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Laguerre based adaptive control of piezoelectric actuator for nanopositioning

This paper considers the Laguerre based adaptive control of piezoelectric actuator for nanopositioning. Laguerre-based adaptive filters provide an attractive alternative to adaptive FIR filters in the sense that they provide better approximation of system with a long impulse response with a restricted order. Laguerre also keeps many of the advantages of adaptive FIR filter, such as unique global minimum and guaranteed stability. In this paper, the Laguerre based model matching problem is studied. A better optimal solution can be achieved by proper chosen pole location of all-pass filter in Laguerre filter. The Least-Mean-Square (LMS) algorithm based on Laguerre structure is then discussed. The results show that with same step size constraint, the Laguerre based LMS algorithm introduces less excessive mean-square-error. The Laguerre-based LMS algorithm is then applied to the adaptive control for reference tracking. Due to the model mismatch, the traditional adaptive feed-forward structure is modified to the adaptive inverse control structure for better tracking performance. The proposed approach is implemented in FPGA with 100kHz sampling rate and applied to piezoelectric actuator for nanopositioning. Experimental results show effectiveness of the proposed approach.