Robust vibration isolation via frequency-shaped sliding control and modal decomposition

A robust controller design is proposed for multi-degree-of-freedom active vibration isolation, which accounts for plant uncertainties and payload disturbances using frequency-shaped sliding control. First, modal decomposition is employed to rewrite the MIMO vibration control problem as a combination of individual SISO control problems in modal coordinates. The modal parameters for decomposition and modelling can be extracted from theoretical or experimental modal analysis. Next, the target frequency-domain performance of isolation, in this case a skyhook model, is recast as a frequency-shaped sliding surface. The practical effects of boundary layer approximation in the resulting controller design are examined. Simulations illustrate that the ideal skyhook effect can indeed be robustly achieved. The frequency-shaped manifold is also extended to adaptive vibration isolation without using model reference. This algorithm has been recently verified by experiments (IEEE Transactions on Control Systems Technology (2005), in press), and has been demonstrated very effective for vibration isolation. The paper also shows, more generally, that the design of a frequency-shaped sliding surface is formally equivalent to a feedback-feedforward compensation problem. Nonlinear target dynamics of the same order as the nominal plant can also be attained.