A graphical tuning method of fractional order proportional integral derivative controllers for interval fractional order plant

Abstract In this paper, a novel graphical tuning method of fractional order proportional integral derivative (FOPID) controllers is proposed for a given interval fractional order plant family. Firstly, an approach is presented to solve the problem of robustly stabilizing the interval fractional order plant using FOPID controller. Moreover, some alternative methods are developed to reduce the computational burden of the presented approach. The results obtained here are general and strict proofs are given on these results. Secondly, a new approach is presented to calculate the complete sets of FOPID controller parameters which guarantee the specified H∞-norm constraint for the interval fractional order plant. The developed approach is convenient and flexible. Finally, a unified design framework is proposed. The aim of the unified design is to compute the biggest region which can simultaneously provide internal stability, maintain the classical gain and phase margin and guarantee the modern H∞-norm constraint for the interval fractional order plant. Examples are followed to illustrate the design procedure.

[1]  Y. Chen,et al.  Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers , 2008 .

[2]  Antonio Visioli,et al.  Tuning rules for optimal PID and fractional-order PID controllers , 2011 .

[3]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[4]  Shang-Hong Shih,et al.  Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay , 2010, Proceedings of the 29th Chinese Control Conference.

[5]  Wei Li,et al.  Tuning of PIλDμ controllers based on sensitivity constraint , 2013 .

[6]  Xiaozhong Liao,et al.  Robust stability criterion of fractional-order functions for interval fractional-order systems , 2013 .

[7]  Truong Nguyen Luan Vu,et al.  Analytical design of fractional-order proportional-integral controllers for time-delay processes. , 2013, ISA transactions.

[8]  Taonian Liang,et al.  Algorithm of robust stability region for interval plant with time delay using fractional order PIλDμ controller , 2012 .

[9]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[10]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .

[11]  Mohammad Haeri,et al.  Robust stability testing function and Kharitonov-like theorem for fractional order interval systems , 2010 .

[12]  Ming-Tzu Ho,et al.  On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty , 2005 .

[13]  Riccardo Caponetto,et al.  A numerical approach for computing stability region of FO-PID controller , 2013, J. Frankl. Inst..

[14]  Mohammad Saleh Tavazoei,et al.  Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations , 2008, IEEE Transactions on Industrial Electronics.

[15]  Boris T. Polyak,et al.  Stability regions in the parameter space: D-decomposition revisited , 2006, Autom..

[16]  Mohammad Bozorg,et al.  Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems , 2011, Autom..

[17]  Nusret Tan,et al.  Robust stability analysis of fractional order interval polynomials. , 2009, ISA transactions.

[18]  Mohammad Haeri,et al.  On robust stability of LTI fractional-order delay systems of retarded and neutral type , 2010, Autom..

[19]  Shiqi Zheng,et al.  Fractional order controllers tuning strategy for permanent magnet synchronous motor servo drive system based on genetic algorithm–wavelet neural network hybrid method , 2014 .

[20]  Christophe Farges,et al.  A stability test for non-commensurate fractional order systems , 2010, Syst. Control. Lett..

[21]  Mohammad Haeri,et al.  Fractional order model reduction approach based on retention of the dominant dynamics: application in IMC based tuning of FOPI and FOPID controllers. , 2011, ISA transactions.

[22]  Serdar Ethem Hamamci.  An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers , 2007, IEEE Transactions on Automatic Control.

[23]  Chyi Hwang,et al.  A numerical algorithm for stability testing of fractional delay systems , 2006, Autom..

[24]  De-Jin Wang,et al.  Stability Margins and H∞ Co‐Design with Fractional‐Order PIλ Controllers , 2013 .

[25]  Shankar P. Bhattacharyya,et al.  Robust and Non-fragile PID Controller Design , 2001 .