By Qingsong Xu, Kok Kiong Tan
This booklet explores rising equipment and algorithms that allow designated regulate 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 keep watch over in line with and unfastened from country commentary. each one paradigm gets committed recognition inside a selected a part of the text.
Readers are proven the best way to layout, validate and observe quite a few new keep an eye on techniques in micromanipulation: hysteresis modelling, discrete-time sliding-mode keep watch over and model-reference adaptive regulate. Experimental effects are supplied all through and increase to a close remedy of functional purposes within the fourth a part of the e-book. The purposes concentrate on keep an eye on of piezoelectric grippers.
Advanced keep watch over of Piezoelectric Micro-/Nano-Positioning Systems will help educational researchers and working towards regulate and mechatronics engineers attracted to suppressing assets of nonlinearity corresponding to hysteresis and waft while combining place and strength keep watch over of precision platforms with piezoelectric actuation.
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Additional resources for Advanced Control of Piezoelectric Micro-/Nano-Positioning Systems
It is observed that the LSSVM approach utilizes the equality constraints instead of the inequality constraints as in the ordinary SVM. Thus, it simplifies the regression to a problem that can be easily solved from a set of linear equations. Assume that Φ is invertible, then b and α can be calculated from Eq. 27): b α = Φ −1 0 . 29) Then, in view of Eq. 30) i=1 where K is the kernel function satisfying Mercer’s condition, xi is the training data, and x denotes the new input data. 3 Hysteresis Modeling 35 with σ > 0 denoting the width parameter (which specifies the kernel sample variance σ 2 ) and · representing the Euclidean distance, the LSSVM model for the hysteresis model estimation becomes N αi exp − y(x) = i=1 x − xi σ2 2 + b.
17) j d ∗j = wsk (d j − dk ), j = 0, 1, . . , m. 3 Hysteresis Modeling with the LSSVM In this section, the hysteresis modeling is treated as a nonlinear regression problem, and the LSSVM is employed to model the piezoelectric hysteresis for the piezoelectric nanopositioning system. Due to the hysteresis effects, one input voltage can produce multiple values of the output displacements. Thus, one challenge lies in how to convert the one-to-many mapping into a one-to-one mapping. 3 Hysteresis Modeling 33 determines a unique output value.
7(3), 408–415 (1991) 42. : Force sensing and control in micromanipulation. IEEE Trans. Syst. Man Cybern. Part C, Appl. Rev. 36(6), 713–724 (2006) 43. : An approach to sliding-mode based control. IEEE Trans. Robot. Automat. 11(5), 754–759 (1995) 44. : Tracking system design based on digital minimum variance control with fuzzy sliding mode. In: Proceeding of 8th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services (TELSIKS 2007), pp. 494–497. Nis, Serbia (2007) 45.
Advanced Control of Piezoelectric Micro-/Nano-Positioning Systems by Qingsong Xu, Kok Kiong Tan