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Analyzing the Impact of Derivative Non-Ideality on the Stability and Performance of Second-Order Nonlinear Systems Controlled by Pd Controllers

Samadani, Mahdi | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57690 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. This research investigates the performance of Proportional-Derivative (PD) controllers in uncertain second-order nonlinear systems and analyzes the impact of non-ideal derivatives on system stability. The findings indicate that using non-ideal approximations of derivatives, even under conditions where closed-loop stability is guaranteed in the ideal case, can lead to system instability. Initially, the mechanisms through which non-ideal derivatives influence system stability were analyzed, and the causes of instability were identified. Subsequently, a theoretical framework was developed to determine suitable parameters to mitigate the adverse effects of non-ideal derivatives. This framework demonstrated that precise parameter tuning could provide sufficient conditions to ensure the stability of the system's equilibrium point. The results of two simulations confirmed the effectiveness of this approach and showed significant improvements in system stability. urthermore, by employing weighted linearization techniques, an enhanced framework was proposed, extending the stability boundaries of uncertain second-order nonlinear systems controlled by non-ideal PD controllers
  9. Keywords:
  10. Stability ; Proportional-Derivative (PD)Controller ; Second-Order Nonlinear Systems ; Weighted Linearization ; Non-Ideal Derivative ; Uncertain Systems

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