Fractional PIλD Controller Design for a Magnetic Levitation System

Currently, there are no formalized methods for tuning non-integer order controllers. This is due to the fact that implementing these systems requires using an approximation of the non-integer order terms. The Oustaloup approximation method of the sα fractional derivative is intuitive and widely adopted in the design of fractional-order PIλD controllers. It requires special considerations for real-time implementations as it is prone to numerical instability. In this paper, for design and tuning of fractional regulators, we propose two methods.The first method relies on Nyquist stability criterion and stability margins. We base the second on parametric optimization via Simulated Annealing of multiple performance indicators. We illustrate our methods with a case study of the PIλD controller for the Magnetic Levitation System. We illustrate our methods’ efficiency with both simulations and experimental verification in both nominal and disturbed operation.

[1]  Mohamed S. Kandil,et al.  Application of Second-Order Sliding-Mode Concepts to Active Magnetic Bearings , 2018, IEEE Transactions on Industrial Electronics.

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

[3]  Jerzy Baranowski,et al.  On Digital Realizations of Non-integer Order Filters , 2016, Circuits Syst. Signal Process..

[4]  Shantanu Das,et al.  Design and implementation of digital fractional order PID controller using optimal pole-zero approximation method for magnetic levitation system , 2018, IEEE/CAA Journal of Automatica Sinica.

[5]  Sandeep Pandey,et al.  Anti-windup Fractional Order $$\textit{PI}^\lambda -\textit{PD}^\mu $$PIλ-PDμ Controller Design for Unstable Process: A Magnetic Levitation Study Case Under Actuator Saturation , 2017 .

[6]  Sandeep Pandey,et al.  A novel 2-DOF fractional-order PIλ-Dμ controller with inherent anti-windup capability for a magnetic levitation system , 2017 .

[7]  Satish Chand,et al.  Fault-tolerant control of three-pole active magnetic bearing , 2009, Expert Syst. Appl..

[8]  Rajiv Tiwari,et al.  Application of active magnetic bearings in flexible rotordynamic systems – A state-of-the-art review , 2018, Mechanical Systems and Signal Processing.

[9]  Jin-Ho Seo,et al.  Design and analysis of the nonlinear feedback linearizing control for an electromagnetic suspension system , 1996, IEEE Trans. Control. Syst. Technol..

[10]  John Chiasson,et al.  Linear and nonlinear state-space controllers for magnetic levitation , 1996, Int. J. Syst. Sci..

[11]  P. Ananthababu,et al.  Design of fractional model reference adaptive PID controller to magnetic levitation system with permagnet , 2016 .

[12]  Waldemar Bauer,et al.  Implementation of Bi-fractional Filtering on the Arduino Uno Hardware Platform , 2017 .

[13]  D. Howe,et al.  Robust control of a magnetic-bearing flywheel using dynamical compensators , 2001 .

[14]  Jerzy Baranowski,et al.  Stability Properties of Discrete Time-Domain Oustaloup Approximation , 2015, RRNR.

[15]  Subhojit Ghosh,et al.  Real time implementation of fractional order PID controllers for a magnetic levitation plant , 2017 .

[17]  M. Lairi,et al.  A neural network with minimal structure for maglev system modeling and control , 1999, Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No.99CH37014).

[18]  Aleksei Tepljakov,et al.  FOMCON: Fractional-Order Modeling and Control Toolbox , 2017 .

[19]  Jerzy Baranowski,et al.  Observer-based feedback for the magnetic levitation system , 2012 .

[20]  Cheol Hoon Park,et al.  Design Aspects of High-Speed Electrical Machines With Active Magnetic Bearings for Compressor Applications , 2017, IEEE Transactions on Industrial Electronics.