Robust design based on complex-order integrator loop gain

In this paper a novel, easy-to-use, robust design method for stable time delay processes is proposed. The purpose is obtaining a desired phase margin at a known crossover frequency. The design methodology is based on complex order integration. Complex order controllers fall into fractional order controllers category. Complex order controllers are the extended version of fractional order controllers in which the order of the transfer function has imaginary and real parts, rather than integer or non-integer real part. Introducing a complex order for the open-loop transfer function makes it possible to fulfill additional specifications of design ensuring a robust performance of the closed-loop system with respect to gain variations. This extra parameter enables designing a controller which makes the phase diagram remain flat around the gain crossover frequency. This leads to a fixed phase margin around the crossover frequency. The design procedure and the validity of the results are illustrated through some examples.

[1]  J. Pontt,et al.  Design of fast and robust current regulators for high-power drives based on complex state variables , 2004, IEEE Transactions on Industry Applications.

[2]  S. Hiti,et al.  Modified Current Control Schemes for High-Performance Permanent-Magnet AC Drives With Low Sampling to Operating Frequency Ratio , 2009, IEEE Transactions on Industry Applications.

[3]  Jan Cvejn,et al.  Sub-optimal PID controller settings for FOPDT systems with long dead time , 2009 .

[4]  Geoff Barton,et al.  Process control: Designing processes and control systems for dynamic performance , 1996 .

[5]  F. Briz,et al.  Analysis and design of current regulators using complex vectors , 1997, IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty-Second IAS Annual Meeting.

[6]  Yangquan Chen,et al.  Fractional order plasma position control of the STOR-1M tokamak , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[7]  Kamran Iqbal,et al.  PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem. , 2005, ISA transactions.

[8]  西本 勝之,et al.  Fractional calculus : integrations and differentiations of arbitrary order , 1984 .

[9]  William L. Luyben,et al.  Process Modeling, Simulation and Control for Chemical Engineers , 1973 .

[10]  Chyi-Tsong Chen,et al.  Design of a sliding mode control system for chemical processes , 2005 .

[11]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[12]  F. Briz,et al.  Dynamic analysis of current regulators for AC motors using complex vectors , 1998, Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242).

[13]  Nabil Derbel,et al.  Analytical Impulse Response of Third Generation CRONE Control , 2010 .

[14]  Dingyu Xue,et al.  PRACTICAL TUNING OF FRACTIONAL ORDER PROPORTIONAL AND INTEGRAL CONTROLLER (I): TUNING RULE DEVELOPMENT , 2007 .

[15]  Suman Saha,et al.  Design of a Fractional Order Phase Shaper for Iso-Damped Control of a PHWR Under Step-Back Condition , 2010, IEEE Transactions on Nuclear Science.

[16]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[17]  C. S. Cox,et al.  Quicktune: A reliable automatic strategy for determining PI and PPI controller parameters using a FOPDT model , 1997 .

[18]  Prabin Kumar Padhy,et al.  Relay based PI-PD design for stable and unstable FOPDT processes , 2006, Comput. Chem. Eng..

[19]  Duarte Valério,et al.  V ARIABLE-ORDER FRACTIONAL DERIVATIVES AND THEIR NUMERICAL APPROXIMATIONS II – COMPLEX ORDERS , 2009 .

[20]  Alain Oustaloup,et al.  Third generation CRONE control , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[21]  Joachim Holtz,et al.  The representation of AC machine dynamics by complex signal flow graphs , 1995, IEEE Trans. Ind. Electron..

[22]  Richard L. Magin,et al.  On the fractional signals and systems , 2011, Signal Process..

[23]  Surekha Kamath,et al.  A comparative study of different types of controllers used for blood glucose regulation system , 2009 .