Hysteresis nonlinearity of piezoelectric actuators degrades the positioning accuracy of micro-/nano-positioning systems. To overcome this problem, an innovative hysteresis compensator based on least squares support vector machine (LSSVM) is proposed in this paper. First, the LSSVM hysteresis modeling is presented using Nonlinear Auto Regressive eXogenous (NARX) structure. To compensate for the hysteresis behavior, two feedforward control schemes according to different inputs of NARX model are proposed and analyzed separately. Then, a hybrid feedforward controller combining both the control schemes is put forward to revise the model input. To further improve the tracking performance, the hybrid feedforward control combined with the feedback control is realized. The comparative study reveals the superior tracking performance of feedforward-feedback control scheme over hybrid feedforward control or feedback control. Moreover, the hybrid feedforward-feedback control scheme is capable of tracking different testing waveforms with negligible errors, which confirms the effectiveness and generalization ability of the proposed approach.

To overcome the low positioning accuracy of piezoelectric actuators (PZAs) caused by the hysteresis nonlinearity, this paper proposes an adaptive weighted least squares support vector regression (AWLSSVR) to model the rate-dependent hysteresis of PZA. Firstly, the AWLSSVR hyperparameters are optimized by using particle swarm optimization. Then an adaptive weighting strategy is proposed to eliminate the effects of noises in the training dataset and reduce the sample size at the same time.Finally, the proposed approach is applied to predict the hysteresis of PZA. The results show that the proposed method is more accurate than other versions of least squares support vector regression for training samples with noises, and meanwhile reduces the sample size and speeds up calculation.

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