D. Zhai, D.K. Rollins, Sr., and N. Bhandari (USA)
Nonlinear systems, continuous-time modeling, sinusoidalinput sequence, Hammerstein model
Discrete-time modeling (DTM) dominates the system engineering literature in the applications of block-oriented modeling. According to Seborg and Henson [1], two major reasons are: (1) the discrete environment of computer-based process control systems and (2) discrete sampling. However, two further reasons include: (3) DTM is easier to obtain because all input changes are approximated by piecewise step input sequences and (4) DTM has a "compact" property that limits its dependence to just a few recent input changes. Nonetheless, DTM has (potentially) two critical drawbacks relative to continuous-time modeling (CTM). DTM requires constant and frequent sampling and is not as accurate as CTM since, at best, DTM can only approximate continuous time processes. In addition, if the error term for a model is stochastically continuous (as in Brownian motion) and must be treated as such, then DTM is not useful. For Hammerstein and Wiener CTM, Bhandari and Rollins [2] introduced a non-compact CTM approach without restriction to the input sequences as well as a compact approach with restriction to piece-wise step inputs. This work extends their work and proposes compact CTM algorithms under various types of sinusoidal input sequences for Hammerstein modeling.
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