By Qingsong Xu, Kok Kiong Tan
This e-book explores rising tools and algorithms that allow specific regulate of micro-/nano-positioning structures. The textual content describes 3 keep watch over techniques: hysteresis-model-based feedforward keep an eye on and hysteresis-model-free suggestions keep an eye on in response to and unfastened from nation commentary. every one paradigm gets committed awareness inside of a selected a part of the text.
Readers are proven the way to layout, validate and practice numerous new keep watch over methods in micromanipulation: hysteresis modelling, discrete-time sliding-mode keep watch over and model-reference adaptive keep watch over. Experimental effects are supplied all through and increase to an in depth remedy of functional functions within the fourth a part of the publication. The functions specialize in regulate of piezoelectric grippers.
Advanced keep an eye on of Piezoelectric Micro-/Nano-Positioning Systems will support educational researchers and practicing regulate and mechatronics engineers attracted to suppressing assets of nonlinearity equivalent to hysteresis and float while combining place and strength keep an eye on of precision platforms with piezoelectric actuation.
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This e-book explores rising equipment and algorithms that permit specific keep an eye on of micro-/nano-positioning structures. The textual content describes 3 keep watch over options: hysteresis-model-based feedforward keep watch over and hysteresis-model-free suggestions regulate according to and loose from kingdom statement. each one paradigm gets devoted cognizance inside of a specific a part of the textual content.
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Extra resources for Advanced Control of Piezoelectric Micro-/Nano-Positioning Systems
N ∂ei ∂L = 0 → wT ϕ(xi ) + b + ei − yi = 0, i = 1, 2, . . 27) Φ where α = [α1 , α2 , . . , α N ]T is called the support vector, whose support values αi are proportional to the residual errors ei by the regularization factor γ ∈ R. In addition, 1 N = [1, 1, . . , 1]T , y = [y1 , y2 , . . , y N ]T , and I N is an identity matrix. Besides, the kernel trick is employed to derive that: Ωi j = ϕ(xi )T ϕ(x j ) = K (xi , x j ), i, j = 1, 2, . . 28) where K is a predefined kernel function. The purpose of introducing the kernel function is to avoid the explicit computation of the map ϕ(·) in dealing with the high-dimensional feature space.
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