A Control Source Structure of Single Loudspeaker and Rear Sound Interference for Inexpensive Active Noise Control

Abstract

Active noise control systems of simple ducts are investigated. In particular, open-loop characteristics and closed-loop performances corresponding to various structures of control sources are compared based on both mathematical models and experimental results. In addition to the standard single loudspeaker and the Swinbanks' source, we propose and examine a single loudspeaker with a rear sound interference as a novel structure of control source, where the rear sound radiated from the loudspeaker is interfered with the front sound in order to reduce the net upstream sound directly radiated from the control source. The comparisons of the control structures are performed as follows. First, the open-loop transfer function is derived based on the standard wave equation, where a generalized control structure unifying the three structures mentioned above is considered. Secondly, by a comparison of the open-loop transfer functions from the first principle modeling and frequency response experiments, it is shown that a certain phase-lag is imposed by the Swinbanks' source and the rear sound interference. Thirdly, effects on control performances of control source structures are examined by control experiments with robust controllers.

Analysis and Optimal Condition of the Rear‐Sound‐Aided Control Source in Active Noise Control

“…The damped wave equation is the wave equation with an additional term of the first partial derivative of pressure in time (see, e.g., [10]). The differences to the existing result of [9] will be explained, since the existing result is based on the (undamped) wave equation. Note that the derivation process of the damped wave equation will be described in this section, since the intermediate equations ( (1) and (2) below) are necessary to exploit the existing result of the transmission line theory.…”

“…(i) The first principle model derived in [9] has not been well consistent with the experimental result of the frequency response.…”

“…Usually, the damped wave equation (3) is solved without considering damping. The resulting undamped solution is used to approximate damping effect by modifying the wave number k := ω/c 0 (real number) to k := (ω/c 0 ) + jα (complex number) [12], which technique has also been used in [9]. The damped wave equation can be obtained by the derivation of (1) with respect to t and (2) with respect to x and combining both 1 c 2 0…”

“…In addition to the Swinbanks' source, the rear-soundaided source has been proposed to achieve similar advantage of Swinbanks' source by using one loudspeaker [9]: the source is composed of a loudspeaker and a subduct which connects the rear side of the loudspeaker to an upstream junction in the main duct in order to attenuate the upstream sound by interfering the rear sound as shown in Figure 1. Experiments demonstrated that the proposed source has an advantage.…”

“…Firstly, the first principle model [9] is derived based on the damped wave equation which later enables comparison of the frequency response of the first principle model with the numerical simulation. In Section 3, the damped wave equation will be directly implemented in a numerical simulation by using finite differences.…”