The document describes an artificial neural network (ANN) model that can estimate distillate composition in a distillation column using secondary measurements like temperature, reflux, and steam flow. The ANN model is tested on a simulated multi-component distillation column and found to provide estimates comparable to using direct composition measurements, with the benefit of being more economical than on-line composition sensors. The document also reviews various other modeling and control techniques that have been developed for distillation columns, including inferential control methods using estimators to indirectly control product quality based on secondary measurements.
HYBRID FUZZY LOGIC AND PID CONTROLLER FOR PH NEUTRALIZATION PILOT PLANTijfls
Use of Control theory within process control industries has changed rapidly due to the increase complexity
of instrumentation, real time requirements, minimization of operating costs and highly nonlinear
characteristics of chemical process. Previously developed process control technologies which are mostly
based on a single controller are not efficient in terms of signal transmission delays, processing power for
computational needs and signal to noise ratio. Hybrid controller with efficient system modelling is essential
to cope with the current challenges of process control in terms of control performance. This paper presents
an optimized mathematical modelling and advance hybrid controller (Fuzzy Logic and PID) design along
with practical implementation and validation of pH neutralization pilot plant. This procedure is
particularly important for control design and automation of Physico-chemical systems for process control
industry.
Comparison of PID Controller with Model Predictive Controller for Milk Pasteu...journalBEEI
Proportional–Integral–Derivative (PID) controllers are used in many of the Industries for various process control applications. PID controller yields a long settling time and overshoot which is not good for the process control applications. PID is not suitable for many of the complex process control applications. This research paper is about developing a better type of controller, known as MPC (Model Predictive Control). The aim of the paper is to design MPC and PID for a pasteurization process. In this manuscript comparison of PID controller with MPC is made and the responses are presented. MPC is an advanced control strategy that uses the internal dynamic model of the process and a history of past control moves and a combination of many different technologies to predict the future plant output. The dynamics of the pasteurization process was estimated by using system identification from the experimental data. The quality of different model structures was checked using best fit with data validation, residual and stability analysis. Auto-regressive with exogenous input (ARX322) model was chosen as a model structure of the pasteurization process and fits about 80.37% with datavalidation. MPC and PID control strategies were designed using ARX322 model structure. The controller performance was compared based on settling time, percent of overshoot and stability analysis and the results are presented.
Data-driven adaptive predictive control for an activated sludge processjournalBEEI
Data-driven control requires no information of the mathematical model of the controlled process. This paper proposes the direct identification of controller parameters of activated sludge process. This class of data-driven control calculates the predictive controller parameters directly using subspace identification technique. By updating input-output data using receding window mechanism, the adaptive strategy can be achieved. The robustness test and stability analysis of direct adaptive model predictive control are discussed to realize the effectiveness of this adaptive control scheme. The applicability of the controller algorithm to adapt into varying kinetic parameters and operating conditions is evaluated. Simulation results show that by a proper and effective excitation of direct identification of controller parameters, the convergence and stability of the implicit predictive model can be achieved.
Analysis and Modeling of PID and MRAC Controllers for a Quadruple Tank System...dbpublications
Multivariable systems exhibit complex dynamics because of the interactions between input variables and output variables. In this paper an approach to design auto tuned decentralized PI controller using ideal decoupler and adaptive techniques for controlling a class of multivariable process with a transmission zero. By using decoupler, the MIMO system is transformed into two SISO systems. The controller parameters were adjusted using the Model Reference Adaptive reference Control. In recent process industries, PID and MRAC are the two widely accepted control strategies, where PID is used at regulatory level control and MRAC at supervisory level control. In this project, LabVIEW is used to simulate the PID with Decoupler and MRAC separately and analyze their performance based on steady state error tracking and overshoot.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijics
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and
robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal
curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc.
Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank
with the outlet connected to a pump is considered for implementation of the PID controllers designed by
the three proposed methods to show the effectiveness of the methods.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijcisjournal
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc. Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank with the outlet connected to a pump is considered for implementation of the PID controllers designed by the three proposed methods to show the effectiveness of the methods.
HYBRID FUZZY LOGIC AND PID CONTROLLER FOR PH NEUTRALIZATION PILOT PLANTijfls
Use of Control theory within process control industries has changed rapidly due to the increase complexity
of instrumentation, real time requirements, minimization of operating costs and highly nonlinear
characteristics of chemical process. Previously developed process control technologies which are mostly
based on a single controller are not efficient in terms of signal transmission delays, processing power for
computational needs and signal to noise ratio. Hybrid controller with efficient system modelling is essential
to cope with the current challenges of process control in terms of control performance. This paper presents
an optimized mathematical modelling and advance hybrid controller (Fuzzy Logic and PID) design along
with practical implementation and validation of pH neutralization pilot plant. This procedure is
particularly important for control design and automation of Physico-chemical systems for process control
industry.
Comparison of PID Controller with Model Predictive Controller for Milk Pasteu...journalBEEI
Proportional–Integral–Derivative (PID) controllers are used in many of the Industries for various process control applications. PID controller yields a long settling time and overshoot which is not good for the process control applications. PID is not suitable for many of the complex process control applications. This research paper is about developing a better type of controller, known as MPC (Model Predictive Control). The aim of the paper is to design MPC and PID for a pasteurization process. In this manuscript comparison of PID controller with MPC is made and the responses are presented. MPC is an advanced control strategy that uses the internal dynamic model of the process and a history of past control moves and a combination of many different technologies to predict the future plant output. The dynamics of the pasteurization process was estimated by using system identification from the experimental data. The quality of different model structures was checked using best fit with data validation, residual and stability analysis. Auto-regressive with exogenous input (ARX322) model was chosen as a model structure of the pasteurization process and fits about 80.37% with datavalidation. MPC and PID control strategies were designed using ARX322 model structure. The controller performance was compared based on settling time, percent of overshoot and stability analysis and the results are presented.
Data-driven adaptive predictive control for an activated sludge processjournalBEEI
Data-driven control requires no information of the mathematical model of the controlled process. This paper proposes the direct identification of controller parameters of activated sludge process. This class of data-driven control calculates the predictive controller parameters directly using subspace identification technique. By updating input-output data using receding window mechanism, the adaptive strategy can be achieved. The robustness test and stability analysis of direct adaptive model predictive control are discussed to realize the effectiveness of this adaptive control scheme. The applicability of the controller algorithm to adapt into varying kinetic parameters and operating conditions is evaluated. Simulation results show that by a proper and effective excitation of direct identification of controller parameters, the convergence and stability of the implicit predictive model can be achieved.
Analysis and Modeling of PID and MRAC Controllers for a Quadruple Tank System...dbpublications
Multivariable systems exhibit complex dynamics because of the interactions between input variables and output variables. In this paper an approach to design auto tuned decentralized PI controller using ideal decoupler and adaptive techniques for controlling a class of multivariable process with a transmission zero. By using decoupler, the MIMO system is transformed into two SISO systems. The controller parameters were adjusted using the Model Reference Adaptive reference Control. In recent process industries, PID and MRAC are the two widely accepted control strategies, where PID is used at regulatory level control and MRAC at supervisory level control. In this project, LabVIEW is used to simulate the PID with Decoupler and MRAC separately and analyze their performance based on steady state error tracking and overshoot.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijics
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and
robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal
curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc.
Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank
with the outlet connected to a pump is considered for implementation of the PID controllers designed by
the three proposed methods to show the effectiveness of the methods.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijcisjournal
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc. Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank with the outlet connected to a pump is considered for implementation of the PID controllers designed by the three proposed methods to show the effectiveness of the methods.
Abstract The deployment of statistical process control (SPC) in manufacturing environments is a prominent global phenomenon. Statistical Process Control is largely used in industries for monitoring the process parameters. It is a standard method for visualizing and controlling processes on the basis of measurements of randomly selected samples. The decisions about what needs to be improved, the possible methods to improve it, and the steps to take after getting results from the charts are all made by humans and based on wisdom and experience. The statistical process control described in this paper gives the details about the SPC, its advantages and limitation, applications and information regarding the control charts. Keywords: Statistical Process Control, Control chart, 5M’s, Capability Indices.
Optimised control using Proportional-Integral-Derivative controller tuned usi...IJECEIAES
Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the underthought which forces exacting constraints on attainable execution. The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-IntegralDerivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor. It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.
Constrained discrete model predictive control of a greenhouse system temperatureIJECEIAES
In this paper, a constrained discete model predictive control (CDMPC) strategy for a greenhouse inside temperature is presented. To describe the dynamics of our system’s inside temperature, an experimental greenhouse prototype is engaged. For the mathematical modeling, a state space form which fits properly the acquired data of the greenhouse temperature dynamics is identified using the subspace system identification (N4sid) algorithm. The obtained model is used in order to develop the CDMPC starategy which role is to select the best control moves based on an optimization procedure under the constraints on the control notion. For efficient evaluation of the proposed control approach MATLAB/Simulink and Yalmip optimization toolbox are used for algorithm and blocks implementation. The simulation results confirm the accuracy of the controller that garantees both the control and the reference tracking objectives.
Controlling a DC Motor through Lypaunov-like Functions and SAB TechniqueIJECEIAES
In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IMC Based Fractional Order Controller for Three Interacting Tank ProcessTELKOMNIKA JOURNAL
In model based control, performance of the controlled plant considerably depends on the
accuracy of real plant being modelled. In present work, an attempt has been made to design Internal
Model Control (IMC), for three interacting tank process for liquid level control. To avoid complexities in
controller design, the third order three interacting tank process is modelled to First Order Plus Dead Time
(FOPDT) model. Exploiting the admirable features of Fractional Calculus, the higher order model is also
modelled to Fractional Order First Order Plus Dead Time (FO-FOPDT) model, which further reduces the
modelling error. Moving to control section, different IMC schemes have been proposed based on the order
of filter. Various simulations have been performed to show the greatness of Fractional order modelled
system & fractional order filters over conventional integer order modelled system & integer order filters
respectively. Both for parameters estimation of reduced order model and filter tuning, Genetic Algorithm
(GA) is being applied.
Performance analysis of a liquid column in a chemical plant by using mpceSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A novel auto-tuning method for fractional order PID controllersISA Interchange
Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Abstract The deployment of statistical process control (SPC) in manufacturing environments is a prominent global phenomenon. Statistical Process Control is largely used in industries for monitoring the process parameters. It is a standard method for visualizing and controlling processes on the basis of measurements of randomly selected samples. The decisions about what needs to be improved, the possible methods to improve it, and the steps to take after getting results from the charts are all made by humans and based on wisdom and experience. The statistical process control described in this paper gives the details about the SPC, its advantages and limitation, applications and information regarding the control charts. Keywords: Statistical Process Control, Control chart, 5M’s, Capability Indices.
Optimised control using Proportional-Integral-Derivative controller tuned usi...IJECEIAES
Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the underthought which forces exacting constraints on attainable execution. The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-IntegralDerivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor. It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.
Constrained discrete model predictive control of a greenhouse system temperatureIJECEIAES
In this paper, a constrained discete model predictive control (CDMPC) strategy for a greenhouse inside temperature is presented. To describe the dynamics of our system’s inside temperature, an experimental greenhouse prototype is engaged. For the mathematical modeling, a state space form which fits properly the acquired data of the greenhouse temperature dynamics is identified using the subspace system identification (N4sid) algorithm. The obtained model is used in order to develop the CDMPC starategy which role is to select the best control moves based on an optimization procedure under the constraints on the control notion. For efficient evaluation of the proposed control approach MATLAB/Simulink and Yalmip optimization toolbox are used for algorithm and blocks implementation. The simulation results confirm the accuracy of the controller that garantees both the control and the reference tracking objectives.
Controlling a DC Motor through Lypaunov-like Functions and SAB TechniqueIJECEIAES
In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IMC Based Fractional Order Controller for Three Interacting Tank ProcessTELKOMNIKA JOURNAL
In model based control, performance of the controlled plant considerably depends on the
accuracy of real plant being modelled. In present work, an attempt has been made to design Internal
Model Control (IMC), for three interacting tank process for liquid level control. To avoid complexities in
controller design, the third order three interacting tank process is modelled to First Order Plus Dead Time
(FOPDT) model. Exploiting the admirable features of Fractional Calculus, the higher order model is also
modelled to Fractional Order First Order Plus Dead Time (FO-FOPDT) model, which further reduces the
modelling error. Moving to control section, different IMC schemes have been proposed based on the order
of filter. Various simulations have been performed to show the greatness of Fractional order modelled
system & fractional order filters over conventional integer order modelled system & integer order filters
respectively. Both for parameters estimation of reduced order model and filter tuning, Genetic Algorithm
(GA) is being applied.
Performance analysis of a liquid column in a chemical plant by using mpceSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A novel auto-tuning method for fractional order PID controllersISA Interchange
Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
2. 786 V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795
computers for distillation calculations was not investigated
up to 1958, although the high speed of computation seemed
to offer economies and present the opportunity of making cal-
culations not otherwise possible. Amundson and Pontinen [1]
in 1958, introduced the use of digital computers to solve the
distillation column problem. For general multi-component
mixtures the coefficients depend in a highly non-linear fash-
ion on compositions also, thus, solution becomes difficult.
The solution obtained should be available for comparison
and should be accurate. This is made possible with the help
of large digital computer.
Choe and Luyben [2] in 1987, took up rigorous dynamic
model of Distillation Column. Most of the dynamic models
assume two simplifications namely negligible vapor holdup
and constant pressure. But in this paper it was demonstrated
that these assumptions lead to erroneous predictions of dy-
namic responses. It happens when pressure of column is
high (i.e. greater than 10 atmosphere) and when column
pressures are low (i.e. vacuum columns). In 1990, Rovaglio
et al. [3] solved the distillation column problem with the
help of rigorous model. Rigorous model is reliable for prac-
tical purposes. An industrial example was taken to show
practical implementation and real economic value of feed
forward control. Feed forward control action reduces the
inherent error when feedback control structure is used to
infer composition. When process dead times are large and
load upsets are frequent and when high quality is required
feedback control cannot serve the purpose alone, then feed
forward control is required to evaluate proper value of ma-
nipulated variables so as to cancel the effects of input varia-
tions.
The control of many industrial processes is difficult be-
cause online measurement of product quality is compli-
cated. This is due to the non-existence of measurement
technology. Weber and Brosilow in 1972 [4] cited one so-
lution to this problem by using secondary measurements
in conjunction with a mathematical model of the process
to estimate product quality. The method includes proce-
dures for selecting the available output measurement to
get an estimator, which is relatively insensitive to model-
ing error and measurement noise. The estimator developed
for control of multi-component distillation column is based
on temperature, reflux and steam flow measurements. The
control achieved with the estimator is comparable to that
achieved with instantaneous composition measurements and
is far superior to composition control achieved by maintain-
ing a constant temperature on any single stage of the col-
umn.
The Weber et al. [4] have designed an estimator in three
steps:
(1) The selection of the appropriate measurements from
those available.
(2) The inversion of the process model so as to obtain an
estimate of the unmeasured process disturbances from
the measurements.
(3) Application of the process model so as to map the esti-
mated and measured process inputs into the estimate of
product quality.
Finally, this model was tested for its validity to 16 stages
distillation column. More important is to develop algorithms
for selecting a subset of the available process output measure-
ments, which will be most appropriate. Joseph and Brosilow
[5] in 1978, presented a method for designing an estimator
to infer unmeasurable product qualities from secondary mea-
surements. The secondary measurements are selected so as
to minimize the number of such measurements required to
obtain an accurate estimate. The application of design proce-
dures to design a static inferential control system to control
product composition is described. Then the dynamic struc-
ture of linear inferential control system term is discussed.
Also the rigorous methods for the design of sub optimal dy-
namic estimators are discussed.
In 1991 and 1992, Marmol and Luyben [6,7] presented
an inferential model based control of multi-component batch
distillation. The model used is described in the paper and two
approaches were explored to estimate the distillate composi-
tion: a rigorous steady state estimator and a quasi-dynamic
non-linear estimator. The models developed provide good
estimation of the distillate composition using only one tem-
perature measurement. Bhagat in 1990 [8], discussed briefly
the neural networks. Two examples were taken to demon-
strate their practical application, these involved CSTR’s. In
the first one, the change in concentration of outlet stream
with the changes in inlet stream concentration was studied.
The second example involved the identification of degree of
mixing in a reactor or vessel.
In 1994, Morris et al. [9] examined the contribution that
various network methodologies can make to the process mod-
eling and control toolbox. Feed forward networks with sig-
moidal activation functions, radial bases function networks
and auto associative networks were reviewed and studied us-
ing data from industrial processes. Finally, the concept of
dynamic networks was introduced with an example of non-
linear predictive control. MacMurray and Himmelblau [13]
in 1994, described the modeling of packed distillation column
with artificial neural network (ANN) and provide a example
of complex modeling. The change in the sign of the gain
was observed under various operating conditions [13]. Ou
and Rhinehart [14] demonstrated a parallel model structure
for general non-linear model predictive control. The model
comprises of a group of sub-models, each providing predic-
tion of one process at one selected future point in time. The
neural network is used for each sub-model and terms the
prediction model as a grouped neural network (GNN). The
work demonstrates implementation of grouped neural net-
work model predictive control (GNNMPC) on a non-linear,
multivariable, constrained pilot scale distillation unit [14].
Tamura and Tateishi [15] have discussed the capabilities
of a neural network with a finite number of hidden units and
shown with the support of mathematical proof that a four-
3. V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795 787
layered feed forward network is superior to three layered
feed forward network in terms of the number of parameters
needed for the training data. Kung and Hwang [16] proposed
algebraic projection analysis and provide an analytical so-
lution for optimal hidden units size and learning rate of the
back propagation neural networks. Murata et al. [17] have
investigated the problem of determining the optimal num-
ber of parameters in neural network from statistical point of
view. The proposed new information criterion (NIC) therein
measures the relative merits of two models having the same
structure but different number of parameters and concludes
whether more number of neurons should be added to the net-
work or not. Kano et al. [18] presented a control scheme to
control the product composition in a multi-component dis-
tillation column. The distillate and bottom compositions are
estimated from online measured process variables. The infer-
ential models for estimation product compositions are con-
structed using dynamic partial least squares (PLS) regression,
on the base of simulated time series data. From the detailed
dynamic simulation results, it is found that the cascade con-
trol system based on a proposed dynamic (PLS) model works
much better than the usual tray temperature control system.
Kano et al. [19] proposed a new inferential control scheme
termed as “Predictive Inferential Control”. In predictive in-
ferential control system, future compositions predicted from
online measured process variables are controlled instead of
the estimates of current compositions. The key concept is to
realize the feed back control with a feed forward effect by
the use of inherent nature of a distillation column.
An approach to fault detection is described by Brydon et
al. [20] which uses neural network pattern classifiers trained
using data from a rigorous differential equation based simula-
tion of a pilot plant column. Two case studies were presented,
both considering only plant data. For two classes of process
data,aneuralnetworkandaK-meansclassifierbothproduced
excellent diagnoses. For additional three classes of plant op-
eration, a neural network again provides accurate classifica-
tions, while a K-means classifier failed to categories the data
[20]. Sbarbaro et al. [21] presented the traditional approach
to include multi-dimensional information into conventional
control systems and proposed a new structure based on pat-
tern recognition. The artificial neural networks and finite state
machines as a frame work for designing the control system is
used. Bakshi and Stephanopoulos [22] derived a methodol-
ogy for pattern based supervisory control and fault diagnosis,
based on multi-scale extraction of trends from process data.
An explicit mapping is learned between the features extracted
at multiple scales, and the corresponding process conditions
using the technique of induction by decision trees.
Taking advantage of technique developed by Kolmogorov,
Kurkova [23] provided a direct proof of the universal approx-
imation capabilities of perceptron type network with two hid-
den layers. Lippmann [24] demonstrated the computational
power of different neural net models and the effectiveness
of simple error correction training procedures. Single and
multi layer perceptrons, which can be used for pattern clas-
sification, are described as well as Kohonen’s feature map
algorithm, which can be used for clustering or as a vector
quantizer.
2. Simulation algorithm
The realistic distillation column [12] consists of non-ideal
column with NC components, non-equimolal overflow, and
inefficient trays. In present paper following assumptions are
made for developing the model.
(1) Liquid on the tray is perfectly mixed and incompressible.
(2) Tray vapor holdups are negligible.
(3) Dynamics of the condenser and the reboiler is neglected.
(4) Vapor and liquid are in thermal equilibrium but not in
phase equilibrium. The departure from phase equilibrium
is described by Murphree vapor efficiency.
Under these assumptions, the steady state operation of
each module is considered by the following equations, com-
monly referred to as the MESH equations. [MESH = material
balance equations, efficiency relations, summation equation,
and heat (enthalpy) balance equations]. Here, the stage num-
ber i takes integer values from 1 to NT.
Li+1 + Vi−1 − Li − Vi = 0
(material balance equations) (1)
yi − yi−1 = ηij[y∗
i (xi, Ti, pi) − yi−1]
(stage efficiency relations) (2)
where
yi =
vi
Vi
and xi =
li
Li
Li =
NC
j=1
lij (summation equations) (3)
Vi =
NC
j=1
vij (4)
Li+1hi+1 + Vi−1Hi−1 − Lihi − Vihi = 0
(enthalpy balance equation) (5)
Eqs. (1)–(5) are used to represent an equilibrium condenser
and an equilibrium reboiler by the removal of variables corre-
sponding to a liquid stream above the condenser and a vapor
stream below a reboiler, and the inclusion of condenser and
reboiler heat duties Qc and QB in the respective enthalpy
balance equations.
For the simulation of a distillation column the quantities
[10], such as feed composition, flow rate, temperature and
4. 788 V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795
pressure, column pressure, stage efficiencies are assumed to
be specified.
The basic steps of the algorithm reflecting the above as-
sumption for the simplified multi-component distillation col-
umn are:
Step 1: Input data for column size, components, physical
properties, feeds, and initial conditions (liquid composi-
tions, liquid flow rates and temperatures on all trays).
Step 2: Calculate initial tray holdups and the pressure pro-
file.
Step 3: Calculate the temperatures and vapor compositions
from the vapor–liquid equilibrium data.
Step 4: Calculate liquid and vapor enthalpies.
Step 5: Calculate vapor flow rates on all trays, starting in
the column base, using the algebraic form of the energy
equations.
Step 6: Evaluate all derivatives of the component continuity
equations for all components on all trays plus the reflux
drum and the column base.
Step 7: Integrate all ODEs (using Euler’s method).
Step 8: Calculate new total liquid holdups from the sum of
the component holdups. Then calculate the new liquid mole
fraction from the component holdups and the total holdups.
Step 9: Calculate new liquid flow rates from the new total
holdups for all trays.
Step 10: Go to step 3 for the next step.
The case under study is a multi-component system (Fig. 1)
(five components) with constant relative volatility through-
out the column and hundred percent efficient trays i.e. the
vapor leaving is in equilibrium with the liquid on the tray. A
single feed stream is fed as saturated liquid on to feed tray NF
(NF = 5). The feed flow rate is F (kmols/h) and composition is
z (mole fraction). The overhead vapor is totally condensed in
a condenser and flows in to the reflux drum, whose holdup of
liquid is MD (kmols). The contents of the drum is assumed to
be perfectly mixed with composition xD (mole fraction). The
liquid in the drum is at it’s bubble point. Reflux is pumped
back to the top tray NT (NT = 15) of the column at a rate R
(kmols/h). Overhead distillate product is removed at a rate D
(kmols/h). At the base of the column, liquid bottoms product
is removed at rate B (kmols/h) and with a composition xB
(mole fraction). The vapor boilup is generated in the reboiler
at rate V (kmols/h).
The algorithm presented is translated into a program using
C language for the distillation column discussed. The main
objective of the above simulation program is to generate pat-
terns. In order to vary reboiler duty QB (KJ/h) for obtaining
various patterns, the following equation is used:
QB = QB + ran(i) (6)
where ran(i) is a random number generated using a library
function srand(). The ran(i) is generated so that it ranges
0.013–0.881. The change in the reboiler duty changes the
temperature profile of the column. With this changed tem-
perature profile we get a changed distillate quality. In this
way, 130 patterns of temperature profile and respective dis-
tillate compositions are generated. These are then used for
training and testing a neural network model.
3. Artificial neural network modeling
3.1. Neuron model
A neuron model consists of a processing element [11] with
synaptic input connections and a single output. The signal
flow of neuron inputs xni is considered to be unidirectional
as indicated by arrows as in a neuron’s output signal flow. A
general neuron symbol is shown in Fig. 2.
The neuron’s output signal is given by the following rela-
tionship
o = f(wt
xn) or o = f
n
i=1
wixni
(7)
where w is weight vector defined as
w
=
[w1 w2 . . . wn ]
t
and xn is the input vector
xn
=
xn1 xn2 · · · xnn
t
The function f(wt xn) is often referred to as an activation func-
tion. The variable net is defined as a scalar product of the
weight and the input vector.
net
=
wt
xn (8)
Using Eq. (8) in Eq. (7), we get
o = f(net) (9)
It is observed from Eq. (7) that the neuron as processing
node performs the operation of summation of its weighted in-
puts. Subsequently, it performs the non-linear operation f(net)
through its activation function. Typical activation functions
used are
f(net)
=
2
1 + exp(−λ net)
− 1 (10)
and
f(net)
=
+1 · · · net 0
−1 · · · net 0
(11)
where λ 0 in Eq. (10) is proportional to neuron gain deter-
mining the steepness of the continuous function f(net) near
net = 0.
By shifting and scaling the bipolar activation function de-
fined by Eqs. (10) and (11), unipolar activation function can
be obtained as
f(net)
=
1
1 + exp(−λnet)
(12)
5. V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795 789
Fig. 1. Schematic diagram of distillation column with instrumentation and control component.
6. 790 V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795
Fig. 2. General symbol of neuron.
Fig. 3. Single layers network with continuous perceptron.
and
f(net)
=
+1 · · · net 0
0 · · · net 0
(13)
3.2. Delta learning rule for multi-perceptron layer
The back propagation-training algorithm allows experi-
ential acquisition of input output mapping knowledge within
multilayer networks. Input patterns are submitted during the
back propagation training sequentially. If a pattern is submit-
ted and its classification or association is determined to be
erroneous, the synaptic weights as well as the thresholds are
adjusted so that the current least mean square classification
error is reduced. The input output mapping comparison of tar-
get and actual values and adjustment, if needed, continue until
all mapping examples from the training are learned within an
acceptable over all error.
During the association or classification phase the trained
neural network itself operate in a feed forward manner. How-
ever, the weight adjustment enforced by the learning rule
propagates exactly backwards from the output layer to the
hidden layer towards the input layer. To formulate the learn-
ing algorithm the simple continuous perceptron network in-
volving K neuron will be considered as shown in Fig. 3 .
o = Γ
Wyn
(14)
where the input and output vector and the weight matrix are
yn =
yn1
yn2
.
.
.
ynJ
o =
o1
o2
.
.
.
oK
W =
w11 w12 · · · w1J
w21 w22 · · · w2J
.
.
.
.
.
.
.
.
.
.
.
.
wK1 wK2 · · · wKJ
and the non-linear diagonal operator Γ [•] is
Γ [•] =
f(•) 0 · · · 0
0 f(•) · · · 0
.
.
.
.
.
.
.
.
.
.
.
.
0 0 · · · f(•)
and the desired output vector is
d
=
d1
d2
.
.
.
dK
netk = Wyn (15)
The generalized error expression include all squared errors
at outputs k = 1, 2, . . ., K.
Ep =
1
2
K
k=1
(dpk − opk)2
=
1
2
dp − op
2
(16)
for a specific pattern p, where p = 1, 2, . . ., P
Let us assume that the gradient decent search is performed
to reduce the error Ep through the adjustment of weights.
Requiring the weight adjustment we compute individual
weight adjustment as follows:
wkj = −η
∂E
∂wkj
(17)
where the error E is defined in Eq. (16) for each node in layer
k, k = 1, 2, . . ., K, we can write using Eq. (15)
netk =
J
j=1
wkjynj (18)
and further using Eq. (14) the neuron’s output is
ok = f(netk) (19)
The error signal term δ is called delta produced by the kth
neuron is defined for this layer as follows:
δok
=
−
∂E
∂(netk)
(20)
It is obvious that the gradient component ∂E/∂Wkj depends
only on the netk of a single neuron, since the error at the output
of the kth neuron is contributed to only by the weights wkj,
7. V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795 791
for j = 1, 2, . . ., J for fixed k value. Thus, using the chain rule
we may write
∂E
∂wkj
=
∂E
∂(netk)
×
∂(netk)
∂wkj
(21)
The second term of product of Eq. (21) in the derivative of
the sum of products of weights and patterns as in Eq. (18).
Since the values of ynj, for j = 1, 2, . . ., J are constant for a
fixed pattern at the input, we obtain
∂(netk)
∂wkj
= ynj (22)
Combining Eqs. (20) and (22) leads to the following form
for Eq. (21)
∂E
∂wkj
= −δokynj (23)
The weight adjustment formula Eq. (17) can be rewritten
using the error signal δok term as below:
wkj = ηδokynj for k = 1, 2, . . . , K and
j = 1, 2, . . . , J (24)
The expression Eq. (24) represents the general formula for
delta training/learning weight adjustments for a single layer
network. It can be noted that wkj in Eq. (24) does not depend
upon the form of an activation function.
To adapt the weights, the error signal term delta δok intro-
duced in Eq. (20) needs to be computed for the kth continuous
perceptron. E is a composite function of netk, therefore, it can
be expressed for k = 1, 2, . . ., K
E(netk) = E[ok(netk)] (25)
Thus, from Eq. (20)
δok = −
∂E
∂ok
×
∂ok
∂(netk)
(26)
Denoting the second term in Eq. (26) as a derivative of acti-
vation function
f
k(netk)
=
∂ok
∂(netk)
(27)
and noting that
∂E
∂ok
= −(dk − ok) (28)
allows rewriting formula Eq. (26) as follows:
δok = (dk − ok)f
k(netk) for k = 1, 2, . . . , K (29)
Eq. (29) shows that the error signal term δok depicts the local
error (dk − ok) at the output of the kth neuron scaled by the
multiplicative factorf
k(netk), which is the slope of the acti-
vation function computed at the following excitation value
netk = f−1
(ok) (30)
The final formula for the weight adjustment of the single
layer network can now be obtained from Eq. (24) as
wkj = η(dk − ok)f
k(netk)ynj (31)
The updated weight values become
w
kj = wkj + wkj for k = 1, 2, . . . , K
j = 1, 2, . . . , J (32)
Formula Eqs. (31) and (32) refers to any form of non-linear
and differentiable activation function f(net) of the neuron.
Let us examine the following two commonly used delta
training rules for the two selected typical activation functions
f(net).For the unipolar continuous activation function defined
in Eq. (12) f(net) can be obtained as
f
(net) =
exp(−net)
[1 + exp(−net)]2
(33)
This can be rewritten as
f
(net) =
1
1 + exp(−net)
×
1 + exp(−net) − 1
1 + exp(−net)
(34)
Again using Eq. (12) in Eq. (34), we get
f
(net) = o(1 − o) (35)
Delta value of the Eq. (29) for this activation function can
be rewritten as
δok = (dk − ok)ok(1 − ok) (36)
Summarizing the above discussion, the updated individual
weights under the delta learning rule can be expressed for
k = 1, 2, . . ., K and j = 1, 2, . . ., J as follows:
w
kj = wkj + η(dk − ok)ok(1 − ok)ynj (37)
for
ok =
1
1 + exp(−netk)
The updated weights under the delta learning rule for the
single layer network can be expressed using vector notation
as
W
= W + ηδoynt
(38)
where the error signal vector δo is defined as the column
vector consisting of the individual error signal terms.
δo
=
δo1
δo2
.
.
.
δoK
8. 792 V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795
4. Proposed ANN based estimator for distillation
column
The ANN model has forward flowing information in pre-
dictive mode back-propagated error corrections in learning
mode. Such nets are usually organized into layer of neurons;
connections are made between neurons of adjacent layers. A
neuron is such connected that it receives signals from each
neuron in immediately succeeding layer. An input layer re-
ceives input. One or more intermediate layers (also called
hidden layers) lie between the input and output layer, which
communicates results externally. ANN based estimator de-
veloped for a distillation column assumes a mixture of NC
components and NT number of trays, the column reboiler in
the bottom and a condenser on the top. An estimator is pro-
posed to estimate the distillate quality from the temperature
profile of the column. We have NT + 2 temperature inputs for
the NT trays, a reflux drum, and the reboiler. The output con-
sists of NC liquid compositions and NC vapor compositions
i.e. 2 × NC outputs. The estimator contains NT + 2 input neu-
rons and 2 × NC output neurons. An input vector of NT + 2
elements (temperature profile of the column) is given to the
input layer of the network. Weights are initially randomized
when the net undergoes training the errors between the re-
sults of the output neurons and the desired corresponding
target values are propagated backward through the net.
The backward propagation of error signals is used to up-
date the connection weights. Finally, a network is achieved
which can predict the output for any input vector. The input
neurons transform the input signal and transmit the resulting
Fig. 4. Proposed neural network for the distillation column.
value to the hidden layer. Each neuron in the hidden layers
individually sums the signals they receive together with the
weighted signal from bias neuron and transmit the result of
each of the neurons in the next layer. Ultimately, the neurons
in the output layer receive weighted signals from neurons
in the penultimate layer sum the signals and emit the trans-
formed sums as output from the net. The output vector is
composed of 2 × NC composition outputs of the distillate.
The temperature profile of the trays in distillation column
is highly non-linear as the system is very complex by having
five-component mixture. To incorporate the non-linearities
in ANN model of these patterns three hidden layers are used
in the proposed estimator. Further for three hidden layers ac-
ceptable accuracy is achieved and increasing the number of
hidden layers beyond three no further improvement in accu-
racy is achieved. Also for less than three hidden layers the
accuracy is not acceptable. The trained network with three
hidden layers is then used to estimate the distillate compo-
sition for any given temperature profile of the distillation
column.
5. Comparison of results
Proposed artificial neural network based estimator is
tested for 15-tray column with a reboiler and a reflux drum
with five component mixture. The 20 temperature profiles
and the corresponding distillate composition used for testing
are the one not used in training. The results obtained with
the help of ANN based estimator are compared with the re-
9. V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795 793
Fig. 5. Liquid composition of components with reboiler temperature.
sults of simulation as obtained using semi rigorous model.
The results for distillate compositions are shown in Fig. 5
and Fig. 6. As seen from Fig. 5 and Fig. 6 the estimated com-
position that from proposed ANN based estimator is close to
the one obtained from semi rigorous model. In Figs. 5 and 6,
the composition of liquid xd5 and vapor compositions yd4 and
yd5, respectively are zero in the distillate product.
6. Discussions and conclusions
The distillate product of distillation control system must
hold composition as near the set point(s) as far as possible
in the faces of upsets. The disturbances are generally in the
flow and composition of feed. The control of the product
composition is difficult because the product quality cannot
be measured economically on line. This is because the in-
strumentation is either infeasible and/or measurement lags
and sampling delays make impossible to design an effective
control system. This problem is solved by using of secondary
measurements in conjunction with a mathematical model of
the process to estimate the product quality. An artificial neural
network based estimator developed here can be used for the
inferential control of distillation column. The developed es-
timator control strategy with minimal computational burden
and high speed can be proposed for the distillation control
system, which is generally non-linear in nature.
As for simulation study program discussed a 15-tray col-
umn with a reboiler and a reflux drum with five-component
mixture is considered for testing the estimator. One hundred
and thirty input-output patterns are generated using simula-
tionprogramandareusedfortrainingthedevelopedestimator
of Fig. 4. Out of the above-generated patterns some of them
are used for testing purpose. Temperature profile taken as in-
put vector consisted of 17 temperature entries of 15 trays,
reboiler and reflux drum. The output vector of the estimator
is constituted by five liquid and five vapor distillate compo-
sitions for the mixture considered. Also the estimator’s input
vector consisted of 17 elements and output vector had 10 ele-
ments. A 5-layered network model is taken with [17, 10, 35,
35, 35] configuration i.e. 17 input neurons, 10 output neurons
and 35 neurons in each of the three hidden layers. The net-
work is trained using 110 patterns and 20 test inputs are given
for testing. Training the estimator took about 60,000 × 110
iterations and about 45 h.
It is observed on 1.2 GHz, Intel Pentium-IV processor, that
developed simulation program takes 0.16 s for its execution
and developed ANN based estimator takes 0.05 s for the same
Fig. 6. Vapor composition of components with reboiler temperature.
10. 794 V. Singh et al. / Chemical Engineering and Processing 44 (2005) 785–795
process, thus, the total time saving of 68.75% can be achieved
using ANN model, without sacrificing the accuracy.
Appendix A. Nomenclature
f(net) activation function
Γ [•] a non-linear diagonal operator
δo error signal vector
δok error signal vector produced by kth neuron
δyj error signal term produced by jth neuron of hidden
layer having output y
v weight increment for hidden layer of neurons
w weight increment for input layer of neurons
f
y column vector for hidden layers
ηi
v vaporization efficiency
η learning parameter (positive constant)
E error gradient vector
ηij Murphree stage efficiency
B bottom product rate (kmols/h)
d desired output vector
dp desired output vector for pth pattern
di desired output from ith neuron
dpk desired output from kth neuron for pth pattern
D distillate product rate (kmols/h)
Ep least squared error for pth pattern
Fi total feed flow rate into ith tray (kmols/h)
hF total molar enthalpy of feed (kJ/kmol)
hfij component feed enthalpy (kJ/kmol)
hi total molar enthalpy of liquid mixture (kJ/kmol)
Hi total molar enthalpy of vapor (kJ/kmol)
hlij component liquid enthalpy (kJ/kmol)
HNi,j hidden neuron for ith hidden layer and jth node
Hvij component vapor enthalpy (kJ/kmol)
INB input neuron for reboiler temperature
IND input neuron for reflux drum temperature
INI input neuron for ith tray temperature
K, L, M number of neurons in three hidden layers respec-
tively
Kij equilibrium constant
Li total liquid flow rate leaving the tray (kmols/h)
lij component liquid flow rate leaving the ith tray
(kmols/h)
MB liquid molar holdup in reboiler (kmols)
MD liquid molar in reflux drum
Mi liquid molar holdup on ith tray (kmols)
NC number of components
net scalar product of weight vector and input vector
netI scalar product of ith weight vector and input vector
NT total number of trays in distillation column
O output vector of neuron
Ok kth output of neurons processing node
ONi output neuron for ith output
QB reboiler heat duty (KJ/h)
QC condenser heat duty (KJ/h)
R reflux rate (kmols/h)
vn updated weights of hidden layer
vnij connection weights of ith node of one layer to jth
node of preceding layer
vn weight vector of hidden layer
V weight matrix of hidden layer
Vi total vapor flow rate from the tray (kmols/h)
vij component vapor flow rate from the tray (kmols/h)
w multiplicative weight vector
wi multiplicative weight for ith input
w updated weights of input layer
wij multiplicative weights for input to ith neuron from
jth input element
W weight matrix
x liquid composition of more volatile component
(mole fraction)
xFij component liquid composition of jth component in
feed (mole fraction)
xij liquid composition if jth component on ith tray
(mole fraction)
xn input vector to neuron
xni ith input to neuron
y vapor composition of more volatile component
(mole fraction)
y* equilibrium vapor composition of more volatile
component (mole fraction)
yij vapor composition of jth component on ith tray
(mole fraction)
yij
* equilibrium vapor composition of jth component on
ith tray (mole fraction)
yn input vector to neuron layer
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