Interconnection and damping assignment passivity based control (IDA-PBC) is a method that has been developed to (asymptotically) stabilize nonlinear systems formulated in portcontrolled Hamiltonian (PCH) structure. This method has gained increasing popularity and has been successfully applied to a wide range of dynamical systems. However, little is known about the robustness of this method in response to the effects of uncertainty which could result from disturbances, noises, and modeling errors. This paper explores the possibility of extending the IDA-PBC method by adopting a robustness perspective, with the aim of maintaining (asymptotic) stability of the system in the presence of such perturbations which exist in any realistic problem. We propose constructive results on Robust IDA-PBC and PID-like controllers for a class of PCH systems. The results extend some existing methods and provide a new framework that allows the implementation of integral action control to underactuated PCH systems that are quite commonly found in practice. The results are applied to a Quanser inertia wheel pendulum and illustrated through numerical simulations.

The structure-borne tones generated by the main gearbox are the primary components of helicopter interior noise. Recently, a kind of periodic strut has been designed to isolate the multispectral vibration from transmitting to the cabin, for their specific stop-band characteristics. Using multicell optimization, the disorders are designed into the strut to obtain better vibration and noise reduction effect. The dynamic model of the periodic strut is firstly established by combining the spectral element method and the transfer matrix method. On this basis, a multi-objective multivariable genetic algorithm is adopted to optimize the geometry by taking the maximum attenuation as the performance objective function. Then, a near-periodic structure is achieved. Compared with the perfect periodic strut, the optimal one has a much wider and deeper stop band, which is critical for a better vibration and noise attenuation effect. In addition, a method is presented to analyze the wave propagation to explore the increase of width and depth of the bandgaps more closely. Experimental investigations are then carried out on a pair of original and optimal struts to validate the improvements. It is shown that 26.22% more attenuation is achieved through this structural optimization.