ℋ_∞ optimization of an integral force feedback controller

Abstract

This paper studies the performance of the classical integral force feedback (IFF) controller for suppressing the forced response of a single degree of freedom (SDOF) system. An ℋ∞ optimization criterion is used to derive the optimal feedback gain of the IFF controller contributed as a complement for the state of the art. This optimal gain is calculated in the closed-form based on a SDOF system which is then applied to a two degrees of freedom system to study its adaptability. It is found that the ℋ∞ optimal gain can be easily transposed into multi-degrees of freedom applications without introducing too many errors. An equivalent mechanical model is also developed to enable a straightforward interpretation of the physics behind the IFF controller.

Active nonlinear energy sink using force feedback under transient regime

“…The control concept is actually built upon the previous developments [22] where the linear double integrator is removed from the chain. In this way, the proposed ANES can be understood to play the same role as a pure mechanical system which consists of a cube root inerter, a linear dashpot and a linear spring according to previous derivations in [22][23][24]. Although the nonlinear assignment of the proposed ANES is different from that of traditional NESs, it is found that ANES and NES behave similarly in terms of vibration mitigation effectiveness.…”

“…For the proposed ANES, the linearised system around the trivial state corresponds to the primary structure coupled with a classical integral force feedback controller. As demonstrated in [24,29], the theoretical gain margin is infinity and the phase margin is p=2 for the linearised system. However, the Lyapunov's linearisation theory is only valid for small range of motions around the equilibrium points (a local stability theorem) and it is not yet clear what are the boundary conditions for the linearisation approximations to hold (global stability theorem is needed).…”

Design and optimization of a novel resonant control law using force feedback for vibration mitigation

“…F I G U R E 5 Impulse response of the coupled system with resonant-force-feedback (RFF) for different values of (a) damping coefficient ξ f , (b) tuning frequency ω f , and (c) feedback gain g f F I G U R E 6 (a) Settling time as a function of the variation of the parameters of resonant-force-feedback (RFF) normalized with respect to their optimal values, (b) a zoom from 0 to 100 s Figure 8a shows the frequency-response-function (FRF) of the performance index with and without control systems. It also compares the performance of RFF with IFF 12 and α-controller 13 when they are optimized based on the method of maximum damping. In order to reveal the difference of using RFF in comparison to IFF and α-controller, Figure 8b presents the evolution of the maximum closed-loop damping ratio under the variation of the stiffness ratio ( k k a ).…”

“…12 It has been shown that IFF is of interest in many engineering applications due to the simplicity of the controller, guaranteed the stability, multimode resonance damping and robustness to resonance uncertainty. Nevertheless, the control performance in terms of maximum achievable damping 12 or maximum amplitude reduction 13 is limited by the distance between the system pole and zero which is a function of the system's stiffness relative to the actuator stiffness. To the best of our knowledge, only a few studies have been focused on the damping improvement of force feedback configurations.…”

Improved integral force feedback controllers for lightweight flexible structures

“…Noted that the IFF has been widely used in several fields of research for its relative simplicity and high robustness to resonance uncertainty of the primary system. In addition, two tuning laws based on maximum damping criterion (Preumont et al, 2016) and H ∞ theory (Zhao et al, 2019) have been used to optimize the feedback gain in a closed-form formulation for a single-degree-offreedom (SDOF) system.…”