MODELING AND TUNING CONTROL OBJECTS WITH NONLINEAR DYNAMICS

UDC 681.53

  • Hryniuk Dzmitry Anatol’yevich – – PhD (Engineering), Associate Professor, Assistant Professor, the Department of Automation of Production Processes and Electrical Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: hryniuk@tut.by

  • Oliferovich Nadezhda Mikhaylovna – Assistant Lecturer, the Department of Automation of Production Processes and Electrical Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: oliferovich@belstu.by

  • Suhorukova Irina Gennad’yevna – Senior Lecturer, the Department of Software Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: irina_x@rambler.ru

DOI: https://doi.org/10.52065/2520-6141-2021-248-2-65-71

Key words: nonlinear dynamics, regulator tuning, transient process.

For citation: Hryniuk D. A., Oliferovich N. M., Suhorukova I. G., Orobei I. O. Modeling and tuning control objects with nonlinear dynamics. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 2 (248), pp. 65–71 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2021-248-2-65-71.

Abstract

The article deals with the problems of analysis of nonlinear control objects. A class of objects, which in the range of possible regulation have a known dependence of the dynamics on the output parameter, is studied. Examples of such objects are given and a structure for their modeling is proposed.

The carried out simulation modeling of a second-order control object with a linear dependence of the time constant on the output parameter demonstrated the asymmetry of the obtained transfer functions along the control channel and a high dependence on the range of the study. At the same time, with an increase in one direction, the presence of a dominant time constant is observed, while in the opposite direction, the minimization of the root-mean-square deviation leads to second-order transfer functions with equal values of the time constant. And even so, the value of the standard deviation of the approximation has a worse value than in the first case.

For the investigated example, the control loop was tuned from the previously obtained transfer functions of the object. To adjust different options, the same integral criterion was used on the proposed nonlinear structure. Transient analysis showed different quality when changing the direction of the task signal. From this, it is concluded that it is rational to have a set of control settings, and change the parameters when changing the direction of exposure. In the extended version, you can change the settings not only when changing the sign, but also the coordinates, as is already used in the table management of industrial systems.

The developed version of the analysis is an intermediate version between the linearization of nonlinear control objects and the use of solving partial differential equations.

Download

References

  1. Hangos K.M., Cameron I.T. Process modelling and model analysis. San Diego, Academic Press Publ., 2001. 543 p.
  2. Smedsrud H. Dynamic model and control of heat exchanger networks. 5th year project work. Norwegian University of Science and Technology. Department of Chemical Engineering Publ., 2007. 50 p.
  3. Dorfman K. D., Prodromos D. Numerical Methods with Chemical Engineering Applications. Cambridge University Press Publ., 2017. 511 p.
  4. Bequette B. W. Process Control: Modeling, Design and Simulation. Upper Saddle River, N. J., Prentice Hall PTR Publ., 1998. 621 p.
  5. Mikles J., Fikar M. Process Modelling, Identification, and Control. Springer-Verlag Berlin Heidelberg Publ., 2007. 497 p.
  6. Boufadene M. Nonlinear Control Systems Using MATLAB. CRC Press. Taylor & Francis Group Publ., 2018. 58 p.
  7. Vepa R. Nonlinear Control of Robots and Unmanned Aerial Vehicles An Integrated Approach. CRC Press. Taylor & Francis Group Publ., 2016. 544 p.
  8. Baldea M., Daoutidis P. Dynamics and Nonlinear Control of Integrated Process Systems. Cambridge, Cambridge University Press Publ., 2012, pp. 2012–257.
  9. Lisauskas, S., Udris, D. and Uznys, D. Direct Torque Control of Induction Drive Using Fuzzy Controller. Elektronika ir Elektrotechnika, 2013, vol. 19 (5), pp. 13‒16.
  10. M. Marozava, D. Hryniuk. Experimental study of the variation dynamic’s for air heat exchanger. Mokslas – Lietuvos ateitis. Science – Future of Lithuania, 2017, vol. 9, no. 3, pp. 297–301.
  11. Hrinyuk D. A. Suhorukova I. G., Oliferovich N. M., Stabletskiy V. A. Assessment of the dynamics of temperature changes along the length of the metal rod. Avtomatizatsiya i energosberezheniye mashinostroitel’nogo i metallurgicheskogo proizvodstv, tekhnologiya i nadezhnost' mashin, priborov i oborudovaniya: materialy Mezhdunar. nauch.-tekhn. konf. [Automation and energy saving of machine-building and metallurgical industries, technology and reliability of machines, instruments and equipment: materials of the XIII International Scientific and Technical Conference]. Vologda, 2018, pp. 85–88 (In Russian).
  12. Hryniuk D., Suhorukova I., Oliferovich N., Orobei I. Complex tuning of the PID controller according to integral criteria. Open Conference Electrical, Electronic and Information Sciences (eStream). Vilnius, 2018, pp. 1–4. DOI: 10.1109/eStream.2018.8394117.
  13. Hryniuk D., Suhorukova I., Orobei I. Non-linear PID controller and methods of its setting. Open Conference Electrical, Electronic and Information Sciences (eStream). Vilnius, 2017, pp. 1–4. DOI: 10.1109/eStream.2017.7950327.
  14. Suhorukova I. G., Hryniuk D. A., Orobei I. O. Application of non-linear error conversion functions in the PID law. Trudy BGTU [Proceedings of BSTU], 2013, no. 6: Physics and Mathematics. Informatics, pp. 95–98 (In Russian).
15.06.2021