Issues in separable identification of continuous-time models with time-delay

Abstract This paper discusses several issues related to the identification of time-delayed continuous-time systems using the refined instrumental variable method. The proposed estimation procedure is iterative where, at each iteration, the rational system parameters and time-delay are estimated separately. The main contribution of this paper covers three aspects. Firstly, conditions for persistent excitation are established, which should be satisfied to guarantee the identifiability of the system parameters and time-delay. Secondly, existence of multiple minima in the loss function is investigated. Due to the nonlinear nature of the loss function to be optimized with respect to the time-delay, initialization is a particularly important issue for correct estimation of the time-delay. Lastly, to reliably initialize the identification algorithm, based on the previous analysis, some guidelines are proposed to facilitate the choice of reliable initial parameters. The main results derived in this paper are verified by means of both theoretical analyses and numerical simulations.

[1]  Yuanqing Xia,et al.  Adaptive parameter identification of linear SISO systems with unknown time-delay , 2014, Syst. Control. Lett..

[2]  Peter C. Young,et al.  Identification and estimation of continuous-time, data-based mechanistic (DBM) models for environmental systems , 2006, Environ. Model. Softw..

[3]  H. Kurz,et al.  Digital parameter-adaptive control of processes with unknown dead time , 1981, Autom..

[4]  Riccardo Scattolini,et al.  On the identifiability of the time delay with least-squares methods , 1996, Autom..

[5]  Wei Xing Zheng,et al.  Identification of linear dynamic systems operating in a networked environment , 2009, Autom..

[6]  P. Young,et al.  Refined instrumental variable methods of recursive time-series analysis Part I. Single input, single output systems , 1979 .

[7]  Svante Björklund,et al.  A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems , 2003 .

[8]  Peter C. Young,et al.  Comment on 'Projection-based identification algorithm for grey-box continuous-time models' by Ichiro Maruta and Toshiharu Sugie , 2014, Syst. Control. Lett..

[9]  G. Carter,et al.  The generalized correlation method for estimation of time delay , 1976 .

[10]  Wei Xing Zheng,et al.  Optimizing search-based identification of stochastic time-delay systems , 1991 .

[11]  Peter C. Young,et al.  The advantages of directly identifying continuous-time transfer function models in practical applications , 2014, Int. J. Control.

[12]  Tore Hägglund,et al.  Advanced PID Control , 2005 .

[13]  T. Söderström,et al.  Instrumental variable methods for system identification , 1983 .

[14]  Rolf Isermann,et al.  Practical aspects of process identification , 1979, Autom..

[15]  Zi-Jiang Yang,et al.  Identification of continuous-time systems with multiple unknown time delays by global nonlinear least-squares and instrumental variable methods , 2007, Autom..

[16]  Hugues Garnier,et al.  Direct continuous-time approaches to system identification. Overview and benefits for practical applications , 2015, Eur. J. Control.

[17]  Wei Xing Zheng,et al.  Convergence analysis of refined instrumental variable method for continuous-time system identification , 2011 .

[18]  Wei Xing Zheng,et al.  Identification problems in distributed parameter neuron models , 1990 .

[19]  Yury Orlov,et al.  On-line identification of SISO linear time-invariant delay systems from output measurements , 2007, Autom..

[20]  P. Young,et al.  Refined instrumental variable methods of recursive time-series analysis Part III. Extensions , 1980 .

[21]  Wei Xing Zheng,et al.  Identification of linear continuous-time systems under irregular and random output sampling , 2015, Autom..

[22]  G. Goodwin,et al.  Identification of continuous-time state-space models from non-uniform fast-sampled data , 2011 .

[23]  Peter C. Young,et al.  Recursive Estimation and Time-Series Analysis: An Introduction , 1984 .

[24]  P. Young,et al.  Refined Instrumental Variable Identification of Continuous-time Hybrid Box-Jenkins Models , 2008 .

[25]  G. Golub,et al.  Separable nonlinear least squares: the variable projection method and its applications , 2003 .

[26]  Ahmad B. Rad,et al.  Simultaneous online identification of rational dynamics and time delay: a correlation-based approach , 2003, IEEE Trans. Control. Syst. Technol..

[27]  Hugues Garnier,et al.  Robust time-domain output error method for identifying continuous-time systems with time delay , 2017, Syst. Control. Lett..

[28]  Sirish L. Shah,et al.  Time delay estimation for MIMO dynamical systems – With time-frequency domain analysis , 2010 .

[29]  Su Whan Sung,et al.  Prediction Error Identification Method for Continuous-Time Processes with Time Delay , 2001 .

[30]  P. Gawthrop,et al.  Identification of time delays using a polynomial identification method , 1985 .

[31]  Marion Gilson,et al.  A Frequency Localizing Basis Function-Based IV Method for Wideband System Identification , 2018, IEEE Transactions on Control Systems Technology.

[32]  Karl Johan Åström,et al.  Relay Feedback Auto-tuning of Process Controllers – A Tutorial Review , 2002 .

[33]  M. Gilson,et al.  Robust identification of continuous-time models with arbitrary time-delay from irregularly sampled data , 2015 .

[34]  Sirish L. Shah,et al.  Parameter and delay estimation of continuous-time models using a linear filter , 2006 .

[35]  Peter C. Young,et al.  Refined instrumental variable estimation: Maximum likelihood optimization of a unified Box-Jenkins model , 2015, Autom..