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  2. 2. OUTLINE <ul><li>Introduction </li></ul><ul><li>Fractional order sytem </li></ul><ul><ul><ul><ul><li>physical system </li></ul></ul></ul></ul><ul><ul><ul><ul><li>fractional order control and fractional calculus </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Fractional differential equations </li></ul></ul></ul></ul><ul><li>FOPID </li></ul><ul><li>Advantages of fractional order pid control </li></ul><ul><li>Applications of FOPID </li></ul><ul><li>FOPID tuning methods </li></ul><ul><li>FOPID tuning using taylor series method </li></ul><ul><li>References </li></ul>
  3. 3. INTRODUCTION <ul><li>A  controller  is a device which monitors and affects the operational conditions of a given dynamic system </li></ul><ul><li>A  proportionalintegralderivativecontroller  ( PID controller ) is a generic control loop  feedback mechanism  </li></ul>
  4. 4. FRACTIONAL ORDER SYSTEM G(s) is trnsfer function of the controlled system Gc(s) is the transfer function of the controller W(s) is input , E(s) is an error , U(s) is controller’s output Y(s) is system’s output Physical system
  5. 5. <ul><li>Fractional order control  or ( FOC ) isa field of control that uses </li></ul><ul><li>  fractional order integrator as part of the control system design toolkit </li></ul><ul><li>Fractional calculus   studies the possibility of taking  real number powers or  complex number powers of the differentiation operator </li></ul><ul><li>Fractional differential equations  are a generalization of differential equations  . </li></ul>
  6. 6. FOPID <ul><li>Substituting integer-order operators by fractional-order </li></ul><ul><li>ones, the FPID controller with transfer function : </li></ul><ul><li>grows up. The FPID controller as so as the classical PID behaves as a band stop filter. </li></ul>
  7. 7. ADVANTAGES OF FRACTIONAL ORDER PID CONTROL <ul><li>The main advantages of introducing FOC to control design are: </li></ul><ul><li>More adequate modeling of dynamic systems </li></ul><ul><li>More clear-cut robust control design </li></ul><ul><li>Advantages of fractional order PID </li></ul><ul><li>Better for fractional systems </li></ul><ul><li>simplicity and compactness </li></ul>
  8. 8. APPLICATIONS OF FOPID <ul><li>1. MOTOR AND GEAR </li></ul>
  9. 9. <ul><li>5.2 PRECISION ACTUATOR </li></ul>
  10. 10. FOPID TUNING METHODS <ul><li>Frequency gain method based on expected gain crossover frequency </li></ul><ul><li>Pole distribution methods </li></ul><ul><li>Tuning based on genetic algorithm </li></ul><ul><li>Particle swarm optimization </li></ul><ul><li>Taylor series </li></ul>
  11. 11. FOPID TUNING USING TAYLOR SERIES EXPANSION <ul><li>This method is based on Taylor series of both actual and </li></ul><ul><li>desired closed-loop transfer function. </li></ul><ul><li>The design parameters of controller are used for matching the same order terms of both desired and actual closed-loop response </li></ul>
  12. 12. <ul><li>FOPID controller has two design parameters, ,λ and µ , morethan PID controller </li></ul><ul><li>Thus two more terms in Taylor series are used to match closed-loop response to desireresponse </li></ul><ul><li>This causes increasing accuracy in tracking the desired response rather than using PID controller </li></ul>
  13. 13. REFERENCES <ul><li>Igor Podlubny, &quot;Fractional-order systems andPID controllers&quot; ,IEEE Transactions on Automatic Control, Vol 44, No. 1, pp.208–213, JANUARY 1999. </li></ul><ul><li>Deepyaman Maiti and Amit Konar IEEE Sponsored Conference on Computational Intelligence ,Control And Computer Vision In Robotics & Automation© IEEE CICCRA 2008149Approximation of a Fractional Order System by an Integer Order Model Using Particle Swarm Optimization Technique. </li></ul><ul><li>YangQuanChen_,1UBIQUITOUSFRACTIONAL ORDER CONTROLS_Center Self-Organizing and Intelligent Systems(CSOIS), Department of Electrical and Computer Eng </li></ul><ul><li>WIKIPEDIA </li></ul><ul><li>STEPPANOPALOUS “CHEMICAL PROCESS CONTROL” </li></ul><ul><li>  </li></ul>
  14. 15. <ul><li>THANK YOU </li></ul>