Applicability analysis of the Laplace integral in evaluating output signals for automatic systems
/ 0
- Details
- Category: Information Technologies
- Last Updated on 07 May 2019
- Published on 24 April 2019
- Hits: 2721
Authors:
A. I. Shvachka, Cand. Sc. (Tech.), orcid.org/0000-0003-1076-6950, State Higher Educational Institution “Ukrainian State University of Chemical Technology”, Dnipro, Ukraine, e‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.
Yu. K. Taranenko, Dr. Sc. (Tech.), Prof., orcid.org/0000-0003-4072-
O. Yu. Oliynik, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0003-2666-3825, State Higher Educational Institution “Ukrainian State University of Chemical Technology”, Dnipro, Ukraine, e‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.
Ye. V. Chernetskyi, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0002-4197-7171, State Higher Educational Institution “Ukrainian State University of Chemical Technology”, Dnipro, Ukraine, e‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.
Abstract:
Purpose. Solving a topical scientific problem of boosting the automatic system accuracy and performance by evaluating the Laplace integral using numerical methods to define transient characteristics in the context of alternating disturbance.
Methodology. Simulation and mathematical modeling methods, the Fourier and Laplace transform apparatus as well as mathematical statistics are at the core of the present research.
Findings. The influence of using the inverse Laplace integral resulted from numerical method calculations on the building accuracy of an automatic control system’s transient characteristic was considered compared to the test dependency. Introducing the Laplace integral enables to implement the transition from the time domain to the frequency domain, and it positively affects the calculation accuracy as compared with the calculations that make use of the Fourier integral. The practicability of using the Laplace integral was proved for numerical transformation of transfer functions of the automatic control system components from the frequency to the time domain which could provide higher accuracy and performance of the system compared with the numerical calculations based on the Fourier integral.
Originality. Within the scope of the research, the use of the Laplace integral in the methods for numerical solving of differential equations of linear systems received solid scientific support, which enables to effectively evaluate the type of the transient characteristic in the course of the technological process and ensures its stability and quality improvement as the process load varies.
Practical value. The decrease in the resulting error rate for solving the differential equation of the system based on the inverse Laplace integral in relation to the test characteristic (the known table equation of the transient process characteristic according to the given research variant) as well as the stability of the transient characteristic of the system is shown. Therefore, as an applied aspect of using the resulting data obtained in the course of the research, we may consider the ability to further improve the principle of retrieving the transient characteristic of a control system. This creates a background of transferring the discovered technological solutions into the field of technical cybernetics.
References.
1. Nikolsky, V., Oliynyk, O., Shvachka, A. and Nachovny, I., 2017. Thermal treatment of concentrated liquid toxic waste and automatic control of process efficiency. Eastern-European Journal of Enterprise Technologies. Ecology, 5/10(89), pp. 26‒31. DOI: 10.15587/1729-4061.2017.111846.
2. Kamenskii, S., 2017. Systems of automatic control, mechatronics and robotics: monograph. Novosibirsk:NSTU Publishing House.
3. Kim, D., 2014. Algebraic methods for the synthesis of automatic control systems: monograph. Moscow:FIZMATLIT.
4. Dovhopolyi, Ya., Manko, G., Trishkin, V. and Shvachka, A., 2017. Development of the program for self-tuning a proportal-integral-differential controller with an additional controlling action. Eastern-European Journal of Enterprise Technologies. Information technology. Industry control systems, 6/2(90), рр. 61‒66. DOI: 10.15587/1729-4061.2017.114333.
5. Filobello-Nino, U., Vazquez-Leal, H., Sarmiento-Reyes, A., Cervantes-Perez, J., Perez-Sesma, A., Jimenez-Fernandez, V., Pereyra-Diaz, D., Huerta-Chua, J., Morales-Mendoza, L., Gonzalez-Lee, M. and Castro-Gonzaleza, F., 2017. Laplace transform–homotopy perturbation method with arbitrary initial approximation and residual error cancellation. Applied Mathematical Modelling, 41, pp. 180‒194. DOI: 10.1007/s40314-013-0073-z.
6. Lotfi, М., Mezrigui, L. and Heyd, R., 2016. Study of heat conduction through a self-heated composite cylinder by Laplace transfer functions. Applied Mathematical Modelling, 40, рр. 10360‒10376. DOI: 10.1016/ J.APM.2016.07.012.
7. Uribe-CamposFelipe, A., 2014. Laplace Synthesis Validation through Measurements on Underground Transmission Cables. Ingeniería, Investigación y Tecnología, 15, рр. 575‒584. DOI: 10.1016/S1405-7743(14)70655-9.
8. Adamek, V., Vales, F. and Cerv, J., 2017. Numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms. Advances in Engineering Software, 113, рр. 120‒129. DOI: 10.1016/j.advengsoft.2016.10.006.
9. Linge, S. and Langtangen, H., 2016. Programming for Computations ‒ Python: A Gentle Introduction to Numerical Simulations with Python. Switzerland:Springer International Publishing.
10. Lubentsova, E., 2014. Control systems with dynamic structure choice, fuzzy logics and neural network models. Stavropol: SKFU.
Archive