A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement

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• 作者：Suman Saha^a ; ^{s_saha@cmeri.res.in} ; Saptarshi Das^b ; ^c ; ^{saptarshi@pe.jusl.ac.in} ; Shantanu Das^d ; ^{shantanu@barc.gov.in} ; Amitava Gupta^b ; ^c ; ^{amitg@pe.jusl.ac.in}
• 关键词：Conformal mapping ; Dominant pole placement ; Fractional order PID controller ; Linear Quadratic Regulator (LQR) ; M-curve ; Root locus
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 期刊代码：89_10075704
• 类别：ph
• 出版时间：September, 2012
• 卷：17
• 期：9
• 页码：3628-3642
• 文件大小：1893 K

摘要

A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PI^位D^渭) controller have been approximated in this paper vis-脿-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PI^位D^渭 controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as 鈥淢-curve鈥? This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller鈥檚 effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.