Zheng Zhang/Olga Kostyukova/Yuanliang Zhang/Kil To Chong
The Journal of Mechanical Science and Technology, vol. 24, no. 3, pp.731-741, 2010

Abstract : A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable.

Keyword : Nonlinear system; Hybrid discretization algorithm; Matrix exponential; Time delay; Taylor series