Iterative Methods for Identification of Multiple Input Continuous-time Systems with Unknown Time Delays

Many practical systems such as thermal processes, chemical processes and biological systems, etc., have inherent time-delay. If the time-delay used in the system model for controller design does not coincide with the actual process time-delay, a closed-loop system may be unstable or exhibits unacceptable transient response characteristics. Therefore, the problem of identifying such a system is of great importance for analysis, synthesis and prediction. Numerous identification methods of time delay systems based on discrete-time models have been proposed [3,32]. However, since physical systems considered in science and engineering are usually continuous in time, it is sometimes desirable to obtain a continuous-time model [12,24,29]. In [9], a general framework of the technique of step-invariant transform from z-to s-domain was proposed , and it was pointed out that the technique may also be applicable to a system with fractional delay which is not an integral multiple of sampling period. There have been some typical approaches to identification of continuous-time models with unknown delay. One approach is based on the approximation of the time-delay in the frequency-domain by a rational transfer function or the padé approximation [1, 4]. This approach requires estimation of more parameters because the order of the approximated system model is increased. And it is not easy to separate the parameters concerned with the time delay from those concerned with the transfer function of the system. Another problem in this method is that it may introduce unacceptable approximation error when the system has a large time-delay. Another approach is based on the nonlinear optimisation method like non-linear least squares (LS) method that searches for the optimum by using a gradient-following technique. In [5, 23], some variations of pure continuous-time on-line nonlinear LS methods were studied. The off-line separable nonlinear least squares (SEPNLS) method was studied in [11], where the time delays were searched exhaustively with spline interpo