Identification and cancellation of sums of narrow-band signals and disturbances

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Predictable and periodic signals occur in a vast array of fields ranging from power systems, metal processing, structural analysis, music, robotic surgery, ventilator control, and diurnal variations in temperatures in petrochemical refining business. As early as 1973, Francis and Wonham at U. of Toronto developed the internal model principle which states that exact matching, and hence cancellation of any exogenous signal in a feedback system is achieved by placing a model of the signal in the loop. However, this requires precise knowledge of the period and decay, but not amplitude or phase, of the signal. The investigator has substantially weakened this requirement by showing how to adaptively identify the frequency and shown how to extend an adaptive internal model principal controller as a signal identification algorithm. The investigator proposes to extend this work in the following directions. i) Many predictable signals are not periodic, but have fixed decay rates. Examples of this are the structural modes of an airplane wing or suspension bridge. The investigator is confident that this decay rate, or damping coefficient can be identified in a manner similar to identifying the frequency. ii) The present approach requires exact knowledge of the number of frequency components in the signal. The investigator believes that this can be learned or adaptively identified in real-time iii) The investigator plans to theoretical examine the behaviour of the algorithm in the presence of colored noise. iv)The investigator plans to apply the algorithm in the fields of tremor control in robotic surgery, identification of structural modes in robots, and music transcription.