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This paper considers the problem of controlling the vibration of a lightweight thin-walled rotor with a distributed actuation magnetic bearing (DAMB). A theoretical flexible rotor model is developed that shows how multiharmonic vibration arises due to small noncircularity of the rotor cross section. This model predicts a series of resonance conditions that occur when the rotational frequency matches a subharmonic of a system natural frequency. Rotor noncircularity can be measured offline, and the measurement data used to cancel its effect on the position sensor signals used for feedback control. A drawback of this approach is that noncircularity is difficult to measure exactly and may vary over time due to changing thermal or elastic state of the rotor. Moreover, any additional multiharmonic excitation effects will not be compensated. To overcome these issues, a harmonic vibration control algorithm is applied that adaptively modifies the harmonic components of the actuator control currents to match a target vibration control performance, but without affecting the stabilizing feedback control loops. Experimental results for a short thin-walled rotor with a single DAMB are presented, which show the effectiveness of the techniques in preventing resonance during operation. By combining sensor-based noncircularity compensation with harmonic vibration control, a reduction in vibration levels can be achieved without precise knowledge of the rotor shape and with minimal bearing forces.

This paper presents a framework for model-based analysis of robust stability and performance for a multi-axis active vibration isolation system with constant but unknown payload and subject to modelling errors associated with structural flexibility. The theoretical treatment involves a linear time-invariant system subject to real parameter uncertainty associated with the unknown payload. A set of performance indices are formulated based on generalized H 2 (H g ) and H 1 measures. A method for stability/performance verification is then developed using a parameter-dependent Lyapunov function that incorporates the kinetic energy of the uncertain payload mass. This allows nonconservative bounds on the performance indices to be established via numerical solution of a corresponding set of matrix inequalities. The approach is especially suitable, and computationally efficient, for multi-degree-of-freedom systems as the overall (symmetric positive-definite) properties of the system mass matrix are accounted for without involving information for each scalar parameter. The associated LMIs can therefore be solved in polynomial time with respect to the number of unknown parameters. Numerical examples for the case of sky-hook damping control and multi-objective H g =H 1 control are provided that demonstrate the effectiveness of the method as a tool for model-based controller evaluation and multi-objective optimization.