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Research Papers

Persistence Filters for Estimation: Applications to Control in Shared-Sensing Reversible Transducer Systems

[+] Author and Article Information
Srikant Sukumar

Systems and Control Engineering,Indian Institute of Technology Bombay,Mumbai, India 400078srikant.sukumar@iitb.ac.in

Maruthi R. Akella

Department of Aerospace Engineering and Engineering Mechanics,  The University of Texas at Austin, 1 University Station, Austin, TX 78712makella@mail.utexas.edu

J. Dyn. Sys., Meas., Control 134(4), 041012 (May 07, 2012) (12 pages) doi:10.1115/1.4005510 History: Received March 10, 2011; Revised September 15, 2011; Published May 04, 2012; Online May 07, 2012

We investigate state observer and feedback control design for systems with state- and time-dependent control or measurement gains. In this framework, we look at reversible transducers that are continually switched between the actuation and sensing modes at some prespecified schedule. Design and analysis of stable state-observers and feedback controllers for these classes of switched/hybrid systems are significantly complicated by the fact that, at any given instant of time, the overall system loses either controllability (during the sensing phase) or observability (during the actuation phase). In this work, we consider systems with scalar time-varying measurement gains and provide a novel observer construction that guarantees exponential reconstruction of state estimates to their true values. We go a step further to derive an exponentially stabilizing controller design that uses the state estimates resulting from our observer. This amounts to the establishment of a rather remarkable separation property of the control design. These developments hinge on a rather mild technical assumption, which can be interpreted for the reversible transducer problem as a persistent dwell time for both the sensing and actuation modes. An important feature here is that the convergence rate can be specified to any arbitrary value. Our theoretical results are validated through numerical simulations of challenging test-cases that include open-loop unstable systems. The paper also illustrates potential for nonlinear extensions of the observer based control design by considering an interesting special case.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simply supported beam with PZT element for vibration suppression

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Figure 2

Switching curves g(t) and gc (t) represented using bump functions

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Figure 3

Persistence observer based controller performance for vibration suppression. The bold and dotted lines in the plots indicate vibrations in the controlled system and the unforced system, respectively.

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Figure 4

Inverted pendulum with dc servo motor for sensing and actuation

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Figure 5

Inverted pendulum stabilization with dc servo motor—angle stabilization, solid lines show noise free case and dashed lines the case with noise

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Figure 6

Inverted pendulum stabilization with dc servo motor—angular velocity stabilization, solid lines show noise free case and dashed lines the case with noise

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Figure 7

Inverted pendulum stabilization with dc servo motor—current stabilization, solid lines show noise free case and dashed lines the case with noise

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Figure 8

Inverted pendulum stabilization with dc servo motor—control voltages, solid lines show noise free case and dashed lines the case with noise

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