Robust stability region of fractional order PI^λ controller for fractional order interval plant

References

• Ahn , HS and Chen , YQ . 2007 . “ Conservatism-free Robust Stability Check of Fractional Order Interval Linear Systems ” . In in Proceedings of the 17th IFAC World Congress, 22 August 2007 15256 – 15261 . Utah State, USA
   Google Scholar
• Ahn , HS and Chen , YQ . 2008 . Necessary and Sufficient Stability Condition of Fractional Order Interval Linear Systems . (Elsevier) Automatica , 44 : 2985 – 2988 .
   Web of Science ®Google Scholar
• H.S. Ahn, Chen, Y.Q., and Podlubny, I. (2006), ‘Robust Stability Checking of a Class of Linear Interval Fractional Order System Using Lyapunov Inequality’, Applied Mathematics and Computation, 187, 27–34
   Google Scholar
• Astrom , KJ and Hagglund , T . 1995 . PID Controllers: Theory, Design and Tuning, Research Triangle Park , Instrument Society of America .
   Google Scholar
• Bartlett , AC , Hollot , CV and Lin , H . 1998 . Root Location of an Entire Polytope of Polynomials: It Suffices to Check the Edges . Math Control Signals Systems , 1 : 61 – 67 .
   Google Scholar
• Batlle , VF , Pérez , RR and Rodríguez , LS . 2007 . Fractional Robust Control of Main Irrigation Canals with Variable Dynamic Parameters . Control Engineering Practice , 15 : 673 – 686 .
   Web of Science ®Google Scholar
• Bhattacharyya , SP , Chapellat , H and Keel , LH . 1995 . Robust Control: The Parametric Approach , Upper Saddle River, NJ: Prentice Hall PTR .
   Google Scholar
• Chapellat , H and Bhattacharyya , SP . 1989 . A Generalisation of Kharitonov's Theorem: Robust Stability of Interval Plants . IEEE Transactions on Automatic Control , 34 : 306 – 11 .
   Web of Science ®Google Scholar
• Chen , YQ , Ahn , HS and Podlubny , I . 2006b . Robust Stability Check of Fractional Order Linear Time Invariant Systems with Interval Uncertainties . (Elsevier) Signal Processing , 86 : 2611 – 2618 .
   Web of Science ®Google Scholar
• Chen , YQ , Dou , H , Vinagre , BM and Monje , CA . 2006a . “ A Robust Tuning Method for Fractional Order PI Controllers ” . In in Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and Its Applications, July 2006 19 – 21 . Porto, Portugal
   Google Scholar
• Cheng , YC and Hwang , C . 2006 . Stabilization of Unstable First-order Time-delay Systems Using Fractional-order PD Controllers . Journal of the Chinese Institute of Engineers , 29 : 241 – 249 .
   Web of Science ®Google Scholar
• Datta , A , Ming , TH and Bhattacharyya , SP . 2000 . Structure and Synthesis of PID Controllers , London : Springer-Verlag .
   Google Scholar
• Delshad , SS , Asheghan , MM and Beheshti , MH . 2010 . Robust Stabilisation of Fractional-order Systems with Interval Uncertainties via Fractional-order Controllers . Advances in Difference Equations , 2010 : 1 – 15 .
   Google Scholar
• Dorcak , L . 1994 . “ Numerical Models for Simulation the Fractional-order Control System ” . In in UeF SAV, The Academy of Science Institute of Experimental Physics , Kosice : Slovak Republic . http://xxx.lanl.gov/abs/math.OC/0204108/
   Google Scholar
• Hamamci , SE . 2007 . An Algorithm for Stabilization of Fractional-order Time Delay Systems using Fractional-order PID Controllers . IEEE Transactions on Automatic Control , 52 : 1964 – 1969 .
   Web of Science ®Google Scholar
• Hamamci , SE . 2008 . Stabilization Using Fractional Order PI and PID Controllers . Nonlinear Dynamics , 51 : 329 – 343 .
   Web of Science ®Google Scholar
• Hamamci , SE , Kanthabhabha , P and Vaithiyanathan , K . 2008 . Computation of All Stabilizing First Order Controllers for Fractional-order Systems . Proceedings of the 27th Chinese Control Conference . 2008 . pp. 123 – 128 . 16–18 July 2008, Kunming, Yunnan, China
   Google Scholar
• Hamamci , SE and Koksal , M . 2010 . Calculation of All Stabilizing Fractional Order PD Controllers for Integrating Time Delay Systems . Computers and Mathematics with Applications , 59 : 1621 – 1629 .
   Web of Science ®Google Scholar
• Ho , MT , Datta , A and Bhattacharyya , SP . 1998 . Design of P, PI and PID Controllers for Interval Plant . Proceedings of the American Control Conference, June 1998 . 1998 . pp. 2496 – 2501 . Philadelphia, PA
   Google Scholar
• Huang , YJ and Wang , YJ . 2000 . Robust PID Tuning Strategy for Uncertain Plants Based on the Kharitonov Theorem . ISA Transaction , 39 : 419 – 431 .
   PubMed Web of Science ®Google Scholar
• Hwang , C and Cheng , YC . 2006 . A Numerical Algorithm for Stability Testing of Fractional Delay Systems . Automatica , 42 : 825 – 831 .
   Web of Science ®Google Scholar
• Hwang , C , Hwang , JH and Leu , JF . 2004 . Tuning PID Controllers for Time-delay Processes with Maximising the Degree of Stability . 5th Asian Control Conference, 20–23 July 2004 . 2004 . Vol. 1 , pp. 466 – 471 .
   Google Scholar
• Johnson , M , Croweand , J and Moradi , MH . 2005 . PID Control: New Identification and Design Methods , London, UK : Springer .
   Google Scholar
• Kang, H. , Il . 2009 . Robust Stabilisation of Commensurate Fractional Order Interval Plants with PID Controllers . IEEE International Conference on Intelligent Computing and Intelligent Systems, 20–22 November 2009 . 2009 . pp. 596 – 599 . Shanghai , , China
   Google Scholar
• Kharitonov , VL . 1979 . Asymptotic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations . Differential Equations , 14 : 1483 – 1485 .
   Google Scholar
• Lazarević , MP and Spasić , AM . 2009 . Finite-time Stability Analysis of Fractional Order Time Delay Systems: Gronwall's Approach . Mathematical and Computer Modelling , 49 : 475 – 481 .
   Web of Science ®Google Scholar
• Li , J and Li , P . 2006 . “ Stability Region Analysis of PID Controllers for Time-delay Systems ” . In in Proceedings of the 6th World Congress on Intelligent Control and Automation, 21–23 June 2006 2219 – 2223 . Dalian, China
   Google Scholar
• Lino , GMP . 2007 . New Tuning Rules for Fractional Order Pi λ Controllers . Nonlinear Dynamics , 49 : 251 – 257 .
   Web of Science ®Google Scholar
• Mckay , J . 1970 . The D-partition Method Applied to Systems with Dead Time and Distributed Lag . Measurement and Control , 3 : 293 – 294 .
   Web of Science ®Google Scholar
• Monje , CA , Vinagre , BM , Chen , YQ and Feliu , V . 2004 . On Fractional PI λ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties . Nonlinear Dynamics , 38 : 369 – 381 .
   Web of Science ®Google Scholar
• Oustaloup , A . 1995 . La Drivation Non Entire , Paris : HERMES .
   Google Scholar
• Petráš , I . 2008 . Stability of Fractional-order Systems with Rational Orders http://arxiv.org/abs/0811.4102
   Google Scholar
• Petráš , I , Chen , YQ and Vinagre , BM . 2002 . A Robust Stability Test Procedure for a Class of Uncertain LTI Fractional Order Systems . International Carpathian Control Conference ICCC'2002, 27–30 May 2002 . 2002 . pp. 247 – 252 . Malenovice, Czech Republic, Beskydy
   Google Scholar
• Petráš , I , Chen , YQ , Vinagre , BM and Podlubny , I . 2005 . Stability of Linear Time Invariant Systems with Interval Fractional Orders and Interval Coefficients . Proceedings of International Conference on Computation Cybernetics(ICCC04) . 2005 . pp. 1 – 4 . Vienna, Austria, Vienna Technical University, 8/30-9/1 2005
   Google Scholar
• Podlubny , I . 1999 . Fractional-order System and PI λ D μ Controllers . IEEE Transactions on Automatic Control , 44 : 208 – 214 .
   Web of Science ®Google Scholar
• Podlubny , I , Dorcak , L and Kostial , I . 1997 . On Fractional Derivatives, Fractional-order Dynamic Systems and PI λDμ-controllers . Proceedings of the 36th Conference on Decision & Control (Vol. 5), December 1997 . 1997 . pp. 4985 – 4990 . San Diego, CA, USA
   Google Scholar
• Saadaoui , K , Elmadssia , S and Benrejeb , M . 2008 . Stability First-order Controllers for n-th Order All Pole Plants with Time Delay . 16th Mediterranean Conference on Control and Automation Congress Centre, 25–27 June 2008 . 2008 . pp. 812 – 817 . Ajaccio, France
   Google Scholar
• Tan , N and Atherton , DP . 2006b . Design of Stabilising PI and PID Controllers . International Journal of Systems Science , 37 : 543 – 554 .
   Web of Science ®Google Scholar
• Tan , N , Kaya , I , Yeroglu , C and Atherton , DP . 2006a . Computation of Stabilising PI and PID Controllers Using the Stability Boundary Locus . Energy Conversion and Management , 47 : 3048 – 3058 .
   Web of Science ®Google Scholar
• Tan , N , Özgüven , ÖF and Özyetkin , MM . 2009 . Robust Stability Analysis of Fractional Order Interval Polynomials . (Elsevier) ISA Transactions , 48 : 166 – 172 .
   PubMed Web of Science ®Google Scholar
• Tavazoei , MS and Haeri , M . 2009 . A Note on the Stability of Fractional Order Systems . Mathematics and Computers in Simulation , 79 : 1566 – 1567 .
   Web of Science ®Google Scholar
• Zhao , C , Xue , D and Chen , YQ . 2005 . A Fractional Order PID Tuning Algorithm for a Class of Fractional Order Plants . Proceedings of the IEEE International Conference on Mechatronics & Automation, July 2005 . 2005 . pp. 216 – 221 . Niagara Falls, Canada
   Google Scholar
• Ziegler , JG and Nichols , NB . 1942 . Optimum Settings for Automatic Controllers . Transactions of the ASME , 64 : 759 – 768 .
   Google Scholar