By Qingsong Xu, Kok Kiong Tan
This ebook explores rising tools and algorithms that allow targeted keep an eye on of micro-/nano-positioning structures. The textual content describes 3 regulate options: hysteresis-model-based feedforward regulate and hysteresis-model-free suggestions keep watch over in response to and unfastened from country commentary. each one paradigm gets committed awareness inside a selected a part of the text.
Readers are proven how you can layout, validate and observe a number of new keep an eye on techniques 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 therapy of useful purposes within the fourth a part of the publication. The functions specialize in keep watch over of piezoelectric grippers.
Advanced keep an eye on of Piezoelectric Micro-/Nano-Positioning Systems will help educational researchers and training keep watch over and mechatronics engineers attracted to suppressing resources of nonlinearity akin to hysteresis and go with the flow whilst combining place and strength keep watch over of precision structures with piezoelectric actuation.
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Extra info for Advanced Control of Piezoelectric Micro-/Nano-Positioning Systems
Therefore, the modified PI operator is derived as follows: z(t) = Γ [u](t) = wsT Sd whT Hr [u, y0 ] (t). 10) A realization of the MPI model using MATLAB/Simulink blocks is shown in Fig. 7. Fig. 3 Inverse MPI Model In order to use the MPI model for the feedforward hysteresis compensation, an inverse model is required to express the voltage as a function of the position. 11) ∗ , w∗ , . . , w∗ ] and w∗ T = [w∗ , w∗ , . . , w∗ ] are the weight where w∗h T = [wh0 s sm s0 s1 h1 hn ∗ , y ∗ , . . , y ∗ ]T is the initial state vector, and the threshold vectors vectors, y∗0 = [y00 01 0n are r∗ = [r0∗ , r1∗ , .
16) −ws j j k=0 wsk j−1 k=0 wsk , j = 1, . . 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.
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