Simultaneous phase control of multiple frequencies of multi-degree-of-freedom systems

This paper presents an innovative method to achieve the simultaneous phase control of multiple resonance frequencies of a linear multi-degree-of-freedom system using only one sensor/actuator pair. Each frequency is manipulated independently by means of a PLL-based control loop which comprises a digital averaging phase detector that combines the two most crucial tasks, namely the phase shift measurement and the frequency separation. The properties of the controller are designed individually for each mode using a linearized model of the control system. The method is applicable to all kinds of oscillators where frequencies near the structure's natural frequencies are to be controlled. To validate the results experimentally, the controller is implemented on a digital signal processor (DSP) and applied to a torsional oscillator. Investigating two different damping conditions, the simultaneous control of five resonance frequencies of the oscillator illustrates the effectiveness and stability of the multiple frequency tracking. The method is able to significantly improve the accuracy and versatility of sensor applications. As an example a method is presented that enables the direct determination of the modal damping by using two frequencies corresponding to one single vibration mode.