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Technical Briefs

Position Control Using Acceleration-Based Identification and Feedback With Unknown Measurement Bias

[+] Author and Article Information
Jaganath Chandrasekar

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140jchandra@umich.edu

Dennis S. Bernstein

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140dsbaero@umich.edu

J. Dyn. Sys., Meas., Control 130(1), 014501 (Dec 05, 2007) (9 pages) doi:10.1115/1.2807180 History: Received January 06, 2005; Revised June 27, 2007; Published December 05, 2007

A position-command-following problem for asymptotically stable linear systems is considered. To account for modeling limitations, we assume that a model is not available. Instead, acceleration data are used to construct a compliance (position-output) model, which is subsequently used to design a position servo loop. Furthermore, we assume that the acceleration measurements obtained from inertial sensors are biased. A subspace identification algorithm is used to identify the inertance (acceleration-output) model, and the biased acceleration measurements are used by the position-command-following controller, which is constructed using linear quadratic Gaussian (LQG) techniques.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Standard problem for designing a position-tracking controller Gc that uses biased acceleration measurements. To facilitate controller synthesis using LQG, the backward-path controller Gbp that is used to reject the sensor bias is included in the Plant G.

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Figure 2

Control architecture for discrete-time LQG position control using acceleration feedback and a backward-path controller Gbp

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Figure 3

Construction of the compliance Ĝcomp by cascading a double integrator with the identified inertance

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Figure 5

Error between the actual position of m1 and the output ypos,1 of the identified compliance model when u1 is an impulse and u2=0. For position-tracking controller synthesis, the identified compliance is used.

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Figure 6

Error between the position of m2 and the output ypos,2 from the identified compliance model when u1=0 and u2 is an impulse

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Figure 7

Magnitude of the diagonal entries of Wr(z)

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Figure 8

Magnitude of the diagonal entries of Gbp(z)

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Figure 9

Position-command following for the two-mass system using an LQG controller and a backward-path controller. The LQG controller Gc produces the control input u to track the position command r, while the backward-path controller with zero dc gain, that is, a zero at z=1, rejects the sensor bias.

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Figure 10

Acceleration measurements of the two masses. The sensor biases in the accelerometers are shown as dashed lines.

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Figure 11

Magnitudes of the diagonal entries of Gsens,r, the sensitivity transfer function between the reference position command r and the position-tracking error zpos. The magnitude of the sensitivity function is low in the required bandwidth between 0.1Hz and 1Hz.

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Figure 12

Magnitudes of the diagonal entries of Gsens,v, the sensitivity function between the bias v and position-tracking error zpos. The inclusion of a backward-path controller with zero dc gain ensures that as k→∞ the position-tracking performance is not affected by the sensor bias v.

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