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Achievable Delay Margin by Using PID Fractional-Order Controllers

Afshari Saleh, Mohammad Hossein | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56636 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. This paper concerns the delay margin achievable using fractional order Proportional_Integral_Derivative controllers for linear time- invariant systems subject to variable, unknown time delays. The basic issue under investigation addresses the question: What is the largest range of time delay so that there exists a single fractional order Proportional_Integral_Derivative controller to stabilize the delay plants within the entire range? Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this research, we develop explicit expressions of the exact delay margin and its upper bounds achievable by a fractional order Proportional_Integral_Derivative controller for low order delay systems, notably the first order unstable systems with unknown constant and possibly time-varying delays. fractional order Proportional_Integral_Derivative controllers are developed versions of Proportional_Integral_Derivative controllers which have been extensively used to control and regulate industrial processes that are typically modeled by first and second order dynamics. Since fractional order Proportional_Integral_Derivative controllers have more degrees of freedom than Proportional_Integral_Derivative controllers, fractional order Proportional_Integral_Derivative controllers are more capable of fulfilling the performance requirements of system than integer order Proportional_Integral_Derivative controllers. While acquiring the fundamental limits of delay within which a Proportional_Integral_Derivative controller may robustly stabilize a delay process, our results should also provide useful guidelines in tuning fractional order Proportional_Integral_Derivative parameters and in the analytical design of fractional order Proportional_Integral_Derivative controllers. 8 distinct structures of fractional order controller that vary in integrator or differentiator order are considered to maximize the delay margin achievable by controlled system and the maximum achievable delay margin by all of these structures are compared with each other and finally the best structure from the viewpoint of delay margin is selected
  9. Keywords:
  10. Fractional Order Controller ; Proportional-Integral-Derivative (PID)Controller ; Frequency Domain Analysis ; Robust Stability ; Input Time Delay Margin ; Time Delay

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