Abstract
The possible approach to the calculating typical controllers for low-order nonlinear non-stationary plants is presented in this paper. It is assumed that the differential channel was put out to the feedback circuit in the stabilization systems. As a result, two control loops are formed in the system. The internal contour contains the proportional and differential components of a typical controller. The output signal derivative implicitly contains all information about the nonlinear and non-stationary characteristics as well as about the external uncontrolled perturbations for the first order plant. For this reason, the inner loop control can be interpreted as a variation of the control law based on the localization method. It is proposed to use the basic relations of this method to calculate the controller components in the feedback circuit. As a result, the inner loop dynamics can be subordinated to a linear equation. For the second order nonlinear plants, it was proposed to introduce an additional differential component to the typical PID controller and consider the PIDD2 controller. In this case, it is also proposed to calculate the inner control loop by means of the localization method. It is shown that after the inner loop stabilization by means of differential components, the calculation of both the PID and PIDD2 controllers can be carried out using the modal approach and the desired roots formation. Thus, we have the system invariant to the external perturbations action for the first and second order nonlinear non-stationary plants. The numerical simulation results in MATLAB illustrate the basic properties of such systems.
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References
Ang, K.H., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 4(13), 559–576 (2005)
Reference materials of PID controller in Simulink (in Russian). http://www.mathworks.com/help/simulink/slref/pidcontroller.html. Accessed 19 Mar 2018
Rotach, V.Ya.: Automatic Control Theory. 5th edn. Publishing House MEI, Moscow (2008)
Denisenko, V.V.: PID controller: principles of construction and modification. STA 4, 66–74 (2006)
Nikulin, E.F.: Fundamentals of Automatic Control Theory. Frequency Methods of Systems Analysis and Synthesis. Publishing BHV-Petersburg, St. Petersburg (2004)
Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 4(13), 291–309 (2003)
Schei, T.S.: Automatic tuning of PID controllers based on transfer function estimation. Automatica 12(30), 1983–1989 (1994)
Wang, Q.-G., Zhang, Z., Astrom, K.J., Chek, L.S.: Guaranteed dominant pole placement with PID controllers. J. Process Control 2(19), 349–352 (2009)
Dorf, R., Bishop, R.: Modern Control Systems. Publishing Laboratory of Basic Knowledge, Moscow (2002)
Zhmud, V.A., Dimitrov, L.V., Taichenachev, A.V., Semibalamut, V.M.: Calculation of PID-regulator for MISO system with the method of numerical optimization. In: International Siberian Conference on Control and Communications SIBCON 2017, pp. 670–676. Astana, Kazakhstan (2017)
Zhmud, V.A., Dimitrov, L.V., Roth, H.: A new approach to numerical optimization of a controller for feedback system. In: 2nd International Conference on Applied Mechanics, Electronics and Mechatronics Engineering, pp. 213–219. DEStech Publications Inc., Beijing (2017)
Zhmud, V.A., Pyakillya, B.I., Liapidevskii, A.V.: Numerical optimization of PID-regulator for object with distributed parameters. J. Telecommun. Electron. Comput. Eng. 2(9), 9–14 (2017)
Vostrikov, A.S., Frantsuzova, G.A.: Synthesis of PID-controllers for nonlinear nonstationary plants. Optoelectron. Instrum. Data Process. 5(51), 471–477 (2015)
Vostrikov, A.S.: Controller synthesis problem for automation systems: state and prospects. Autometriya 2(46), 3–19 (2010)
Kotova, E.P., Frantsuzova, G.A.: Application PI2D controller in automatic control systems. In: International Siberian Conference on Control and Communications SIBCON 2017, pp. 692–695. Astana, Kazakhstan (2017)
Frantsuzova, G.A.: PI2D-controllers synthesis for nonlinear non-stationary plants. In: 14th International Scientific-Technical Conference APEIE, vol.1, pp. 212–216. NSTU, Novosibirsk (2018)
Zhmud, V.A., Zavoryn, A.N.: Fractional-exponent PID-controllers and ways of their simplification with increasing control efficiency. Autom. Softw. Eng. 1, 30–36 (2013)
Vostrikov, A.S., Utkin, V.I., Frantsuzova, G.A.: Systems with state-vector derivative in control. Autom. Remote Control 3, 22–25 (1982)
Vostrikov, A.S.: Control Systems Synthesis by Localization Method. Publishing NSTU, Novosibirsk (2007)
Yurkevich, V.D.: Calculation and tuning of controllers for nonlinear systems with different-rate processes. Optoelectron. Instrum. Data Process. 5(48), 447–453 (2012)
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Frantsuzova, G., Zhmud, V., Vostrikov, A. (2019). Possibilities of Typical Controllers for Low Order Non-linear Non-stationary Plants. In: Dolinina, O., Brovko, A., Pechenkin, V., Lvov, A., Zhmud, V., Kreinovich, V. (eds) Recent Research in Control Engineering and Decision Making. ICIT 2019. Studies in Systems, Decision and Control, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-030-12072-6_43
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DOI: https://doi.org/10.1007/978-3-030-12072-6_43
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