A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems

The control of a special class of Single Input Single Output (SISO) switched fractional order systems (SFOS) is addressed from the viewpoints of the Generalized Proportional Integral (GPI) feedback control approach and a sliding mode based Σ − Δ modulation implementation of an average model based designed feedback controller. Alternatively, a Pulse Width Modulation (PWM) duty ratio synthesis approach is also developed for the approximate discontinuous control of the same class of systems. A fractional order GPI controller is proposed which transforms the average model of the system into a pure, integer order, chain of integrations with desired closed loop dynamics achieved through a classical compensation network robustly acting in the presence of constant load perturbations. A sliding mode based Σ − Δ modulation and a PWM based Σ − Δ modulation implementation of the continuous, bounded, dynamic average output feedback control signal is adopted for the switched system. An illustrative simulation example dealing with an electric radiator system is presented.

[1]  Sunil K. Agrawal,et al.  Differentially Flat Systems , 2004 .

[2]  N. Retiere,et al.  Half-order modelling of supercapacitors , 2004, Conference Record of the 2004 IEEE Industry Applications Conference, 2004. 39th IAS Annual Meeting..

[3]  R. Steele,et al.  Delta Modulation Systems , 1975 .

[4]  T. Hartley,et al.  Dynamics and Control of Initialized Fractional-Order Systems , 2002 .

[5]  Arkadiĭ Khaĭmovich Gelig,et al.  Stability and Oscillations of Nonlinear Pulse-Modulated Systems , 1998 .

[6]  Hebertt Sira-Ramírez.  SLIDING MODES, Δ‐MODULATORS, AND GENERALIZED PROPORTIONAL INTEGRAL CONTROL OF LINEAR SYSTEMS , 2008 .

[7]  I. Podlubny.  Fractional differential equations , 1998 .

[8]  A. Oustaloup.  La dérivation non entière , 1995 .

[9]  T. Poinot,et al.  Identification of Fractional Systems Using an Output-Error Technique , 2004 .

[10]  Alain Oustaloup,et al.  Motion Control by ZV Shaper Synthesis Extended for Fractional Systems and Its Application to CRONE Control , 2004 .

[11]  H. Sira-Ramírez.  A geometric approach to pulse-width modulated control in nonlinear dynamical systems , 1989 .

[12]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

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

[14]  Hebertt Sira-Ramírez,et al.  Sliding mode control of DC‐to‐DC power converters using integral reconstructors , 2002 .

[15]  M. Fliess,et al.  CORRECTEURS PROPORTIONNELS-INT EGRAUX G EN ERALIS ES , 2002 .

[16]  M. Fliess,et al.  Correcteurs proportionnels-intégraux généralisés , 2002 .