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Research Papers

Robust Optimal Consensus State Estimator for a Piezoactive Distributed Parameter System

[+] Author and Article Information
Ehsan Omidi

Nonlinear Intelligent Structures Laboratory,
Department of Mechanical Engineering,
University of Alabama,
Tuscaloosa, AL 35487-0276
e-mail: eomidi@crimson.ua.edu

S. Nima Mahmoodi

Nonlinear Intelligent Structures Laboratory,
Department of Mechanical Engineering,
University of Alabama,
Tuscaloosa, AL 35487-0276
e-mail: nmahmoodi@eng.ua.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 27, 2015; final manuscript received March 24, 2016; published online June 8, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(9), 091011 (Jun 08, 2016) (10 pages) Paper No: DS-15-1401; doi: 10.1115/1.4033312 History: Received August 27, 2015; Revised March 24, 2016

This paper proposes a consensus state estimator for sensor networks of distributed parameter structures. A thin beam with clamped–clamped boundary conditions enhanced by piezoelectric sensors is considered, and individual observers are assigned for each of these sensors. The so-called estimation agents are then connected to one another in a network with certain directed topology, and consensus is enforced between the agents estimated output in observers dynamics. Observer gains are optimized using algebraic Riccati equations (AREs), and robustness to measurement disturbances is applied via H design. The consensus state estimator is then numerically investigated for a sensor network of five agents. According to the results of the optimal and robust designs, the proposed consensus observer successfully estimates the modal system states in finite time, whereas the estimation output is resilient to measurement disturbances. Implementation of the consensus sensor network increases the robustness of the estimation, due to its inherent redundancy.

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Figures

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Fig. 1

Beam structure and implemented piezoelectric sensors

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Fig. 2

Communication topology of the sensor network on the beam 10

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Fig. 3

Simulated beam response to the disturbance input

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Fig. 4

Measured vibration amplitudes by the sensors versus estimated output amplitudes by the agents at the position of (a) sensor no. 1, (b) sensor no. 2, (c) sensor no. 3, (d) sensor no. 4, and (e) sensor no. 5

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Fig. 5

Output estimation error of the consensus observer agents

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Fig. 6

Local disagreement norm of each agent 15

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Fig. 7

Measured vibration amplitudes by the sensors versus estimated output amplitudes by the agents at the position of (a) sensor no. 1, (b) sensor no. 2, (c) sensor no. 3, (d) sensor no. 4, and (e) sensor no. 5

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Fig. 8

Output estimation error of the optimized consensus observer agents

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Fig. 9

Local disagreement norm of each agent in the optimal consensus

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Fig. 10

Output estimation error of each agent for its corresponding sensor in the presence of the 20 disturbance at (a) agent no. 1, (b) agent no. 2, (c) agent no. 3, (d) agent no. 4, and (e) agent no. 5

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Fig. 11

Output estimation error of the robust system in the presence of the disturbance at (a) agent no. 1, (b) agent no. 2, (c) agent no. 3, (d) agent no. 4, and (e) agent no. 5

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