Abstract
A method for designing a model of PID controllers for high-order systems based on the modal method for linear systems is proposed taking into account the assignment of the roots of the characteristic polynomial of the corrected automatic feedback control system. From the stability condition of the system, the coefficients of the characteristic polynomial must be positive. It is provided to set the test conditions of the positive values of the coefficients of the PID regulators. The calculation of the controller parameters is performed according to transition characteristics of the system. Functionality test of method has provided by the example of synthesis of PID controllers parameters of the control system of third order object.
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References
Prokopev, A.P., Ivanchura, V.I., Emelianov, R.T., Palchikov, P.A.: Implementation of the concept of automation and intellectualization of management of road construction processes. Vestnik MGSU. 2018, 13(1) (112), 61–70 (2018)
Prokopev, A.P., Ivanchura, V.I., Emelyanov, R.T.: Synthesis PID controller for objects second order with regard to the location poles. Zhurnal SFU. Tech. Technol. 9(1), 50–60. https://doi.org/10.17516/1999-494x-2016-9-1-50-60 (2016)
Ziegler, J.G., Nichols, N.B.: Optimum settings for automatic controllers. Trans. Am. Soc. Mech. Eng. 64, 759–768 (1942)
Astrom, K.J., Hagglund, T.: Advanced PID Control. Research Triangle Park, North Carolina: The Instrumentation, Systems, and Automation Society, 354 p (2006)
Vadutov, O.S.: Design of PID controller for delayed systems using optimization technique under pole assignment constraints. News of Tomsk Polytechnic University. Inf. Technol. 325(5), 16–22 (2014)
Filips, Ch., Kharbor, R.: Feedback control systems. Moscow, Basic knowledge laboratory Publ., 2001, 616 p (2001)
Voronov, A.A.: Fundamentals of the Theory of Automatic Control. Automatic control of continuous linear systems. Energiya Publ., Moscow, 309, p (1980)
Lukas, V.A.: Automatic Control Theory. Nedra Publ., Moscow, 416 p (1990)
O’Dwyer, A.: Handbook of PI and PID Controller Tuning Rules. Imperial College Press, London, 564 p (2006)
O’Dwyer, A.: Handbook of PI and PID controller tuning rules. Imperial College Press, London, 623 p (2009)
Zamyatin, D.V., Lovchikov, A.N.: The time optimal systems synthesis methodic. Vestnik SibGAU, 4, 28–30 (2005)
Besekersky, V.A., Popov, E.P.: Theory of automatic control systems. Moscow, Publishing House “Nauka”, 768 p (1975)
Zamyatin, D.V., Lovchikov, A.N.: Correctional unit parameters obtaining for time optimal four order system. Vestnik SibGAU, 4(11), 18–20 (2006)
Zamyatin, D.V., Lovchikov, A.N.: Synthesis of time optimal systems of high order. Vestnik SibGAU, 2(48), 24–28 (2013)
Ivanchura, V.I., Prokopiev, A.P.: Optimization of a tracker system of automatic control. Vestnik SibGAU, 5(38), 44–49 (2011)
Prokopev, A.P., Ivanchura, V.I., Emelyanov, R.T.: Features of the synthesis of controller for nonlinear system control. Mathematical methods in engineering and technology. MMTT-27: XXVII international scientific conference: proceedings. Section 2. The Ministry of education and science of the Russian Federation, Tambov state technical. University [etc.]. Tambov: [b. I.], 2014 (2014)
Prokopev A.P., Ivanchura V.I.: Features of the synthesis of controller electro-hydraulic control system XII All-Russia meeting on control problems VCPU-2014. Moscow, June 16–19, 2014: Proceedings. Moscow, Institute of control them. V.A. Trapeznikov Academy of Sciences, 2014, pp. 307–317 (2014)
Prokopev, A.P., Ivanchura, V.I., Emelyanov R.T.: Identification of nonlinear control systems with the PID control, SICPRO’15, Moscow, pp. 387–397; http://www.sicpro.org/sicpro15/code/r15_08.htm (2015)
Prokopiev, A.P., Ivanchura, V.I., Emelianov, R.T., Scurihin, L.V.: The technique of synthesis of regulators for objects of the second order. Vestnik SibGAU, 17(3), 618–624 (2016)
Efimov, S.V., Zamyatin, S.V., Gayvoronskiy, S.A.: Synthesis of the PID controller with respect to the location of zeros and poles of the system of automatic control. News of Tomsk Polytechnic University, 317(5), 102–107 (2010)
Efimov, S.V., Gayvoronskiy, S.A., Zamyatin, S.V.: Root tasks of analysis and synthesis and synthesis of automatic control systems. News Tomsk. Polytech. Univ. 316(5), 16–20 (2010)
Uderman, E.G.: Root Locus Method in the Theory of Automatic Systems. Gosenergoizdat Publ., Moscow-Leningrad 112 p (1963)
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Prokopev, A., Nabizhanov, Z., Ivanchura, V., Emelyanov, R. (2020). Parametric Synthesis Method of PID Controllers for High-Order Control Systems. In: Kravets, A., Bolshakov, A., Shcherbakov, M. (eds) Cyber-Physical Systems: Industry 4.0 Challenges. Studies in Systems, Decision and Control, vol 260. Springer, Cham. https://doi.org/10.1007/978-3-030-32648-7_8
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