Fractional order model for control system and design of fractional order PI^λD^μ controller

For the delay performance of the higher order dynamic system model in the process of system analysis and design, first or second order plus time delay system model are used to make approximations for it, but the described system accuracy and control performance are reduced because of oversize error of the model. A new non-integer order plus time delay (NIOPTD) system model was designed, then the traditional model and the NIOPTD model were received to take the place of a higher order system, and the advantages of the NIOPTD system model were given via comparisons. A new method of fractional order controller parameter tuning in frequency domain was given for the three system models (first order, second order system and NIOPTD). Simulations results illustrate that the best control performance and robust stability can be performed as desire by utilizing NIOPTD system model.