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The parameter estimation problem for the Hammerstein systems with asymmetric preload nonlinearity is considered in this paper. The nonlinearity is described by the piecewise function, which brings difficulty to the identification. By introducing a switching function, the static nonlinearity is described by an expression with unknown preload points and slopes. By using the key term separation technique, the unknown parameters from the nonlinear block and linear block are decoupled and collected in a parameter vector. Under the gradient iterative (GI) algorithm with finite measured data, the estimates of unknown parameters are obtained. Furthermore, combining the ideas of the recursive and iterative algorithms, a dynamic sliding window is designed. By updating the training data, the sliding window removes the oldest data and adds the newest sampled data to keep the length of the training data unchanged. The sliding window gradient-based iterative algorithm is proposed to estimate the unknown parameters. Moreover, compared with the stochastic gradient algorithm, the sliding window GI algorithm can improve the accuracy of parameter estimation and the utilization of the system data. The numerical simulation example is employed to validate the effectiveness of the proposed algorithms.

Sliding Window Iterative Identification of Systems With Asymmetric Preload Nonlinearity Based on the Key Term Separation