Robust saturated control of human-induced floor vibrations via a proof-mass actuator

This paper is concerned with the design of a robust active vibration control system that makes use of a proof-mass actuator for the mitigation of human-induced vibrations in floor structures. Ideally, velocity feedback control (VFC) is unconditionally stable and robust to spillover effects, interlacing of poles and zeros of collocated control is then accomplished. However, the use of a proof-mass actuator influences the system dynamics and the alternating pole-zero pattern of the system formed by the actuator and structure is no longer fulfilled. However, a controlled migration of the two zeros of the root locus plot at the origin, resulting from the acceleration output, can be achieved by adding a feed-through term (FTT) to the structure acceleration output. That is, the FTT enables us to control the position of a pair of complex conjugate zeros (an anti-resonance in the frequency domain). This paper proposes the introduction of an FTT designed in such a way that the anti-resonance at the origin is located between the actuator resonance and the structure fundamental resonance. Hence, an integral controller leads to infinite gain margin and significant phase margin. Simulation and experimental results on a concrete slab strip have validated the proposed control strategy. Significant improvements in the stability properties compared with VFC are reported.