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The problem of curse-of-dimensionality in finite state and action Markov decision processes is considered using iterative clustering of closed-loop data and repeated discretization of the state space process model. The performance of the control design approach is demonstrated using a multi-input van der Vusse continuous stirred tank reactor control benchmark. It is demonstrated that the finite state description provides a simple implementation of Bayesian state estimation using cell filters, and dynamic programming gives means to conduct optimization of closed-loop performance of a nonlinear stochastic multidimensional chemical plant.

Simulation-based non-linear active suspension control design for MacPherson systems is considered. A nonlinear dynamic model for the MacPherson suspension system is derived. The model nonlinearities and the dynamic behaviour of the system is illustrated by simulations. The design of controllers and state estimators using finite state Markov models is briefly outlined, and applied for nonlinear active suspension control system. The study illustrates the potential of the finite Markov chains approach in non-linear active suspension control, emphasizing the possibility to move computational load due to simulations to off-line design.

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.

This paper deals with regulation control on the basis of genealogical decision trees (GDTs). GDTs are a population-based random search technique for solving sequential multimodal and multivariable trajectory tracking problems, when gradient information is not available or does not exist. A direct application of GDT results in an open-loop control. In this paper, feedback regulation based on GDT is considered. In the proposed scheme, GDTs are used for solving off-line a number of predictive control problems; a finite set of initial states is then constructed from these simulations, for each of which an optimal control sequence has been computed. Natural handling of missing state vector measurements is provided. Numerical examples dealing with the van der Vusse CSTR illustrate the feasibility and the efficiency of this feedback control algorithm. A discussion on alternative approaches and a numerical comparison with the Markov-decision-process-based optimal policy are provided. Copyright © 2008 John Wiley & Sons, Ltd.

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.

Polynomial artificial neural networks (PANN) have been shown to be powerful for forecasting nonlinear time series. The training time is small compared to the time used by other algorithms of artificial neural networks and the capacity to compute relations between the inputs and outputs represented by every term of the polynomial. In this paper a new structure of polynomial is presented that improves the performance of this type of network considering only non-integers exponents. The architecture adaptation uses genetic algorithm (GA) to find the optimal architecture for every example. Some examples of sunspots and chaotic time series are presented.

The goal of this paper is to design a new control algorithm for open-loop control of complex systems. This control approach is based on a genealogical decision tree for both regulation and tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges on probability. A numerical example dealing with the control of a fluidized bed combustion power plant illustrates the feasibility and the performance of this control algorithm.

A new control algorithm for open-loop control of complex systems is suggested. The approach is based on a genealogical decision tree for tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges in probability. A numerical example illustrates the feasibility and the performance of this control algorithm.

A distributed Wiener logic processor model structure is considered. Each fuzzy Wiener model consists of a succession of a linear dynamic part and a static steady-state (non-linear) logical part. The model structure and the necessary gradients required by gradient-based parameter estimation methods are given. Parameter projection and a modified threshold method are discussed. A simulation example illustrates the approach in the identification of a nonlinear, non-minimum phase CSTR process where a van der Vusse reaction takes place.

This paper presents an algorithm for optimization. This algorithm is based on a team of learning stochastic automata. Each automaton is characterized by two actions providing a binary output (0 or 1). The action of the team of automata consists of a digital number which represents the environment input. The probability distribution associated which each automaton is adjusted using a modified version of the Bush-Mosteller reinforcement scheme. This adaptation scheme uses a continuous environment response and a time-varying correction factor. A normalization procedure is used in order to preserve the probability measure. The asymptotic properties of this optimization algorithm are presented. A numerical example illustrates the feasibility and the performance of this optimization algorithm.

Modelling of dynamic non-linear processes using the Wiener approach is considered. Models are constructed based on sampled measurements from the process, as well as a priori information of the characteristics of the process. Prior information is expressed by a set of constraints, which leads to an optimisation problem of parameter estimation under constraints. Modelling of a two-tank system Illustrates the performance of the approach

The identification of multiple-input single-output Wiener models is considered in this paper. The non-linear memoryless part is described by a parametrized steady state model. In this paper two representations for the linear dynamic part that preserve the unit steady state gain are discussed and compared: finite step response and transfer function with a feedback polynomial. The steps necessary for estimating the parameters of the Wiener model are presented. In the simulation examples with data from a pneumatic valve model, distillation column model and a pilot pump-valve system, the performance of the approach is examined, and the use of various kinds of non-linear black-box and grey-box structure for the modelling of the static part is illustrated.

This paper deals with the design and analysis of a modified version of the Bush-Mosteller reinforcement scheme applied by partners in a zero-sum repeated game with random pay-offs. The suggested study is based on the learning automata paradigm and a limiting average reward criterion is tackled to analyse the arising Nash equilibrium. No information concerning the distribution of the pay-off is a priori available. The novelty of the suggested adaptive strategy is related to the incorporation of a 'normalization procedure' into the standard Bush-Mosteller scheme to provide a possibility to operate not only with binary but also with any bounded rewards of a stochastic nature. The analysis of the convergence (adaptation) as well as the convergence rate (rate of adaptation) are presented and the optimal design parameters of this adaptive procedure are derived. The obtained adaptation rate turns out to be of o(n 1/3 ).

This paper concerns process modelling using fuzzy neural networks. In distributed logic processors (DLP) the rule base is parameterised. The DLP derivatives required by gradient-based training methods are given, and the recursive prediction error method is used to adjust the model parameters. The power of the approach is illustrated with a modelling example where NOx-emission data from a full-scale fluidised-bed combustion district heating plant are used. The method presented in this paper is general, and can be applied to other complex processes as well.

Control is a subject that heavily relies on mathematics and physics. High level theoretical treatments are more easily understood and digested when accompanied by concrete examples. In this study, two important phenomena, namely linearization and integration are chosen as two cases that are important in industrial processes. Examples of teaching approaches are demonstrated around these two cases. Some simple examples are chosen, for easy demonstration, without the loss of generality. The approaches are believed to be effective in teaching engineering students and especially engineers working in industry.

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.

The paper concerns the estimation under constraints of the parameters of distributed logic processors (DLP). This optimization problem under constraints is solved using stochastic approximation techniques. DLPs are fuzzy neural networks capable of representing nonlinear functions. They consist of several logic processors, each of which performs a logical fuzzy mapping. A simulation example, using data collected from an industrial fluidized bed combustor, illustrates the feasibility and the performance of this training algorithm.

Wiener type of models consist of linear dynamics followed by a static non-linear part. In this paper, a restricted class of Wiener models is considered where the static mapping represents a steady-state model for the process. A Wiener model structure is suggested for the identification of a MISO steady-state static model with linear FIR (finite impulse response) dynamics for each input. Unit steady-state gain is obtained by using a reduced FIR model, consisting of a unit gain plus FSR (finite step response) dynamics. The necessary derivatives required by gradient-based parameter estimation techniques are given. Simulation examples with data from a distillation column model and a pump-valve system, using sigmoid neural networks to model the non-linearities, illustrate the behaviour of the approach.

This paper presents a constrained predictive control strategy using artificial neural networks (ANN). In this control scheme two ANN are used. The recurrent ANN is used as a multi-step ahead predictor. The control action is provided by the multilayer feedforward ANN. The weights of this ANN are estimated at each control step using a stochastic approximation (SA) algorithm by minimizing a quadratic control objective which is based on a series of the future predictions and future control actions, and by preventing violations of process constraints. Simulation results demonstrate the usefulness and the robustness of this predictive control algorithm.

A long-range predictive control strategy using artificial neural networks ( ANNs) is represented. Both unconstrained and constrained control problems are considered. In this control scheme a recurrent ANN and a multilayer feedforward ANN are used. The recurrent ANN is used as a multi-step ahead predictor. For training this network the backpropagation through the time is used. The control action is provided by the multilayer feedforward ANN which uses the predictions of the output of the process to be controlled. The weights of this ANN are estimated at each control step using a stochastic approximation ( SA) algorithm by minimizing a quadratic control objective which is based on a series of the future predictions and future control actions, and by preventing violations of process constraints. To demonstrate the feasibility and the performance of this control scheme, a continuous biochemical reactor and a fixed bed tubular chemical reactor are chosen as realistic nonlinear case studies. Simulation...

A new algorithm for training the parameters of a distributed logic processor is suggested, based on learning automata. A fuzzy inference system is implemented on a multilayer perceptron platform. Various possibilities for assigning learning automata are discussed and two assignment strategies are proposed. The behaviour of the resulting algorithm is illustrated using flue-gas NO/sub x/ emission data measured from an industrial-size fluidised-bed combustor.

The behaviour of a stochastic automaton operating in an S-model environment is described. The environment response takes an arbitrary value in the closed segment [0, 1] (continuous response). The learning automaton uses a reinforcement scheme to update its action probabilities on the basis of the reaction of the environment. The complete set of actions is divided into a collection of non-empty subsets. The action set is changing from instant to instant. Each action set is selected according to a given probability distribution. Convergence and convergence rate results are presented. These results have been derived using quasimartingales theory.

This paper presents the Generalized Predictive Control (GPC) strategy based on Artificial Neural Network (ANN) plant model. To obtain the step and the free process responses which are needed in the generalized predictive control strategy we iteratively use a multilayer feedforward ANN as a one-step-ahead predictor. A bioprocess was chosen as a realistic nonlinear SISO system to demonstrate the feasibility and the performance of this control scheme. A comparison was made between our approach and the adaptive GPC (AGPC).

This paper concerns the process modelling based on fuzzy logic neural networks. Fuzzy systems are implemented in the form of distributed logic processors. Derivatives required by gradient descent training methods are given, and recursive prediction error training method is used to adjust the model parameters. The approach is illustrated with a modelling example where nitrogen emission (x) data from a fluidized-bed combustion district heating plant is used. The method presented in this paper is general, and can be applied to other complex processes as well.

This paper concerns the adaptive selection of the optimal order of linear regression models using a variable-structure stochastic learning automaton. The Alaike criterion is derived for stationary and non-stationary cases, and it is shown that the optimal order minimizes a loss function corresponding to the evaluation of this criterion. The order of the regression model belongs to a finite set. Each order value is associated with an action of the automaton. The Bush-Mosteller reinforcement scheme with normalized automaton input is used to adjust the probability distribution. Simulation results illustrate the feasibility and performance of this model order selection approach

This paper deals with the optimization of an autogenous grinding circuit using a random search technique. This technique is based on a hierarchical structure of learning automata operating in a random environment constituted by the autogenous circuit to be optimized. The ore feed rate to the mill is considered as the control variable while the mass flow rate of the concentrate of the subsequent separation process constitutes the controlled variable. The variation domain of the manipulated variables is discretized into a set of regions which are associated to the actions of the automata of the last level of the hierarchical learning system. A probability is associated to each action (region). The learning system selects one of the available actions and, based on the response of the environment, modifies the strategy (the probabilities associated to the set of actions) using an adaptation procedure called reinforcement scheme. Numerical results illustrate the feasibility and the performance of this self-adjusting optimization algorithm.

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.

Autogenous grinding is characterized by non-linearities, time-varying dynamics and a high level of uncertainties, conditions which usually originate from the variability of the ore feed characteristics (hardness and grade). These characteristics make this grinding operation particularly appealing for some type of knowledge-based control. This paper discusses the application of the dynamic matrix control algorithm to an autogenous grinding operation. This control algorithm is a long-range predictive control algorithm which has been successfully applied to other processes. The study was carried out using an empirical simulator calibrated with industrial data. The simulation results were compared to those obtained using PID and learning controllers. The ability of the dynamic matrix control to improve the efficiency of this complex and highly sensitive process is clearly demonstrated.

This paper presents the results of the application of a new process control technique, the Learning Control, to a mineral processing operation. A hierarchical system of learning automata is used as a model of the controller. An empirical simulator capable of reproducing the dynamic of the autogenous grinding process is considered as the random environment in which the hierarchical system of automata operates. A probability distribution is associated to the manipulated variable. This distribution is continuously adjusted by the learning system using a reinforcement scheme. Numerical results have demonstrated its control properties, transparent tuning and robustness, while requiring minimal computational load.

Student's studies can be seen as consisting of chains or sequences of courses, the learning activities of a student along these lines make his study path. In this paper, methods for detection, analysis and control of learning activities are developed, based on students' credit record data. A central aim of the work is to support the supervision of students using currently available data bases.

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...

Publisher Summary Artificial intelligence is the science of intelligence and is connected to systems sciences through the basic assumptions of computational psychology. Computational intelligence includes fields such as neural networks, fuzzy systems, evolutionary computing, and artificial life. The various types of fuzzy neural networks can also be considered. Neuro-fuzzy systems are tools for engineering technical processes, having an interest in engineering applications. Models are needed for training the process operators and for the development of soft sensors. Standard modeling approaches include two main streams: the first-principle (white-box) approach and the identification of a parameterized black-box model. The first-principle approach denotes models based on laws about physical and chemical phenomena, derived on the basis of the first principles whereas in the black-box models, the model structure is a priori selected. Based on experimental data, an identification algorithm is used for estimating the unknown parameters. The neuro-fuzzy methods are most useful in the identification of nonlinear and poorly known processes when measurement data giving examples of the process behavior are available. The fuzzy features in the approach also make it useful when knowledge is available in the form of human experimental knowledge. The integration of fuzzy methods with optimization, systems identification, and parameter estimation techniques offers robust and efficient tools for the modeling of real-world industrial processes. This chapter illustrates a unified representation including logic processors (LP), and multilayer perceptron (MLP) neural networks. It discusses gradient-based parameter estimation techniques, learning-automata-based techniques, and identification of a nonlinear plant.

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 describes multilevel automata systems for the implementation of hierarchical reinforcement schemes. The advantages of multilevel systems of automata are the acceleration of the learning process and the simplification of their implementation. In a hierarchical structure of learning automata, the selection of the control action is performed in several sequential stages. The algorithms, used to modify the probability density functions are called hierarchical reinforcement schemes and the systems, used to implement these algorithms, are called multilevel systems of automata. The efficiency of such a hierarchical control strategy can be greatly improved when a priori information on the hierarchical structure of the problem is available. A priori information may significantly help to specify the structure of the multilevel system of automata in order to accelerate the convergence of the learning process. A two-level hierarchical learning system of automata consists of a hierarchy of stochastic variable-structure automata with different control actions. The first level consists of one probabilistic automaton. The second level of the hierarchy interacts with the random environment where the two-level hierarchical system of learning automata operates.

This chapter discusses the applications of learning automata. The applications of learning automata cover a wide range of problems such as absorption columns, bioreactors, communication, computers, drying furnaces, fluidized bed reactors, image processing, irrigation canals, and liquid–liquid extraction columns. Learning automata should, by collecting and processing current information regarding the environment, be capable of changing their structure and parameters as time evolves to achieve the desired goal or the optimal performance in some sense. Learning systems have made a significant impact on all areas of engineering problems arising from complexity and uncertainty. They are attractive methods for solving process control, optimization, pattern recognition, image processing, telecommunications, and scheduling. They are very simple to implement and need little prior knowledge. The only calculation required for the implementation of learning system is the relatively simple adjustment of the state probability distribution. In the control context, it is not necessary to construct a model for the process to be controlled. The number of learning systems applications has increased with the advent of highly integrated computers that made the technology cost-effective.

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.