1.School of Electromechanical Engineering, Xidian University, Xi’an, Shaanxi 710071, China
2.Northwest Institute of Mechanical & Electrical Engineering, Xianyang, Shaanxi 712099, China
3. Shaanxi Electronic Industrial Technology Research Institute, Xi’an, Shaanxi 710065, China
Abstract：The influence of frequency characteristic and step response performance for the fractional order control system while the integral order λand differential order μ are changed in the range of 0<λ,μ<2for the fractional order PIλDμcontroller are analyzed.The reasonable ranges of orders are also obtained.Firstly, the numerical solution of fractional order differential equation is adopted to compute the numerical solution for the fractional order closed control system.The fractional order differential and integral operators are replaced by the approximate recurrent evaluate operator.Secondly, fractional order PIλand PDμ controller are adopted to analyze the performance of control system which adopt the frequency characteristic and step response for fractional order control system while the integral order λand differential order μ change, respectively.The analyses of frequency characteristic are accord with the result of practical step response, which shown the integral order λand differential order μ of fractional order PIλDμcontroller have the better range.
［1］Ziegler J G, Nichols N B. Optimum Settings for Automatic Controllers［J］.Transactions of the ASME, 1942, 64: 759-768.
［2］Oustaloup A.La Dè rivation non Entière［M］.Paris: HERMES, 1995.
［3］Dorcak L.Numberical models for simulation the fractional order control systems［R］.UEF-04-94, 1994.
［4］Podlubny I. Fractional-order system and PIλDμ controllers［J］.IEEE Transactions on Automatic Control, 1999, 44(1): 208-214.
［5］Podlubny I, Dorcak L, Kostial I. On fractional derivatives, fractional-order dynamic systems and PIλDμ-controllers［C］//Proceeding of the 36th Conference on Decision & Control.San Diego, California, 1997.
［6］Hamamci S E. Stabilization using fractional-order PI and PID controllers［J］.Nonlinear Dynamic, 2008, 51(1-2): 329-343.
［7］Hamamci S E. An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers［J］.IEEE Transactions on Automatic Control,2007, 52(10): 1964-1969.
［8］Chen Y Q, Dou H F, Vinagre B M, et al. A robust tuning method for fractional order PI controller［C］//Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications.Porto, Portugal,2006.
［9］Podlubny I. Fractional differential equations［M］.San Diego: Academic Press, 1999.
［10］Petras I, Cheng Y Q, Vinagre B M, et al. Stability of linear time invariant systems with interval fractional orders and onterval coefficients［C］//Proceedings of International Conference on Computation Cybernetics. Vienna, 2004.
2012, Vol. 33 
