Undirectional JMC actuators and their aproximations in the active attenuation of noise in ducts

This report deals with a fundamental problem of feedforward active noise control systems in ducts, the acoustic feedback from the canceling actuator to the reference detector. A natural solution to this problem is to use a unidirectional actuator. The starting point of this study is the JMC source that is an ideal unidirectional actuator but is difficult to realize. Potential unidirectional three-element actuator systems are surveyed systematically by modifying and approximating the JMC source in various ways. As a result, one realizable ideal unidirectional three-element source configuration and four nearly unidirectional approximations of it are discovered. Also two-element unidirectional JMC actuators are handled, in which the elements act as a dipole with the monopole effect included in the same elements. As a result, one ideal unidirectional two-element solution and six approximations of it are found. The inter-channel delay in the control structure of the two-element actuators is optimized so that the residual sound pressure downstream or upstream from the unidirectional source will be mini-mized, or the delay is omitted altogether. The two-element ideal solution and its approximations are derived for each three ways of handling the delay. The output volume velocities of all the three variations of two-element Ideal Source are mutually identical and independent of the inter-channel delay optimization, and are also identical with those of Swinbanks' two-element actuator, although the procedure of attaining them is quite different. Especially the delayless version of two-element Ideal Source has the advantage of no separate phase shift between the volume velocities of the elements, which turns out to be advantageous in the practical implementation of digital control systems. Using the unidirectional solutions with no inter-channel delays makes is possible to achieve simplified control algorithms and reduce the computing time or improve the performance. Digital control of some of the structures and their practical limitations are considered. Examples of realizable digital control systems are given.