The Analysis of Controllability and Stability of an Approximate Model of Heat Transfer in an Autoclave
Sergey A. Mokrushin
Valeri S. Khoroshavin
Sergey I. Ohapkin
Alexander V. Zotov
Victor S. Grudinin
Introduction.Ensuring the safety of country food industry in terms of the duration of storage and the quality of products is impossible without sterilizing products in autoclaves. The effectiveness of the sterilization processes depends on the degree of their automation. In the last twenty years, the improvement of automatic and automated control systems was primarily based on the development of technical means for automation without theoretical justification of decision-making. The proposed work is aimed at identifying the links between the parameters and connections of the sterilization process and the choice of structural and parametric features of the control system.
Materials and Methods. A qualitative analysis is carried out based on the modern theory of automatic control for an approximative model of the thermal process of steam heating in an autoclave, taking into account the laws of heat transfer and the sufficiency of using a twodimensional model depending upon the structural and functional features of the model, which have regard to the parameters and relationships of the process, namely, the Kalman’s controllability properties of the model in the time domain in the state-space representation (the transition from the transfer function with zeros in the numerator to the normal differential system differential equations is also described). There were also analized the stability properties of the model in the frequency domain by means of transfer functions and structural transformations and the relationship of parameters in the form of inequalities with the subsequent choice of proportional-integral-differential configuration components for a real autoclave using the matrix of expert estimates.
Results. It is shown that to make a qualitatively study of the issues of controllability and stability of the approximative model of the thermal process of water heating by steam in an autoclave, depending on the process parameters, it is necessary to represent the model the time domain (in the state-space representation) and in the frequency domain (in the form of transfer functions). The analysis of the controllability of the process is based on three approaches: the first (formalized) approach is based on the representation of the model in the form of a normal system of ordinary differential equations in the Cauchy form with the development of a method of decreasing the order of the higher derivatives of coordinates and introducing additional control signals taking into account the control derivatives; the second (unformalized) is based on the exclusion of management derivatives through structural transformation; the third (direct) approach uses the first-order heat balance and heat conduction equations derived from physical considerations. Under the conditions of Kalman’s controllability, dependencies between the parameters of the process and the degree of its controllability have been obtained.The analysis of the stability of the process is based on studying the poles of the transfer functions in the frequency domain and the characteristic roots of the equations of state in the time domain. On the basis of structural transformations, a closed canister heating loop with water with inertia, depending on the autoclave charging parameters, is isolated. Transient processes in this circuit take an amplifying, aperiodic or integral character, which affects the nature of the transient processes of the control system as a whole. The formalized choice of the components of the proportional-integral-differential regulation law is carried out depending on the frequency of application of the degree of loading and the need for the components of the proportional-integral-differential regulator using the matrix of expert estimates.
Conclusions. The results of the research will serve as the material for the development of a real model of the autoclaving process, taking into account the static and dynamic characteristics of measuring, conversion and actuating elements, investigating the influence and compensation of inertia and nonlinearities of real elements, followed by the development of an automated system for controlling the sterilization process in autoclaves. The results of the work can be used to study general and applied problems of optimal control in both food and other industries, for example, in the production of building materials and the production of rubber products.
Keywords: heat transfer, heat conductivity, concentrated model, controllability, stability, transfer function, normal system of differential equations, rules for transformation of structural schemes, proportional-integral-differential regulation law, matrix of expert estimates
For citation: Mokrushin S. A., Khoroshavin V. S., Ohapkin S. I., Zotov A. V., Grudinin V. S. The Analysis of Controllability and Stability of an Approximate Model of Heat Transfer in an Autoclave. Vestnik Mordovskogo universiteta = Mordovia University Bulletin. 2018; 28(3):416–428. DOI: https://doi.org/10.15507/0236-2910.028.201803.416-428
Authors’ contribution: С. S. A. Mokrushin – process model and literature review; V. S. Khoroshavin – statement of the problem and the choice of methods of solution; S. I. Ohapkin – analysis of materials on the research topic; A. V. Zotov – controllability analysis; V. S. Grudinin – stability analysis.
All authors have read and approved the final version of the paper.
Received 06.02.2018; revised 02.04.2018; published online 20.09.2018
СПИСОК ИСПОЛЬЗОВАННЫХ ИСТОЧНИКОВ
1. Asmaev M. P., Lebed B. N., Vyskubov Ye. V. [Structural-parametric identification of the model of the process of canning sterilization in batch autoclaves]. Izvestiya vuzov. Pishchevaya tekhnologiya = Proceedings of High Schools. Food Technology. 1996; 1–2:48–50. (In Russ.)
2. Filimonov A. B., Filimonov N. B. Concerning the problems of synthesis of coordinated systems of automatic control. Izvestiya YuFU. Tekhnicheskie nauki = Izvestiya SFedU. Engineering Sciences. 2012; 128(3):172–180. (In Russ.)
3. Mokrushin S. A. Sterilization of canning products. Avtomatizatsiya i proizvodstvo = Automation and Production. 2010; 1(10):30–31. (In Russ.)
4. Kirgin D. S. Control algorithms for the technological process of vulcanization of autoclave installation. Vestnik IrGTU = Irkutsk State Technical University Bulletin. 2011; 55(8):195–199. (In Russ.)
5. Mokrushin S. A., Khoroshavin V. S., Filatova Ye. S., Rusyaeva T. L. Management of food processing processes. Sovremennye problemy nauki i obrazovaniya = Modern Problems of Science and Education. 2012; 6.
6. Kaychenov A. V., Vlasov A. V., Vlasova A. R., Grokhovskiy V. A., Kuranova L. K. Comparison of modernized and traditional ways of sterilization of canned food. Vestnik MGTU = Bauman Moscow State Technical University Bulletin. 2013; 16(3):560–565.
7. Mokrushin S. A., Ohapkin S. I., Khoroshavin V. S. Investigation of the process of sterilization of canning products for the purpose of further automation. Nauchnyy zhurnal NIU ITMO. Ser. “Protsessy i apparaty pishchevykh proizvodstv” = Scientific Journal NRU ITMO. Series “Processes and Food Production Equipment”. 2015; 4:62–72.
8. Klymenko O., Tregub V. Mathematical modeling of periodic processes in counterpressure autoclaves. Naukovі pratsі NUKhT = Scientific Works of National University of Food Technologies. 2014; 20(6):14–20.
9. Taricco T. Autoclave cure systems. ASM International, Engineered Materials Handbook. 1987; 1:645–648.
10. Gonçalves E. C., Minim A., Coimbra J. S. R., Minim V. P. R. Modeling sterilization process of canned foods using artificial neural networks.Chemical Engineering and Processing: Process Intensification. 2005; 44(12):1269–1276.
11. Khoroshavin V. S., Zotov A. V., Mokrushin S. A. Khoroshavin V. S., Zotov A. V., Mokrushin S. A. Advance Science. 2017; 2.
12. Pikina G. A., Burtseva Yu. S. Non-search tuning of linear regulators to a minimum of the quadratic criterion. Teploenergetika = Heat Power Engineering. 2014; 3:23–27.
13. Alonso A. A., Banga J. R., Perez-Martin R. Modeling and adaptive control for batch sterilization. Computers & Chemical Engineering. 1998; 22(3):445–458
This work is licensed under a Creative Commons Attribution 4.0 License.