A frequency-domain method for solving linear time delay systems with constant coefficients

In an active control system, time delay will occur due to processes such as signal acquisition and transmission, calculation,and actuation. Time delay systems are usually described by delay differential equations（DDEs）. Since it is hard to obtain an analytical solution to a DDE, numerical solution is of necessity. This paper presents a frequency-domain method that uses a truncated transfer function to solve a class of DDEs. The theoretical transfer function is the sum of infinite items expressed in terms of poles and residues. The basic idea is to select the dominant poles and residues to truncate the transfer function,thus ensuring the validity of the solution while improving the efficiency of calculation. Meanwhile, the guideline of selecting these poles and residues is provided. Numerical simulations of both stable and unstable delayed systems are given to verify the proposed method, and the results are presented and analysed in detail.

Time-delay identification for linear controlled systems

A new approach for time-delay identification is proposed in linear controlled systems. The delay is derived from the control loop in the system. The frequency-response function of the system is presented in terms of the impedance matrix. It is proved that the inverse form of the function may be expressed in the harmonic function, which is used to fit those data from the experiment. As an example, an isolator with the delayed feedback control is schemed to acquire such data. Using least square algorithm yields that the identified delay can reach any required accuracy.

Simultaneous determination of ten taste and odor compounds in drinking water by solid-phase microextraction combined with gas chromatography-mass spectrometry

Taste and odor （T＆O） problems in drinking water frequently occur because of many compounds present in the water, of which trans-1,10-dimethyl-trans-9-decalol （geosrnin） and 2-methylisoborneol （MIB） are well-known. In this study, a fast and effective method was established for simultaneous determination of 10 T＆O compounds, including geosmin, MIB, 2,4,6-trichloroanisole （TCA）, 2-methylbenzofuran, 2-isopropyl-3-methoxypyrazine （IPMP）, 2-isobutyl-3-methoxypyrazine （IBMP）, cis-3-hexenyl acetate, trans,trans-2,4-heptadienal, trans, cis-2,6-nonadienal, and trans-2-decenal in water samples by headspace solid-phase microextraction （SPME） coupled with gas chromatography-mass spectrometry. An orthogonal array experimental design was used to optimize the effects of SPME fiber, extraction temperature, stirring rate, NaC1 content, extraction time, and desorption time. The limits of detection ranged from 0.1 to 73 ng/L were lower than or close to the odor threshold concentrations （OTCs）. All the 10 T＆O compounds were detected in the 14 water samples including surface water, treatment process water and tap water, taken from a waterworks in Lianyungang City, China. MIB and geosmin were detected in most samples at low concentration. Six T＆O compounds （IPMP, IBMP, trans,cis-2,6-nonadienal, 2-methylbenzofuran, trans-2-decenal, and TCA） were effectively decreased in water treatment process （sedimentation and filtration） that is different from cis-3-hexenyl acetate, MIB and geosmin. It is noted that the TCA concentrations at 15.9-122.3 ng/L and the trans,cis-2,6-nonadienal concentrations at 79.9-190.1 ng/L were over 10 times higher than their OTCs in tap water. The variation of the analytes in the all water samples, especially distribution system indicated that distribution system cannot be ignored as a T＆O compounds source.