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Research Papers

Robust Control of a Parallel- Kinematic Nanopositioner

[+] Author and Article Information
Jingyan Dong, Srinivasa M. Salapaka, Placid M. Ferreira

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Dyn. Sys., Meas., Control 130(4), 041007 (Jun 09, 2008) (15 pages) doi:10.1115/1.2936861 History: Received January 30, 2007; Revised November 28, 2007; Published June 09, 2008

This paper presents the design, model identification, and control of a parallel-kinematic XYZ nanopositioning stage for general nanomanipulation and nanomanufacturing applications. The stage has a low degree-of-freedom monolithic parallel-kinematic mechanism featuring single-axis flexure hinges. The stage is driven by piezoelectric actuators, and its displacement is detected by capacitance gauges. The control loop is closed at the end effector instead of at each joint, so as to avoid calibration difficulties and guarantee high positioning accuracy. This design has strongly coupled dynamics with each actuator input producing in multiaxis motions. The nanopositioner is modeled as a multiple input and multiple output (MIMO) system, where the control design forms an important constituent in view of the strongly coupled dynamics. The dynamics that model the MIMO plant is identified by frequency domain and time-domain identification methods. The control design based on modern robust control theory that gives a high bandwidth closed loop nanopositioning system, which is robust to physical model uncertainties arising from flexure-based mechanisms, is presented. The bandwidth, resolution, and repeatability are characterized experimentally, which demonstrate the effectiveness of the robust control approach.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 6

Frequency response of the models from time domain (solid) and frequency domain (dotted) identifications

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Figure 7

Frequency response of the identified models at different operating points

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Figure 8

Hankel singular values of the balancing realized model

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Figure 9

Comparison of frequency response between the original model (solid) and the reduced rank model (dashed)

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Figure 10

(a) Multiplicative output uncertainty and (b) singular value for uncertainty function E0 from model reduction

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Figure 11

(a) Closed loop system with weighted outputs and (b) weighting transfer function

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Figure 12

Closed loop sensitivity function with different models. Target sensitivity function (dashed). Achieved sensitivity functions (solid). (a) Nominal model and (b) perturbed model (original model).

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Figure 13

Examples of bode plots of closed loop transfer functions. (a) A diagonal function (x reference to x output). (b) An off-diagonal function (x reference to y output).

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Figure 14

Hysteresis in (a) open loop configuration and (b) closed loop configuration

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Figure 15

Creep in open loop and closed loop configurations

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Figure 16

Capacitance sensor measurements of steady state positions: (a) open loop and (b) closed loop. PSD of the output (no input case) plot: (c) open loop and (d) closed loop.

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Figure 17

Small step response with a 10nm step. (a) Step command and (b) step response.

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Figure 18

Closed loop bandwidth from the singular value plot of (a) sensitivity transfer function, (b) complementary sensitivity function, and (c) the response of a step input.

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Figure 19

Tracking of (a) triangular and (b) sinusoidal waves at (a1) and (b1) 5Hz, (a2) and (b2) 10Hz, (a3) and (b3) 20Hz, and (a4) and (b4) 40Hz using an H∞ controller. Reference: dotted. Output: solid.

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Figure 20

(a) Contouring error of tracking a 45deg line. (b) An example of following errors for two axes at a speed of 1000μm∕s.

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Figure 21

Bode plot of closed loop transfer functions

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Figure 22

Bode plot of the controller

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Figure 2

Piezoelectric actuator assembly

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Figure 1

The PKXYZNP prototype. Left top: flexure structure with actuators. Right top: fully assembled stage. Bottom: kinematic scheme of the XYZ stage (14).

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Figure 3

Control system setup for the PKM XYZ stage

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Figure 4

Time domain identification example (from actuator A to X motion). (a) Input command signal for identification. (b) Measured output from the stage. (c) Simulated output from the identified model. (d) A close comparison between the actual output (solid line) and the model output (dashed line).

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Figure 5

Frequency response of the identified model

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