line estimation technique of the main uncertainties of a fermentation processes (e.g. specific growth rate, biomass concentration and yield coefficient) based on a mass balance, to generate a linearising feedback control law that provides a robust stabilisation against uncertainties. By numerical simulations the performance of the closed-loop system and the controller design procedure is illustrated.