Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis

Čelikovský, Sergej; Papáček, Štěpán; Herrera, Alejandro Cervantes; Leon, Javier Ruiz

doi:10.1109/cdc.2008.4738726

Cited by 9 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Modelling in a predictive way the photosynthetic response in the threedimensional flow field seems unrealistic today, because the global response depends on numerous interacting intracellular reactions, with various time-scales. In our previous works [2][3][4][5], we examined an adequate multi-scale lumped parameter model, describing well the principal physiological mechanisms in microalgae: photosynthetic light-dark reactions and photoinhibition. Now our main goal is the development and implementation of a mathematical model of microalgae growth in a general gas-liquid-solid PBR as a tool in PBR design and optimization of its performance.…”

Section: Introductionmentioning

confidence: 99%

Growth impact of hydrodynamic dispersion in a Couette–Taylor bioreactor

Papáček

Štumbauer

Štys

et al. 2011

Mathematical and Computer Modelling

View full text Add to dashboard Cite

a b s t r a c tThe development of a distributed parameter model of microalgae growth is presented. Two modelling frameworks for photo-bioreactor modelling, Eulerian and Lagrangian, are discussed and the complications residing in the multi-scale nature of transport and reaction phenomena are clarified. It is shown why is the mechanistic two time-scale model of photosynthetic factory the adequate model for biotechnological purposes. For a special laboratory Couette-Taylor bioreactor with cylindrical geometry, we reached reliable simulation results using a steady-state Eulerian approach and the finite difference scheme. Moreover, we prove numerically that the resulting photosynthetic production rate in this reactor goes, for growing inner cylinder angular velocity, to a certain limit value, which depends on the average irradiance only.

show abstract

Section: Introductionmentioning

confidence: 99%

Growth impact of hydrodynamic dispersion in a Couette–Taylor bioreactor

Papáček

Štumbauer

Štys

et al. 2011

Mathematical and Computer Modelling

View full text Add to dashboard Cite

show abstract

“…The addition of dissolved CO 2 decreases the pH of the media. Since it can take 2-3 seconds for carbon to completely dissolve and only a fraction of the input CO 2 dissolves before leaving the vent, there are some dynamics associated with the pH in the media, which are captured by the first order dynamics (transfer function) in eqn (16). The pH model is linearized about a pH of 7.3.…”

Section: E Water Chemistry Subsystemmentioning

confidence: 99%

“…However, there has been significantly less publications on flat panel reactors, which is the style of reactor addressed in this paper. Model based controls have been developed in [9], [16], [17], [18], [19], [20]. Most of these papers model growth as a function light using a Monod kinetics model.…”

Section: Introductionmentioning

confidence: 99%

Microalgae growth modeling and control for a vertical flat panel photobioreactor

Buehner

Young

Willson

et al. 2009

2009 American Control Conference

View full text Add to dashboard Cite

Abstract-Microalgae have the potential to produce enough biofuels to meet the current US fuel demands. In order to achieve this potential, photobioreactors (PBRs) need to be developed that are efficient, scalable, and affordable. Models are an analytical tool that can be used to evaluate various PBRs. In this article, a dynamic model is developed for growing microalgae in a vertical flat panel photobioreactor (PBR) that may be used to measure PBR efficiency for various architectures independent of scale. The growth model is used to estimate the microalgae growth and byproduct production and consumption as a function of incident light. A feed-forward controller is developed that uses the estimated amount of CO2 consumed to determine the amount of additional CO2 to add to the system during photosynthesis. An overall controller structure that uses both feed-forward and feedback control is presented for growing microalgae inside a PBR.

show abstract

“…The VSI dynamics can be divided into two parts: the fast internal current control loop, called the fast boundary layer, and the slow external voltage loop, called the slow quasi-steady state [46]- [50]. From the vantage point of the slow quasi-steady state, the grid current can be seen to have reached the reference current because it is in the fast boundary layer and significantly faster in comparison.…”

Section: B Dynamic Analysis Of the Proposed Droop Controllermentioning

confidence: 98%

“…Thus, in this section the stability of the proposed closed-loop control system is explored. The stability of the closed-loop control system is analysed through singular perturbation control theory, which allows a nonlinear dynamical system to be broken down into subsystems with different time scales [56]- [60]. This approach is particularly suited towards systems with state variables that have different rates of change.…”

Section: B Optimized Dc-bus Voltage Adaptive Droop Controlmentioning

confidence: 99%

An Adaptive Droop DC-Bus Voltage Controller for a Grid-Connected Voltage Source Inverter With LCL Filter

Eren

Pahlevani

Bakhshai

et al. 2015

IEEE Trans. Power Electron.

View full text Add to dashboard Cite

This paper presents a very fast DC-bus voltage controller for a single-phase grid-connected Voltage Source Inverter (VSI) with an LCL output filter used in renewable energy applications. In single-phase grid-connected inverters, the design of the DC-bus voltage control scheme is very challenging due to the presence of a second harmonic ripple across the DC-bus voltage. The proposed DC-bus voltage control scheme is able to address the difficulties introduced by the second harmonic ripple. The DC-bus voltage controller is based on an adaptive droop control technique, which is able to provide a very fast transient response for the closed-loop system and ensures the optimal operation of the VSI during steady-state conditions. Also, the simple structure of the controller makes it very practical for grid-connected VSIs used in renewable energy power conditioning systems. Theoretical analysis and experimental results demonstrate the superior performance of the proposed control approach compared to conventional DCbus voltage control schemes.

show abstract

Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis

Cited by 9 publications

References 0 publications

Growth impact of hydrodynamic dispersion in a Couette–Taylor bioreactor

Growth impact of hydrodynamic dispersion in a Couette–Taylor bioreactor

Microalgae growth modeling and control for a vertical flat panel photobioreactor

An Adaptive Droop DC-Bus Voltage Controller for a Grid-Connected Voltage Source Inverter With LCL Filter

Contact Info

Product

Resources

About