Passive Voice Coil Feedback Control of Closed

Passive Voice Coil Feedback Control of Closed
Passive voice coil feedback control of closed-box
subwoofer systems
C-Y Cben', G T-C Cbiu2, C-C Cheng*' and H Peng3
'Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan
2School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA
3Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor,
Michigan, USA
Abstract: In this paper, the feasibility of using a voice coil back-electromotive voltage (back-e.m.f.)
signal as feedback information for closed-loop control was investigated. A dual voice coil closed-box
subwoofer system is used to demonstrate the effectiveness of back-e.m.f. feedback control. A secondorder filter is developed to extract the velocity information from the coil back-e.m.f. signal. A proportional-plus-derivative (PD) controller is well suited for reducing the harmonic distortion and
extending the subwoofer bass response. Experimental results verified that the proposed control
scheme effectively extended the bass response of the subwoofer system by one octave and at the same
time reduced harmonic distortion by more than 6 dB. The proposed feedback and control scheme can
be easily implemented using inexpensive analogue components, which can further reduce the cost and
complexity of the system.
Keywords: bandwidth, feedback control, harmonic distortion, loudspeaker, passive coil
Laplace transform of cone acceleration, x(t)
effective damping coefficient of the subwoofer
forcing factor or back-e.m.f. constant of the
electromechanical system
transfer function of the controller
compliance of the speaker box (m/N)
feedfonvard path gain
resonant frequency for the closed-box
resonant frequency for the open-air loudspeaker
transfer function from input voltage to passive
coil terminal voltage
transfer function from input voltage to cone
active coil current
passive coil current
equivalent suspension stiffness of the subwoofer
differential gain of the proportional-plusderivative (PD) controller
d.c. gain of the filter
proportional gain of the PD controller
d.c. gain offset of the dominating system
self-inductance of the two coils for the
equivalent mass of the subwoofer
mutual inductance of the two coils for the
d.c. voice coil resistance for the subwoofer
effective piston area of the cone (m2)
Laplace transform of the input voltage U(t)
applied voltage supplied by the audio
enclosed air volume (m3)
equivalent volume of compliance, which
specifies a volume of air having the same
compliance as the suspension system of the
volume of the sealed enclosure
Laplace transform of the passive coil terminal
voltage Vs(t)
voltage across the passive coil
moving coil position of the subwoofer
The MS was received on 23 October 1998 and was accepted after revision
for publication on 28 July 1999.
*Corresponding author: Department of Mechanical Engineering,
National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan.
damping ratio of the dominating system
time constant of the high-frequency first-order
resonant frequency of the dominating
C08298 6IMechE2OOO
Proc Instn Mech Engrs Vo1214 Part C
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