Design and Analysis of a Nonlinear Stabilizing Controller for a Mass Structured Cell Population Balance Model With Input Constraints

The dynamics of population balance systems are described by partial integro-differential equations. In this paper we are interested in the design and analysis of a nonlinear stabilizing control scheme based on Lyapunov design techniques in order to stabilize the steady state of the cell population balance model in a continuous bioreactor by manipulating the dilution rate. In this specific instance, the model consists of a partial integro-differential equation, describing cell growth, and an ordinary integro-differential equation, accounting for substrate consumption

Global input constrained adaptive lambda-tracking with application to a nonlinear distributed parameter exothermic chemical reaction models in tubular reactor

We consider input constrained adaptive output feedback control for exothermic chemical tubular reactor with axial dispersion. we use a non linear distributed parameter model with boundary control for both the evolution of the temperature and concentration. Our objective is the set point control of the output i.e, the temperature of the reaction. Practical consideration lead us to work in the presence of input constraints. we apply a λ-tracking controller, we show that for all initial temperature and under a simple feasibility assumptions that the tracking error tends asymptotically to a ball centred at the reference temperature and of arbitrary prescribed radius

Adaptive λ-tracking controller for an exothermic chemical plug flow tubular reactor

This paper deals with the tracking of a prespecified profile temperature for exothermic chemical tubular reactor whose dynamics is described by a set of nonlinear partial differential equations where the state variables are the reactor temperature and the reactant concentration. The coolant temperature, the inlet temperature and the inlet concentration are considered as control actions. For practical reasons, it is preferable to consider a non distributed control law to achieve the control objective. In contrast to our previous work that considers fully distributed control actions where the three control inputs are assumed to be distributed along the reactor, here the last two control inputs are applied at the reactor inlet and only the coolant temperature is distributed along the reactor. We show that the temperature of the reactor tends asymptotically to a ball of arbitrary prescribed radius λ>0, centred at the given temperature profile

Global adaptive l-tracking of a temperature profile in tubular reactor

This paper deals with the control design for a class of nonlinear distributed parameter systems, i.e. convection-diffusion-reaction systems, encountered under the form of non-isothermal tubular reactors in chemical engineering applications. More specifically the design concentrates on the boundary control of the temperature profile in an exothermic chemical reactor under input constraints. Our objective is to analyze the global stability of the closed-loop system by considering a simple control structure, i.e. an adaptive λ-tracking controller. It is shown that for all initial temperature and under simple feasibility assumptions, the tracking error tends asymptotically to a ball of arbitrary prescribed radius λ> 0, centered at the given temperature profile

Extremum seeking control for a mass structured cell population balance model in a bioreactor

This paper is concerned with the design of an adaptive extremum seeking control scheme for a mass structured cell population balance model in a bioreactor. The feed substrate concentration is considered as the manipulated input to drive system states to the desired setpoints that maximize the value of an objective function of the cell density. We assume limited knowledge on the objective function and we use the substrate concentration measurements to estimate this function. We use the Lyapunov's stability theorem and a persistency of excitation condition to show that the proposed adaptive extremum seeking control achieves the exponential convergence to the desired set points. Numerical simulation has been performed to illustrate the performance of the proposed approach

Factorial Design Statistical Analysis and Optimization of the Adsorptive Removal of COD from Olive Mill Wastewater Using Sugarcane Bagasse as a Low-Cost Adsorbent

This work highlights the elimination of chemical oxygen demand (COD) from olive mill wastewater using sugarcane bagasse. A 25−1 fractional factorial design of experiments was used to obtain the optimum conditions for each parameter that influence the adsorption process. The influence of the concentration of sugarcane bagasse, solution pH, reaction time, temperature, and agitation speed on the percent of COD removal were considered. The design experiment describes a highly significant second-order quadratic model that provided a high removal rate of 55.07% by employing optimized factors, i.e., a temperature of 60 °C, an adsorbent dose of 10 g/L, a pH of 12, a contact time of 1 h, and a stirring speed of 80 rpm. The experimental data acquired at optimal conditions were confirmed using several isotherms and kinetic models to assess the solute interaction behavior and kind of adsorption. The results indicated that the experimental data were properly fitted with the pseudo-first-order kinetic model, whereas the Langmuir model was the best model for explaining the adsorption equilibrium