An Error Learning Scenario-Based Scheme to Quantized Identification in Wiener-Hammerstein Systems Subject to Deadzone Nonlinearity

Most of the existing estimation methods for nonlinear systems have been developed by using non-self-error data (e.g., prediction error and observation error, etc.), potentially resulting in a tricky problem. In this paper, we propose a new estimator design for nonlinear Wiener-Hammerstein systems subject to quantised measurements, where the self-error data (i.e., initial error and estimation error) are used. For this purpose, the estimation error information is derived by introducing several auxiliary variables with an error feedback filter. Then, a compensated estimation error variable is designed to remove the hostile effect of the regressor matrix on the estimator. A novel adaptive parameter estimation learning law is proposed based on a performance evaluation function, where the compensated estimation error term, initial error term and several restraint conditions are used to construct the aforementioned evaluation function. In addition, the online verification of persistent excitation (PE) condition is also provided. Finally, the efficiency and availability of the proposed scheme are validated through numerical examples and experiment in comparison with the available estimation algorithms
Note to Practitioners
—This study was motivated by the system modelling and identification problem of the servomechanism but is also uses to other nonlinear systems that have deadzone, saturation, backlash and hysteresis nonlinearity characteristics. Available methods to use common error data to establish an estimator that produces biased estimate and initial-value problems. This study introduces a new scheme using the self-error data to establish an estimator, to provide a new framework of identification method design, and to improve above-mentioned problems. The self-error data are directly related to parameter adaptive updates, thus giving positive estimation performance. In this study, we mathematically characterize the dynamical equations for the servomechanism. We introduce how to extract self-error data from the input and output data of system. This is the key step for us to construct an estimator in the future. Then, based on self-error data and several constraint conditions, a novel estimator is provided using recursive pattern. Preliminary practical experiments indicate that the proposed method is feasible but it has not yet been tested in the complex industrial production.