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Performance Analysis of Proximate Time-Optimal Control for Undamped Harmonic Oscillator in the Presence of Unmodelled Dynamics

Sarmasti, Tooraj | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52448 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. A servomechanism is a system with the objective of to controlling the position or velocity of a mechanical device. In many servomechanisms, one of the major performance measures is tracking the reference input in the shortest time possible. In practice, due to reasons such as modeling error and existence of disturbances, time-optimal control strategy, which is obtained using the classical calculus of variations methods, leads to the undesirable chattering phenomenon. The Proximate Time-Optimal Servomechanism control method is among the practical approaches proposed to obtain responses arbitrarily close to time-optimal, and at the same time avoid chattering. This methodology has found successful applications in areas such as control of Hard Disk Drives. On the other hand, in applications such as Atomic Force Microscopy, as a result of physical properties of the controlled system, arriving at an accurate model is difficult. It is in such applications that studying the stability of the Proximate Time-Optimal Servomechanism control methodology in the presence of unmodelled dynamics is of critical significance. In this thesis, the stability of the Proximate Time-Optimal Servomechanism control methodology applied to a high-order system that was approximated by an undamped harmonic oscillator was studied. Using an upper bound on the magnitude of the time response of the unmodelled dynamics to step input, a number of constraints were found that the controller design parameters and this upper bound must meet in order for the stability of the control method to be guaranteed. Hence, tracking of step inputs with fast response and negligible asymptotic error, and at the same time avoidance of chattering, were guaranteed
  9. Keywords:
  10. Servomechanism ; Servo Control ; Time Optimal Control ; Chattering Avoidance ; Controller Robustness Analysis

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