Hierarchical Control for Vibration Suppression Through Decoupling of Traveling/Reflected Waves

Vibration suppression has attracted interest in achieving fast, stable motion control in industrial fields. This study uses the wave partial differential equation (PDE) to model resonant systems and connects a lumped load and the PDE model in series. The lumped load is governed by the ordinary differential equation (ODE). This integrated model replaces the conventional two-mass resonant model, referred to as the PDE-ODE model in this study. A matrix representation of the PDE model is eigenvalue decomposed. The decomposition provides the basis transformation of the variables on the actual space into those on a wave space. Based on this transformation, the proposed controller equips the decoupling of the traveling/reflected waves for vibration suppression. Impedance matching explains the conditions necessary for the decoupling and control of vibration. The suppression method requires only the PDE part's parameter, making the control system resistant to inertial variations.