Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ and Active Disturbance Rejection Control of Nonlinear Two-Mass Drive System

This study presents the application of a fractional-order <formula formulatype="inline"><tex Notation="TeX">$\hbox{PI}^{ \lambda}\hbox{D}^{\mu}$</tex></formula> and an active disturbance rejection (ADR) controller to a nonlinear two-mass system. A complete state-space mathematical model for a nonlinear two-mass system is first developed. Then, a fractional-order <formula formulatype="inline"><tex Notation="TeX">$\hbox{PI}^{\lambda}\hbox{D}^{\mu}$</tex></formula> controller and an ADR controller are both designed to regulate the speed of the system. Design procedures for both controllers are given in detail. Finally, corresponding results are compared. The extended state observer in the ADR controller is tested for torsional torque and the load machine speed with open-loop and closed-loop control structures. Performance analysis for both of the proposed controllers is confirmed by experimental results. Obtained results are also compared with the results given in the literature for the same system.

[1]  Alain Oustaloup,et al.  The CRONE Control of Resonant Plants: Application to a Flexible Transmission , 1995, Eur. J. Control.

[2]  Teresa Orlowska-Kowalska,et al.  Adaptive Sliding-Mode Neuro-Fuzzy Control of the Two-Mass Induction Motor Drive Without Mechanical Sensors , 2010, IEEE Transactions on Industrial Electronics.

[3]  H. Grotstollen,et al.  COMPARISON OF METHODS FOR STATE ESTIMATION AND ON-LINE IDENTIFICATION IN SPEED AND POSITION CONTROL LOOPS , 1999 .

[4]  Dan Wu,et al.  Design and Analysis of Precision Active Disturbance Rejection Control for Noncircular Turning Process , 2009, IEEE Transactions on Industrial Electronics.

[5]  Yong Zhang,et al.  Non-linear auto-disturbance rejection control of parallel active power filters , 2009 .

[6]  Teresa Orlowska-Kowalska,et al.  Vibration Suppression in a Two-Mass Drive System Using PI Speed Controller and Additional Feedbacks—Comparative Study , 2007, IEEE Transactions on Industrial Electronics.

[7]  Nobuyuki Matsui,et al.  GA-based evolutionary identification algorithm for unknown structured mechatronic systems , 2005, IEEE Transactions on Industrial Electronics.

[8]  Nobuyuki Matsui,et al.  Optimal design of robust vibration suppression controller using genetic algorithms , 2002, 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No.02TH8623).

[9]  D. Yoo,et al.  Optimal fast tracking observer bandwidth of the linear extended state observer , 2007, Int. J. Control.

[10]  Ivo Petraÿs,et al.  FRACTIONAL - ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[11]  Yuanqing Xia,et al.  Active disturbance rejection control for uncertain multivariable systems with time-delay , 2007 .

[12]  Leang-San Shieh,et al.  Load Disturbance Resistance Speed Controller Design for PMSM , 2006, IEEE Transactions on Industrial Electronics.

[13]  Yuichi Matsumoto,et al.  Analysis and experimental validation of force bandwidth for force control , 2003, IEEE International Conference on Industrial Technology, 2003.

[14]  Duarte Valério,et al.  Rule-based fractional control of an irrigation canal , 2009 .

[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]  Koksal Erenturk,et al.  Nonlinear two-mass system control with sliding-mode and optimised proportional-integral derivative controller combined with a grey estimator , 2008 .

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

[18]  Mingxing Fang,et al.  Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach , 2008, IEEE Transactions on Industrial Electronics.

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

[20]  Teresa Orlowska-Kowalska,et al.  FPGA Implementation of the Multilayer Neural Network for the Speed Estimation of the Two-Mass Drive System , 2011, IEEE Transactions on Industrial Informatics.

[21]  Hans Schuster,et al.  PI-Funnel Control for Two Mass Systems , 2009, IEEE Transactions on Automatic Control.

[22]  Dong Sun,et al.  Comments on Active Disturbance Rejection Control , 2007, IEEE Trans. Ind. Electron..

[23]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[24]  Mark Sumner,et al.  Control of an AC Dynamometer for Dynamic Emulation of Mechanical Loads With Stiff and Flexible Shafts , 2006, IEEE Transactions on Industrial Electronics.

[25]  Frede Blaabjerg,et al.  Reduced-order extended luenberger observer based sensorless vector control driven by matrix converter with nonlinearity compensation , 2006, IEEE Transactions on Industrial Electronics.

[26]  Vicente Feliu,et al.  On Fractional PID Controllers: A Frequency Domain Approach , 2000 .

[27]  Teresa Orlowska-Kowalska,et al.  Neural-Network Application for Mechanical Variables Estimation of a Two-Mass Drive System , 2007, IEEE Transactions on Industrial Electronics.

[28]  Zhiqiang Gao,et al.  Frequency Response Analysis of Active Disturbance Rejection Based Control System , 2007, 2007 IEEE International Conference on Control Applications.

[29]  C. Yeroglu,et al.  Note on fractional-order proportional–integral–differential controller design , 2011 .

[30]  Vicente Feliu-Batlle,et al.  Fractional robust control of main irrigation canals with variable dynamic parameters , 2007 .

[31]  K. Peter,et al.  Robust output-feedback H/sub /spl infin//-control with a nonlinear observer for a two-mass system , 2002, Conference Record of the 2002 IEEE Industry Applications Conference. 37th IAS Annual Meeting (Cat. No.02CH37344).

[32]  Yoichi Hori,et al.  Vibration suppression in 2- and 3-mass system based on the feedback of imperfect derivative of the estimated torsional torque , 1996, IEEE Trans. Ind. Electron..

[33]  K. Jezernik,et al.  Improved design of VSS controller for a linear belt-driven servomechanism , 2005, IEEE/ASME Transactions on Mechatronics.

[34]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[35]  Seung-Ki Sul,et al.  Kalman filter and LQ based speed controller for torsional vibration suppression in a 2-mass motor drive system , 1995, IEEE Trans. Ind. Electron..

[36]  Giansalvo Cirrincione,et al.  Sensorless Control of Induction Motors by Reduced Order Observer With MCA EXIN + Based Adaptive Speed Estimation , 2007, IEEE Transactions on Industrial Electronics.

[37]  M.A. Valenzuela,et al.  Evaluation of torsional oscillations in paper machine sections , 2004, IEEE Transactions on Industry Applications.

[38]  Ying Luo,et al.  Lateral directional fractional order (PI) π control of a small fixed-wing unmanned aerial vehicles: controller designs and flight tests , 2011 .

[39]  Teresa Orlowska-Kowalska,et al.  Damping of Torsional Vibrations in Two-Mass System Using Adaptive Sliding Neuro-Fuzzy Approach , 2008, IEEE Transactions on Industrial Informatics.

[40]  Zhiqiang Gao,et al.  Active disturbance rejection control: a paradigm shift in feedback control system design , 2006, 2006 American Control Conference.

[41]  Duarte Valério,et al.  Introduction to single-input, single-output fractional control , 2011 .

[42]  Daniel Hissel,et al.  Enhanced Servo-Control Performance of Dual-Mass Systems , 2007, IEEE Transactions on Industrial Electronics.

[43]  Xavier Moreau,et al.  Principles and Synthesis of Hydractive CRONE Suspension , 2004 .

[44]  S. Manabe.  A Suggestion of Fractional-Order Controller for Flexible Spacecraft Attitude Control , 2002 .

[45]  Mehmet Önder Efe,et al.  Neural Network Assisted Computationally Simple PI$^\lambda$D$^\mu$ Control of a Quadrotor UAV , 2011, IEEE Transactions on Industrial Informatics.

[46]  Xavier Moreau,et al.  The CRONE Suspension: Management of the Dilemma Comfort-Road Holding , 2004 .

[47]  Jingqing Han,et al.  From PID to Active Disturbance Rejection Control , 2009, IEEE Trans. Ind. Electron..

[48]  M. Ehsani,et al.  Simple Derivative-Free Nonlinear State Observer for Sensorless AC Drives , 2006, IEEE/ASME Transactions on Mechatronics.

[49]  Zhiqiang Gao,et al.  Discrete implementation and generalization of the extended state observer , 2006, 2006 American Control Conference.

[50]  Ivo Petráš,et al.  FRACTIONAL – ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[51]  K. Erenturk,et al.  Hybrid Control of a Mechatronic System: Fuzzy Logic and Grey System Modeling Approach , 2007, IEEE/ASME Transactions on Mechatronics.

[52]  Shantanu Das,et al.  Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power with a Robust PIλDμ Controller , 2012, ArXiv.

[53]  An-Chen Lee,et al.  Rejection of Limit Cycles Induced From Disturbance Observers in Motion Control , 2006, IEEE Transactions on Industrial Electronics.

[54]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[55]  Slobodan N. Vukosavic,et al.  Suppression of torsional oscillations in a high-performance speed servo drive , 1998, IEEE Trans. Ind. Electron..

[56]  Zhiqiang Gao,et al.  A DSP-based active disturbance rejection control design for a 1-kW H-bridge DC-DC power converter , 2005, IEEE Trans. Ind. Electron..

[57]  B. Orlik,et al.  Robust output-feedback H/sub /spl infin//-control with a nonlinear observer for a two-mass system , 2002 .

[58]  Masoud Karimi-Ghartemani,et al.  Method for designing PI λ D μ stabilisers for minimum-phase fractional-order systems , 2010 .