Grey Box Identification of Fractional-order System Models from Frequency Domain Data

In the following paper, the grey box system identification method is applied to the problem of fractional-order model identification from available frequency domain data. Oftentimes, this is the only feasible approach in case of industrial system identification where the capacity to perform time domain experiments is limited due to associated expenses. In this work, we comment on the potential of this approach and investigate the model parameter estimation method based on frequency domain data. Then, the implementation of the method in FOMCON toolbox for MATLAB is described. Finally, the resulting application is validated on the basis of a relevant academic example.

[1]  Y. Chen,et al.  A fractional order PID tuning algorithm for a class of fractional order plants , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[2]  Manuel Duarte Ortigueira,et al.  Identifying a Transfer Function From a Frequency Response , 2007 .

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

[4]  M. Amairi,et al.  A direct fractional order bias eliminated least squares method for the fractional closed-loop system identification , 2015, 2015 IEEE 12th International Multi-Conference on Systems, Signals & Devices (SSD15).

[5]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[6]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[7]  Lennart Ljung,et al.  Closed-loop identification revisited , 1999, Autom..

[8]  Eduard Petlenkov,et al.  FOMCON: Fractional-order modeling and control toolbox for MATLAB , 2011, Proceedings of the 18th International Conference Mixed Design of Integrated Circuits and Systems - MIXDES 2011.

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

[10]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[11]  Eduard Petlenkov,et al.  Closed-loop identification of fractional-order models using FOMCON toolbox for MATLAB , 2014, 2014 14th Biennial Baltic Electronic Conference (BEC).

[12]  Bruce J. West.  Fractional Calculus View of Complexity: Tomorrow’s Science , 2015 .

[13]  Tom T. Hartley,et al.  Fractional-order system identification based on continuous order-distributions , 2003, Signal Process..

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

[15]  Aleksei Tepljakov,et al.  Fractional-order Modeling and Control of Dynamic Systems , 2017 .

[16]  Yong Wang,et al.  Frequency domain subspace identification of commensurate fractional order input time delay systems , 2011 .

[17]  Cheng-Ching Yu.  Autotuning of PID Controllers , 1999 .

[18]  YangQuan Chen,et al.  Frequency domain modelling and control of fractional-order system for permanent magnet synchronous motor velocity servo system , 2016 .

[19]  Kevin L. Moore,et al.  Relay feedback tuning of robust PID controllers with iso-damping property , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[20]  Inés Tejado,et al.  Identifying a non-commensurable fractional transfer function from a frequency response , 2015, Signal Process..

[21]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[22]  J. J. Moré,et al.  Levenberg--Marquardt algorithm: implementation and theory , 1977 .