Fractional order control: a tutorial

  • Authors:

  • YangQuan Chen;Ivo Petráš;Dingyü Xue

  • Affiliations:

  • Center for Self-Organizing and Intelligent Systems, Department of Electrical and Computer Engineering, Utah State University, Logan, UT;Institute of Control and Informatization of Production Processes, BERG Faculty, Technical University of Košce, Košice, Slovak Republic;Faculty of Information Sciences and Engineering, Northeastern University, Shenyang, P. R. China

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of noninteger order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.