Design Of Optimal Fractional Order PID Controller For Fractional Order Systems With Time-delay

Fractional order system is the hot topic of current control domain. But in the fractional control domain, few researches of complex time-delay fractional order system are done right now. Time-delay fractional order system is selected as the research object. Two methods are presented to solve the step-response of time-delay fractional order system. Parameters optimization method for minimize integral index is used to design time-delay fractional order optimal PIλDμ controller in this thesis Several simulations of typical time-delay fractional order system are made to verify the method’s effectiveness. The time-delay fractional order optimal PIλDμ controller in this thesis can provide theoretical support for the control of fractional network system. Meanwhile it can provide new method for fractional higher order system to reduce order to NIOPTD-I model or turning PIλDμ controller’s parameters of NIOPTD-II model in frequency domain design. The main work and innovation of the thesis are as follow:(1) A lot of papers have been studied on fractional control domain, focusing on the fractional control.(2) The mathematical method which is numerical inverse Laplace transformation to solve the problem of time-delay fractional order system is introduced. Based on the numerical inverse Laplace transformation method, parameters optimization method for minimize integral index is used to design time-delay fractional order optimal PIλDμ controller.(3) For the problem of description time-delay fractional order system, the method using Simulink block diagram to construct is performed. Fractional order system’s approximate model and controller’s approximate model are designed. Parameters optimization method for minimize integral index is used to design time-delay fractional order optimal PIλDμ controller.4. Two methods for design the time-delay fractional order optimal PIλDμcontroller in the thesis are used to typical fractional order system. The experimental results show that the design of optimal PIλDμ controller based on the inverse Laplace transformation or Simulink block diagram can control the time-delay fractional order system effectively and it has good robust characteristic.