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A novel centralized controller design method is proposed for multivariable systems, whether square or nonsquare processes. First, the relationship between equivalent transfer function (ETF) and the pseudo-inverse of multivariable transfer matrix is derived. Second, the relative normalized gain array (RNGA)-based ETF parametrization method is extended to the nonsquare processes. Finally, a centralized proportional integral/proportional integral derivative (PI/PID) multivariable controller is obtained from the Maclaurin expansion. The effectiveness of the proposed approach is verified by analysis of several multivariable industrial processes; better overall performance is demonstrated compared with other centralized control methods.

We describe diffraction effects in acoustic ultrasound attenuation coefficient estimation using an insertion technique. We characterize the estimation error produced by diffraction as a function of distance and nominal attenuation values. Two new methods for correcting for the diffraction effect are presented. They are termed the Theoretical Diffraction Correction (TDC) and Experimental Diffraction Correction (EDC) techniques, respectively. Experimental validation of the two techniques is also presented, using two different sets of ultrasound measurements obtained with 1 MHz and 500 kHz transducer pairs, respectively. Significant improvement in the accuracy of the acoustic attenuation coefficient is demonstrated using both techniques.

A comparison study is reported on the ultrasonic assessment of human trabecular and bovine trabecular bone samples. Both ultrasonic velocity and ultrasonic attenuation were evaluated through a transmission insertion technique and correlated with bone mineral density as determined with single photon absorptiometry. For a 1-MHz ultrasonic transducer pair and the human cancellous bone samples the correlations were 0.91 and 0.89 between density and velocity and attenuation, respectively. For a 500-kHz ultrasonic transducer pair the correlations were 0.89 and 0.81 between density and velocity and attenuation, respectively. For the bovine bone samples, the correlations were 0.90 and -0.31 for the velocity and attenuation, respectively, for the 1 MHz transducer pair. For the 500-kHz transducers, the correlations were 0.85 and -0.17 for the velocity and attenuation, respectively. By combining both velocity and attenuation in a multivariate regression, an improvement was achieved in the estimation of bone density in the human samples for both the 500-kHz and 1-MHz transducer pairs. No significant improvement was achieved in the multivariate regressions for the bovine bone samples. In conclusion, the results indicate that ultrasonic measurements are in general highly correlated with bone mineral density in trabecular bone samples. This correlation is more consistent and strong in relatively low density human samples compared with the higher density bovine samples.

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