Abstract
In this paper, a recursive closed-loop subspace identification method for Hammerstein nonlinear systems is proposed. To reduce the number of unknown parameters to be identified, the original hybrid system is decomposed as two parsimonious subsystems, with each subsystem being related directly to either the linear dynamics or the static nonlinearity. To avoid redundant computations, a recursive least-squares (RLS) algorithm is established for identifying the common terms in the two parsimonious subsystems, while another two RLS algorithms are established to estimate the coefficients of the nonlinear subsystem and the predictor Markov parameters of the linear subsystem, respectively. Subsequently, the system matrices of the linear subsystem are retrieved from the identified predictor Markov parameters. The convergence of the proposed method is analyzed. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed method.
Highlights
Hammerstein systems can effectively represent and capture the nonlinearity and linear dynamics of many real-world nonlinear processes, e.g., turntable servo systems [1], voltage management systems [2], and blast furnace ironmaking systems [3]
The focus of this paper is on the subspace identification methods (SIMs) for Hammerstein state space systems
The parsimonious SIMs based on a truncated SVD decomposition have been proposed to reduce the number of unknown parameters to be estimated. These methods are developed by using different regression iterative or recursive algorithms to retrieve the underlying system matrices of the nonlinear subsystem and dynamic linear subsystem, separately
Summary
Hammerstein systems can effectively represent and capture the nonlinearity and linear dynamics of many real-world nonlinear processes, e.g., turntable servo systems [1], voltage management systems [2], and blast furnace ironmaking systems [3]. J. Hou et al.: Recursive Parsimonious Subspace Identification for Closed-Loop Hammerstein Nonlinear Systems parameters are slowly time-varying, recursive OPM-like SIMs were proposed [18]–[20]. The parsimonious SIMs based on a truncated SVD decomposition have been proposed to reduce the number of unknown parameters to be estimated These methods are developed by using different regression iterative or recursive algorithms to retrieve the underlying system matrices of the nonlinear subsystem and dynamic linear subsystem, separately. A few efforts have been done for iterative subspace identification, for example, reference [21] developed a Gauss-Newton iteration based SIM for closed-loop Hammerstein state space models in innovation form. A recursive parsimonious SIM is first proposed for closed-loop Hammerstein state space models in innovation form.
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