A feedback temperature control in a chemical reactor with high inertia of its cooling system

1984 ◽  
Vol 49 (7) ◽  
pp. 1642-1652 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Mathematical Model ◽  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Time Derivative ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
The One ◽  
The Mathematical Model ◽  
The Given

In this work we compare simple algorithms for the one-off feedback temperature control of the reaction mixture in a batch reactor during an exothermic reaction. The aim of the control was to maintain the temperature of the mixture within the given range, and simultaneously, to minimize the number of the regulator switchings. The temperature control of the mixture was being performed at conditions when working states of the reactor in an open regulation loop are unstable and when the response of the cooler to regulation is slow. The following control algorithms were compared: P - regulator, PD - regulator and algorithms based on a prediction mathematical model including its adaptive variant. The results indicate that the algorithms based on the mathematical model are more efficient. However, the precision of the control can be diminished due to error in the time derivative of the temperature of the reaction mixture which forms the input to the prediction model. The adaptive variant of the algorithms was advantageous in cases when it was necessary to make up for significant errors in initial estimates of parameters of the prediction mathematical model.

A simplified method of temperature control maximizing productivity of the batch reactor; The effect of inertia of the cooling system

1982 ◽  
Vol 47 (2) ◽  
pp. 454-464 ◽  
Author(s):  
František Jiráček ◽  
Josef Horák
Keyword(s):  
Mathematical Model ◽  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Cooling Capacity ◽  
Variable Activity ◽  
Simplified Method ◽  
Opening And Closing ◽  
Time Of Operation

The effect has been studied of the inertia of the cooling system on the reliability of control of the temperature of the reaction mixture. The study has been made using a mathematical model of the batch reactor with an exothermic reaction. The temperature has been controlled by a two-level controller opening and closing the flow of the coolant. The aim of the control has been to maintain a constant value of the degree of utilization of the cooling capacity of the reactor. The instantaneous value of the degree of utilization has been assessed from the ratio of times for which the cooling system is idle to the time of operation. The reliability of control has been studied for variable activity of the catalyst.

Temperature control in chemical reactors with slow response of the cooling system; Definition of coefficients of control safety

1983 ◽  
Vol 48 (3) ◽  
pp. 711-721 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček
Keyword(s):  
Temperature Control ◽  
Cooling System ◽  
Operating Temperature ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
Loop Control ◽  
Information Safety ◽  
Definition Of ◽  
Reactor Operating

Coefficients of static, dynamic and information safety are defined. They cold be used for consideration of how difficult is the feedback of temperature control in a chemical reactor with exothermic reaction. An analysis is made for a batch reactor which should be kept in a pseudostationary state which is unstable at the open control loop. Control is based on measurement of the reaction mixture temperature and on evaluation of temperature derivative with time. The action quantity is flow rate of the carrier in the cooling system. The result of an analysis is the highest operating temperature of the mixture at which the safety of the reactor operation is still secured and further the trajectory on which it is possible to reach in the shortest time the given operating temperature at preserving safety of the reactor operating.

scholarly journals Methodology of Supervision by Analysis of Thermal Flux for Thermal Conduction of a Batch Chemical Reactor Equipped with a Monofluid Heating/Cooling System

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Ghania Henini ◽  
Fatiha Souahi ◽  
Ykhlef Laidani
Keyword(s):  
Thermal Conduction ◽  
Cooling System ◽  
Batch Reactor ◽  
Thermal Flux ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
Thermal Control ◽  
Ride Quality ◽  
Heating And Cooling

We present the thermal behavior of a batch reactor to jacket equipped with a monofluid heating/cooling system. Heating and cooling are provided respectively by an electrical resistance and two plate heat exchangers. The control of the temperature of the reaction is based on the supervision system. This strategy of management of the thermal devices is based on the usage of the thermal flux as manipulated variable. The modulation of the monofluid temperature by acting on the heating power or on the opening degrees of an air-to-open valve that delivers the monofluid to heat exchanger. The study shows that the application of this method for the conduct of the pilot reactor gives good results in simulation and that taking into account the dynamics of the various apparatuses greatly improves ride quality of conduct. In addition thermal control of an exothermic reaction (mononitration) shows that the consideration of heat generated in the model representation improve the results by elimination any overshooting of the set-point temperature.

Adaptive temperature control in chemical reactors a simplified method maximizing productivity of the batch reactor

1982 ◽  
Vol 47 (1) ◽  
pp. 251-261 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Mathematical Model ◽  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Cooling Capacity ◽  
Present Value ◽  
Chemical Reactors ◽  
Exothermal Reaction ◽  
Variable Activity ◽  
Simplified Method

A simplified method has been proposed in the paper of adaptive temperature control in a batch reactor with an exothermal reaction. The control has been effected by a two-level controller enabling the degree of utilization of the cooling capacity of the reactor to be maintained on a present value. The degree of utilization of the cooling capacity was evaluated from the ratio of the time for which the cooling system was in action to that during it was idled. The method has been applied to reactors with a small inertia of the cooling system. The study has been based on the simulation by a mathematical model of the system. Experimental verification of results of the simulation has been caried out a laboratory batch reactor with variable activity of the catalyst.

A two-point regulator control of a chemical reactor; Cooling system with a large inertia - PD algorithm

1983 ◽  
Vol 48 (9) ◽  
pp. 2627-2635 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Chemical Reactor ◽  
Slow Response ◽  
Practical Utilization ◽  
Laboratory Scale Reactor ◽  
Combined Simulation ◽  
Rate Of Response

The effect has been investigated of the gain of the derivative element of a PD controller on the quality of the temperature control of an exothermal reaction mixture in a batch reactor. The investigation concerned a reactor equipped with a cooling system whose rate of response could be varied in the range of several orders of magnitude. The results have lead to the conclusion that a slow response of the coolong system is difficult to make up for by using more sophisticated control algorithms. For the slow response of the cooling system the range of gain of the controller providing for a safe temperature control is narrow leaving essentially no margin for its practical utilization. The study combined simulation on a mathematical model with experimental verification of a laboratory scale reactor cooled by a submersible retractable cooler.

Temperature control in a chemical reactor through variable area of the heat transfer surface. Experimental verification

1982 ◽  
Vol 47 (2) ◽  
pp. 446-453
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Batch Reactor ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
Open Loop ◽  
Heat Transfer Surface ◽  
Laboratory Reactor ◽  
Hysteresis Control ◽  
Relay With Hysteresis ◽  
Rate Of Response ◽  
The Ideal

A possibility has been tested in the paper of the feed back control of temperature of the reaction mixture in a batch reactor with an exothermic reaction through the variable area of the cooling surface. The measurement were carried out in a laboratory reactor with a retractable cooler which was being immersed into the reaction mixture. The speed of motion of the cooler was sufficiently high permitting the process of immersion to be regarded as practically instantaneous. The aim of the control was to stabilize the set point temperature of the reaction mixture by a two-point controler. In dependence on the rate of response of the system to a change of the section variable either the ideal relay or the relay with hysteresis control algorithmus were used. The results of measurements showed that with the aid of a retractable cooler the temperature could be controlled safely even in those cases, in which the control by the variable flow rate of the coolant was unfeasible. The verification was carried out in the open-loop instable operating point of the reactor.

scholarly journals Mathematical modeling of physical processes in the complex for testing of induction machines

2018 ◽  
Vol 239 ◽  
pp. 01055 ◽  
Author(s):  
Viktor Kharlamov ◽  
Denis Popov
Keyword(s):  
Mathematical Model ◽  
Frequency Converter ◽  
Electrical Energy ◽  
Induction Machines ◽  
Test Scheme ◽  
Load Testing ◽  
Variable Parameters ◽  
Asynchronous Machines ◽  
The Mathematical Model ◽  
The Given

The paper is devoted to the simulation of the test complex designed for energy-efficient load testing of induction machines by the method of mutual load with the exchange of electrical energy through the network. It is noted that for other similar test schemes, the mathematical model will have a slightly different form, but it will be identical in terms of asynchronous machines, network and frequency converter. The compiled mathematical model of the test complex allows studying the variable parameters of the system in all elements of the test scheme in static and dynamic modes of operation as well. The synthesized mathematical model can be used to determine the parameters of the equipment in the designed test complexes if the parameters of the test and load machines are known. The results of simulation of the test complex for the given parameters of the test and load induction machines are obtained.

Mathematical model of the artificial muscle with two actuators

2020 ◽  
pp. 095440622094156
Author(s):  
Ljubinko B Kevac ◽  
Mirjana M Filipovic ◽  
Ana M Djuric
Keyword(s):  
Mathematical Model ◽  
Control Structure ◽  
Artificial Muscle ◽  
Parallel Robot ◽  
Simulation Results ◽  
Proportional Derivative Controller ◽  
Definition Of ◽  
The Mathematical Model ◽  
The Given ◽  
Very High

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

scholarly journals Chaos Predictability in a Chemical Reactor

2020 ◽  
Vol 30 (11) ◽  
pp. 2050221
Author(s):  
Marek Berezowski
Keyword(s):  
Mathematical Model ◽  
Chemical Reactor ◽  
Transient Chaos ◽  
Distant Future ◽  
State Variable ◽  
First Case ◽  
Start Up ◽  
System Temperature ◽  
Intermittent Chaos ◽  
The Mathematical Model

The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor.

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