Separating the Identifications of Nonlinear and Linear Parts In Block-Oriented Nonlinear Models Using Subspace Identification Approach

Wednesday, October 19, 2011
Exhibit Hall B (Minneapolis Convention Center)
Jyh-Cheng Jeng, Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, Taipei, Taiwan

In the last decades, a considerable amount of research has been carried out on modeling, identification, and control of nonlinear systems. Most dynamical systems can be better represented by nonlinear models, which are able to describe the global behavior of the system over wide ranges of operating conditions, rather than by linear ones that are only able to approximate the system around a given operating point. One of the most frequently studied classes of nonlinear models are the so-called block-oriented nonlinear models, which involve a cascade combination of a linear dynamic block and a nonlinear static (memoryless) one. Such models are related very closely to linear ones and can be easily adapted to linear control techniques. Two typical block-oriented model structures are the Hammerstein and Wiener models. In the Hammerstein structure, the linear dynamic element is preceded by the nonlinear static element. The order of connection is reversed in the Wiener structure. These model structures have been successfully used to describe nonlinear systems in a number of practical applications in the areas of chemical processes, biological processes, signal processing, communications, and control.

Many approaches have been proposed in the literature for the identification of Hammerstein and/or Wiener models, and they fall into two main groups. The first group is simultaneous parameter identification of the linear and nonlinear elements, which usually leads to iterative procedures or nonlinear optimization problems. The major difficulty is that the convergence of parameter estimates to the actual values is not always warranted. The second group is elaborated to separate the identification of the nonlinear static part from that of the linear dynamic part. This often involves a special design of the test input signal that enables the decoupling of the linear and nonlinear parts. The requirement on the test signal would cause extra implementation complexity during the identification test.

To overcome the aforementioned drawbacks in the existing methods, this work develops a novel method for the identification of block-oriented nonlinear models (Hammerstein and Wiener models). The linear dynamic element is represented as its finite impulse response (FIR) model, and the static nonlinearity is approximated by expansions of basis functions. The identification problem is to estimate the unknown FIR model and expansion coefficients characterizing the linear and the nonlinear parts, respectively, from a data set of observed input-output measurements. Notice that the intermediate variable between blocks is non-accessible. The algorithm is derived from the subspace identification method (SIM) with a proper selection of the future horizon. In comparison with other works, the proposed method has three advantages: (1) special design of the test input signal is not required; (2) parameter estimations of the nonlinear and linear parts are decoupled; (3) iterative and/or nonlinear optimization procedures are avoided. These features significantly reduce the identification complexities in process test and computation, which makes the proposed method more suitable for practical applications. Simulation examples will be provided to demonstrate the effectiveness of the proposed method. Finally, it is noted that the proposed method is also applicable to multivariable systems. 

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