Design and optimization of a novel resonant control law using force feedback for vibration mitigation. Issue 6 (3rd February 2022) - Paknejad, Ahmad; Zhao, Guoying; Chesné, Simon; Deraemaeker, Arnaud; Collette, Christophe
Summary: Integral‐force‐feedback (IFF) is a popular control law in active vibration damping of mechanical system when a force sensor is collocated with a force actuator. While it is simple, robust to resonance uncertainty and stable for any feedback gains, its efficiency is limited by system's parameters and in particular the stiffness ratio between the structure and the actuator. Therefore, the control authority decreases at high frequency resonances or when the actuator is weakly coupled to the structure. It has been shown that the use of double integrator with a real zero, named α ‐controller, can improve the control authority of a target mode. However, this technique like IFF cannot be easily implemented in practice because of low frequency saturation issue induced by significantly amplifying the low frequency content during the integration process. This paper proposes a new control law, named resonant‐force‐feedback (RFF), based on a second order low pass filter to damp a target mode resonance. Through the mechanical analogy of the proposed system, RFF can be seen as an active realization of an inerter‐spring‐damper (ISD) system. In addition, the parameters of RFF are optimized based on two methods, that is, maximum damping criterion and H ∞ optimization which consists in minimizing the settling time of the impulse response and the peak amplitude in the frequency domain, respectively. It is shown that RFF always provides a higher control authority of a target mode in comparison to IFF for a given stiffness ratio and in particular when the stiffness ratio is low. Despite the fact that the performance of the system, in terms of the closed‐loop damping ratio or the amplitude reduction, obtained by RFF is very close to that of α ‐controller, RFF requires less control effort in comparison to α ‐controller. The stability of the proposed system is also assessed in terms of the gain margin and the phase margin although the system is unconditionally stable. Moreover, the robustness of the designed RFF is compared to that of IFF under stiffness uncertainty. Although IFF can tolerate a higher level of uncertainty, the performance of RFF is superior to that of IFF for almost 50% of changes in the stiffness of the primary system.