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Optimal Design of Implementable Fractional-order PI and PID Controllers for Time-delay LTI Systems

Ashjaei Sanzighi, Mehrdad | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50028 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. Benefiting from the great potential of the mathematical tool of fractional calculus, fractional order proportional integral (FOPI) and proportional integral derivative (FOPID) controllers have been proposed as the next generations for the popular PI and PID controllers. On the other hand, the integral performance indices such as the integral square error (ISE), integral square time error (ISTE), integral absolute error (IAE) and integral time absolute error (ITAE) are commonly used in design and evaluate of the performance of practical control systems. Considering these points, the present thesis deals with optimal tuning of the free parameters of fractional order PI and PID controllers, to be used in control of first order plus dead time (FOPDT) processes in a unity negative control structure, on the basis of ISE and ISTE performance indices. Using the approach of “tuning based on the implementable form of the controller” instead of the approach of “tuning based on the ideal form of the controller” causes that no incompatibility is seen between the ideal behavior of the controller and the behavior of the implementable controller. Also, to avoid approximation error in calculation of assumed cost functions, algebraic relations are used for analytically finding the values of ISE and ISTE in the under study time delay control systems. In fact, the main contribution of the project is to propose simple tuning rules for implementable fractional order PI and PID controllers with the aim of achieving an optimal control systems in the viewpoint of the ISE and ISTE performance criteria. These rules are obtained by iteratively using the steepest descent optimization algorithm with the constraint of optimizing the step size in each iteration. The proposed rules for tuning of the free parameters of implementable FOPI and FOPID controllers yield in a control systems whose performances is better than the control systems with optimal PI and PID controllers, respectively. These points are successfully confirmed by some numerical examples
  9. Keywords:
  10. Control System ; Proportional-Integral-Derivative (PID)Controller ; Proportional-Integral (PI)Controller ; Time Delay ; Implementation ; Optimal Tuning ; Integral Square Error (ISE)Performance Index ; Integral Square Time Error (ISE)Performance Index

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