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Cognition and control processes share many similar characteristics, and decisionmaking and learning under the paradigm of multiple models has increasingly gained attention in both fields. The controlled finite Markov chain (CFMC) approach enables to deal with a large variety of signals and systems with multivariable, nonlinear, and stochastic nature. In this article, adaptive control based on multiple models is considered. For a set of candidate plant models, CFMC models (and controllers) are constructed off-line. The outcomes of the CFMC models are compared with frequentist information obtained from on-line data. The best model (and controller) is chosen based on the Kullback–Leibler information. This approach to adaptive control emphasizes the use of physical models as the basis of reliable plant identification. Three series of simulations are conducted: to examine the performace of the developed Matlab-tools; to illustrate the approach in the control of a nonlinear nonminimum phase van der Vusse CSTR plant; and to examine the suggested model selection method for the adaptive control.

An application of a linear quadratic self-tuning control approach to a pulsed liquid-liquid extraction column is described. The control algorithm is derived from the minimization of a quadratic cost function. The resulting Riccati equation is iterated until the closed-loop poles belong to a predefined stability domain included in the unit circle. Based upon the certainty equivalence principle, the adaptive control algorithm involves a parameter identification procedure and a feedback control law which uses the estimated parameters. Several experiments are carried out on a pulsed liquid-liquid extraction column. Such extractors are being increasingly used in several industries because they are not energy-consuming and they lead to high product purity. The column considered has the same dimensions as those currently used in fine chemical processes. The control objective is to optimize the column behaviour. The selected control variables are the pulse frequency and the conductivity measured at the bottom of the column. The experiments have been carried out with a mixture of water and toluene. The physical model developed for the column is too complex to use for control purposes. To represent the complex behaviour of the column, a single-input/single-output discrete-time linear model was adopted. The parameters in the model are estimated on-line with normalized data. The forgetting factor is also adjusted to maintain a constant trace of the estimator gain matix. The results obtained show the ability of this algorithm to improve the efficiency of the process considered. Finally, some details on practical implementation are provided.

This paper considers the use of adaptive learning systems for multimodal functions optimization and process control. The learning system collects and processes the available data to achieve the desired control objective. The environment where the automaton operates corresponds to the function to be optimized (the process to be controlled) which is assumed to be unknown function of a single parameter x. The admissible region of x (control variable) is quantized into N levels. These levels are associated with the actions of the automaton. The set of these actions is further decomposed into nonempty subsets. The action set is changing from instant to instant. At each time an action set is selected according to a probability distribution. The action and the action set probabilities are adjusted using learning algorithms (reinforcement schemes). This optimization and control approach is tested using two numerical examples (multimodal function and a chemical reactor). However, the concept can be applied to other examples as well. Simulation results illustrate the feasibility and the performance of this adaptive automaton.

This paper deals with distributed adaptive generalized predictive control of a grinding circuit. This multivariable system is commonly used in mineral industries for size reduction. It is characterized by time varying dynamics owing to changes in ore properties and operating conditions. The fresh ore feed rate, the water addition rate, the circulating load and the product fineness are respectively selected as control and controlled variables. The parameters of two single input-single output discrete models are identified using a least-squares algorithm, taking into account the requirements for long-term adaptive control. Numerical results have been carried out using a simulator based on phenomenological models derived from mass balance considerations. The adaptive controller is compared to a fixed parameter controller. These results illustrate the self-tuning ability and the continuous adaptivity of the control strategy. They also highlight that adaptive control is particulary suitable for distributed control.

This paper deals with the generalized predictive control with partial state reference model, of an absorption packed column. The packed column is the most popular equipment used for process absorption. The absorption column is used to decrease the concentration of CO 2 in a gas mixture below a desired value. A solution of Diethanolamine (DEA) is used as the absorbent. The flow rate of the absorbent and the concentration of CO 2 in the gas mixture are respectively considered as control and controlled variables. The process model has been built from considerations of mass balances, of transport phenomena and of chemical reaction in the liquid phase. This model describes the complex dynamics of the absorption column considered. It consists of three non-linear partial differential equations. The dynamics associated respectively with the gas and the liquid phases are quite different. The control design is based on a simple low order linear discrete model with unknown and possibly time-varying parameters. The parameters of this model are estimated from deviation of the input-output measurements, using a constant trace identification algorithm which ensures an upper bound of the covariance matrix. Several procedures such as filtering, normalization, U/D factorization, etc., have been introduced to improve the robustness of the estimation scheme towards the unmodelled dynamics, round-off errors, etc. An extended horizon control policy, based on the plant output prediction over several steps and on the minimization (in a receeding horizon sense) of a criterion, is used for feedback control. This criterion is a quadratic cost function of the input and output tracking errors, An assumption about the future of the input tracking error increments is made. This assumption is more realistic than that considered in the standard Generalized Predictive Control algorithm (GPC). The control algorithm have been implemented using an IBM-PC. Several simulation studies highlight the applicability of the involved adaptive control algorithm.

Some critical computations in pole-placement design and in that of many model reference adaptive systems are described. These numerical problems are associated with the resolution of the diophantine equation. They occur when the assumption of no common poles and zeros is violated. Regularization techniques which cope with ill-conditioning are presented. The resulting algorithm combines a standard indirect pole-placement adaptive control algorithm and a dimension-free regularization procedure of the design equations, thus avoiding the pole-zero cancellation problem and yet retaining the other properties of the algorithm. The application of this control scheme in a pulsed liquid-liquid extraction column is described. The control objective is to optimize the column behaviour. Extraction columns are subject to changes in feed compositions, feed flow-rates, physical properties of the solvent (the extractor) and the solute (liquid mixture) and various disturbances. The column exhibits highly non-linear and time...

This chapter discusses the behavior of learning automata for different reinforcement schemes. It describes a number of recurrent reinforcement schemes for solving the problem of adaptive control of static systems. The nonprojectional algorithm of Narendra and Shapiro, of Luce, and of Varashavskii and Vomtsova, can be used to solve learning problems associated with binary loss functions. The algorithm of Luce has the highest convergence rate. However, a high convergence rate cannot be guaranteed for all average loss functions. The reinforcement scheme of Varashavskii and Vorontsova is a modification of the algorithm of Luce. With this algorithm, the widest range of average loss functions can be considered. The Bush–Mosteller reinforcement scheme can solve the adaptive control problem only when the average loss functions of the optimal strategy is equal or tends to zero. The projectional algorithms, for solving problems with continuous loss functions in the interval (-∞, ∞) are introduced in the chapter. These algorithms are significantly more complex and require the solution of a quadratic programming problem using the projection operator at each step.

This chapter discusses reinforcement schemes for average loss function minimization. The standard problem of average loss function minimization is formulated as a linear programming problem. This formulation considers the problem of adaptive control as a minimization of a linear function on a simplex. The recurrent control algorithms are classified into two categories: nonprojectional and projectional algorithms. For every reinforcement scheme, the pseudogradient condition must be fulfilled to guarantee the property of learning. The chapter presents all known reinforcement schemes and their classification from the point of view of fulfilling of pseudogradient condition. Following the definitions of different types of automata behavior, it is shown that the majority of learning automata possess symptotically an optimal behavior only in a special class of environments. The analysis of the behavior of learning automata is carried out using the martingale theory. The reinforcement scheme is the heart of the learning automaton. It is the mechanism used to adapt the probability distribution. The reinforcement schemes can be classified on the basis of the properties that they induce in the learning automaton or on the basis of their own characteristics.

This chapter presents basic notions and definitions. The basic notions are: (1) controlled finite system and its dynamic characteristics, (2) control strategies and their classification, and (3) adaptive control strategy and learning automata. The chapter also presents simple control problems of static systems that are close to the problem of synthesis of adaptive neural networks using the learning automata theory. It discusses classification of problems of adaptive control of finite systems. The problem of finite system adaptive control is of major importance in the theory of adaptive systems. The objective of adaptive system theory is the development of adaptive algorithms that optimize the behavior of a system under uncertainty conditions. All of these algorithms specify how to use the current information to improve the performance of the system. This current information corresponds to a realization of some loss functions associated to the adaptive strategy.

An application of self-tuning control to a fluidized bed reactor for ammoxydatlon of propylene to acrylonitrile is studied. The acrylonitrile is one of the main raw mateAial used for the fabrication of synthetic rubbers and fibres. The main reaction is highly exothermic. The highest yield of acrylonitrile occurs in temperature range of 480-510°C. Thecatalyst is very fragile at high temperature and does not resist to large and sudden temperature variations. The purpose of the control is to maintain the temperature of the reactor closeto a desired value [490°C] in order to facilitate the phenomenologlcal study (isothermal model building) is well as to avoid risks of destruction of the catalyst. The velocity of a ventilator whose.function is to carry away some, of the produced heat was considered as the control variable. The reactor has been interfaced with an Apple II micro-computer. The host programm used in the control is written in Pascal. Itcall external assembly language routines related to real time control such that : date acquisition routine, digital-analog converter routine, and the clock reading routine for sampling period. A simplified single input-single output model ofthe complex dynamics of the reactor was assumd. A constant trace algorithm is combined with an extented minimal variance controller including the set point action. The self-tuning controller gives improved control performance, compared to that achieved using proportional plus integral plusderivative (P.I.D.) control.

This paper describes the application of the long-range predictive control with pole placement and double serie-parallel reference model to mecanically agitated Kuhni columns. In previous works (Carrier, 1981) it has been stated that the flooding conditions of a pulsed column for liquid-liquid extraction might be controlled by measuring the conductivity of the liquid medium at a place located between the dispersed phase inlet and the continuous phase outlet. The pulsing intensity was the command variable. In this paper, it is demonstrated that the same control strategy may be similarly applied to a very different type of agitated column, the Kuhni contactor which is a major representative of the rotary mixed columns. The controlled variable remains the conductivity measured at a similar location in the column, whereas the pulsing frequency has been replaced by the rotation speed of the central shaft which wears the mixing turbines. The same single input-output linear discrete model with time varying parameters has been adopted in order to model the even more complicated dynamic behaviour of the column. Good results have been obtained, allowing to conclude that the proposed strategy might be of valuable interest whatever the kind of mechanically agitated contactor involved.

This paper presents a study on the control of a fluidized bed catalytic reactor. In this study, the model reference adaptative control algorithm with independent tracking and regulation objectives as presented by Landau-Lozano (1981) has been investigated. The purpose of the control is to maintain the temperature of the reactor as near as possible to a desired set value (490°C). Some of the heat produced as a result of the exothermal reaction tacking place between propylene, ammonia and oxygen is carried away by a ventilator. The control action is based on a simple mathematical lower order with time varying unknown parameters. This method of control results in a significantly improved control for both servo and regulatory control.

Many chemical plants have to be controlled such that their responses are within given tolerances under various operating conditions including variation in plant parameters and disturbances. It is therefore desirable to have adaptive controllers which can compensate for changes in process parameters due to varying working conditions or initial indeterminateness. The high effort in development and implementation as well as operation of such control systems is justified economically if significant improvements in operation can be achieved The examples discussed in this paper are aimed to showing the different steps in the development and application of single variable and multivariable adaptive control for different types of processes The applications show that, at the present time, adaptive control has reached a high degree of maturity, making it a very powerful tool for the experienced control engineer. However, for making adaptive control accessible to the broad field of process engineers, the degrees of freedom have to be reduced by simplifying the elements of the adaptive controller. To clarify this, further research has to be undertaken

The simulation of the operation of an industrial sugar crystallization unit under a generalized predictive controller is reported. The feed flow rate of sugar liquor or syrup and the vacuum pressure have been selected as input control variables. The aim is to force the operation into following optimal profiles of brix and temperature. The state vector in the dynamic model includes temperature, dissolved sucrose and dissolved impurities in liquor, mass of sucrose crystals and the moments of order zero to five in the characterization of crystal size distribution. Main intensive variables such as brix, supersaturation, crystal content and masscuite consistency are calculated from the set of state variables. The control algorithm first predicts the plant output over several steps. It then determines the future control inputs to the plant in order to minimize a quadratic function of the future errors and control, assuming that after some periods nul increments for the control vector. A linear discrete model with time-varying parameters was adopted as a representation of the complex dynamics of the crystallizer. The model parameters are estimated by a constant trace algorithm. Several modifications like the U/D factorization, the normalisation and an information measure (to detect when the information carried out by data is poor) have been introduced to improve the robustness of the parameter estimator towards round-off errors, unmodelled dynamics etc. The dynamic model gives an accurate representation of the industrial behaviour of this batch crystallizer. Control simulations show an improved performance of the proposed control algorithm over classical alternatives (P.I.D.), hence suggesting its industrial implementation.

The problem of ill conditioning of the design equations involved in adaptive pole placement control algorithms is addressed. A regularization procedure is proposed and analysed through numerical simulations.

This paper deals with the application of a general predictive controller to a pulsed liquid-liquid extraction column. The control purpose is to maintain the column in its optimal behaviour zone in spite or flowrates and physical properties of solvent and solute fluctuations. The complex dynamics of the column is modeled by a low order linear discrete model with time varying parameters which are recursively identified. Based on these estimates, the control policy is adapted on line. The obtained results illustrate the successful application of such an adaptive algorithm.

This paper presents a study on the control of a fluidized bed catalytic reactor. In this study, the model reference adaptative control algorithm with independent tracking and regulation objectives as presented by Landau-Lozano (1981) has been investigated. The purpose of the control is to maintain the temperature of the reactor as near as possible to a desired set value (490°C). Some of the heat produced as a result of the exothermal reaction tacking place between propylene, ammonia and oxygen is carried away by a ventilator. The control action is based on a simple mathematical lower order with time varying unknown parameters. This method of control results in a significantly improved control for both servo and regulatory control.

Many chemical plants have to be controlled such that their responses are within given tolerances under various operating conditions including variation in plant parameters and disturbances. It is therefore desirable to have adaptive controllers which can compensate for changes in process parameters due to varying working conditions or initial indeterminateness. The high effort in development and implementation as well as operation of such control systems is justified economically if significant improvements in operation can be achieved. The examples discussed in this paper are aimed to showing the different steps in the development and application of single variable and multivariable adaptive control for different types of processes. The applications show that, at the present time, adaptive control has reached a high degree of maturity, making it a very powerful tool for the experienced control engineer. However, for making adaptive control accessible to the broad field of process engineers, the degrees of freedom have to be reduced by simplifying the elements of the adaptive controller. To clarify this, further research has to be undertaken.