Nonisothermal control of a batch reactor with exothermic reaction using a mathematical model

1986 ◽  
Vol 51 (6) ◽  
pp. 1268-1278
Author(s):  
Josef Horák ◽  
Petr Beránek ◽  
Dagmar Maršálková
Keyword(s):  
Mathematical Model ◽  
Temperature Difference ◽  
Control Algorithm ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Coolant Temperature ◽  
Inlet Temperature ◽  
A Value ◽  
Total Model

A method of nonisothermal control of a batch reactor with exothermic reaction is suggested and tested. The control algorithm is based on jump changes in the inlet temperature of coolant, which is chosen so that the highest difference between the temperature of the reaction mixture and the temperature of entering coolant is held at a value near the highest temperature difference at which the stable pseudostationary state still exists. A total model of the system is used for the prediction of the entering coolant temperature.

Intensification of cooling in a batch reactor with an exothermic reaction by nonisothermal control in stable pseudostationary states

1984 ◽  
Vol 49 (11) ◽  
pp. 2566-2578 ◽  
Author(s):  
Josef Horák ◽  
Petr Beránek ◽  
Dagmar Maršálková
Keyword(s):  
Batch Reactor ◽  
Exothermic Reaction ◽  
Reaction Model ◽  
Order Reaction ◽  
Zero Order ◽  
Coolant Temperature ◽  
Inlet Temperature ◽  
Adaptive Parameter ◽  
Zero Order Reaction ◽  
Set Up

An algorithm is set up and tested for the temperature control of a batch reactor consisting in jump changes in the inlet temperature of entering coolant. This temperature is so chosen that its difference from the temperature of the reaction mixture is near the highest difference at which the stable pseudostationary state of the system still exists. For the prediction of the new coolant inlet temperature, a zero-order reaction model is used with an adaptive parameter estimated from the experimentally established value of the maximum of the reaction mixture overheating at the previous coolant temperature.

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.

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.

Nonisothermal control of batch reactor with reaction by digital computer. Experimental verification of the control algorithm based on mathematical model of the system

1983 ◽  
Vol 48 (9) ◽  
pp. 2473-2483
Author(s):  
František Jiráček ◽  
Josef Horák
Keyword(s):  
Mathematical Model ◽  
Heat Carrier ◽  
Reaction Temperature ◽  
Flow Rate ◽  
Control Algorithm ◽  
Operating Temperature ◽  
Batch Reactor ◽  
Time Derivative ◽  
Reactor Model ◽  
Operating Reactor

Two-position feedback temperature control of the mixture in a batch reactor with the strongly exothermic autocatalytic reaction is studied. The control is based on continuous measurement of reaction temperature, evaluation of its time derivative and periodical determination of conversion of the reactant. On basis of numerical solution of equations of the mathematical model of the reactor is then evaluated the highest operating temperature of the mixture at which is still secured a safe operation of the reactor and trajectories along which the given operating temperature could be reached in the shortest time period. The manipulated variable was the flow rate of heat carrier into the cooler. Sampling of the reaction temperature and two-position switching over of flow rate of the heat carrier was performed in real time by use of the digital measuring center Hewlett-Packard 3052A. In the experiments has been verified the effect of changes in reactivity of the mixture, accuracy of the mathematical reactor model and effect of additional noise in the measured reaction temperature on control safety. Results of the experiments have proved that the proposed control algorithm enables safe control of the reaction temperature also in cases when the operating reactor states are unstable at the open control loop and when the cooler has a slow response to changes in the manipulated variable.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

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.

Construction of an Elementary Model for the Dynamic Analysis of a Pressurized Water Reactor

2013 ◽  
Vol 284-287 ◽  
pp. 652-656 ◽  
Author(s):  
Chiung Wen Tsai ◽  
Chun Kuan Shih ◽  
Jong Rong Wang
Keyword(s):  
Transfer Functions ◽  
Feedback Loops ◽  
Dynamic Responses ◽  
Coolant Temperature ◽  
Inlet Temperature ◽  
Pressurized Water Reactor ◽  
Elementary Model ◽  
Pressurized Water ◽  
Water Reactor ◽  
Neutron Kinetics

A lumped-parameter numerical model was constructed based on the conservation laws of mass and energy and the point neutron kinetics with 6 groups of delayed neutron to represent the dynamics of primary loop of a pressurized water reactor (PWR) core. On the viewpoint of control theory, the coupled phenomenon of neutron kinetics and thermohydraulics can be recognized as a dynamic system with feedback loops which is caused by the Doppler effect and the coolant temperature difference. Scilab was implemented to representing the equivalent transfer functions and associated feedback loops of a PWR core. The dynamic responses were performed by the perturbations of coolant inlet flow, coolant inlet temperature, and reactivity insertion.

Increasing the mobility of a high-speed tracked vehicle based on a controlled skid algorithm

2020 ◽  
pp. 29-33
Author(s):  
S. V. Kondakov ◽  
O.O. Pavlovskaya ◽  
I.D. Ivanov ◽  
A.R. Ishbulatov
Keyword(s):  
Mathematical Model ◽  
Dynamic Stability ◽  
Simulation Modeling ◽  
Automatic System ◽  
High Speed ◽  
Control Algorithm ◽  
Loss Of Stability ◽  
Tracked Vehicle ◽  
Hydrostatic Transmission ◽  
The Mathematical Model

A method for controlling the curvilinear movement of a high-speed tracked vehicle in a skid without loss of stability is proposed. The mathematical model of the vehicle is refined. With the help of simulation modeling, a control algorithm is worked out when driving in a skid. The effectiveness of vehicle steering at high speed outside the skid is shown. Keywords: controlled skid, dynamic stability, steering pole displacement, hydrostatic transmission, automatic system, fuel supply. [email protected]

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