Mihaela-Iuliana Sbarciog

Nonlinear Predictive Control of processes with variable time delay. A temperature control case study

Material or fluid transportation is a commonly encountered phenomenon in industrial applications, generating variable time delay that makes the design of feedback control loops more difficult. This paper investigates the applicability of MPC (Model Predictive Control) strategies to this type of processes. The experimental setup consists of a heated tank, of which the outlet temperature (measured at a certain distance from the tank) is controlled by manipulating the outlet flow. The nonlinear EPSAC (Extended Prediction Self-Adaptive Control) approach is used, which reduces the complexity of nonlinear optimization to iterative quadratic programming. It is shown that developing a process model in which dynamics are decoupled from the variable time delay leads to a Smith predictor-like control structure, that allows the proper operation of the control loop with fixed control parameters. The performance of the predictive controller is compared on the pilot plant to the performance of classic control approaches for systems with time delay.

Steady state multiplicity of two-step biological conversion systems with general kinetics

This study analyses the steady state behaviour of biological conversion systems with general kinetics, in which two consecutive reactions are carried out by two groups of micro-organisms. The model considered is a realistic description of wastewater treatment processes. A step-wise procedure is followed to reveal the mechanisms affecting the occurrence of steady states in terms of the process input variables. It is clearly demonstrated how taking into account inhibition effects by simply including additional inhibition terms to the kinetic expressions, a common practice, influences the models long term behaviour. The overall steady state behaviour of the model has been summarized in easy-to-interpret operating diagrams, depicting the occurrence of steady states in terms of the reactor dilution rate and the influent substrate concentration, with well-defined boundaries between distinct operating regions. This knowledge is crucial for modelers as steady state multiplicity--in the sense that more than one steady state can be reached depending on the initial conditions--may remain undetected during simulation. The obtained results may also serve for experimental design and for model validation based on experimental findings.

The Estimation of Stability Boundaries for an Anaerobic Digestion System

Abstract The operation of biochemical reaction systems requires substantial expertise and a good understanding of system dynamics. Due to various inhibition effects, these systems usually possess several equilibrium points. Selecting the initial state of the system is as important as selecting the systems inputs for a proper operation and for achieving the technological goal. This paper presents an anaerobic digestion system with two biochemical reactions, which possesses six equilibria for some ranges of systems inputs. The systems stability boundary separates the set of initial states from which the system converges to the desired operating point and the set of initial states which lead the system to a totally undesired condition, the acidification point. A methodology for estimating this stability boundary is described. Additionally, a procedure for visualizing the extent of the estimated boundary in a lower dimensional space is introduced. The algorithms are simple and provide accurate estimates. Moreover, the results may be displayed as two-dimensional diagrams that can be easily understood by the systems operator.

Optimality and stability in a class of bang–bang controlled biochemical reaction systems

This paper deals with the optimization of biochemical reaction systems of rank one. Two optimization problems are solved: the problem of optimal operation for maximum productivity in steady state and the problem of the start-up to the optimal steady state. Application of Pontryagins maximum principle shows that the controller is of the bang–bang type, with no singular intervals. The determination of the optimal switching surface involves the solution of a two point boundary value problem. Solving such a difficult problem is avoided by choosing candidate switching surfaces on a heuristic basis. This study shows that switching on the stability boundary of the nominal operating point corresponding to the maximum dilution rate is the best choice. Here the value of the cost index is minimum amongst the various switching surfaces considered and the stability boundary satisfies the conditions imposed on a candidate switching surface for proper operation. Simple, robust algorithms are formulated for accurately estimating the systems stability boundary. The obtained results display the influence of feedback control on the stability of the set point. The bang–bang controller substantially increases the set points region of attraction in state space as compared to the uncontrolled bioreactor.

Convergence and Stability of Biochemical Reaction Systems of Rank One

The dynamics of biochemical reaction systems of rank one are studied. The global convergence of the set of equilibrium points is investigated and the local stability properties of the equilibria are analysed. The problem of stability boundary estimation is addressed and an algorithm for the visualization of the boundaries is proposed. The theoretical results and the effectiveness of the proposed algorithms are verified by two examples.

Optimization of microorganisms growth processes

Microorganisms growth processes are encountered in many biotechnological applications. For an increased economic benefit, optimizing their productivity is of great interest. Often the growth is inhibited by the presence in excess of other components. Inhibition determines the occurrence of multiple equilibrium points, which makes the optimal steady state reachable only from a small region of the system state space. Thus dynamic control is needed to drive the system from an initial state (characterized by a low concentration of microorganisms) to the optimal steady state. The strategy presented in this paper relies on the solutions of two optimization problems: the problem of optimal operation for maximum productivity in steady state (steady state optimization) and the problem of the start-up to the optimal steady state (transient optimization). Steady state optimization means determining the optimal equilibrium point (the amount of microorganisms harvested is maximum). The transient optimization is solved using the maximum principle of Pontryagin. The proposed control law, which drives the bioreactor from an initial state to the optimal steady state while maximizing the productivity, consists of switching the manipulated variable (dilution rate) from the minimum to the maximum value and then to the optimal value at well defined instants. This control law substantially increases the stability region of the optimal equilibrium point. Aside its efficiency, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any microorganisms growth process which involves only one biochemical reaction. This means that the sequence of the control levels does not depend on the structure and parameters of the reaction kinetics, the values of the yield coefficients or the number of components in the bioreactor.

Anticipating Operational and Wash out Conditions in Biotechnological Reactors

Algorithms are developed which compute the stability boundaries of the equilibrium points of biotechnological reaction systems and which visualize these boundaries in a high dimensional state space. The algorithms predict the ultimate process behaviour from its present state and from the control input levels, using an analytical model of the system. In particular, they allow to forecast whether the process will converge to a nominal operational state or to a condition of biological wash out. The paper concentrates on systems of rank two, which encompass a wide range of potential industrial applications.

An optimal operation strategy for a bioprocess: robustness evaluation

This paper investigates the influence of parameter uncertainty in the reaction rate function on the efficiency of a bang‐bang control strategy for a microorganism’s growth process. The bang‐bang controller is developed to drive the bioreactor from an initial state to a small neighbourhood (target set) of the optimal steady state, while maximizing the productivity. Once the target set is reached, the control effort is switched to the optimal dilution rate, which allows the process to converge to the optimum. This simple control strategy uses a model of the process i) to determine when the switching in the control effort must occur, ii) to determine which initial states will lead the system to an optimal steady state, and iii) to predict the optimal equilibrium point. For certain kinetic coefficients of the model a wide region in the process’s kinetic coefficients space is identified, for which the bang‐bang control will perform reasonably. Moreover, the productivity of the process will be higher than the one predicted by the model in almost the entire robustness region.

Optimization of a Microorganisms Growth Process

Abstract This paper presents an optimization strategy for a microorganisms growth process with inhibition kinetics. Two optimization problems are solved: the problem of optimal operation for maximum productivity in steady state and the problem of the start-up to the optimal steady state. The proposed control law is of bang-bang type with no singular intervals. It drives the bioreactor from an initial state to a small neighbourhood (target set) of the optimal steady state while maximizing the productivity. Once the target set is reached, the control effort is switched to the optimal dilution rate, which allows the process to converge to the optimum. The bang-bang controller substantially increases the stability region of the optimal equilibrium point.