Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares(ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

Time delay recursive neural network-based direct adaptive control for a piezo-actuated stage

Piezo-actuated stage is a core component in micro-nano manufacturing field.However,the inherent nonlinearity,such as rate-dependent hysteresis,in the piezo-actuated stage severely impacts its tracking accuracy.This study proposes a direct adaptive control(DAC)method to realize high precision tracking.The proposed controller is designed by a time delay recursive neural network.Compared with those existing DAC methods designed under the general Lipschitz condition,the proposed control method can be easily generalized to the actual systems,which have hysteresis behavior.Then,a hopfield neural network(HNN)estimator is proposed to adjust the parameters of the proposed controller online.Meanwhile,a modular model consisting of linear submodel,hysteresis submodel,and lumped uncertainties is established based on the HNN estimator to describe the piezoactuated stage in this study.Thus,the performance of the HNN estimator can be exhibited visually through the modeling results.The proposed control method eradicates the adverse effects on the control performance arising from the inaccuracy in establishing the offline model and improves the capability to suppress the influence of hysteresis on the tracking accuracy of piezo-actuated stage in comparison with the conventional DAC methods.The stability of the control system is studied.Finally,a series of comparison experiments with a dual neural networks-based data driven adaptive controller are carried out to demonstrate the superiority of the proposed controller.