Synthesis and implementation of λ-approach of slide control in heat-consumption system
https://doi.org/10.17586/2226-1494-2022-22-3-501-508
Abstract
The paper proposes an essentially new approach to synthesis and implementation of dynamic objects with three-position relay control. The approach consists in organization of differentiation procedure on the relay element involved into feedback. We considered synthesis of the relay element feedback in tasks of robust and time optimal control of heatconsumption systems. To demonstrate the effectiveness of the proposed approach, a comparative assessment of the results of modeling heat consumption systems with three-position relay control and a traditional linear–quadratic regulator is presented. We attached transient processes plots of active heat-consumption systems which confirm the effectiveness of the synthesized relay control.
About the Authors
A. A. ShilinRussian Federation
Aleksandr A. Shilin — D. Sc. (Eng.), Professor; Software Engineer
Tomsk, 643050
Tomsk, 634009
sc 56330899200
V. G. Bukreev
Russian Federation
Viktor G. Bukreev — D. Sc., Full Professor
Tomsk, 643050
sc 7005611043
F. V. Perevoshchikov
Russian Federation
Filipp V. Perevoshchikov — Student
Tomsk, 643050
sc 57216875510
References
1. Poznyak A.S. Sliding mode control in stochastic continuos-time systems: μ-zone MS-convergence. IEEE Transactions on Automatic Control, 2017, vol. 62, no. 2, pp. 863–868. https://doi.org/10.1109/TAC.2016.2557759
2. Alibeji N., Sharma N. A PID-type robust input delay compensation method for uncertain Euler-Lagrange systems. IEEE Transactions on Control Systems Technology, 2017, vol. 25, no. 6, pp. 2235–2242. https://doi.org/10.1109/TCST.2016.2634503
3. Guo X., Ren H.P. Robust variable structure control for three-phase PWM converter. Zidonghua Xuebao/Acta Automatica Sinica, 2015, vol. 41, no. 3, pp. 601–610. (in Chinese). https://doi.org/10.16383/j.aas.2015.c140421
4. Zhu Q.D., Wang T. An improved design scheme of variable structure control for discrete-time systems. Zidonghua Xuebao/Acta Automatica Sinica, 2010, vol. 6, no. 6, pp. 885–889. (in Chinese). https://doi.org/10.3724/SP.J.1004.2010.00885
5. Parra-Vega V., Fierro-Rojas J.D. Sliding PID uncalibrated visual servoing for finite-time tracking of planar robots. Proc. of the 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), 2003, vol. 3, pp. 3042–3047. https://doi.org/10.1109/ROBOT.2003.1242058
6. Choi H.H. LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems. IEEE Transactions on Automatic Control, 2007, vol. 52, no. 4, pp. 736–742. https://doi.org/10.1109/TAC.2007.894543
7. Huang Y. J., Kuo T.C., Chang S.H. Adaptive sliding-mode control for nonlinear systems with uncertain parameters. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2008, vol. 38, no. 2, pp. 534–539. https://doi.org/10.1109/TSMCB.2007.910740
8. Abdulgalil F., Siguerdidjane H. PID based on sliding mode control for rotary drilling system. Proc. of the EUROCON 2005 — The International Conference on “Computer as a Tool”, 2005, vol. 1, pp. 262–265. https://doi.org/10.1109/EURCON.2005.1629911
9. Utkin V. I. Sliding Modes in Control and Optimization. Berlin, Germany, Springer, 1992, 299 p.
10. Li X.B., Ma L., Ding S.H. A new second-order sliding mode control and its application to inverted pendulum. Zidonghua Xuebao/Acta Automatica Sinica, 2015, vol. 41, no. 1, pp. 193–202. (in Chinese). https://doi.org/10.16383/j.aas.2015.c140263
11. Li Y., Xu Q. Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezodriven micromanipulator. IEEE Transactions on Control Systems Technology, 2010, vol. 18, no. 4, pp. 798–810. https://doi.org/10.1109/ TCST.2009.2028878
12. Mu C.X., Yu X.H., Sun C.Y. Phase trajectory and transient analysis for nonsingular terminal sliding mode control systems. Zidonghua Xuebao/Acta Automatica Sinica, 2013, vol. 39, no. 6, pp. 902–908. (in Chinese). https://doi.org/10.3724/SP.J.1004.2013.00902
13. Bartolini G., Pydynowski P. An improved, chattering free, V.S.C. scheme for uncertain dynamical systems. IEEE Transactions on Automatic Control, 1996, vol. 41, no. 8, pp. 1220–1226. https://doi.org/10.1109/9.533691
14. Bartolini G., Ferrara A., Usai E. Chattering avoidance by secondorder sliding mode control. IEEE Transactions on Automatic Control, 1998, vol. 43, no. 2, pp. 241–246. https://doi.org/10.1109/9.661074
15. Bartolini G., Ferrara A., Usai E., Utkin V.I. On multi-input chatteringfree second-order sliding mode control. IEEE Transactions on Automatic Control, 2000, vol. 45, no. 9, pp. 1711–1717. https://doi.org/10.1109/9.880629
16. Zhang Y., Ma G.F., Guo Y.N., Zeng T.Y. A multi power reaching law of sliding mode control design and analysis. Zidonghua Xuebao/Acta Automatica Sinica, 2016, vol. 42, no. 3, pp. 466–472. (in Chinese). https://doi.org/10.16383/j.aas.2016.c150377
17. Kim N., Cha S., Peng H. Optimal control of hybrid electric vehicles based on Pontryagin’s minimum principle. IEEE Transactions on Control Systems Technology, 2011, vol. 19, no. 5, pp. 1279–1287. https://doi.org/10.1109/TCST.2010.2061232
18. Klyuev A.S., Kolesnikov A.A. Optimization of Automatic Control Systems by Speed. Moscow, Energoizdat, 1982, 239 p. (in Russian)
19. Kirk D.D. Optimal Control Theory. An Introduction. Englewood Cliffs, NJ, Prentice-Hall, 1970, 472 p.
20. Li Y., Wang Z., Zhu L. Adaptive neural network PID sliding mode dynamic control of nonholonomic mobile robot. Proc. of the IEEE International Conference on Information and Automation, 2010, pp. 753–757. https://doi.org/10.1109/ICINFA.2010.5512467
21. Khalil H.K. Nonlinear Systems. 3nd ed., Upper Saddle River, NJ, Prentice Hall, 2002, 750 p.
22. Liu T., Liu H.P. Quasi-sliding-mode control based on discrete reaching law with dead zone. Zidonghua Xuebao/Acta Automatica Sinica, 2011, vol. 37, no. 6, pp. 760–766. (in Chinese). https://doi.org/10.3724/SP.J.1004.2011.00760
23. Shilin A.A., Bukreev V.G. The reduction of the multidimensional model of the nonlinear heat exchange system with delay. Communications in Computer and Information Science, 2014, vol. 487, pp. 387–396. https://doi.org/10.1007/978-3-319-13671-4_44
24. Shilin A.A., Bukreev V.G., Prohorov S. Pressure pump power control in the primary circuit of the heat exchange system. MATEC Web of Conferences, 2016, vol. 91, pp. 01043. https://doi.org/10.1051/matecconf/20179101043.
25. Savrasov F.V., Prokhorov S.V., Shilin A.A. The computer simulation of hoar-frost’s clearing process in the air recuperation system. Journal of Physics: Conference Series, 2017, vol. 803, no. 1, pp. 012134. https://doi.org/10.1088/1742-6596/803/1/012134
Review
For citations:
Shilin A.A., Bukreev V.G., Perevoshchikov F.V. Synthesis and implementation of λ-approach of slide control in heat-consumption system. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2022;22(3):501-508. https://doi.org/10.17586/2226-1494-2022-22-3-501-508