Sliding-mode control of fermentation processes

Continuous fermentation processes described by two nonlinear differential equations with uncertain parameters are considered. Sliding mode control design for these processes is proposed. The control design is carried out with direct use of nonlinear model, expert knowledge and on-line measurement of output variable only. Chattering phenomena are avoided by realizing the sliding mode with respect to the control input derivative. The excellent performance of presented control is proved through simulation investigations.     

Non-linear control of continuous bioreactors

Control of bioreactors has achieved importance in the recent years. This may be due to the fact that they are difficult to control which may be attributed to its nonlinear dynamic behavior. The model parameters of the bioreactor also vary in an unpredictable manner. The complexity of the biochemical processes inhibits the accurate modeling and also the lack of suitable sensors make the process state difficult to characterize. Considerable emphasis has been placed on the control of fed-batch fermentors because of their prevalence in industries. However, when production of biomass is to be optimized, continuous operation is desirable. Several procedures are available for the nonlinear control of processes, viz., differential geometric approach, internal model control approach, reference synthesis technique, predictive control design, etc., but the major disadvantage of these approaches is the computational time required to perform the prediction optimization. In this study, a nonlinear controller based on a polynomial discrete time model (NARMAX) is evaluated for its performance on a fermentor. It can be shown that a nonlinear self-tuning controller based on NARMAX model can be extended to the control of fermentors. The response is smooth for both load and setpoint changes even when process parameters are assumed to be zero and uncertainty in parameters are present and in the presence of controller constraints. The control action can be made more or less robust by changing the design parameters appropriately. Therefore, nonlinear self-tuning controller is suitable for control of industrial processes.     

Dynamic output feedback stabilization for nonlinear systems based on standard neural network models

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.     

Metabolic engineering in silico

This review briefs on the main directions in the field of mathematical modeling of metabolic processes aimed at a rational design of genetically modified organisms. The class of generalized Hill functions is described, and their application to modeling of nonlinear processes in Escherichia coli metabolic systems is illustrated by several examples. A model for the pyrimidine biosynthesis in E. coli, taking into account the nonlinear effects of a negative allosteric regulation of enzyme activities involved in the control of the subsequent stages by the end products of synthesis, is considered. It has been shown that the model displays its own continuous oscillation mode of functioning with a period of approximately 50 min, which is close to the duration of E. coli cell cycle. The need in considering the nonlinear effects in the models as essential elements in the function of metabolic systems far from equilibrium is discussed.     

LFT models of continuous biotechnological processes

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.     

On the modeling of the performances of the human brain in a two-choice task involving decoding and memorization of simple visual patterns

The quantitative, aspects of the decoding and storage processes of simple visual patterns by the human brain are considered, on the basis of the performances obtained in a set of two-choice experiments. Strings of patterns (colored lights or simple geometrical patterns) were used in which the densities of the two patterns throughout the string were either constant or asymmetric. The subjects were required to indicate the pattern which was presented more frequently. A nonlinear model for the storage and decision processes was devised from these data which accurately predicted the performance under experimental conditions different from those originally used. Among the prominent features of the brain processes suggested by the model are the necessity for a nonlinear summation of the decoded information and its decay with time.Finally, it is shown that the experimental design allows a quantitative evaluation of those factors which are relevant to the decoding of patterns of different complexities.     

Foundations for the design and implementation of synthetic genetic circuits

Synthetic gene circuits are designed to program new biological behaviour, dynamics and logic control. For all but the simplest synthetic phenotypes, this requires a structured approach to map the desired functionality to available molecular and cellular parts and processes. In other engineering disciplines, a formalized design process has greatly enhanced the scope and rate of success of projects. When engineering biological systems, a desired function must be achieved in a context that is incompletely known, is influenced by stochastic fluctuations and is capable of rich nonlinear interactions with the engineered circuitry. Here, we review progress in the provision and engineering of libraries of parts and devices, their composition into large systems and the emergence of a formal design process for synthetic biology.     

Machine learning-based model predictive controller design for cell culture processes

The biopharmaceutical industry continuously seeks to optimize the critical quality attributes to maintain the reliability and cost-effectiveness of its products. Such optimization demands a scalable and optimal control strategy to meet the process constraints and objectives. This work uses a model predictive controller (MPC) to compute an optimal feeding strategy leading to maximized cell growth and metabolite production in fed-batch cell culture processes. The lack of high-fidelity physics-based models and the high complexity of cell culture processes motivated us to use machine learning algorithms in the forecast model to aid our development. We took advantage of linear regression, the Gaussian process and neural network models in the MPC design to maximize the daily protein production for each batch. The control scheme of the cell culture process solves an optimization problem while maintaining all metabolites and cell culture process variables within the specification. The linear and nonlinear models are developed based on real cell culture process data, and the performance of the designed controllers is evaluated by running several real-time experiments.     

Design of Full-Adder and Full-Subtractor Using Metal-Insulator-Metal Plasmonic Waveguides

The metal-insulator-metal (MIM) waveguides are considered best among all plasmonic waveguides for propagation of optical signal to deep sub-wavelength scale. In this paper, MIM plasmonic waveguides based Mach-Zehnder interferometer (MZI) is developed. It possesses nonlinear Kerr material in one of its linear arm for controlling of optical signal with light intensity. Self phase modulation (SPM) and cross phase modulation (XPM) processes inside nonlinear MZI are used to design novel and compact full-adder and full-subtractor. Analysis and verification of proposed devices are carried out using FDTD and MATLAB simulations.     

Connection of the tangents of the regression slope of the heart rate graph with linear and nonlinear dynamics in stationary short-time series

The connection of the regression slope of heart rate graph (b1) with linear and nonlinear dynamics in stationary short-time series (256 points) was studied. A new index for the estimation of nonlinear dynamics in stationary short-time series was used, which is based on the correlation dimension. The results of the study indicated that the dynamics of heart rate in stationary short-time series can be represented as the sum of linear (periodic) and nonlinear (stochastic) processes. A relation of b1 with both linear and nonlinear dynamics of heart rate was found. The formulas for the calculation of absolute and relative (to the amplitude of periodic fluctuations) noise levels in heart rate dynamics were derived. A comparative analysis of nonlinear dynamics of heart rate in stationary short-time series for different functional states of humans was performed. The increase in the relative noise level in heart rate dynamics with increasing breathing frequency is related not only to a decrease in control breathing amplitude but also to an increase in the noise amplitude. The decrease in the absolute noise level for nervous excitation, fatigue, and mental stress were found. The predominance of nonlinear (stochastic) processes over linear (periodic) processes in the relaxed state was established.     

Microbial production of enzymes: Nonlinear state and kinetic reaction rates estimation

The nonlinearity of the biotechnological processes and the absence of cheap and reliable instrumentation require an enhanced modelling effort and estimation strategies for the state and the kinetic parameters. This work approaches nonlinear estimation strategies for microbial production of enzymes, exemplified by using a process of lipase production from olive oil by Candida rugosa. First, by using a dynamical mathematical model of this process, an asymptotic observer which reconstructs the unavailable state variables is proposed. The design of this kind of observers is based on mass and energy balances without the knowledge of kinetics being necessary; only minimal information concerning the measured concentrations is used. Second, a nonlinear high-gain observer is designed for the estimation of imprecisely known kinetics of the bioprocess. An important advantage of this high-gain estimator is that the tuning is reduced to the calibration of a single parameter. Numerical simulations in various scenarios are provided in order to test the behaviour and performances of the proposed nonlinear estimation strategies.     

Multi-input multi-output control of a continuous fermenter using nonlinear model based controllers

Internal Model Control (IMC) and Model Predictive Control (MPC), the two most important members of model based controllers, are favourable alternatives for control of nonlinear processes. However, the performance of these controllers deteriorates drastically in the presence of substantial process-model mismatch. Hu and Rangaiah (1998) proposed feedback augmentation for nonlinear IMC (hence named Augmented IMC, AuIMC) for improving control in the presence of modelling errors, and demonstrated its success on a neutralization process. In the present study, IMC, MPC and AuIMC strategies are tested in a more difficult case of multi-input multi-output (MIMO) operation of a highly nonlinear continuous fermenter. A new control configuration is introduced as the conventional configuration is not applicable. Simulation results for different modelling errors show that IMC is better than MPC for fermenter control. The advantage of augmentation as in AuIMC manifests in the significantly improved regulatory control of the fermenter.     

Mathematical analysis of multienzyme systems. II. Steady state and transient control.

The control theory of steady states, previously presented for linear enzymatic systems (Heinrich and Rapoport, 1974) is extended to nonlinear systems. On the basis of three theorems a new procedure for the calculation of the control strength and of the control matrix is developed. The theory is applied to the extended model of glycolysis of erythrocytes, which includes also ATP-consuming processes. Also in this model the glycolytic flux is mainly controlled by the hexokinase-phosphofructokinase-system. The control strengths of the pyruvate kinase and of the enzymes of the 2.3 P2G-bypass are negligibly small. The control strength of the ATPase is negative, i.e. an activation of this enzyme leads to a decrease of the flux. For transition states of multienzyme systems definitions are given for the mean time required for the transition of the metabolites and for the "transient control" of enzymes. Enzymes with a pronounced influence on the transition time are called time-limiting enzymes. Enzymes which excert strong control on the time-dependent processes may have little influence under steady state conditions and vice versa. The transition times of ATP have been calculated for transient states of glycolysis.     

Neural chaos and schizophrenia

Recent data indicate that random-like processes are related to the defects in the organization of semantic memory in schizophrenia which is more disorganized and less definable than those of controls with more semantic links and more bizarre and atypical associations. These aspects of schizophrenic cognition are similar to characteristics of chaotic nonlinear dynamical systems. In this context, the hypothesis tested in this study is that dynamic changes of electrodermal activity (EDA) as a measure of brain and autonomic activity may serve as a characteristic which can be used as an indicator of possible neural chaotic process in schizophrenia. In the present study, bilateral EDA in rest conditions were measured in 40 schizophrenic patients and 40 healthy subjects. Results of nonlinear and statistical analysis indicate left-side significant differences of positive largest Lyapunov exponents in schizophrenia patients compared to the control group. This might be interpreted that the neural activity during rest in schizophrenic patients is significantly more chaotic than in the control group. The relationship was confirmed by surrogate data testing. These data suggest that increased neural chaos in patients with schizophrenia may influence brain processes that can cause random-like disorganization of mental processes.     

The nature of robustness in development

A trait is robust to a genetic or environmental variable if its variation is weakly correlated with variation in that variable. The source of robustness lies in the fact that the developmental processes that give rise to complex traits are nonlinear. A consequence of this nonlinearity is that not all genes are equally correlated with the trait whose ontogeny they control. Here we explore how developmental mechanisms determine and alter the correlation structure between genes and the traits that they control. A formula is developed by which the correlation of a gene or environmental variable with a trait can be calculated if the mechanism that gives rise to the trait is known. The nature of robustness and the ways in which robustness can evolve are discussed in the context of the problems that arise in the analysis of inherently nonlinear systems.     

Adaptive fuzzy control with output feedback for H infinity tracking of SISO nonlinear systems

Observer-based adaptive fuzzy H(infinity) control is proposed to achieve H(infinity) tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The key ideas in the design of the proposed controller are (i) to transform the nonlinear control problem into a regulation problem through suitable output feedback, (ii) to design a state observer for the estimation of the non-measurable elements of the system's state vector, (iii) to design neuro-fuzzy approximators that receive as inputs the parameters of the reconstructed state vector and give as output an estimation of the system's unknown dynamics, (iv) to use an H(infinity) control term for the compensation of external disturbances and modelling errors, (v) to use Lyapunov stability analysis in order to find the learning law for the neuro-fuzzy approximators, and a supervisory control term for disturbance and modelling error rejection. The control scheme is tested in the cart-pole balancing problem and in a DC-motor model.     

A fully symbolic design and modeling of nonlinear glucose control with Control System Professional Suite (CSPS) of Mathematica

In this case study a fully symbolic design and modeling method are presented for blood glucose control of diabetic patients under intensive care using Mathematica. The analysis is based on a modified two-compartment model proposed by Bergman et al. The applied feedback control law decoupling even the nonlinear model leads to a fully symbolic solution of the closed loop equations. The effectivity of the applied symbolic procedures being mostly built-in the new version of Control System Professional Suite (CSPS) Application of Mathematica have been demonstrated for controller design in case of a glucose control for treatment of diabetes mellitus and also presented for a numerical situation described in Juhász. The results are in good agreement with the earlier presented symbolic-numeric analysis by Benyó et al.     

Mathematical modeling and parameters estimation of anaerobic fermentation processes

In the paper some problems of the mathematical modeling of anaerobic (methane) fermentation of animal waste in stirred tank bioreactors are considered. Laboratory experiments are carried out with highly concentrated organic pollutants and transient step responses of the control output for continuous methane fermentation are obtained. The dynamic behavior of this process is described by sets of deterministic nonlinear differential equations from 2nd order with different structures. Static characteristics are obtained with these models analytically. Investigations by computer simulation of the methane fermentation are performed with the aim to chose appropriate models for automatic control system design of this process.