Advertisement

Possibilities of Typical Controllers for Low Order Non-linear Non-stationary Plants

  • Galina FrantsuzovaEmail author
  • Vadim Zhmud
  • Anatoly Vostrikov
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)

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.

Keywords

Typical controllers Nonlinear plant Perturbations Localization method Invariant system 

References

  1. 1.
    Ang, K.H., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 4(13), 559–576 (2005)Google Scholar
  2. 2.
    Reference materials of PID controller in Simulink (in Russian). http://www.mathworks.com/help/simulink/slref/pidcontroller.html. Accessed 19 Mar 2018
  3. 3.
    Rotach, V.Ya.: Automatic Control Theory. 5th edn. Publishing House MEI, Moscow (2008)Google Scholar
  4. 4.
    Denisenko, V.V.: PID controller: principles of construction and modification. STA 4, 66–74 (2006)Google Scholar
  5. 5.
    Nikulin, E.F.: Fundamentals of Automatic Control Theory. Frequency Methods of Systems Analysis and Synthesis. Publishing BHV-Petersburg, St. Petersburg (2004)Google Scholar
  6. 6.
    Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 4(13), 291–309 (2003)CrossRefGoogle Scholar
  7. 7.
    Schei, T.S.: Automatic tuning of PID controllers based on transfer function estimation. Automatica 12(30), 1983–1989 (1994)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Dorf, R., Bishop, R.: Modern Control Systems. Publishing Laboratory of Basic Knowledge, Moscow (2002)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    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)Google Scholar
  13. 13.
    Vostrikov, A.S., Frantsuzova, G.A.: Synthesis of PID-controllers for nonlinear nonstationary plants. Optoelectron. Instrum. Data Process. 5(51), 471–477 (2015)CrossRefGoogle Scholar
  14. 14.
    Vostrikov, A.S.: Controller synthesis problem for automation systems: state and prospects. Autometriya 2(46), 3–19 (2010)Google Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Vostrikov, A.S., Utkin, V.I., Frantsuzova, G.A.: Systems with state-vector derivative in control. Autom. Remote Control 3, 22–25 (1982)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Vostrikov, A.S.: Control Systems Synthesis by Localization Method. Publishing NSTU, Novosibirsk (2007)Google Scholar
  20. 20.
    Yurkevich, V.D.: Calculation and tuning of controllers for nonlinear systems with different-rate processes. Optoelectron. Instrum. Data Process. 5(48), 447–453 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations