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Technical Briefs

Source Seeking With Very Slow or Drifting Sensors

[+] Author and Article Information
Nima Ghods1

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411nimaghods@gmail.com

Miroslav Krstic

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411krstic@ucsd.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(4), 044504 (Apr 11, 2011) (8 pages) doi:10.1115/1.4003639 History: Received December 16, 2008; Revised October 28, 2010; Published April 11, 2011; Online April 11, 2011

Slow sensors arise in many applications, including sensing chemical concentrations in tracking of contaminant plumes. Slow sensors are often the cause of poor performance and a potential cause of instability. In this paper, we design a modified extremum seeking scheme to account and exploit slow sensor dynamics. We also consider the worst case, which is sensor dynamics governed by a pure integrator. We provide stability results for several distinct variations of an extremum seeking scheme for one-dimensional optimization. Then we develop a design for source seeking in a plane using a fully actuated vehicle, prove its closed-loop convergence, and present simulation results. We use metal oxide microhotplate gas sensors as a real world example of slow sensor dynamics, model the sensor based on experimental data, and employ the identified sensor model in our source seeking simulations.

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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Sensors
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Figures

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Figure 1

(a) An example of metal oxide sensor TGS2602 responding to four different concentrations of ethanol. (b) Comparison of the first order sensor model and the real sensor reaction to ethanol.

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Figure 2

Extremum seeking block diagrams. The modified extremum seeking algorithm (b) applies both to the case with a slow sensor (ε>0) and to the case with a sensor modeled as a pure integrator, which we also refer to as a “drifting sensor” (ε=0). In both cases (ε>0 and ε>0), the washout filter is optional (both h>0 and h=0 are permissible).

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Figure 3

Gas concentration distribution along the pipe with gas leak at position 0

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Figure 4

Simulation results for modified extremum seeking with slow sensor dynamics. (a) Output of the nonlinear map. (b) The sensor position relative to θ∗. (c) The signal after the high pass filter. (d) The slow sensor reading.

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Figure 5

Simulation results for extremum seeking with Gsensor(s)=b/s with washout filter. (a) Output of the nonlinear map. (b) The sensor position relative to θ∗. (c) The signal after the high pass filter.

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Figure 6

Simulation results for extremum seeking with Gsensor(s)=b/s and without washout filter. (a) Output of the nonlinear map. (b) The sensor position relative to θ∗.

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Figure 7

Modified ES for 2D point mass vehicle with slow sensor. The scheme applies both to the case with a slow sensor (ε>0) and to the case with a sensor modeled as a pure integrator, which we also refer to as a “drifting sensor” (ε=0), and with both h>0 and h=0 being permissible.

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Figure 8

Simulation results for extremum seeking on a 2D point mass with a slow sensor. (a) Vehicle trajectory with the intensity of the nonlinear map in the background. (b) Output of the nonlinear map. (c) The slow sensor output. (e) The output of the washout filter. ((d) and (f)) The control input of x-axis and y-axis before the addition of the perturbation, respectively.

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