This work presents the temperature control of a nonlinear batch reactor with constrains in the manipulated
variable by means of adaptive feedback-based iterative learning control (ILC). The strong nonlinearities
together with the constrains of the plant can lead to a non-monotonic convergence of the l2-norm of the
error, and still worse, an unstable equilibrium signal e(t) can be reached. By numeric simulation this
works shows that with the adaptive feedback-based ILC is possible to obtain a better performance in the
controlled variable than with the traditional feedback and the feedback based-ILC.
FUZZY LOGIC Control of CONTINUOUS STIRRED TANK REACTOR ProfDrDuraidAhmed
This document describes the use of fuzzy logic control for a continuous stirred tank reactor (CSTR). It begins with an abstract that summarizes modeling the CSTR system using mass and energy balances, and designing a fuzzy logic controller to control the reactor temperature. It then provides more details on mathematical modeling of the CSTR, the basic operations of fuzzy set theory, and the design of the fuzzy logic controller. The controller design involves choosing membership functions to classify the error signal and change in error, then developing fuzzy rules relating the error terms to the control output. Simulation results showed the fuzzy logic controller provided better tracking and regulation than a traditional PID controller.
This document presents a method for driving a chemical process output to a new operating level in minimum time using bang-bang control. The method involves:
1) Modeling the process using a second-order model with time delay and fitting the model parameters to process response data.
2) Calculating the switching times between maximum and minimum input levels using the model to achieve an optimal response time.
3) Implementing the bang-bang control by switching the input at the calculated times to drive the process output to the new level, then returning to conventional control.
The method provides improved set-point responses for processes compared to conventional control, without requiring detailed process dynamics information.
Linking Ab Initio-Calphad for the Assessment of the AluminiumLutetium SystemIRJESJOURNAL
Abstract: First-principles calculations within density functional theory (DFT) were used to investigate intermetallics in the Al-Lu system at 0 K. The five compounds of the system were investigated in their observed experimental structures. Thermodynamic modelling of the Au–Lu system was carried out by means of the CALPHAD (calculation of phase diagrams) method. The liquid phase and the intermetallic compounds Al3Lu, Al2Lu, AlLu, Al2Lu3 and AlLu2 are taken into consideration in this optimization. The substitutional solution model was used to describe the liquid phase. The five compounds are treated as stoichiometric phases. The enthalpies of formation of the compounds were found by the ab initio calculations and used in the optimization of the phase diagram.
The document discusses various methods for analyzing experimental rate data from chemical reactions, including integral methods, differential methods, and the method of initial rates. It covers analyzing data from batch reactors as well as determining reaction orders and rate constants. Rate equations can be first-order, second-order, or nth-order depending on the mechanism and can be determined by plotting concentration or conversion versus time from batch reactor experiments.
This document summarizes a study that models and compares fuzzy PID and PSD controllers for regulating temperature in a discrete thermodynamic system. It describes the design of the thermodynamic system and measurement chain used, which includes temperature and humidity sensors connected to control software. Transient characteristics of the system were determined and fitted to a first-order model. The PSD controller coefficients were then calculated using Kuhn's method for a first-order system. The fuzzy PID controller structure and use of fuzzy logic for control is also discussed.
Coalfired power plant boiler unit decision support systemAlexander Decker
This document discusses a decision support system developed for the boiler unit of a coal-fired thermal power plant. The boiler unit consists of five subsystems arranged in series and parallel configurations. A mathematical model was developed using a Markov birth-death process and probabilistic approach to analyze the system. Differential equations were generated and solved to determine the steady state availability. Decision matrices were developed showing the availability levels for different failure and repair rate combinations of the subsystems. The results indicate the re-heater subsystem has the greatest impact on availability and should be the highest repair priority. The model helps quantitatively manage maintenance decisions.
11.coalfired power plant boiler unit decision support systemAlexander Decker
This document discusses a decision support system developed for the boiler unit of a coal-fired thermal power plant. The boiler unit consists of five subsystems arranged in series and parallel configurations. A mathematical model was developed using a Markov birth-death process and probabilistic approach to analyze the system. Differential equations were generated and solved to determine the steady state availability. Decision matrices were developed showing the availability levels for different failure and repair rate combinations of the subsystems. The results indicate the re-heater subsystem has the greatest impact on availability and should be the highest repair priority. The model helps quantitatively manage maintenance decisions.
FUZZY LOGIC Control of CONTINUOUS STIRRED TANK REACTOR ProfDrDuraidAhmed
This document describes the use of fuzzy logic control for a continuous stirred tank reactor (CSTR). It begins with an abstract that summarizes modeling the CSTR system using mass and energy balances, and designing a fuzzy logic controller to control the reactor temperature. It then provides more details on mathematical modeling of the CSTR, the basic operations of fuzzy set theory, and the design of the fuzzy logic controller. The controller design involves choosing membership functions to classify the error signal and change in error, then developing fuzzy rules relating the error terms to the control output. Simulation results showed the fuzzy logic controller provided better tracking and regulation than a traditional PID controller.
This document presents a method for driving a chemical process output to a new operating level in minimum time using bang-bang control. The method involves:
1) Modeling the process using a second-order model with time delay and fitting the model parameters to process response data.
2) Calculating the switching times between maximum and minimum input levels using the model to achieve an optimal response time.
3) Implementing the bang-bang control by switching the input at the calculated times to drive the process output to the new level, then returning to conventional control.
The method provides improved set-point responses for processes compared to conventional control, without requiring detailed process dynamics information.
Linking Ab Initio-Calphad for the Assessment of the AluminiumLutetium SystemIRJESJOURNAL
Abstract: First-principles calculations within density functional theory (DFT) were used to investigate intermetallics in the Al-Lu system at 0 K. The five compounds of the system were investigated in their observed experimental structures. Thermodynamic modelling of the Au–Lu system was carried out by means of the CALPHAD (calculation of phase diagrams) method. The liquid phase and the intermetallic compounds Al3Lu, Al2Lu, AlLu, Al2Lu3 and AlLu2 are taken into consideration in this optimization. The substitutional solution model was used to describe the liquid phase. The five compounds are treated as stoichiometric phases. The enthalpies of formation of the compounds were found by the ab initio calculations and used in the optimization of the phase diagram.
The document discusses various methods for analyzing experimental rate data from chemical reactions, including integral methods, differential methods, and the method of initial rates. It covers analyzing data from batch reactors as well as determining reaction orders and rate constants. Rate equations can be first-order, second-order, or nth-order depending on the mechanism and can be determined by plotting concentration or conversion versus time from batch reactor experiments.
This document summarizes a study that models and compares fuzzy PID and PSD controllers for regulating temperature in a discrete thermodynamic system. It describes the design of the thermodynamic system and measurement chain used, which includes temperature and humidity sensors connected to control software. Transient characteristics of the system were determined and fitted to a first-order model. The PSD controller coefficients were then calculated using Kuhn's method for a first-order system. The fuzzy PID controller structure and use of fuzzy logic for control is also discussed.
Coalfired power plant boiler unit decision support systemAlexander Decker
This document discusses a decision support system developed for the boiler unit of a coal-fired thermal power plant. The boiler unit consists of five subsystems arranged in series and parallel configurations. A mathematical model was developed using a Markov birth-death process and probabilistic approach to analyze the system. Differential equations were generated and solved to determine the steady state availability. Decision matrices were developed showing the availability levels for different failure and repair rate combinations of the subsystems. The results indicate the re-heater subsystem has the greatest impact on availability and should be the highest repair priority. The model helps quantitatively manage maintenance decisions.
11.coalfired power plant boiler unit decision support systemAlexander Decker
This document discusses a decision support system developed for the boiler unit of a coal-fired thermal power plant. The boiler unit consists of five subsystems arranged in series and parallel configurations. A mathematical model was developed using a Markov birth-death process and probabilistic approach to analyze the system. Differential equations were generated and solved to determine the steady state availability. Decision matrices were developed showing the availability levels for different failure and repair rate combinations of the subsystems. The results indicate the re-heater subsystem has the greatest impact on availability and should be the highest repair priority. The model helps quantitatively manage maintenance decisions.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Iaetsd design and implementation of intelligentIaetsd Iaetsd
This document describes the design and implementation of intelligent controllers for a continuous stirred tank reactor (CSTR) system. The CSTR is used to control the concentration of ethylene glycol by manipulating the concentration of ethylene oxide. Various controllers like PI, PID, fuzzy logic, and genetic algorithms are analyzed for controlling the concentration. Modeling is done in MATLAB Simulink. Genetic algorithms are found to provide better concentration control compared to other controllers. The paper discusses CSTR modeling and problem formulation. Controller design methods like PID and modified PID are also covered.
This document discusses the mathematical modeling of a continuous stirred tank reactor (CSTR). It begins by describing a CSTR and its approximation as a continuously ideally stirred tank reactor. It then presents the mass and energy balances used to develop a model of a CSTR, including a list of variables and assumptions. The balances derived are for total mass, mass of component A, and total energy in the reactor. The document concludes by referencing additional sources on control systems modeling.
This document proposes a new one-step method for tuning PI/PID controllers based on closed-loop experiments. It derives simple correlations between data from a proportional-only closed-loop step response experiment and PI/PID settings that provide good performance and robustness. Specifically:
1) A proportional-only controller is used to generate a step response with 10-60% overshoot. The gain, overshoot, peak time, and steady-state change are recorded.
2) Simulations show the proposed controller gain is proportional to the proportional gain used in the experiment, with the ratio dependent only on overshoot. Simple equations are derived relating overshoot and peak time to the PI/PID settings.
3
Modeling and simulation of temperature profiles in a reactiveAlexander Decker
This document summarizes a study that developed a mathematical model to simulate temperature profiles in a reactive distillation system for the esterification of acetic anhydride and methanol. The model was based on reaction kinetics determined from experimental temperature data. Simulation results showed good agreement with experiments, with deviations less than 4%. An overview of the experimental setup and procedures for thermistor calibration and reactor calibration are also provided.
NEED FOR THE SECOND LAW OF THERMODYNAMICS - STATEMENT - CARNOT CYCLE - REFRIGERATOR CONCEPT - CONCEPT OF ENTROPY - FREE ENERGY FUNCTIONS - GIBB'S HELMHOLTZ EQUATIONS - MAXEWELL'S RELATIONS - THERMODYNAMICS EQUATION OF STATE - CRITERIA OF SPONTANITY - CHEMICAL POTENTIAL - GIBB'S DUHEM EQUATION
Optimization through Mathematical Modelling of Irreversibility and Other Para...IRJET Journal
This document discusses optimization of irreversibility and other parameters in a simple vapor compression refrigeration cycle using the refrigerant R-134a through mathematical modeling. It summarizes previous research that analyzed refrigeration cycles using exergy analysis and the second law of thermodynamics. The study establishes relationships between evaporator temperature and performance parameters like COP, total exergy change, irreversibility, ECOP, and second law efficiency. It analyzes these parameters for different evaporator temperatures to develop a mathematical model to calculate one parameter given a value for another. The model aims to optimize irreversibility and other factors in the refrigeration cycle.
Control tutorials for matlab and simulink introduction pid controller desig...ssuser27c61e
This document introduces PID (proportional-integral-derivative) controllers and how they can be used to improve closed-loop system performance. It describes how each of the P, I, and D terms affect rise time, overshoot, settling time, and steady-state error. An example using a mass-spring-damper system demonstrates how to design PID controllers manually and use MATLAB's automatic tuning tools to design controllers. The document provides guidelines for designing PID controllers and introduces PID controller objects and functions in MATLAB.
This document discusses various optimization strategies for an air separation unit (ASU) using gPROMS software. It begins with examples of steady-state optimization of continuous stirred tank reactors (CSTRs) and dynamic optimization of a batch reactor. It then provides an overview of air separation processes and simulations before examining different optimization approaches for an ASU, including steady-state, dynamic, dynamic under uncertainty, and economics-based dynamic optimization. The goal is to develop computational tools and algorithms to optimize ASUs and address some industrial issues through various optimization techniques.
Design of a self tuning regulator for temperature control of a polymerization...ISA Interchange
The temperature control of a polymerization reactor described by Chylla and Haase, a control engineering benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. The conventional cascade control provides a robust operation, but often lacks in control performance concerning the required strict temperature tolerances. The self-tuning control concept presented in this contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature in order to follow a predefined trajectory of the reactor temperature. The reaction heat and the heat transfer coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Two simple physically motivated relations are employed, which allow the non-delayed estimation of both quantities. Simulation results under model uncertainties show the effectiveness of the self-tuning control concept.
STABILIZATION AT UPRIGHT EQUILIBRIUM POSITION OF A DOUBLE INVERTED PENDULUM W...ijcsa
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed
method gave results which were better when compared without time delay wherein the calculated values
indicated the issues when incorporating time delay
The document discusses chemical kinetics and provides information about:
- The factors that affect the speed of a chemical reaction, including concentration, temperature, and catalysts.
- How to determine the rate law, rate constant, order, and mechanism of reactions from experimental data.
- The relationship between concentration and time for reactions of different orders (zero, first, and second order).
- How to calculate half-life, effect of temperature on reaction rate using the Arrhenius equation, and the role of homogeneous and heterogeneous catalysts.
Chem 2 - Chemical Kinetics IV: The First-Order Integrated Rate LawLumen Learning
This document discusses first-order chemical kinetics. It defines the differential and integrated rate laws for first-order reactions and shows that the integrated rate law results in an exponential decay equation. It also describes how to experimentally determine reaction order by plotting the natural log of concentration versus time and identifying linear trends. The half-life of a first-order reaction is derived and shown to be 0.693/k, where k is the rate constant, meaning half-life does not depend on initial concentration.
Brain emotional learning based intelligent controller and its application to ...Alexander Decker
This document discusses applying a Brain Emotional Learning Based Intelligent Controller (BELBIC) to control a Continuous Stirred Tank Reactor (CSTR). BELBIC is an intelligent controller modeled after the limbic system of the brain. The document provides background on CSTRs and their typical uses. It also outlines the mathematical model for a CSTR, including mass and energy balances. Parameters for a sample CSTR system are provided. The goal is to use BELBIC to control the concentration and temperature of the CSTR by manipulating the feed flow and temperature. BELBIC is described as being based on the architecture of the limbic system and aims to provide emotional learning-based control.
The document describes the design of a fractional order PIλDλ controller for liquid level control of a spherical tank modeled as a fractional order system. A fractional order proportional integral derivative (FOPID) controller is designed and its performance is compared to a traditional integer order PID controller designed for the same spherical tank modeled as a first order plus dead time system. Simulation results show that the fractional order controller designed using frequency domain specifications achieves improved performance over the integer order controller. The fractional order controller provides extra tuning parameters that allow it to better match the dynamics of the fractional order plant model.
The document analyzes the performance of different bin-packing heuristics. It finds that the Next-Fit heuristic is the fastest, taking O(n) time, while First-Fit and First-Fit-Decreasing are the slowest at O(n^2) time. The Max-Rest heuristic can be optimized to O(n log n) time by using a priority queue. Various optimizations are discussed that improve the performance of heuristics like using mapping/lookup tables or sorting objects by size.
A Self-Tuned Simulated Annealing Algorithm using Hidden Markov ModeIJECEIAES
Simulated Annealing algorithm (SA) is a well-known probabilistic heuristic. It mimics the annealing process in metallurgy to approximate the global minimum of an optimization problem. The SA has many parameters which need to be tuned manually when applied to a specific problem. The tuning may be difficult and time-consuming. This paper aims to overcome this difficulty by using a self-tuning approach based on a machine learning algorithm called Hidden Markov Model (HMM). The main idea is allowing the SA to adapt his own cooling law at each iteration, according to the search history. An experiment was performed on many benchmark functions to show the efficiency of this approach compared to the classical one.
This document discusses methods for assessing the energy performance of heat exchangers over time. It describes calculating the overall heat transfer coefficient U to determine if fouling or other issues have reduced efficiency. The procedure involves monitoring operating parameters, calculating thermal properties, and determining U by measuring the heat duty, surface area, and log mean temperature difference. An example application to a liquid-liquid exchanger is provided, comparing test data to design specifications to identify potential fouling issues.
Adaptive predictive functional control of a class of nonlinear systemsISA Interchange
This document summarizes an adaptive predictive functional control algorithm for nonlinear systems.
1) It uses a concept called pseudo-partial derivative (PPD) to dynamically linearize the nonlinear system model based on input-output data.
2) It predicts future outputs using an internal model based on the estimated PPD.
3) Predictive functional control (PFC) is used to design the control algorithm, where only two coincidence points are used to calculate the manipulated variable.
4) The proposed algorithm provides bounded inputs/outputs and setpoint tracking without steady-state error using a simple structure that is easy to tune for real-time control of nonlinear systems.
This document summarizes a study that determined the bio-kinetic parameters for a sequencing batch reactor (SBR) type sewage treatment plant. Five bench-scale SBRs were operated under different biomass retention times ranging from 2 to 10 days. Samples from the influent, mixed liquor, and effluent were analyzed using standard methods. The study found that the kinetic parameters, including yield coefficient, organism decay rate, BOD removal rate, half velocity constant, and maximum specific growth rate, were within normal ranges for activated sludge. A higher sludge yield and lower organism decay showed that excess sludge production was high in the plants. The biomass retention time was determined to be a useful operating parameter instead of adjusting
This document discusses the design of chemical reactors, including batch and continuous stirred-tank reactors (CSTR). It covers key concepts like space time, space velocity, and accumulation equations for CSTR design. Examples are provided for solving first and second order reaction systems using a graphical approach, including determining rate constants from concentration-rate graphs and applying variable volume systems.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Iaetsd design and implementation of intelligentIaetsd Iaetsd
This document describes the design and implementation of intelligent controllers for a continuous stirred tank reactor (CSTR) system. The CSTR is used to control the concentration of ethylene glycol by manipulating the concentration of ethylene oxide. Various controllers like PI, PID, fuzzy logic, and genetic algorithms are analyzed for controlling the concentration. Modeling is done in MATLAB Simulink. Genetic algorithms are found to provide better concentration control compared to other controllers. The paper discusses CSTR modeling and problem formulation. Controller design methods like PID and modified PID are also covered.
This document discusses the mathematical modeling of a continuous stirred tank reactor (CSTR). It begins by describing a CSTR and its approximation as a continuously ideally stirred tank reactor. It then presents the mass and energy balances used to develop a model of a CSTR, including a list of variables and assumptions. The balances derived are for total mass, mass of component A, and total energy in the reactor. The document concludes by referencing additional sources on control systems modeling.
This document proposes a new one-step method for tuning PI/PID controllers based on closed-loop experiments. It derives simple correlations between data from a proportional-only closed-loop step response experiment and PI/PID settings that provide good performance and robustness. Specifically:
1) A proportional-only controller is used to generate a step response with 10-60% overshoot. The gain, overshoot, peak time, and steady-state change are recorded.
2) Simulations show the proposed controller gain is proportional to the proportional gain used in the experiment, with the ratio dependent only on overshoot. Simple equations are derived relating overshoot and peak time to the PI/PID settings.
3
Modeling and simulation of temperature profiles in a reactiveAlexander Decker
This document summarizes a study that developed a mathematical model to simulate temperature profiles in a reactive distillation system for the esterification of acetic anhydride and methanol. The model was based on reaction kinetics determined from experimental temperature data. Simulation results showed good agreement with experiments, with deviations less than 4%. An overview of the experimental setup and procedures for thermistor calibration and reactor calibration are also provided.
NEED FOR THE SECOND LAW OF THERMODYNAMICS - STATEMENT - CARNOT CYCLE - REFRIGERATOR CONCEPT - CONCEPT OF ENTROPY - FREE ENERGY FUNCTIONS - GIBB'S HELMHOLTZ EQUATIONS - MAXEWELL'S RELATIONS - THERMODYNAMICS EQUATION OF STATE - CRITERIA OF SPONTANITY - CHEMICAL POTENTIAL - GIBB'S DUHEM EQUATION
Optimization through Mathematical Modelling of Irreversibility and Other Para...IRJET Journal
This document discusses optimization of irreversibility and other parameters in a simple vapor compression refrigeration cycle using the refrigerant R-134a through mathematical modeling. It summarizes previous research that analyzed refrigeration cycles using exergy analysis and the second law of thermodynamics. The study establishes relationships between evaporator temperature and performance parameters like COP, total exergy change, irreversibility, ECOP, and second law efficiency. It analyzes these parameters for different evaporator temperatures to develop a mathematical model to calculate one parameter given a value for another. The model aims to optimize irreversibility and other factors in the refrigeration cycle.
Control tutorials for matlab and simulink introduction pid controller desig...ssuser27c61e
This document introduces PID (proportional-integral-derivative) controllers and how they can be used to improve closed-loop system performance. It describes how each of the P, I, and D terms affect rise time, overshoot, settling time, and steady-state error. An example using a mass-spring-damper system demonstrates how to design PID controllers manually and use MATLAB's automatic tuning tools to design controllers. The document provides guidelines for designing PID controllers and introduces PID controller objects and functions in MATLAB.
This document discusses various optimization strategies for an air separation unit (ASU) using gPROMS software. It begins with examples of steady-state optimization of continuous stirred tank reactors (CSTRs) and dynamic optimization of a batch reactor. It then provides an overview of air separation processes and simulations before examining different optimization approaches for an ASU, including steady-state, dynamic, dynamic under uncertainty, and economics-based dynamic optimization. The goal is to develop computational tools and algorithms to optimize ASUs and address some industrial issues through various optimization techniques.
Design of a self tuning regulator for temperature control of a polymerization...ISA Interchange
The temperature control of a polymerization reactor described by Chylla and Haase, a control engineering benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. The conventional cascade control provides a robust operation, but often lacks in control performance concerning the required strict temperature tolerances. The self-tuning control concept presented in this contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature in order to follow a predefined trajectory of the reactor temperature. The reaction heat and the heat transfer coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Two simple physically motivated relations are employed, which allow the non-delayed estimation of both quantities. Simulation results under model uncertainties show the effectiveness of the self-tuning control concept.
STABILIZATION AT UPRIGHT EQUILIBRIUM POSITION OF A DOUBLE INVERTED PENDULUM W...ijcsa
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed
method gave results which were better when compared without time delay wherein the calculated values
indicated the issues when incorporating time delay
The document discusses chemical kinetics and provides information about:
- The factors that affect the speed of a chemical reaction, including concentration, temperature, and catalysts.
- How to determine the rate law, rate constant, order, and mechanism of reactions from experimental data.
- The relationship between concentration and time for reactions of different orders (zero, first, and second order).
- How to calculate half-life, effect of temperature on reaction rate using the Arrhenius equation, and the role of homogeneous and heterogeneous catalysts.
Chem 2 - Chemical Kinetics IV: The First-Order Integrated Rate LawLumen Learning
This document discusses first-order chemical kinetics. It defines the differential and integrated rate laws for first-order reactions and shows that the integrated rate law results in an exponential decay equation. It also describes how to experimentally determine reaction order by plotting the natural log of concentration versus time and identifying linear trends. The half-life of a first-order reaction is derived and shown to be 0.693/k, where k is the rate constant, meaning half-life does not depend on initial concentration.
Brain emotional learning based intelligent controller and its application to ...Alexander Decker
This document discusses applying a Brain Emotional Learning Based Intelligent Controller (BELBIC) to control a Continuous Stirred Tank Reactor (CSTR). BELBIC is an intelligent controller modeled after the limbic system of the brain. The document provides background on CSTRs and their typical uses. It also outlines the mathematical model for a CSTR, including mass and energy balances. Parameters for a sample CSTR system are provided. The goal is to use BELBIC to control the concentration and temperature of the CSTR by manipulating the feed flow and temperature. BELBIC is described as being based on the architecture of the limbic system and aims to provide emotional learning-based control.
The document describes the design of a fractional order PIλDλ controller for liquid level control of a spherical tank modeled as a fractional order system. A fractional order proportional integral derivative (FOPID) controller is designed and its performance is compared to a traditional integer order PID controller designed for the same spherical tank modeled as a first order plus dead time system. Simulation results show that the fractional order controller designed using frequency domain specifications achieves improved performance over the integer order controller. The fractional order controller provides extra tuning parameters that allow it to better match the dynamics of the fractional order plant model.
The document analyzes the performance of different bin-packing heuristics. It finds that the Next-Fit heuristic is the fastest, taking O(n) time, while First-Fit and First-Fit-Decreasing are the slowest at O(n^2) time. The Max-Rest heuristic can be optimized to O(n log n) time by using a priority queue. Various optimizations are discussed that improve the performance of heuristics like using mapping/lookup tables or sorting objects by size.
A Self-Tuned Simulated Annealing Algorithm using Hidden Markov ModeIJECEIAES
Simulated Annealing algorithm (SA) is a well-known probabilistic heuristic. It mimics the annealing process in metallurgy to approximate the global minimum of an optimization problem. The SA has many parameters which need to be tuned manually when applied to a specific problem. The tuning may be difficult and time-consuming. This paper aims to overcome this difficulty by using a self-tuning approach based on a machine learning algorithm called Hidden Markov Model (HMM). The main idea is allowing the SA to adapt his own cooling law at each iteration, according to the search history. An experiment was performed on many benchmark functions to show the efficiency of this approach compared to the classical one.
This document discusses methods for assessing the energy performance of heat exchangers over time. It describes calculating the overall heat transfer coefficient U to determine if fouling or other issues have reduced efficiency. The procedure involves monitoring operating parameters, calculating thermal properties, and determining U by measuring the heat duty, surface area, and log mean temperature difference. An example application to a liquid-liquid exchanger is provided, comparing test data to design specifications to identify potential fouling issues.
Adaptive predictive functional control of a class of nonlinear systemsISA Interchange
This document summarizes an adaptive predictive functional control algorithm for nonlinear systems.
1) It uses a concept called pseudo-partial derivative (PPD) to dynamically linearize the nonlinear system model based on input-output data.
2) It predicts future outputs using an internal model based on the estimated PPD.
3) Predictive functional control (PFC) is used to design the control algorithm, where only two coincidence points are used to calculate the manipulated variable.
4) The proposed algorithm provides bounded inputs/outputs and setpoint tracking without steady-state error using a simple structure that is easy to tune for real-time control of nonlinear systems.
This document summarizes a study that determined the bio-kinetic parameters for a sequencing batch reactor (SBR) type sewage treatment plant. Five bench-scale SBRs were operated under different biomass retention times ranging from 2 to 10 days. Samples from the influent, mixed liquor, and effluent were analyzed using standard methods. The study found that the kinetic parameters, including yield coefficient, organism decay rate, BOD removal rate, half velocity constant, and maximum specific growth rate, were within normal ranges for activated sludge. A higher sludge yield and lower organism decay showed that excess sludge production was high in the plants. The biomass retention time was determined to be a useful operating parameter instead of adjusting
This document discusses the design of chemical reactors, including batch and continuous stirred-tank reactors (CSTR). It covers key concepts like space time, space velocity, and accumulation equations for CSTR design. Examples are provided for solving first and second order reaction systems using a graphical approach, including determining rate constants from concentration-rate graphs and applying variable volume systems.
The document discusses the design of an ideal batch reactor for converting chemical A into product R through a liquid reaction. It provides the stoichiometry and rate equation for the reaction and asks the reader to calculate the reaction time needed for the concentration of A to drop from an initial concentration of 1.3 mol/liter to a final concentration of 0.3 mol/liter based on the information given.
This experiment involves conducting a saponification reaction between sodium hydroxide (NaOH) and ethyl acetate (Et(Ac)) in a continuous stirred tank reactor (CSTR) to determine the effect of residence time on conversion. A calibration curve will be prepared to relate conductivity measurements to conversion values for the 0.1M NaOH and 0.1M Et(Ac) reaction. The objectives are to determine conversion, the reaction rate constant, and the effect of residence time on conversion.
This document summarizes saponification of ethyl acetate and sodium hydroxide in an isothermal batch reactor. It describes the basic design of a batch reactor where reactants are placed inside and allowed to react over time before removing products. The general mass balance equation and basic design equation for a batch reactor are provided. Kinetic parameters like rate of reaction, concentration, and temperature are also discussed. Procedures for a titration experiment to determine concentration are outlined. Tips are given to ensure accurate measurements in experiments.
The experiment studied the effect of temperature on the saponification reaction of ethyl acetate and sodium hydroxide in a batch reactor. Calibration curves were plotted at different temperatures to determine conductivity and conversion levels. Reactants were added to a jacketed reactor and stirred at 30°C and 50°C, with conductivity readings recorded. The data showed lower temperatures resulted in higher conversions as evidenced by lower conductivity readings. Batch reactors are useful for small-scale testing but have high operating costs and variable product quality compared to continuous reactors.
The document discusses various topics related to chemical reactor design including:
1. Reactor classification into homogeneous and heterogeneous types and examples like batch, continuous stirred tank, plug flow, and semi-batch reactors.
2. Factors to consider for reactor design like heat of reaction, operating temperature and pressure, and use of internal or external heating/cooling.
3. Methods for controlling temperature like adiabatic, isothermal, auto-thermal reactors.
4. Key principles of chemical equilibrium and kinetics that influence choice of process conditions.
This document summarizes and compares various tuning methods for a PID controller for temperature control of an electric oven. It describes the Ziegler-Nichols first and closed loop tuning methods, and a genetic algorithm tuning method. The genetic algorithm approach was able to automatically tune the PID controller gains to minimize error for the temperature control system, and its performance was compared to the other methods. The document also discusses identifying the parameters of the oven plant through open loop step response testing.
MODEL BASED ANALYSIS OF TEMPERATURE PROCESS UNDER VARIOUS CONTROL STRATEGIES ...Journal For Research
This paper analyze the temperature process in an empirical model. From the empirical model the system behavior is determined by transfer function and the basic controller strategies Ziegler-Nichols & Cohen-Coon method are implemented in it. With these tuning methods the best control strategies are obtained at the final stage by interfacing the system with NI-myRIO kit.
Simulation analysis of Series Cascade control Structure and anti-reset windup...IOSR Journals
This document presents a simulation analysis of series cascade control structure and anti-reset windup technique for a jacketed continuous stirred tank reactor (CSTR). It discusses modeling and linearization of a CSTR process. It then analyzes series cascade control structure and designs PID controllers using auto-tuning. Next, it explains an anti-reset windup protection technique to address issues like overshoot and windup. Simulation results showing step responses indicate that responses with anti-windup have less overshoot and shorter settling time compared to the conventional cascade control system. In conclusion, the anti-reset windup technique improves closed-loop performance for the CSTR process.
Current predictive controller for high frequency resonant inverter in inducti...IJECEIAES
This document discusses current predictive control for a high frequency resonant inverter used in induction heating applications. It begins with modeling the inductor-load system powered by the inverter. It then discusses generalized predictive control (GPC), including using a prediction model, minimizing a cost function to determine the optimal control signal, and applying the first value of the control signal sequence. Simulation results show the GPC controller provides accurate current tracking with fast response times and no overshoot, even when the reference current amplitude varies. The control is robust to parameter changes in the inductor-load system.
EHR ATTRIBUTE-BASED ACCESS CONTROL (ABAC) FOR FOG COMPUTING ENVIRONMENTcsandit
Liquid level tanks are employed in many industrial and chemical areas. Their level must be keep
a defined point or between maximum-minimum points depending on changing of inlet and outlet
liquid quantities. In order to overcome the problem, many level control methods have been
developed. In the paper, it was aimed that obtain a mathematical model of an installed liquid
level tank system. Then, the mathematical model was derived from the installed system
depending on the sizes of the liquid level tank. According to some proportional-integralderivative
(PID) parameters, the model was simulated by using MATLAB/Simulink program.
After that, data of the liquid level tank were taken into a computer by employing data
acquisition cards (DAQs). Lastly, the computer-controlled liquid level control was successfully
practiced through a written computer program embedded into a PID algorithm used the PID
parameters obtained from the simulations into Advantech VisiDAQ software
A new approach for Tuning of PID Load Frequency Controller of an Interconnect...Editor IJMTER
This document describes a new approach for tuning PID load frequency controllers in an interconnected power system consisting of three areas. It begins by describing the structure and components of PID controllers used for load frequency control. It then provides details on the three-area power system model consisting of different turbine types in each area. The document then explains the Ziegler-Nichols and Pessen Integral Rule methods for tuning the PID controllers in each area. The controller gains for each plant in the system are calculated using both classical and proposed PID tuning methods. Simulation results show the proposed controller provides better dynamic performance than the classical PID controller.
Metamodel-based Optimization of a PID Controller Parameters for a Coupled-tan...TELKOMNIKA JOURNAL
Liquid flow and level control are essential requirements in various industries, such as paper
manufacturing, petrochemical industries, waste management, and others. Controlling the liquids flow and
levels in such industries is challenging due to the existence of nonlinearity and modeling uncertainties of
the plants. This paper presents a method to control the liquid level in a second tank of a coupled-tank plant
through variable manipulation of a water pump in the first tank. The optimum controller parameters of this
plant are calculated using radial basis function neural network metamodel. A time-varying nonlinear
dynamic model is developed and the corresponding linearized perturbation models are derived from the
nonlinear model. The performance of the developed optimized controller using metamodeling is compared
with the original large space design. In addition, linearized perturbation models are derived from the
nonlinear dynamic model with time-varying parameters.
A STUDY ON PERFORMANCE OF DIFFERENT OPEN LOOP PID TUNNING TECHNIQUE FOR A LIQ...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired operating condition ,safety, and efficiently while satisfying the environmental and product quality. Like the Level, Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in
process plant. This paper mainly concern about the single tank liquid flow process and designing the controller with different PID tunning methods. Many process plants controlled by the PID controller with similar dynamics to find out the possible set of satisfactory controller parameters from the less plant
information but from the mathematical model. With minimum effort adjust the controller parameters by using three open loop PID controller IMC,CHR & AMIGO and compare their output response in real time flow tank system
A Study on Performance of Different Open Loop PID Tunning Technique for a Liq...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired
operating condition ,safety,and efficiently while satisfying the environmental and product quality.Like the
Level,Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in
process plant. This paper mainly concern about the single tank liquid flow process and designing the
controller with different PID tunning methods.Many process plants controlled by the PID controller with
similar dynamics to find out the possible set of satisfactory controller parameters from the less plant
information but from the mathematical model.With minimum effort adjust the controller parameters by
using three open loop PID controller IMC,CHR & AMIGO and compare their output response in real time
flow tank system.
A STUDY ON PERFORMANCE OF DIFFERENT OPEN LOOP PID TUNNING TECHNIQUE FOR A LI...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired operating condition ,safety,and efficiently while satisfying the environmental and product quality. Like the Level,Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in process plant. This paper mainly concern about the single tank liquid flow process and designing the controller with different PID tunning methods.Many process plants controlled by the PID controller with similar dynamics to find out the possible set of satisfactory controller parameters from the less plant information but from the mathematical model.With minimum effort adjust the controller parameters by using three open loop PID controller IMC,CHR & AMIGOand compare their output response in real time flow tank system.
This document describes using Simulink block diagrams to model and solve mathematical equations for controlling temperature in a stirred tank heater. It presents the equations for an energy balance on the tank, a model of the thermocouple measurement including dead time, and a PID controller model. Simulation results are shown for an open loop system and systems with proportional and PI control, demonstrating how the controller parameters affect the ability to maintain the set point temperature.
Online Adaptive Control for Non Linear Processes Under Influence of External ...Waqas Tariq
In this paper a novel temperature controller, for non linear processes, under the influence of external disturbance, has been proposed. The control process has been carried out by Neural Network based Proportional, Integral and Derivative (NNPID). In this controller, two experiments have been conducted with respect to the setpoint changes and load disturbance. The first experiment considers the change in setpoint temperature in steps of 10oC from 50oC to 70oC for three different rates of flow of water. In the second experiment the load disturbance in terms of addition of 100ml/min of water at three different time intervals is introduced in the system. It has been shown that, in these situations, the proposed controller adjusts NN weights which are equivalent to PID parameters in both the cases to achieve better control than conventional PID. In the proposed controller, an error less than 0.08oC have been achieved under the effect of the load disturbance. Moreover, it is also seen that the present controller gives error less than 0.11oC, 0.12oC and 0.12oC, without overshoot for 50oC, 60oC and 70oC, respectively, for all three rate of flow of water.
Design of Controllers for Continuous Stirred Tank ReactorIAES-IJPEDS
The objective of the project is to design various controllers for temperature control in Continuous Stirred Tank Reactor (CSTR) systems. Initially Zeigler-Nichols, modified Zeigler-Nichols, Tyreus-Luyben, Shen-Yu and IMC based method of tuned Proportional Integral (PI) controller is designed and comparisons are made with Fuzzy Logic Controller. Simulations are carried out and responses are obtained for the above controllers. Maximum peak overshoot, Settling time, Rise time, ISE, IAE are chosen as performance index. From the analysis it is found that the Fuzzy Logic Controller is a promising controller than the conventional controllers.
This document summarizes a study comparing three control methods - PID, IMC, and IMC-PID - for controlling a first-order motor-tachometer system. The key findings are:
1) IMC performs better than PID when near system limitations, as PID can exhibit reset windup causing poor control. IMC avoids this issue.
2) Both IMC and IMC-PID effectively control the system under normal operation. However, IMC has less noise than IMC-PID.
3) When a large disturbance occurs, IMC returns to the setpoint faster than IMC-PID, which overshoots due to integral windup.
This document compares the performance of PID and FOPID controllers for automatic voltage regulation (AVR) systems. It presents models for the components of an AVR system and describes integer and fractional order PID controllers. Classical tuning methods like Ziegler-Nichols and Cohen-Coon are discussed for PID tuning. Ziegler-Nichols type rules are presented for FOPID tuning. Simulation results show that a FOPID controller tuned by Ziegler-Nichols methods provides better performance than PID controllers tuned by Ziegler-Nichols or Cohen-Coon, with less overshoot, faster settling time, and reduced rise time.
This document presents a digital implementation of a fractional order PID controller for a boost DC-DC converter. It begins with an introduction to DC-DC converters and why fractional order PID controllers could improve performance over existing controllers. It then describes the mathematical model of a boost converter and proposes a fractional order PID control law. Tuning algorithms are presented to optimize the fractional orders μ and λ. Simulation and experimental results demonstrate the effectiveness of the proposed controller in providing less overshoot and faster recovery than conventional controllers under load and voltage variations.
comparative analysis of pid and narma l2 controllers for shell and tube heat...INFOGAIN PUBLICATION
The application of this paper firstly simplified mathematical model for heat exchanger process has been developed and used for the dynamic analysis and control design. A conventional PID controller and Advanced Artificial Neural Network NARMA L2 Controller for Shell and Tube heat exchanger is proposed to control the cold water outlet temperature and test the best efficiency of NARMA L2 and PID controller.The control problem formulated as outlet cold water temperature is controlled variable and the inlet hot water temperature is manipulated variable the minimum possible time irrespective of load and process disturbances.Simulation and verified the mathematical model of the controller has been done in MATLAB Simulink. From the simulation results the prime controller has been chosen by comparing the criteria of the response such as settling time, rise time, percentage of overshoot and steady state error.The Neural NetworkNARMA L2 controller is founded to give finest performance for Shell and Heat exchanger problem like temperature control. Later Need to compare Conventional PID and Advance Artificial Neural NetworkNARMA L2 Controller results which lead to decide which one is best for Chosen has a better performance than other.
Disturbance Rejection with a Highly Oscillating Second-Order Process, Part I...Scientific Review SR
This research paper aims at investigating disturbance rejection associated with a highly oscillating
second-order process. The PD-PI controller having three parameters are tuned to provide efficient rejection of a
step input disturbance input. Controller tuning based on using MATLAB control and optimization toolboxes.
Using the suggested tuning technique, it is possible to reduce the maximum time response of the closed loop
control system to as low as 0.0095 and obtain time response to the disturbance input having zero settling time.
The effect of the proportional gain of the PD-PI controller on the control system dynamics is investigated for a
gain ≤ 100. The performance of the control system during disturbance rejection using the PD -PI controller is
compared with that using a second-order compensator. The PD-PI controller is superior in dealing with the
disturbance rejection associated with the highly oscillating second-order process
This document presents a new control structure using a PID controller for load frequency control of power systems. The control structure places the PID controller in the feedback loop to improve disturbance rejection and robustness against plant parameter uncertainties. A relay feedback method is used to identify lower order transfer function models with time delay from typically higher order power system models. The PID controller parameters are then tuned using Laurent series expansion of the closed loop transfer function to provide improved performance for disturbance rejection while maintaining robustness. Simulation results on single-area and multi-area power system models demonstrate the effectiveness of the proposed control structure and PID controller design method.
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8th International Conference of Information Technology, Control and Automation (ITCA 2020) will provide an excellent international forum which contributes new results in all areas of Information Technology (IT), Control Systems and Automation Engineering. The conference focuses on all technical and practical aspects of IT, Control Systems and Automation with applications in real-world engineering and scientific problems. The goal of this conference is to bring together researchers and practitioners from academia and industry to focus on information technology, control engineering, automation, modeling concepts and establishing new collaborations in these areas.
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An angular momentum spinner includes two or more rotating arms loaded with an adjustable sliding block
for each arm and laid symmetrically about a rotating center. Each sliding block is controlled to move
along the corresponding rotating arm. Such a spinner can display the conservation of angular momentum
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A STUDY ON APPLICATION OF BAYES’ THEOREM IN APPIN TECHNOLOGYijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
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International Journal of Instrumentation and Control Systems (IJICS)ijics
International Journal of Instrumentation and Control Systems (IJICS) is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Instrumentation Engineering and Control Systems. The journal focuses on all technical and practical aspects of Instrumentation Engineering and Control Systems. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced instrumentation engineering, control systems and automation concepts and establishing new collaborations in these areas. Authors are solicited to contribute to this journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the Instrumentation Engineering.
International Journal of Instrumentation and Control Systems (IJICS)ijics
International Journal of Instrumentation and Control Systems (IJICS) is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Instrumentation Engineering and Control Systems. The journal focuses on all technical and practical aspects of Instrumentation Engineering and Control Systems. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced instrumentation engineering, control systems and automation concepts and establishing new collaborations in these areas. Authors are solicited to contribute to this journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the Instrumentation Engineering.
International Journal of Instrumentation and Control Systems (IJICS)ijics
International Journal of Instrumentation and Control Systems (IJICS)
ISSN : 2249 - 1147 [Online]; 2319 - 412X [Print]
http://airccse.org/journal/IJICS/ijics.html
Call For Papers
Important Dates
· Submission Deadline : January 11, 2020
· Acceptance Notification : February 11, 2020
· Final Manuscript Due : February 19, 2020
International Journal of Instrumentation and Control Systems (IJICS)ijics
International Journal of Instrumentation and Control Systems (IJICS) is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Instrumentation Engineering and Control Systems. The journal focuses on all technical and practical aspects of Instrumentation Engineering and Control Systems. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced instrumentation engineering, control systems and automation concepts and establishing new collaborations in these areas. Authors are solicited to contribute to this journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the Instrumentation Engineering.
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Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Nonlinear batch reactor temperature control based on adaptive feedback based ilc
1. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
DOI : 10.5121/ijics.2015.5101 1
NONLINEAR BATCH REACTOR TEMPERATURE
CONTROL BASED ON ADAPTIVE FEEDBACK-BASED
ILC
Eduardo J. Adam1
1
Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santa Fe, Argentina
ABSTRACT
This work presents the temperature control of a nonlinear batch reactor with constrains in the manipulated
variable by means of adaptive feedback-based iterative learning control (ILC). The strong nonlinearities
together with the constrains of the plant can lead to a non-monotonic convergence of the l2-norm of the
error, and still worse, an unstable equilibrium signal e∞(t) can be reached. By numeric simulation this
works shows that with the adaptive feedback-based ILC is possible to obtain a better performance in the
controlled variable than with the traditional feedback and the feedback based-ILC.
KEYWORDS
Batch reactor, Adaptive control, PID control, ILC
1. INTRODUCTION
Batch processes have received important attention during the past two decades due to incipient
chemical and pharmaceutical products, new polymers, and recent bio-technological processes.
The control of such processes is usually given as a tracking problem for a time-variant reference
trajectories defined in a finite interval. Usually, the engineers talk about that a batch process has
three operative stages clearly different, startup, batch run and, shutdown. While these three stages
are widely studied by the engineers for each particular batch process, it is important to remark
that in a widely number of cases, the most industries have managed to successfully operate these
processes, but this operation is clearly far from optimal. Only with the experience of operators
and engineers and, the repeated runs can be improved the operation control and the product
quality.
Thus, one aspect of batch operation unexplored is how the control engineer can use repetitive
nature of the operation to reach a better performance in the controlled variable. And, this is
exactly the central point in which ILC theoretical framework is supported.
ILC associates three interesting concepts. Iterative refers to a process that executes the same
setpoint trajectory over and over again. Learning refers to the idea that by repeating the same
thing, the system should be able to improve the performance. Finally, control emphasizes that the
result of the learning is used to control the plant.
For this reason, ILC constitutes the adequate theoretical framework to renew efforts in order to
study new alternatives for the batch process control.
The first contribution to ILC was introduced by Uchiyama [24]. Since then, ILC has received
considerable attention in the automatic control community. Important contributions to the ILC
2. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
2
theory appeared with [3], [5], [6], among others. The main idea behind the ILC technique is to use
the previous trail information to progressively reach a better performance with every new
iteration.
Thus, ILC has shown to be appropriate in processes whose operation is repeated over an over
again, and it found a strong application field in the robotics area because of the repetitive nature
of robot operations. Accordingly, interesting application examples are presented in the literature
such as those of [3] and [9], among others. Afterwards, other authors [13], [14], [11] and [12])
extended this idea to industrial batch processes in chemical engineering for the same reason.
While, several authors obtain interesting results when the ILC scheme is implemented in real
processes ([3]; [11]; [12]; [8]; among others), ILC can reach unsatisfactory results when the
nonlinearities are strong, due to in many cases the linearities hypothesis cannot be sustained. In
order to avoid a possible poor performance, [1], [2] and, [18] proposed to include an optimal
learning algorithm to achieve a reduction of the l2-norm of the error at each trail.
On the other hand, the idea of combining adaptive control with ILC was presented by several
authors [7]; [22]; among others) especially with robotics applications but, outside of chemical
engineering research. This paper present an adaptive feedback-based ILC scheme applied to a
batch reactor with acceptable results where the l2-norm of the error is reduced at each trail and an
almost monotonic convergence is achieved.
The organization of this work is as follows. Next section presents the non-linear batch reactor
here studied. Section 3 an Adaptive PI control is implemented. Section 4 includes a theoretical
framework presentation related to adaptive feedback-based ILC scheme here studied. Then,
Section 5 presents by means of numeric simulations the behavior of the batch reactor in closed
loop when the designer pretends to apply the adaptive ILC linear theory to a nonlinear system.
Finally, in Section 6 the conclusions are summarized.
2. NON-LINEAR BATCH REACTOR
Consider a batch reactor with a nonlinear dynamic where an exothermic and irreversible second
order chemical reaction A → B takes place. It is assumed that the reactor has a cooling jacket
whose temperature can be directly manipulated. The goal is to control the reactor temperature by
means of inlet coolant temperature. Furthermore, the manipulated variable has minimum and
maximum constrains. That is, Tcmin ≤ Tc ≤ Tcmax, Tcmin = -10, Tcmax = 20 and, Tc is written in
deviation variable.
So as to clarify the understanding of this work, the dynamic equations and the nominal values of
the batch reactor are included in this section.
The reactor dynamic is modelled by the following equations:
dt
dcA
= – k0e-ER/T
cA² ,
(1)
dt
dT
= –
Mcp
∆H
k0e-ER/T
cA² –
Mcp
UA
(T – Tc) .
(2)
Also, it must be noted that the reaction rate kinetic is rA = kcA
2
with k = k0e-E/RT
and the nominal
batch reactor values are summarized in Table 1 and, they are based on data from literature [13].
Table 1. Nominal batch reactor values.
3. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
3
parameter nomenclature value
feed concentration cAe 0.9 mol m-3
feed temperature Te 298.16 K
inlet coolant temperature Tc 298.16 K
heat transfer term UA/Mcp 0.0288 l min-1
reaction rate constant k0 4.7 10+19
l mol-1
s-1
activation energy term E/R 13550 K-1
heat reaction term ∆H/Mcp -5.79 K l mol-1
A simple test was applied for determining of the linear transfer function parameters. This test
consists of introducing a step change in cooling jacket temperature (manipulated variable) and the
reactor temperature time response is registered. This numerical experiment is showed in Fig. 1
and the nonlinearity of the batch reactor is clearly evidenced.
In Fig. 1, the reader can notice that the transfer function structure of the batch reactor changes
according to operation point of the reactor. For 28°C ≤ Tc < 31°C a good linear approximation is a
first order plus zero while, for 31°C ≤ Tc < 32°C a better approximation is a simple first order.
Thus, by simplicity and taking into a account that the batch reactor operates around 30°C, a first
order transfer function was accepted as a first approximation to tune the controller parameters
explained in the next section. Consequently, the transfer function parameters were computed
using a Matlab optimization toolbox based on a multiparametric optimization algorithm.
Accordingly, they result to be, the gain process K = 1, and the time constant T = 1.4370.
0 50 100 150 200
25
26
27
28
29
30
31
32
Time (min.)
coolingjacketandreactortemperature
cooling jacket temperature test
reactor temperature response
Figure 1. Batch reactor identification tests for different step changes in the cooling jacket temperature.
3. ADAPTIVE PI CONTROL
In this work, firstly, it is proposed to combine an on-line parameter identification of the plant in
order to implement an adaptive PI controller. The classical literature ([4]; among others) presents
two schemes clearly different to implement adaptive control, one of these is i) the Model
Reference Adaptive Control (MRAC) and the other one is ii) the Self-Tuning Regulator (STR).
4. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
4
Due to the necessity to obtain on-line process data for the implementation of the ILC (presented
in Section 4), it took advantage of these data to implement a STR scheme.
As for the identification procedure, the algorithms used for the on-line parameter estimation are
the extreme importance. Here, it is considered that the system is perfectly deterministic and there
are no disturbances and noises.
Now, consider the model,
( ) ( ) ( ) ( ) ( )ndkub++dkub=nkya++kyaky n1n −−−−−−+ LL 111 , (3)
it is possible to write in a vectorial form,
( ) ( )θkψ=ky T
, (4)
where
( ) ( ) ( ) ( ) ( ) ( )[ ]ndku,,dku,nky,,ky,ky=kψT
−−−−−−−−− LL 121 , (5)
and
[ ]n1,n b,bb,a,aa=θ LL 2,2,1, , (6)
Then, 2n parameters must be found, and in consequence, 2n data of u(k) and y(k) are necessary.
Thus, a linear equation system can be written where ai and bj are unknown parameters. That is,
( ) ( )θkψ=ky T
( ) ( )θ+kψ=+ky T
11
MM =
θΨ=Y T
kk
(7)
or well,
θΨ=Y kk (8)
where N = 2n,
( ) ( ) ( )[ ]TTTT
k N+kψ,,+kψ,kψ=Ψ 11 −L (9)
and Yk = [y(k), y(k+1), …, y(k+N-1)]T
. Then, the solution of (8) is given by,
k
1
k YΨ=θ − (10)
As a particular case, considering the transfer function of the reactor indicated in the Section 2
then, the (3) has two parameters to estimate, that is, a1 and b1. In consequence, the vectors
( )kψT
, kΨ ,and θ result to be,
( ) ( ) ( )[ ]11 −−−− ku,ky=kψT (11)
( ) ( )[ ]1+kψ,kψ=Ψ TT
k
(12)
and
[ ]T
ba=θ 11, . (13)
Finally, based on a1 and b1 it is possible to calculate K and T by means of the following
expressions,
( )11/ ab=K 1 − . (14)
and
1ln/ aT=T s− (15)
5. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
5
where Ts is the sample time.
Finally, based on the estimated parameters, it is possible to tune on line the controller parameters
following a criterion for controller design. In this work, the PI controller was designed via
optimal control theory as it is shown in the next subsection.
3.1. The Adaptive PI Implemented
The performance at steady state is extreme importance in the process control, i.e., the control
system ability to absorb disturbances without leaving the desired operating point or, reach without
error new steady state operating points.
Also, the classical literature ([17], [20] among others) presents alternative which combine an
optimal design by state feedback and offset elimination.
A new fictitious state ξ is added to a linear system under state space representation (A, B, C) (but
keeping the linearization around a fixed point) and, an augmented linear system can be defined as,
( ) )(
1
0
)(
00
0
.
.
tr+tu
B
+tx
C
A
=
ξ
x k
k
k
−
.
(16)
where is defined
( ) ( ) ( ) ( )tCxtr=tytr=ξ −−& . (17)
Here, k denote that Ak, Bk and Ck are updated at each sample time.
For this system and holding the traditional cost function given by algebraic Ricatti equation
(ARE), the resulting PI control law is
( ) ( )tξk+txk=xK=u ip−− ~ˆ . (18)
where [ ]i'k
1
kK=PBR=K ˆˆˆ −
, pk=K ,
( )
( )
tξ
tx
=x~ , with states x(t) coming from the real process
and Pˆ a solution of the ARE written with the extended linear system
− 0
0ˆ
k
k
k
C
A
=A and
0
ˆ k
k
B
=B .
Notice that, the PI control law has time variant modes as a result of solving a infinite-horizon
optimal control problem in each time interval according to identified parameter of the plant in
each instant.
Thus, the following procedure was implemented:
Design Procedure 1:
• Step 1. Using sample data, compute ( )kψT
and kΨ according to Eqs. (5) and (9) or well,
for a simple case by using Eqs. (11) and (12).
• Step 2. Compute θ with Eq. (10) and then, compute kAˆ and kBˆ and at each sampling
time.
• Step 3. Finally, compute the PI controller parameters kp and ki.
• Step 4. If t = Tf with Tf the final time for the batch reactor operation then, stop the
algorithm; the otherwise, increment the k-time and go to step 1.
6. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
6
4. LEARNING CONTROL APPLIED TO BATCH PROCESSES
4.1. The Basic Idea of the Adaptive ILC
The ILC scheme was initially developed as a feedforward action applied directly to the open-loop
system ([3], [10]). However, if the system is integrator or unstable to open loop, or well, it has
wrong initial condition, the ILC scheme to open loop can be inappropriate. Thus, the feedback-
based ILC has been suggested in the literature as a more adequate structure ([19], [15], [21],
[23]).
In this work, a traditional self-tuning regulator (STR) is combined with feedback-based ILC and,
the basic idea is shown in Fig. 2
Notice that, in the block diagram of Fig. 2 it is possible to distinguish three blocks related to: i)
data acquisition and parameters estimation of the plant, ii) adaptation mechanism for the
controller design and iii) the controller with autotuning parameters.
This scheme operates as follows. Consider a plant, which is operated iteratively with the same
setpoint trajectory over and over again, as a robot or an industrial batch process. During the i-th
trail an input-signal ui(t) is applied to the plant, producing the output signal yi(t). Both signals are
stored in the memory devise. Thus, two vectors with length Tf are available for the next iteration.
If the system of Fig. 2 operates to open loop, using ui(t) in the i+1-th trail it is possible to obtain
the same output again. But, if the i+1 iteration includes ui(t) and ei(t) information then, new
ui+1(t) and yi+1(t) can be obtained. The importance of the input-signal modification is to reduce
the tracking error as the iterations are progressively increased. That is, 01 ≥∀≤ iee i+i .
Thus, the purpose of an ILC algorithm is to find a unique equilibrium input signal u∞(t) which
minimizes the tracking error.
C P
R
Vk
Uk
Ek
Yk
Memory Device
Q
Vk+1
Parameter
Estimation
Controller
Parameter
Calculation
Figure 2. Schematic diagram of STR combined with feedback-based ILC. Here, continuous lines denote
the signals used during the k-th trail, dashed lines denote signals will be used in the next iteration and
doted lines belong to STR scheme.
Due to the existing strong nonlinearities in the chemical systems, the ILC scheme by itself cannot
lead to a monotonic decrease of the error (in many cases). For such reason, an adaptive scheme is
added in order to obtain a stable decreasing error l2-norm of the error at each trail as it shows in
the next section. The STR scheme here implemented follows the traditional recommendations
given by classical authors as [4], among others.
4.2. The Tracking ILC Formulation
The ILC formulation uses an iterative updating formula and the most common algorithm
suggested by several authors ([3], [9], [5], [23] among others) is given by
7. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
7
Vi+1 = Q(Vi, + CEi) (19)
where V1 = 0, C denotes the controller transfer function and Q is a linear filter1
.
A major issue in ILC is the convergence, and each type of ILC has its own convergence criterion.
The tracking error ei(t) is defined as
ei(t) := r(t) – yi(t) (20)
where the subscript i denotes the run number and ei represents (finite-length) output error
trajectory for i-th trail.
The idea is to find an input trajectory uk which minimizes the output error,
∥ ei ∥ → ε e
u
min= (21)
as i →∞, where ∥∥is some vector norm.
Clearly, ε is a inferior level to be reached by feedback based-ILC as i-index is increased.
DEFINITION 1. The feedback based-ILC system is said to have monotonic convergence if
∀i ≥ 0: ε ≤ ∥ei+1 ∥≤ ∥ei ∥ (22)
Then, the tracking error e∞(t) is an equilibrium signal reached by the control system if the system
has this error signal for all future trails.
DEFINITION 2. The equilibrium signal e∞(t) is said to be stable if
( ) ( ) b<tete>b>B ∞−∃∀ 00,0, => ( ) ( ) B<tetek k ∞−∀ 0, , (23)
where e0(t) is the initial tracking error.
Definition 3. An equilibrium signal e∞(t) is said to be asymptotically stable if it is stable and
( ) ( ) b<tete>b ∞−∃ 00, => ( ) ( ) 0lim =− ∞
∞→
tetei
i
(24)
The definitions presented before can be founded in the literature ([5], [16]).
Notice that, there exists a unique input u∞(t) that yields the desired output r(t), with a minimum
tracking error e∞(t).
4.3. A Simple Iterative Updating Formula
Now, Fig. 2, Ui = Vi + CEi. Then,
Vi+1 = QUi (25)
is a simple update formula in Laplace domain. Thus,
Ei+1 = S(1 – Q)R + SQEi (26)
Being Ei+1 = R - Yi+1 then,
Ei+1 = R - Yi+1 = R – PUi+1 = R - P(QUi + CEi+1) (27)
where P denotes the plant transfer function and
Ei+1(1+PC) = R – PQUi = (1 - Q)R - PQUi + QEi + PQUi (28)
Being S := 1/(1+PC) the sensitivity function, the last equation can be written as,
Ei+1 = S(1 - Q)R + SQEi (29)
According to latter equation, it is possible to write
(R - Yi+1) = S(1 - Q)R + SQ(R - Yi) (30)
and being Yi+1 = PUi+1, the last equation can be rewritten as
PUi+1 = R - S(1 - Q)R - SQR + SQPUi = TR + SQPUi (31)
where T := 1 - S is denoted as complementary sensitivity function. In consequence,
1 In this paper variables in time domain are denoted with small letters and variables in s-domain are denoted with capital letters.
8. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
8
i+i SQU+R
P
T
=U 1
(32)
Also, based on [23], the following remark for LTI system without model uncertainty can be
enunciated:
Remark 1. Consider a feedback-based ILC scheme in Fig. 2 with the updating formula (25) and
the plant is a LTI system without model uncertainty. If there exists C(s) such that the nominal
stability is satisfied, then by adopting Q such that ||SQ ||∞ ≤ 1 the tracking error is reduced as i is
increased and it is bounded for all +
i Ζ∈ and converges uniformly to
( ) ( )
−
−
= −
∞→
R
SQ
QS
Lte=te 1
ii
1
1
)(lim
i
(33)
when i → ∞ in the sense of the l2-norm.
Proof It is easy to proff this remark for nominal stability following similar steps to authors
mentioned above [23].
By similar reasoning and according to (32) and taking into account that limi →∞ Ui+1(s) = limi →∞
Ui(s) = U∞,
( ) ∞∞ SQU+R
P
T
=tU
(34)
or
( )
( )
R
SQP
T
=tU
−
∞
1
(35)
Based on E∞ = S(1 – Q)/(1 - SQ) R and (35) the following remark can be enunciated:
Remark 2. Consider the feedback-based ILC scheme in Fig. 2 with the updating formula (22)
and the plant is a LTI system without model uncertainty. If there exists C(s) such that the nominal
stability is satisfied, then by adopting Q = 1 the perfect control can be reached as i → ∞.
Proff According to (29) then E∞ = S(1 - Q)R + SQE∞. Thus, from (34) note that, if Q = 1, then E∞
= 0 and U∞ = (1/P)R, and in consequence Y∞ = R.
4.4. Adaptive PI Feedback Based-ILC
Based on the last remarks the following design procedure is enunciated:
Design Procedure 2 (Nominal Case):
• Step 1. Estimate the PI controller parameters according to Procedure 1 such that the
nominal stability, the performance and the restriction are satisfied.
• Step 2. Set Q = 1 or well Q(s) to be low pass filter such that, |Q(ω)| → 1 ∀ ω ∈ [0, ωc],
and |Q(ω)| → 0 ∀ ω > ωc with ωc a cut-off frequency.
• Step 3. Use the ILC updating formula (19) or (25).
• Step 4. Compute the control signal ui.
• Step 5. If t = Tf, where Tf is the fixed interval time for every iteration, stop the procedure;
otherwise, go to Step 1.
5. NUMERICAL SIMULATION
In this section, the non-linear batch reactor control with strong parametric uncertainty is studied
by means of numeric simulation using adaptive feedback based-ILC presented in previous
section.
9. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
9
As it was remarked above, every batch reactor has an operation sequence which consists of three
stages, start-up, run and shutdown. Assuming that, the controlled temperature inside the reactor
is monitored during these three stages and, the adaptive feedback based-ILC scheme was
implemented by means of the combination of the design procedures 1 and 2. Furthermore, an
additional hypothesis related to the batch reactor behaviour has been added. Here, it is considered
that the chemical reaction begins when the temperature inside the reactor is equal 30°C. This
consideration makes more attractive the physical system here studied.
5.1. Example 1. Without constrain in the manipulated variable
Firstly, let it considers the batch reactor presented in the Section 2 where the manipulated variable
(cooling jacket temperature) can change without saturation and, a feedback-bases ILC without
adaptive scheme is implemented, that is the PI controller has fixed parameters calculated with an
initial identification.
Figure 3 shows l2-norm2
ratio between dynamic error and the maximum l2-norm of the dynamic
error obtained when the traditional feedback is implemented alone, that is when i = 0 (|| e ||2,0).
Clearly, the || e ||2,i is reduced as k is incremented, and in consequence, the convergence of the
error is monotonic and the definitions 1, 2 and 3 could be reached.
Clearly, when there are no limits for the manipulated variable, the adaptive scheme is not
necessary because of the feedback-based ILC with fixed parameter has the capacity to control the
system in spite of non-linearities.
Notice that, ||e||2,i is approximately reduced in a more than 80% for i = 10 with respect to || e ||2,0.
In addition, the l2-norm could be further reduced because the manipulated variable can change
without saturation.
Figure 4 compares the performance obtained with the traditional feedback (i = 0) and tenth
iteration for the feedback-based ILC with PI with fixed parameter. Notice that, i) when the
feedback-based ILC is implemented during the start-up and the shutdown, the ramp tracking error
is very small; ii) the overshoot produced during the reaction starting time is reduced because of
the unbounded manipulated variable and in consequence, the system has an unbounded capacity
to extract energy; therefore, iii) l2-norm of the error is considerably reduced with only 10
iterations.
2
The l2-norm refers to the Euclidean norm defined in the traditional form.
10. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
10
0 1 2 3 4 5 6 7 8 9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Unbounded Problem
i-Iteration
||e||2,i
/||e||2,0
Figure 3. Ratio between || e ||2,i and || e ||2,0 vs. i-trail when the feedback-base ILC is implemented with an
unbounded manipulated variable.
0 50 100 150 200
24
25
26
27
28
29
30
31
32
33
34
Setpoint
SetpointandControlledTemperature(ºC)
PI with fixed parameters (i = 0)
PI with fixed parameters (i = 10)
Time (min.)
Start up Operation Shut down
Figure 4. Setpoint and controlled temperature for iteration 0 (traditional feedback) and 10 when the
manipulated variable is unbounded.
11. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
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5.2. Example 2. With constrain in the manipulated variable
Now, let it considers the same batch reactor of the previous section but now the manipulated
variable is bounded between the maximum and minimum specified in Section 2.
Figure 5 compares the performance obtained with the traditional feedback (i = 0) and tenth
iteration for the feedback-based ILC when there are constrains in the manipulated variable. For
this case, the reader can notice that the performance is not considerably improved in spite of the
control system had 10 iterations to learn.
Figure 6 shows the controlled temperature performance obtained by a traditional PI feedback and
it is compared with the one obtained by means of adaptive PI feedback-based ILC
implementation according to Section 4.4. It is possible to distinguish that the controlled
temperature can follow the reference with a acceptable exactitude when the adaptive feedback
based-ILC is implemented. Furthermore, the reader can note that there is not strong difference as
i is increased.
0 50 100 150 200
24
25
26
27
28
29
30
31
32
33
34
Setpoint
SetpointandControlledTemperature(ºC)
Time (min.)
PI with fixed parameters (i = 0)
PI with fixed parameters (i = 10)
Start up Operation Shut down
Reaction starting time
Figure 5. Setpoint and controlled temperature for iteration 0 (traditional feedback) and 10 (Feedback-based
ILC) with limit in the manipulated variable.
Figure 7 shows the dynamic errors obtained with the three cases presented in the Fig. 6. Clearly,
the dynamic error is considerably smaller when the adaptive feedback based-ILC is implemented.
12. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
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0 50 100 150 200
24
25
26
27
28
29
30
31
32
33
34
PI with fixed parameters (i = 0)
Adaptive PI (i = 2)
Adaptive PI (i = 30)
Start up Operation Shut down
Time (min.)
Reaction starting time
ReactorTemperature(ºC)
Reference
Figure 6. Controlled temperature inside the batch reactor when traditional feedback and adaptive feedback
based-ILC are implemented.
0 50 100 150 200
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Adaptive PI (i = 30)
Adaptive PI (i = 2)
PI with fixed parameters (i = 0)
Time (min.)
Errorse(t)
Figure 7. Dynamic errors for the cases studied in Fig. 6.
13. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
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From a practical point of view, the error is practically zero in almost all the time interval,
excepting a small interval associated to the reaction starting time. Neither the traditional feedback
control nor the adaptive feedback based-ILC can reject that disturbance due to the saturation of
the manipulated variable. This phenomenon is showed in Fig. 8. Notice that when the reaction
begins both control schemes try to correct the increase of temperature in the reactor, but quickly
the manipulated variable is saturated and as consequence, the peak of temperature observed
cannot be avoided. On the other hand, outside of the time interval of the manipulated variable
saturation, the correction of adaptive feedback based-ILC is better than the traditional feedback
due to the control system is learning.
0 20 40 60 80 100 120 140 160 180 200
24
26
28
30
32
34
0 20 40 60 80 100 120 140 160 180 200
-10
-5
0
5
10
15
20
Manipulated variable saturation
Time (min.)
ManipulatedVariable(ºC)ReactorTemperature(ºC)
PI with fixed parameters (i = 0)
Adaptive PI (i = 2)
Time (min.)
PI with fixed parameters (i = 0)
Adaptive PI (i = 2)
Reaction starting time
Figure 8. Temperature reaction response and manipulated variable for the traditional feedback and adaptive
feedback based-ILC during the second iteration.
Figure 9 compares the l2-norm ratio between dynamic errors obtained with the ILC schemes and
the traditional feedback as a function of the iteration index i. Here, two ILC schemes were used,
one of them was a feedback based-ILC implemented with PI controller with fixed parameter and,
the other one was a feedback based-ILC implemented with an adaptive PI controller according to
Section 3.1. Here || e ||2,i denotes the l2-norm of the error obtained with the i-iteration while, || e
||2,0 denotes the of the error obtained with the traditional feedback with PI controller with fixed
parameter.
Notice that, the feedback based-ILC scheme with fixed parameter PI controller does not have a
monotonic convergence of the || e ||2 and the Defns. 1, 2 and 3 are not satisfied. In other words,
the equilibrium signal is not stable for this case but, this fact does not imply that the control
system is unstable during the batch operation. On the contrary, when the adaptive feedback
based-ILC is implemented an almost monotonic convergence of the || e ||2 is reached. Only in few
points, the requirement || ei+1 ||2 ≤ || ei ||2 ∀ i ≥ 0 is not fulfilled but, a decreasing error is reached in
almost every iteration. Clearly, Fig. 6 is showing an improvement in the performance because of
adaptive scheme introduced. Certainly, if the designer wants a monotonic convergence of the || ei
||2, an optimal learning algorithm should be introduced as it is suggested by [1], [2] and [18]. But,
14. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
14
this last objective is not pretended in this work. Without doubt, if the optimal learning algorithm
had been implemented, the behaviour that shown in Fig. 8 could not have been manifested.
0 5 10 15 20 25 30
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
PI with fixed parameters
Adaptive PI
i-Iteration
||e||2,i
/||e||2,0
Figure 9. Ratio between || e ||2,i and || e ||2,0. Notice that, || e ||2,i is approximately reduced in a 20% for i ≥ 3
with respect to || e ||2,0. In addition, the l2-norm could not be further reduced because of the saturation of the
manipulated variable.
Finally, notice that the tracking equilibrium error does not indeed tend to zero as i → ∞ and, it is
associated to manipulated variable saturation during a small time interval. However, the only
way to extract the maximum possible energy is saturating the manipulated variable (at least for a
period of time), achieving maximum benefit in terms of energy. In other words, implementing an
optimal learning algorithm and allowing the saturation of the manipulated variable, the monotonic
convergence of the error (Defn. 1) could have been reached but, the batch reactor never will reach
|| e∞ ||2 = 0 (Defn. 3) because the system has bounded capability to extract energy. In addition, the
reader may note that the maximum possible performance and the equilibrium signal are next to
being achieved with a few iterations.
6. CONCLUSIONS
In this work firstly, it is important to remark that without the necessity of considering a robust
design, the adaptive PI feedback-based ILC was justified by means of using a nominal model
which is identified on line. Furthermore, the adaptive capacity of the control strategy is reached
because the linear model is updated at each sampling time.
Secondly, it was presented a minimal review of ILC theory and it was possible to extend
theoretical results obtained by [23] for the feedback-based ILC by introducing the Rems. 1 and 2
for a nominal case.
15. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.1, January 2015
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Based on the results from different numeric simulations, it is possible to conclude that the control
system can reach the maximum possible performance (in practical terms) with a few iterations
when the adaptive feedback-based ILC is implemented in this reactor. On the contrary, if the
feedback-based ILC is implemented alone, a stable equilibrium signal with a monotonic terminal
convergence will be little probable, especially if the non-linearities of the system are considerably
strong.
The methodology of combining the STR scheme with feedback-based ILC has showed to be an
attractive alternative for chemical engineering problems with good results.
ACKNOWLEDGEMENTS
The author would like to the Universidad Nacional del Litoral for the financial support received.
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Authors
He was born in Argentina and he received his PhD degrees at National University of
Litoral in 1996. Then, did a postdoctoral residence at University of Florida during 1999-
2000. He is involved in academic and research activities in areas such as control system
theory, robust and predictive control and fault diagnosis.