Several investigators have taken advantage of electromagnetic shunt-tuned mass dampers to achieve concurrent vibration mitigation and energy harvesting. For nonlinear structures such as the Duffing oscillator, it has been shown that the novel nonlinear electromagnetic resonant shunt-tuned mass damper inerter (NERS-TMDI) can mitigate vibration and extract energy for a wider range of frequencies and forcing amplitudes when compared to competing technologies. However, nonlinear systems such as the NERS-TMDI are known to exhibit complex stability behavior, which can strongly influence their performance in simultaneous vibration control and energy harvesting. To address this problem, this paper conducts a global stability analysis of the novel NERS-TMDI using three approaches: the multi-parametric recursive continuationWe emphasize that these assume method, Floquet theory, and Lyapunov exponents. A comprehensive parametric analysis is also performed to evaluate the impact of key design parameters on the global stability of the system. The outcome indicates the existence of complex nonlinear behavior, such as detached resonance curves, and the transition of periodic stable solutions to chaotic solutions. Additionally, a parametric study demonstrates that the nonlinear stiffness has a minimal impact on the linear stability of the system but can significantly impact the nonlinear stability performance, while the transducer coefficient has an impact on the linear and nonlinear stability NERS-TMDI. Finally, the global sensitivity analysis is performed relative to system parameters to quantify the impact of uncertainty in system parameters on the dynamics. Overall, our findings show that simultaneous vibration control and energy harvesting come with a considerable instability trade-off that limits the range of operation of the NERS-TMDI.

We investigate the effectiveness of a vibration absorber on the vortex-induced vibration response of turbine blades during the frequency lock-in phase. A reduced-order model of a turbine blade and van der Pol oscillator is used to represent the fluid–blade interaction caused by the vortex shedding. A spring-mass-damper system is considered to model the vibration absorber. The advantage of the vibration absorber is demonstrated by simulating the nonlinear coupled four-degree-of-freedom aeroelastic system for the different sets of system parameters. We observe the dominance of a nonlinear vibration absorber over the linear vibration absorber only for the higher coupling parameter values. The analytical solution of the nonlinear coupled system is obtained through the method of multiple scales for the case of 1:1 internal resonance to identify the critical design parameters of the vibration absorber. We observe the high sensitivity of the system's frequency response to the distance of the vibration absorber from the elastic axis, along with the absorber's damping, stiffness, and mass. Finally, we perform a parametric analysis on the lock-in of the stability region to better understand the effect of the vibration absorber on the instability region.

We propose a robust adaptive controller for the safe and accurate trajectory tracking control of upper limb rehabilitation exoskeletons. The proposed controller can adapt to the inertia and load uncertainties, and compensate for their effects. The $H_\infty$ robustness of the controller in $l_2$ perturbation/disturbance attenuation is realized by nonlinear robust control theory via inverse optimality. We mathematically prove the asymptotic stability and optimality of the controller by stabilizing a Lyapunov function and minimizing a meaningful cost function, respectively. We then demonstrate the performance of the controller with the simulations of two different exoskeleton control systems. The results show that the controller can identify and compensate for model uncertainties, and realize good tracking performance in the presence of perturbations and disturbances. These qualities are crucial to the reliability and safety of exoskeleton operations. In addition to rehabilitation exoskeletons, the proposed framework can also be applied to the control of other multibody robotic systems.