On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements

It is well known that, in some industrial process identification situations, measurements can be collected from closed-loop experiments for several reasons such as stability, safety, and performance constraints. In this paper, we investigate the problem of identifying continuous-time fractional closed-loop linear parameter varying systems. The simplified refined instrumental variable method is developed to estimate both coefficients and differentiation orders. This method is established to provide consistent estimates when the output and the scheduling variable are contaminated by additive measurements noise. The proposed scheme is evaluated in comparison with other approaches in terms of a simulation example.

[1]  Hugues Garnier,et al.  Parameter and differentiation order estimation in fractional models , 2013, Autom..

[2]  Saeed Tavakoli,et al.  Fractional order PID control design for semi-active control of smart base-isolated structures: A multi-objective cuckoo search approach. , 2017, ISA transactions.

[3]  Mohamed Aoun,et al.  Instrumental variable based methods for continuous-time linear parameter varying system identification with fractional models , 2016, 2016 24th Mediterranean Conference on Control and Automation (MED).

[4]  Alain Oustaloup,et al.  Synthesis of fractional Laguerre basis for system approximation , 2007, Autom..

[5]  Régis Ouvrard,et al.  Parameter Estimation of Fractional Systems: Application to the Modeling of a Lead-Acid Battery , 2000 .

[6]  Mohamed Aoun,et al.  On the Closed-Loop System Identification with Fractional Models , 2015, Circuits Syst. Signal Process..

[7]  Y. Chen,et al.  Tuning fractional order proportional integral controllers for fractional order systems , 2010 .

[8]  J. Gabano,et al.  Identification of a thermal system using continuous linear parameter-varying fractional modelling , 2011 .

[9]  Mehdi Dalir,et al.  Applications of Fractional Calculus , 2010 .

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

[11]  M. Amairi,et al.  Indirect approach for closed-loop system identification with fractional models , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

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

[13]  Mohamed Aoun,et al.  A bias correction method for fractional closed-loop system identification , 2015 .

[14]  D. Matignon.  Stability properties for generalized fractional differential systems , 1998 .

[15]  Hugues Garnier,et al.  An optimal instrumental variable method for continuous-time fractional model identification , 2008 .

[16]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[17]  Mohamed Aoun,et al.  Model-based fractional order controller design , 2017 .

[18]  Yuquan Chen,et al.  Stability for nonlinear fractional order systems: an indirect approach , 2017 .

[19]  Thierry Poinot,et al.  LPV continuous fractional modeling applied to ultracapacitor impedance identification , 2015 .

[20]  A. Oustaloup,et al.  Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction , 2000 .

[21]  A. Oustaloup,et al.  Fractional state variable filter for system identification by fractional model , 2001, 2001 European Control Conference (ECC).

[22]  M. Tavazoei,et al.  Proportional stabilization and closed-loop identification of an unstable fractional order process , 2014 .

[23]  Yong Wang,et al.  Modulating function-based subspace identification for continuous-time fractional order systems , 2017, 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC).