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Positive Position Feedback (PPF) Control

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Control of Noise and Structural Vibration

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Abstract

This chapter presents the design of a positive position feedback (PPF) controller based on low-pass filters and band-pass filters. In Sect. 6.1, the principle of the PPF controller is presented based on the single degree of freedom (SDOF) case. In Sect. 6.2, the loudspeaker–duct model is developed, several model interconnection methods in MATLAB are presented, and then the influence of loudspeaker dynamics is discussed. In Sect. 6.3, for the loudspeaker/microphone pair at the same location, the design of a PPF controller with an all-pass filter as phase compensation is presented. The Nyquist diagram, gain and phase margin, and root locus analysis are used to analyze the stability of the PPF controller. In Sect. 6.4, the PPF controller is extended for non-collocated loudspeaker/microphone pair. The calculation results show that the similar sound pressure reduction can be obtained by using a PPF controller with a non-collocated loudspeaker/microphone pair. In Sect. 6.5, the multimode control is discussed by using a single loudspeaker/microphone pair. In Sect. 6.6, a GUI program is given to design and analyze the PPF controller for a loudspeaker–duct model. And then we discuss how to share data between Simulink and GUI programs. In Sect. 6.7, the analog circuit for design of PPF controllers and all-pass filters are presented. Finally, some experimental results are presented to verify the simulation results.

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References

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Author information

Authors and Affiliations

  1. School of Aircraft Engineering, Nanchang HangKong University, Nanchang, China, People’s Republic

    Qibo Mao PhD

  2. Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland

    Stanislaw Pietrzko DSc, Dr. sc. techn. ETH

Authors
  1. Qibo Mao PhD
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  2. Stanislaw Pietrzko DSc, Dr. sc. techn. ETH
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Problems

Problems

  1. P.6.1

    Consider a SDOF system with PPF controller K, as shown in Fig. 6.6. The controller natural frequency ω f is set to be the same as the natural frequency of the structure ω s . Design a MATLAB GUI program to display the control performance and Nyquist diagram with different gain and damping ratio of the controller.

  2. P.6.2

    Consider a simply supported uniform beam with a collocated point force actuator and displacement sensor. The beam has an elastic modulus of 109 N/m2, a density of 2,700 kg/m3 and a thickness of 4 mm. The dimensions of the beam are 0.05 m × 0.6 m.

  1. (a)

    Design the optimal parameters for PPF controller to control the second structural mode of the beam. Assume that the collocated actuator/sensor pair is located at x s  = 0.1 m.

  2. (b)

    Check the stability of the control system.

  1. P.6.3

    Reconsider Problem 6.2, if the actuator and sensor is non-collocated, such as actuator is located at x a = 0.15 m and the sensor is located at x s = 0.35 m.

  1. (a)

    Design an optimal all-pass filter for phase compensation as discussed in Sect. 6.3.

  2. (b)

    Calculate the control performance of the second-order PPF controller with and without all-pass filter.

  3. (c)

    Compare the control performance for the different order of PPF controller with optimal all-pass filter.

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Mao, Q., Pietrzko, S. (2013). Positive Position Feedback (PPF) Control. In: Control of Noise and Structural Vibration. Springer, London. https://doi.org/10.1007/978-1-4471-5091-6_6

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  • DOI: https://doi.org/10.1007/978-1-4471-5091-6_6

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5090-9

  • Online ISBN: 978-1-4471-5091-6

  • eBook Packages: EngineeringEngineering (R0)

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