Partial pole assignment using rank-one control and receptance in second-order systems with time delay

Abstract

In this note, a partial pole assignment approach is presented for second-order systems with time delay. The method uses the versatile system receptance for designing state-feedback, rank-one controllers for second-order systems with time delay in the measurements or actuation. The stability of the closed-loop system is pursued throughout an optimization problem formulated with basis on the classical frequency domain technique known as the Nyquist stability criterion. Besides the partial pole assignment, robustness measured in terms of phase and gain margins can be achieved using a genetic algorithm to solve the optimization problem. The proposed approach is shown to provide effective solutions for systems with different time delays in the measurements of displacements and velocities, and with singular mass matrix. Numerical examples are presented to illustrate the benefits of the approach.

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Funding

Carlos E.T. Dórea receives the Grant #309862/2019-1 from Conselho Nacional de Desenvolvimento Científico e Tecnológico.

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Correspondence to Jose M. Araujo.

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Dantas, N.J.B., Dorea, C.E.T. & Araujo, J.M. Partial pole assignment using rank-one control and receptance in second-order systems with time delay. Meccanica 56, 287–302 (2021). https://doi.org/10.1007/s11012-020-01289-w

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Keywords

  • Pole assignment
  • Receptance
  • Active vibration control
  • Frequency response