Strictly Positive Real Condition and Pseudo-Strictly Positive Real Condition

1989 ◽  
Vol 25 (7) ◽  
pp. 751-757 ◽  
Author(s):  
Tsutomu MITA ◽  
Yuichi CHIDA ◽  
Jing Wen WANG
Keyword(s):  
Positive Real ◽  
Real Condition ◽  
Strictly Positive Real

Active Helmholtz Resonator With Positive Real Impedance

2006 ◽  
Vol 129 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Jing Yuan
Keyword(s):  
Noise Control ◽  
Helmholtz Resonator ◽  
Control Device ◽  
Positive Real ◽  
Noise Field ◽  
Strictly Positive Real ◽  
Control Devices ◽  
Passive Noise ◽  
Active Resonator ◽  
Electronic Resonance

The impedance of a passive noise control device is strictly positive real, if the device is installed in noise fields with weak mean flows. Passive noise control devices are, therefore, more reliable than active ones. Active control may be applied to a Helmholtz resonator to introduce electronic resonance. It will affect the impedance Zact of the resonator. A controller may be designed such that (a) Zact is small and resistive at some tunable frequencies; and (b) Re{Zact}⩾0 in the entire frequency range of interest. If criterion (a) is satisfied, the active resonator can suppress duct noise at tunable frequencies. It is difficult to design a controller to satisfy criterion (b) because parameters of the controller depend on acoustic parameters of the noise field. A new method is proposed here to design an active controller to meet both criteria simultaneously. The satisfaction of criterion (b) implies a positive real Zact and a robust active resonator with respect to parameter variation in the noise field. Experimental results are presented to verify the performance of the active resonator.

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