Robust control approach for a nonlinear 2-DOF quasi-zero stiffness vibration isolator

Meta materials are widely used as vibration isolators, where various combinations of springs and dampers are employed to mitigate vibrations. Unlike passive meta materials, active meta materials incorporate sensors and actuators to actively suppress vibrations. Vibration isolators with low dynamic and high static stiffness offer better isolation than conventional linear devices. This article analyzes the dynamic characteristics of a one-degree and two-degree-freedom bottom spring grounded vibration isolator with quasi-zero stiffness (QZS). The optimal control feedback mechanism is studied to improve the vibration isolation performance of a two-degree-of-freedom bottom spring grounded nonlinear vibration isolator. The performance of the active vibration isolator is analyzed using optimal control techniques such as H ∞ and μ -synthesis methods and further compared its response with pole placement based controller. The numerical results show that the μ -synthesis controller outperforms both the H ∞ and pole placement controllers. The H ∞ controller achieves convergence with a state-space order of 8 and a γ value of 6.518, whereas the μ -synthesis controller, with an order of 11, reaches a significantly lower γ value of 1.3552. The D - K iteration also reveals a significant reduction in the structured singular value μ , from 13.88 to 1.768, indicating enhanced robustness. While comparing the response of the trial-and-error based pole placement method with robust strategies such as H ∞ and μ -synthesis, it is observed that by selecting the desired poles [−1.8 + 1.63 i , − 1.8 − 1.63 i , − 1.7 + 1.14 i , − 1.7 − 1.14 i ] and the corresponding gain K = [−1464.5, 196.7, − 5.0, 210.0], the system response closely matches with the robust controllers response. The pole locations are iteratively refined until the response approaches that of closer to H ∞ and μ − synthesis over 5–7 iterations.