H∞ control design for a magnetostrictive transducer

Magnetostrictive transducers are becoming increasingly prevalent in industrial applications including high speed milling and hybrid motor design due to their broadband, large force capabilities. To achieve the level of performance required by such applications, however, these transducers must operate in nonlinear and hysteretic regimes. To accommodate this nonlinear behavior, models and control laws must incorporate known physics and be sufficiently robust to operate under realistic operating conditions. We develop here an H_∞ robust control design for a prototypical magnetostrictive transducer but note that the design is sufficiently general to be utilized for several commonly used smart materials including piezoceramics and shape memory alloys. The performance of the control strategy is illustrated through a numerical example.