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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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References

Omidi, E. , Korayem, A. H. , and Korayem, M. H. , 2013, “ Sensitivity Analysis of Nanoparticles Pushing Manipulation by AFM in a Robust Controlled Process,” Precis. Eng., 37(3) pp. 658–670. [CrossRef]
Van Auken, R. M. , 2015, “ Development and Comparison of Laplace Domain Models for Nonslender Beams and Application to a Half-Car Model With Flexible Body,” ASME J. Dyn. Syst. Meas. Control, 137(7), p. 071001. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2015, “ Multimode Modified Positive Position Feedback to Control a Collocated Structure,” ASME J. Dyn. Syst. Meas. Control, 137(5), p. 051003. [CrossRef]
Pedersen, H. C. , Andersen, T. O. , and Nielsen, B. K. , 2015, “ Comparison of Methods for Modeling a Hydraulic Loader Crane With Flexible Translational Links,” ASME J. Dyn. Syst. Meas. Control, 137(10), p. 101012. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2015, “ Nonlinear Vibration Suppression of Flexible Structures Using Nonlinear Modified Positive Position Feedback Approach,” Nonlinear Dyn., 79(2), pp. 835–849. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2015, “ Sensitivity Analysis of the Nonlinear Integral Positive Position Feedback and Integral Resonant Controllers on Vibration Suppression of Nonlinear Oscillatory Systems,” Commun. Nonlinear Sci. Numer. Simul., 22(1–3), pp. 149–166. [CrossRef]
Samiei, E. , Butcher, E. A. , and Sanyal, A. K. , 2015, “ Attitude Stabilization of Rigid Spacecraft With Minimal Attitude Coordinates and Unknown Time-Varying Delay,” Aerosp. Sci. Technol., 46, pp. 412–421. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2015, “ Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures,” IEEE/ASME Trans. Mechatron., 20(4), pp. 1790–1797. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2014, “ Vibration Control of Collocated Smart Structures Using ℋ∞ Modified Positive Position and Velocity Feedback,” J. Vib. Control (published online).
Seigler, T. , and Ghasemi, A. , 2012, “ Specified Motion of Piezoelectrically Actuated Structures,” ASME J. Vib. Acoust., 134(2), p. 021002. [CrossRef]
Alessandroni, S. , Andreaus, U. , and Dell'Isola, F. , 2004, “ Piezo-ElectroMechanical (PEM) Kirchhoff–Love Plates,” Eur. J. Mech., A/Solids, 23(4) pp. 689–702. [CrossRef]
Porfiri, M. , Dell'Isola, F. , and Mascioli, F. M. F. , 2004, “ Circuit Analog of a Beam and Its Application to Multimodal Vibration Damping, Using Piezoelectric Transducers,” Int. J. Circuit Theory Appl., 32(4) pp. 167–198. [CrossRef]
Noshadi, A. , Shi, J. , and Lee, W. S. , “ Robust Control of an Active Magnetic Bearing System Using H and Disturbance Observer-Based Control,” J. Vib. Control (published online).
Hidayat, Z. , Babuska, R. , and De Schutter, B. , 2011, “ Observers for Linear Distributed-Parameter Systems: A Survey,” IEEE International Symposium on Robotic and Sensors Environments, Montreal, Canada, Sept. 17–18, pp. 166–171.
Schaum, A. , Moreno, J. A. , and Fridman, E. , 2014, “ Matrix Inequality-Based Observer Design for a Class of Distributed Transport-Reaction Systems,” Int. J. Robust Nonlinear Control, 24(16), pp. 2213–2230. [CrossRef]
Patan, M. , 2012, Optimal Sensor Networks Scheduling in Identification of Distributed Parameter Systems, Springer, Berlin.
Olfati-Saber, R. , and Murray, R. M. , 2004, “ Consensus Problems in Networks of Agents With Switching Topology and Time-Delays,” IEEE Trans. Autom. Control, 49(9), pp. 1520–1533. [CrossRef]
Olfati Saber, R. , and Murray, R. M. , 2003, “ Consensus Protocols for Networks of Dynamic Agents,” American Control Conference, Denver, CO, Vol. 2, pp. 951–956.
Demetriou, M. A. , 2009, “ Natural Consensus Filters for Second Order Infinite Dimensional Systems,” Syst. Control Lett., 58(12), pp. 826–833. [CrossRef]
Li, Z. , Duan, Z. , and Chen, G. , 2010, “ Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint,” IEEE Trans. Circuits Syst. I, 57(1), pp. 213–224. [CrossRef]
Demetriou, M. A. , 2010, “ Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of Distributed Parameter Systems,” IEEE Trans. Autom. Control, 55(7), pp. 1570–1584. [CrossRef]
Spinello, D. , and Stilwell, D. J. , 2014, “ Distributed Full-State Observers With Limited Communication and Application to Cooperative Target Localization,” ASME J. Dyn. Syst. Meas. Control, 136(3), p. 031022. [CrossRef]
Mehrabian, A. , and Khorasani, K. , 2015, “ Cooperative Optimal Synchronization of Networked Uncertain Nonlinear Euler–Lagrange Heterogeneous Multi-Agent Systems With Switching Topologies,” ASME J. Dyn. Syst. Meas. Control, 137(4), p. 041006. [CrossRef]
Dong, Y. , and Huang, J. , 2014, “ Cooperative Global Robust Output Regulation for Nonlinear Multi-Agent Systems in Output Feedback Form,” ASME J. Dyn. Syst. Meas. Control, 136(3), p. 031001. [CrossRef]
Rastgoftar, H. , and Jayasuriya, S. , 2015, “ Swarm Motion as Particles of a Continuum With Communication Delays,” ASME J. Dyn. Syst. Meas. Control, 137(11), p. 111008. [CrossRef]
Omidi, E. , and Mahmoodi, S. N. , 2015, “ Multiple Mode Spatial Vibration Reduction in Flexible Beams Using H2- and H∞-Modified Positive Position Feedback,” ASME J. Vib. Acoust., 137(1), p. 011004. [CrossRef]
Han, S. M. , Benaroya, H. , and Wei, T. , 1999, “ Dynamics of Transversely Vibrating Beams Using Four Engineering Theories,” J. Sound Vib., 225(5) pp. 935–988. [CrossRef]
Rao, S. S. , 2007, Vibration of Continuous Systems, Wiley, Hoboken, NJ.
Howard, C. Q. , 2007, “ Modal Mass of Clamped Beams and Clamped Plates,” J. Sound Vib., 301(1–2), pp. 410–414. [CrossRef]
Hwu, C. , Chang, W. C. , and Gai, H. S. , 2004, “ Vibration Suppression of Composite Sandwich Beams,” J. Sound Vib., 272(1–2), pp. 1–20. [CrossRef]
Ren, W. , and Beard, R. W. , 2005, “ Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies,” IEEE Trans. Autom. Control, 50(5), pp. 655–661. [CrossRef]
Liu, Y. , Jia, Y. , and Du, J. , 2009, “ Dynamic Output Feedback Control for Consensus of Multi-Agent Systems: An H Approach,” American Control Conference, St. Louis, MO, June 10–12, pp. 4470–4475.
Lewis, F. , Zhang, H. , and Hengster-Movric, K. , 2014, Cooperative Control of Multi-Agent Systems, Springer-Verlag, London.
Lewis, F. L. , Vrabie, D. , and Syrmos, V. L. , 2012, Optimal Control, Wiley, New York.
Zhang, H. , Lewis, F. L. , and Das, A. , 2011, “ Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback,” IEEE Trans. Autom. Control, 56(8) pp. 1948–1952. [CrossRef]
Jin, Z. , and Murray, R. M. , 2004, “ Double-Graph Control Strategy of Multi-Vehicle Formations,” IEEE Conference on Decision and Control (CDC), Nassau, Bahamas, Dec. 14–17, Vol. 2, pp. 1988–1994.
Li, H. , and Fu, M. , 1997, “ A Linear Matrix Inequality Approach to Robust H Filtering,” IEEE Trans. Signal Process., 45(9), pp. 2338– 2350. [CrossRef]

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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