Elsevier

Systems & Control Letters

Volume 5, Issue 4, February 1985, Pages 267-271
Systems & Control Letters

Identification of time delays using a polynomial identification method

https://doi.org/10.1016/0167-6911(85)90020-9Get rights and content

Abstract

An algorithm for the exact least-squares identification of an approximate continuous-time time-delay system is derived and its operation verified by simulation.

References (6)

There are more references available in the full text version of this article.

Cited by (72)

  • Optimal state-delay control in nonlinear dynamic systems

    2022, Automatica
    Citation Excerpt :

    Some important practical problems such as delay estimation problems (Banks et al., 1981) and delayed feedback controller design problems (Guan et al., 2007) are of this type. For optimal state-delay control problems with linear dynamics and a single fixed delay, the optimal delay can be determined using various computational approaches, such as least-squares optimization (Gawthrop & Nihtilä, 1985), steepest descent (Diop et al., 2001), or genetic algorithms (Pan et al., 2003). The nonlinear case is far more challenging, but several gradient-based optimization algorithms have been developed in Chai et al. (2013a, 2013b), Liu et al. (2014), and Loxton et al. (2010).

  • Useful redundancy in parameter and time delay estimation for continuous-time models

    2018, Automatica
    Citation Excerpt :

    A simple approach is to consider the impulse response data, e.g. estimate the time delay by finding where the impulse response becomes nonzero (Carlemalm, Halvarsson, Wigren, & Wahlberg, 1999) or by noting the delay where the correlation between input and output is maximum (Carlemalm et al., 1999; Carter, 1987). Another approach is to model the delay by a rational polynomial transfer function using a Padé or similar approximation and then estimate the time delay as part of the system parameters (Agarwal & Canudas, 1987; Ahmed, Huang, & Shah, 2006; Gawthrop & Nihtil, 1985). In Baysse, Carrillo, and Habbadi (2011, 2012) and Yang, Iemura, Kanae, and Wada (2007), the time delay and system parameters of a Multiple Input Single Output CT system are estimated in a separable way using an iterative global nonlinear least-squares or instrumental variable method.

  • Recursive parameter estimation of exhaust gas oxygen sensors with input-dependent time delay and linear parameters

    2015, Control Engineering Practice
    Citation Excerpt :

    However, these approaches suffer from the drawback that they are restricted to rather small time delays, compared to the sampling interval of the system (only few multiples of the sampling interval). To overcome this drawback, various heuristic extensions of these approaches have been developed, which for instance can be found in the publications (Agarwal & Canudas, 1987; Durbin, 1985; Gawthrop & Nihtilä, 1985; Jones, 2004; O׳Dwyer & Ringwood, 1994; Björklund & Ljung, 2009; Fischer & Medvedev, 1999; Hidayat & Medvedev, 2012; Isaksson et al., 2001). Another approach for time delay estimation is the overparameterization method as presented for instance in Kurz and Goedecke (1981).

View all citing articles on Scopus

On leave from the Helsinki University of Technology, Otaniemi, Otakaari 5a, 02150 Espoo 15, Finland

View full text