Nonlinear output control in hysteretic, saturating materials

The problem of determining the drive waveform that produces a desired outpu t from a hysteretic, saturating material is considered both theoretically a nd experimentally. The specific problem of interest is the production of a high-amplitude, but monofrequency, sinusoidal polarization response. (The t echniques presented could also be used to control other physical variables, such as the strain, if desired.) Two sample materials were considered, one of which is characterized by relatively low hysteresis tan delta approxima te to0.03) and tested using mechanical prestresses of 20.7 MPa (3 kpsi) and 41.4 MPa (6 kpsi), and the other of which is characterized by relatively h igh hysteresis (tan (delta approximate to0.11), and tested without a prestr ess. Both samples were fabricated from the electrostrictive material lead m agnesium niobate (PMN), although a magnetostrictive material (such as Terfe nol-D) could have been tested instead. The samples were subjected to a bias voltage and prestress in order to simulate conditions that might arise in a full transducer. By analytically inverting a theory of hysteresis [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 106, 3317-3327 (1999) and J. Acoust Soc. Am. 106, 3328-3334 (1999)], the required (predistorted) driv e waveform was determined. Both semi-major and minor hysteresis loops, in b oth polarization and strain, were measured and the parameters of the theory determined by least-squares fitting. The measurements were obtained under quasi-static conditions, with drive frequencies at or below 10 Hz. The obse rved fits of theory to data are of high quality. The theory was then invert ed analytically to determine the drive required to produce the desired mono frequency polarization response, having a peak polarization value approxima tely equal to that achieved using a biased sinusoid of AC amplitude equal t o the bias. The total harmonic distortion (THD) in the output polarization resulting from the inverting drive, computed using 10 harmonics, was experi mentally observed to be about an order of magnitude less than that resultin g from a biased sinusoid in all cases. It is shown that the hysteresis loop arising when using the distortion-reducing drive is of smaller area than t hat obtained when driving with a sinusoid to achieve the same polarization amplitude. Thus, the distortion-reducing drive results in a smaller loss pe r cycle than is obtained with a sinusoidal drive. (C) 2001 Acoustical Socie ty of America.