Limiting Values of the Stability Margins in the Parametric Synthesis of PID-Controllers

  • Goerun Ayazyan
  • Elena TaushevaEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 260)


The problem of parametric synthesis of PID controllers of integer and fractional orders is solved. PID-controllers are an integral part of many cyber-physical systems. Two well-known methods of synthesis are considered—for a relative stability margin and a maximum value of the sensitivity function. Algorithms have been developed for calculating the limiting values of the differential gain of the controller, at which the boundary of the region of a given stability margin has a cusp. In the case of using the criterion for low-frequency disturbance rejection (LFDR), the limiting values of the relative stability margin and the maximum value of the sensitivity function are determined.


PID-controller Fractional order Relative stability margin Maximum value of the sensitivity function Cyber-physical systems Maple 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Ufa State Petroleum Technological UniversityUfaRussia

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