41 resultados para adaptive control simulation
em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland
Resumo:
Adaptive control systems are one of the most significant research directions of modern control theory. It is well known that every mechanical appliance’s behavior noticeably depends on environmental changes, functioning-mode parameter changes and changes in technical characteristics of internal functional devices. An adaptive controller involved in control process allows reducing an influence of such changes. In spite of this such type of control methods is applied seldom due to specifics of a controller designing. The work presented in this paper shows the design process of the adaptive controller built by Lyapunov’s function method for the Hydraulic Drive. The calculation needed and the modeling were conducting with MATLAB® software including Simulink® and Symbolic Math Toolbox™ etc. In the work there was applied the Jacobi matrix linearization of the object’s mathematical model and derivation of the suitable reference models based on Newton’s characteristic polynomial. The intelligent adaptive to nonlinearities algorithm for solving Lyapunov’s equation was developed. Developed algorithm works properly but considered plant is not met requirement of functioning with. The results showed confirmation that adaptive systems application significantly increases possibilities in use devices and might be used for correction a system’s behavior dynamics.
Resumo:
There exist several researches and applications about laser welding monitoring and parameter control but not a single one have been created for controlling of laser scribing processes. Laser scribing is considered to be very fast and accurate process and thus it would be necessary to develop accurate turning and monitoring system for such a process. This research focuses on finding out whether it would be possible to develop real-time adaptive control for ultra-fast laser scribing processes utilizing spectrometer online monitoring. The thesis accurately presents how control code for laser parameter tuning is developed using National Instrument's LabVIEW and how spectrometer is being utilized in online monitoring. Results are based on behavior of the control code and accuracy of the spectrometer monitoring when scribing different steel materials. Finally control code success is being evaluated and possible development ideas for future are presented.
Resumo:
Concerning process control of batch cooling crystallization the present work focused on the cooling profile and seeding technique. Secondly, the influence of additives on batch-wise precipitation process was investigated. Moreover, a Computational Fluid Dynamics (CFD) model for simulation of controlled batch cooling crystallization was developed. A novel cooling model to control supersaturation level during batch-wise cooling crystallization was introduced. The crystallization kinetics together with operating conditions, i.e. seed loading, cooling rate and batch time, were taken into account in the model. Especially, the supersaturation- and suspension density- dependent secondary nucleation was included in the model. The interaction between the operating conditions and their influence on the control target, i.e. the constant level of supersaturation, were studied with the aid of a numerical solution for the cooling model. Further, the batch cooling crystallization was simulated with the ideal mixing model and CFD model. The moment transformation of the population balance, together with the mass and heat balances, were solved numerically in the simulation. In order to clarify a relationship betweenthe operating conditions and product sizes, a system chart was developed for anideal mixing condition. The utilization of the system chart to determine the appropriate operating condition to meet a required product size was introduced. With CFD simulation, batch crystallization, operated following a specified coolingmode, was studied in the crystallizers having different geometries and scales. The introduced cooling model and simulation results were verified experimentallyfor potassium dihydrogen phosphate (KDP) and the novelties of the proposed control policies were demonstrated using potassium sulfate by comparing with the published results in the literature. The study on the batch-wise precipitation showed that immiscible additives could promote the agglomeration of a derivative of benzoic acid, which facilitated the filterability of the crystal product.
Resumo:
This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.
Resumo:
Control applications of switched mode power supplies have been widely investigated. The main objective ofresearch and development (R&D) in this field is always to find the most suitable control method to be implemented in various DC/DC converter topologies. Inother words, the goal is to select a control method capable of improving the efficiency of the converter, reducing the effect of disturbances (line and load variation), lessening the effect of EMI (electro magnetic interference), and beingless effected by component variation. The main objective of this research work is to study different control methods implemented in switched mode power supplies namely (PID control, hysteresis control, adaptive control, current programmed control, variable structure control (VSC), and sliding mode control (SMC). The advantages and drawbacks of each control method are given. Two control methods, the PID and the SMC are selected and their effects on DC/DC (Buck, Boost, and Buck-Boost) converters are examined. Matlab/SimulinkTM is used to implement PID control method in DC/DC Buck converter and SMC in DC/DC (Buck, and Buck Boost) converters. For the prototype, operational amplifiers (op-amps) are used to implement PID control in DC/DC Buck converter. For SMC op-amps are implemented in DC/DC Buck converter and dSPACETM is used to control the DC/DC Buck-Boost converter. The SMC can be applied to the DC/DC (Buck, Boost, and Buck-Boost) converters. A comparison of the effects of the PID control and the SMC on the DC/DC Buck converter response in steady state, under line variations, load variations, and different component variations is performed. Also the Conducted RF-Emissions between the PID and SMC DC/DC Buck Converter are compared. The thesis shows that, in comparison with the PID control, the SMC provides better steady-state response, better dynamic response, less EMI, inherent order reduction, robustness against system uncertainty disturbances, and an implicit stability proof. Giving a better steady-state and dynamic response, the SMC is implemented in a DC/DC resonant converter. The half-wave zero current switching (HWZCS) DC/DC Buck converter is selected as a converter topology. A general guideline to select the tank component values, needed for the designing of a HWZCS DC/DC Buck, is obtained. The implementation of the SMC to a HWZCS DC/DC Buck converter is analysed. The converter response is investigated in the steady-state region and in the dynamic region.
Resumo:
The pumping processes requiring wide range of flow are often equipped with parallelconnected centrifugal pumps. In parallel pumping systems, the use of variable speed control allows that the required output for the process can be delivered with a varying number of operated pump units and selected rotational speed references. However, the optimization of the parallel-connected rotational speed controlled pump units often requires adaptive modelling of both parallel pump characteristics and the surrounding system in varying operation conditions. The available information required for the system modelling in typical parallel pumping applications such as waste water treatment and various cooling and water delivery pumping tasks can be limited, and the lack of real-time operation point monitoring often sets limits for accurate energy efficiency optimization. Hence, alternatives for easily implementable control strategies which can be adopted with minimum system data are necessary. This doctoral thesis concentrates on the methods that allow the energy efficient use of variable speed controlled parallel pumps in system scenarios in which the parallel pump units consist of a centrifugal pump, an electric motor, and a frequency converter. Firstly, the suitable operation conditions for variable speed controlled parallel pumps are studied. Secondly, methods for determining the output of each parallel pump unit using characteristic curve-based operation point estimation with frequency converter are discussed. Thirdly, the implementation of the control strategy based on real-time pump operation point estimation and sub-optimization of each parallel pump unit is studied. The findings of the thesis support the idea that the energy efficiency of the pumping can be increased without the installation of new, more efficient components in the systems by simply adopting suitable control strategies. An easily implementable and adaptive control strategy for variable speed controlled parallel pumping systems can be created by utilizing the pump operation point estimation available in modern frequency converters. Hence, additional real-time flow metering, start-up measurements, and detailed system model are unnecessary, and the pumping task can be fulfilled by determining a speed reference for each parallel-pump unit which suggests the energy efficient operation of the pumping system.
Resumo:
Työssä toteutettiin C-kielellä luistonestojärjestelmä ja elektroninen tasauspyörästö Simulinkmallien pohjalta hybridityökoneeseen. Hybridityökoneen sähkökäytöt mahdollistavat tarkan vääntömomentin säädön, joka mahdollistaa työssä kuvatun kaltaisen järjestelmän toteuttamisen. Toteutettua järjestelmää simuloitiin MeVEA Oy:n ajoneuvomallinnukseen kehitetyssä simulaattorissa. Lisäksi järjestelmästä kehitettiin Visedo Oy:n sähkökäyttösimulaattoriin sopiva versio, jota testattiin Visedon sähkökäyttöjä simuloivan ohjelman kanssa. Simulointituloksien mukaan luistonesto estää vetäviä pyöriä luistamasta liukkaalla alustalla eikä toisaalta vähennä aiheetta kuljettajan asettamaa vääntömomenttia. Myös sähköinen tasauspyörästö toimi kuten oli suunniteltu. Työssä kehitetty luistonesto tarvitsee toimiakseen tiedon ajoneuvon kokonaismassasta, joten työssä kehitettiin myös tapa ajoneuvon massan estimoimiseksi ajoneuvon kiihdyttäessä. Massan estimointia testattiin pitävällä ja liukkaalla alustalla. Massan estimointi toimi simulaattoriympäristössä hyvällä tarkkuudella.
Resumo:
The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.
Resumo:
Industry's growing need for higher productivity is placing new demands on mechanisms connected with electrical motors, because these can easily lead to vibration problems due to fast dynamics. Furthermore, the nonlinear effects caused by a motor frequently reduce servo stability, which diminishes the controller's ability to predict and maintain speed. Hence, the flexibility of a mechanism and its control has become an important area of research. The basic approach in control system engineering is to assume that the mechanism connected to a motor is rigid, so that vibrations in the tool mechanism, reel, gripper or any apparatus connected to the motor are not taken into account. This might reduce the ability of the machine system to carry out its assignment and shorten the lifetime of the equipment. Nonetheless, it is usually more important to know how the mechanism, or in other words the load on the motor, behaves. A nonlinear load control method for a permanent magnet linear synchronous motor is developed and implemented in the thesis. The purpose of the controller is to track a flexible load to the desired velocity reference as fast as possible and without awkward oscillations. The control method is based on an adaptive backstepping algorithm with its stability ensured by the Lyapunov stability theorem. As a reference controller for the backstepping method, a hybrid neural controller is introduced in which the linear motor itself is controlled by a conventional PI velocity controller and the vibration of the associated flexible mechanism is suppressed from an outer control loop using a compensation signal from a multilayer perceptron network. To avoid the local minimum problem entailed in neural networks, the initial weights are searched for offline by means of a differential evolution algorithm. The states of a mechanical system for controllers are estimated using the Kalman filter. The theoretical results obtained from the control design are validated with the lumped mass model for a mechanism. Generalization of the mechanism allows the methods derived here to be widely implemented in machine automation. The control algorithms are first designed in a specially introduced nonlinear simulation model and then implemented in the physical linear motor using a DSP (Digital Signal Processor) application. The measurements prove that both controllers are capable of suppressing vibration, but that the backstepping method is superior to others due to its accuracy of response and stability properties.
Resumo:
Nowadays the energy efficiency has become one of the most concerned topics. Compressors are the equipment, which is very common in industry. Moreover, they tend to operate during long cycles and therefore even small decrease in power consumption can significantly reduce electricity costs during the year. And therefore it is important to investigate ways of increasing the energy efficiency of the compressors. In the thesis rotary screw compressor alongside with different control approaches is described. Simulation models for various control types of rotary screw compressor are developed. Analysis of laboratory equipment is conducted and results are compared with simulation. Suggestions of the real laboratory equipment improvement are given.
Resumo:
Usingof belt for high precision applications has become appropriate because of the rapid development in motor and drive technology as well as the implementation of timing belts in servo systems. Belt drive systems provide highspeed and acceleration, accurate and repeatable motion with high efficiency, long stroke lengths and low cost. Modeling of a linear belt-drive system and designing its position control are examined in this work. Friction phenomena and position dependent elasticity of the belt are analyzed. Computer simulated results show that the developed model is adequate. The PID control for accurate tracking control and accurate position control is designed and applied to the real test setup. Both the simulation and the experimental results demonstrate that the designed controller meets the specified performance specifications.
Resumo:
The active magnetic bearings present a new technology which has many advantages compared to traditional bearing designs. Active magnetic bearings, however, require retainer bearings order to prevent damages in the event of a component, power or a control loop failure. In the dropdown situation, when the rotor drops from the magnetic bearings to the retainer bearings, the design parameters of the retainer bearings have a significant influence on the behaviour of the rotor. In this study, the dynamics of an active magnetic bearings supported electric motor during rotor drop on retainer bearings is studied using a multibody simulation approach. Various design parameters of retainer bearings are studied using a simulation model while results are compared with those found in literature. The retainer bearings are modelled using a detailed ball bearing model, which accounts damping and stiffness properties, oil film and friction between races and rolling elements. The model of the ball bearings includes inertia description of rollingelements. The model of the magnetic bearing system contains unbalances of the rotor and stiffness and damping properties of support. In this study, a computationally efficient contact model between the rotor and the retainer bearings is proposed. In addition, this work introduces information for the design of physicalprototype and its retainer bearings.
Resumo:
The aim of the study is to developa novel robust controller based on sliding mode control technique for the hydraulic servo system with flexible load and for a flexible manipulator with the lift and jib hydraulic actuators. For the purpose of general control design, a dynamic model is derived describing the principle physical behavior for both the hydraulic servo system and the flexible hydraulic manipulator. The mechanism of hydraulic servo systems is described by basic mathematical equations of fluid powersystems and the dynamics of flexible manipulator is modeled by the assumed modemethod. The controller is constructed so as to track desired trajectories in the presence of model imprecision. Experimental and simulation results demonstratethat sliding mode control has benefits which can be used to guarantee stabilityin uncertain systems and improve the system performance and load tolerance.
Resumo:
Thedirect torque control (DTC) has become an accepted vector control method besidethe current vector control. The DTC was first applied to asynchronous machines,and has later been applied also to synchronous machines. This thesis analyses the application of the DTC to permanent magnet synchronous machines (PMSM). In order to take the full advantage of the DTC, the PMSM has to be properly dimensioned. Therefore the effect of the motor parameters is analysed taking the control principle into account. Based on the analysis, a parameter selection procedure is presented. The analysis and the selection procedure utilize nonlinear optimization methods. The key element of a direct torque controlled drive is the estimation of the stator flux linkage. Different estimation methods - a combination of current and voltage models and improved integration methods - are analysed. The effect of an incorrect measured rotor angle in the current model is analysed andan error detection and compensation method is presented. The dynamic performance of an earlier presented sensorless flux estimation method is made better by improving the dynamic performance of the low-pass filter used and by adapting the correction of the flux linkage to torque changes. A method for the estimation ofthe initial angle of the rotor is presented. The method is based on measuring the inductance of the machine in several directions and fitting the measurements into a model. The model is nonlinear with respect to the rotor angle and therefore a nonlinear least squares optimization method is needed in the procedure. A commonly used current vector control scheme is the minimum current control. In the DTC the stator flux linkage reference is usually kept constant. Achieving the minimum current requires the control of the reference. An on-line method to perform the minimization of the current by controlling the stator flux linkage reference is presented. Also, the control of the reference above the base speed is considered. A new estimation flux linkage is introduced for the estimation of the parameters of the machine model. In order to utilize the flux linkage estimates in off-line parameter estimation, the integration methods are improved. An adaptive correction is used in the same way as in the estimation of the controller stator flux linkage. The presented parameter estimation methods are then used in aself-commissioning scheme. The proposed methods are tested with a laboratory drive, which consists of a commercial inverter hardware with a modified software and several prototype PMSMs.
Resumo:
The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.