Symposium on Fractional Signals and Systems

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Symposium on Fractional Signals and Systems

• Expanding Gain-Phase Margin Specifiable Area In
  Control of Unstable Processes via Fractional
  Calculus Based Techniques
• Mohammad Saleh Tavazoei
• Electrical Engineering Department, Sharif
  University of Technology
• (tavazoei_at_sharif.edu)

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Contents
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes

• Introduction
• PI Stabilization of First-Order Plus Dead Time
  Unstable Processes
• Gain-Phase Margin Specifiable Area in PI Control
  based Stabilization
• Stabilization of First-Order Plus Dead Time
  Unstable Processes Using a Fractional-Order
  Controller
• Gain-Phase Margin Specifiable Area in
  FractionalOrder Control based Stabilization
• Conclusions

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Introduction
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes

• Conventional PI and PID controllers have been
  extensively used for achieving different control
  objectives in control of stable processes.
• Moreover, these controllers have been used to
  stabilize unstable processes.
• The free parameters of these conventional
  controllers can be tuned in order to have desired
  values for specifications such as gain margin,
  phase margin or maximum peak response.

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Introduction
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes

• It is obvious that any controller has some
  limitations in fulfilling the mentioned
  specifications, and consequently the desired
  values for these specifications can be selected
  in special areas.
• Our aim is to show that the area in that the
  desired values for some specifications can be
  chosen can be expanded by applying fractional
  calculus based techniques.

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PI Stabilization of First-Order Plus Dead Time
Unstable Processes
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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PI Stabilization of First-Order Plus Dead Time
Unstable Processes
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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PI Stabilization of First-Order Plus Dead Time
Unstable Processes
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in PI Control
based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in PI Control
based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in PI Control
based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in PI Control
based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Stabilization of First-Order Plus Dead Time
Unstable Processes Using a Fractional-Order
Controller
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Stabilization of First-Order Plus Dead Time
Unstable Processes Using a Fractional-Order
Controller
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Stabilization of First-Order Plus Dead Time
Unstable Processes Using a Fractional-Order
Controller
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Stabilization of First-Order Plus Dead Time
Unstable Processes Using a Fractional-Order
Controller
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Stabilization of First-Order Plus Dead Time
Unstable Processes Using a Fractional-Order
Controller
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in
FractionalOrder Control based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in
FractionalOrder Control based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in
FractionalOrder Control based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in
FractionalOrder Control based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Gain-Phase Margin Specifiable Area in
FractionalOrder Control based Stabilization
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
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Conclusions
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes

• A fractional order controller as a modified
  version of the traditional PI controller was
  introduced and it was used in stabilization of
  unstable processes which are described by
  first-order plus dead time models.
• The introduced controller in comparison to the
  conventional PI controller can be used for
  controlling a wider range of unstable processes.
• When one uses the proposed fractional order
  controller the desired phase and margin
  specifications can be chosen in a wider area.
• Fractional calculus based techniques can be
  applied in enhancing the performance of
  conventional controllers.

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The End
Expanding Gain-Phase Margin Specifiable Area In
Control of Unstable Processes
Thank You! Any Question?