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Laboratory Demonstration Hardware for AVC

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Model Predictive Vibration Control

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Abstract

A laboratory demonstration hardware for the verification of model predictive control (MPC) algorithms in active vibration control (AVC) is introduced in detail. The laboratory device featured in the experiments comparing model predictive vibration control algorithms is a simple clamped cantilever beam with piezoelectric actuation. Despite of its elementary physical construction such a lightly damped vibrating device models the dynamics of a class of real-life applications, such as helicopter rotor beams, wing surfaces, antenna masts, manipulators and others. After a brief summary of this laboratory device, its experimental identification procedure is discussed. Some of the characteristic properties of the device are introduced as well, such as actuator linearity and noise tolerance. As finite element modeling (FEM) of vibrating structures is a valuable tool for the engineering practitioner, some of the results of the preliminary FEM analyses performed on the device are also presented. The chapter is closed with a section on hardware component details, which can be an aid to those who are unfamiliar with the components of such AVC demonstrators and are planning to build one.

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Notes

  1. 1.

    Courtesy of The Boeing Company.

  2. 2.

    See Fig. 1.4. on p. 9 for another photograph depicting the same smart helicopter rotor structure with AVC.

  3. 3.

    See the description of the host PC in Sect. 5.5.4.1.

  4. 4.

    That is 262 144 data points.

  5. 5.

    See the initial deflection, frequency domain and other experiments on the controlled system, as described in Sects. 12.2, 12.3.2, 12.4.

  6. 6.

    Presuming initial disturbance is removed and the system is able to settle on its own or under control.

  7. 7.

    see Sect. 12.1 for LQ, Sect. 12.2 and others for NRMPC and MPMPC.

  8. 8.

    Not actually plotted. The three different experiments produced random noise with the same specifications.

  9. 9.

    Actual quantization may differ significantly, possibly encoding potential polarity and others. For example a 10 V span can be divided into 1.5 mV portions.

  10. 10.

    Accelerometers and amplifiers registering both excitation and response.

  11. 11.

    Laser reference output is directly proportional to the measured value, in this case, there is a 1.5 mm/V gain.

  12. 12.

    Modes (3) and (5) are twisting modes and cannot be measured nor controlled with the sensor/actuator configuration assumed throughout this book.

  13. 13.

    An MPC control would provide significantly better performance than LQ given a MIMO vibration control system, where the real performance of the linear quadratic controller would be degraded due to the saturation limits not included in the original optimization task.

  14. 14.

    See (5.5.1) for more details on amplifier safety measures.

  15. 15.

    Considering the first three transversal vibration modes instead of five at design stage would be more suitable for this application. However, the issues regarding the size of the region of attraction and unexpected levels of NRMPC suboptimality were at this time unknown. See Sects.  11.1 and 11.4 for more details.

  16. 16.

    Actuator marked as PZT1, see Sect. 5.1 for details.

  17. 17.

    As of its current version: Release 13.0.

  18. 18.

    This safety limit is given in RMS, not peak values.

  19. 19.

    Courtesy of Thomas Huber.

  20. 20.

    See Sect. 5.3.2 for a measured mechanical noise and disturbance sample.

  21. 21.

    This computer has been used to compute the task execution times of various predictive controller featured in Sect. 12.5.

  22. 22.

    Formerly known as PCI-MIO-16XE-10.

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  1. Faculty of Mechanical Engineering, Institute of Automation, Measurement and Applied Informatics, Slovak University of Technology in Bratislava, Námestie slobody 17, 812 31, Bratislava 1, Slovakia

    Gergely Takács & Boris Rohal’-Ilkiv

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Takács, G., Rohal’-Ilkiv, B. (2012). Laboratory Demonstration Hardware for AVC. In: Model Predictive Vibration Control. Springer, London. https://doi.org/10.1007/978-1-4471-2333-0_5

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