Development of an Analog Controller for Tuning an Adaptive-Passive Control Device

Abstract

Adaptive-passive devices such as adaptive Helmholtz Resonators (HR) and tunable vibration absorbers have been shown to be suitable for controlling both narrowband disturbances and lightly damped structural/acoustic modes driven by broadband disturbances. In order to track changes in the disturbance or changes in the modes, the natural frequency of the absorber, ωn, is tuned to match the observed signals. This is achieved by altering some physical parameter of the control device such as the stiffness of a vibration absorber or the neck cross-sectional area of a Helmholtz resonator. In order to automatically adjust these devices, control systems and tuning algorithms have been developed, most of which involve a digital controller. However, this paper looks specifically at the development of a simple analog controller used to drive a DC motor in order to tune a mechanical device. A two sensor dot product method is employed where one sensor is placed inside of the control device, such as a Helmholtz Resonator, and the other on/in the system under control, such as in a room. The outputs from the two sensors are multiplied together and subsequently low passed in order to extract a low frequency “DC” voltage which acts as an error signal. The error signal is related to the relative phase of the two sensor signals and determines the direction in which the device should be tuned. When the two signals are 90° apart, the system is tuned (i.e. the inner product produces zero DC level). If the drive frequency ω is different than the tuned frequency, then the system is mis-tuned. The relationship between the mis-tuning, ωn-ω, and the error is not linear, but for small perturbations a linear approximation can be used to investigate the stability and performance of the system. The gradient of the function is shown to be largest when the mis-tuning error is zero and is inversely proportional to the damping level in the control device. Once stability of the system has been ensured the ability of the system to track changes in drive frequency is investigated experimentally. The control system is demonstrated using an adaptive Helmholtz resonator which has a variable cross-sectional neck via an iris diaphragm. The iris is controlled using a small DC motor; two microphones (one mounted internally and one externally) are used to supply the driving signal to the circuit.