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)


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.


Typical controllers Nonlinear plant Perturbations Localization method Invariant system 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

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