Identification of Lifted Models for General Dual-Rate Sampled-Data Systems Using N4SID Algorithm
The technological and the economical reasons often make the researchers and engineers encounter the so-called multirate sampled-data systems which include multiple sampleddata mechanisms with different sampling periods. As a class of multi-rate systems, general dual-rate systems are very attractive because the contributions in the literature of the dual-rate systems can be easily extended to the whole scope of multi-rate sampled system. In this research, we consider the identification problems for the general dual-rate systems. A general dual-rate system is illustrate Fig. 1. In Fig. 1, u(kT1) and y(kT2) are the dual-rate system input and output signals and the sampling period T1 = T2. y(kT2) is corrupted by a stochastic noise v(kT2). The measurement of the output is denoted by z(kT2) . ZOH is a zero order holder with period T1. ADC is a sampler with period T2. Pc is a linear time-invariant(LTI) continuous-time process. Suppose that the samplers and zero order holders are synchronized at time t = 0. Most typical identification algorithms only handle the identification problems of single-rate systems. However, a single-rate LTI isomorphism can be obtained for the dualrate system in Fig.1 by the lifting technique. The isomorhpism is the so-called lifted model, Although there are several contributions in the literature for the identification problems of the lifted models, most of them need detailed prior information about the dual-rate system, e.g. observability structure indexes which cannot be obtained in many cases. In contrast, Subspace State-Space IDentification(4SID) algorithms need no prior information about the systems under investigation. Unfortunately, it is commented that the 4SID type algorithm cannot be used to the lifted models because of the causality constraints.