A frequency-domain method for solving linear time delay systems with constant coefficients
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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.
KeywordsTime delay system Delay differential equation Approximate solution Transfer function
This work was supported by the National Natural Science Foundation of China (11272235).
- 6.Qin, Y.X.: The Motion Stability of Dynamical Systems with Time-delay, 2nd edn. Science Press, Beijing (1984). (In Chinese)Google Scholar
- 13.Falbo, C.E.: Analytic and numerical solutions to the delay differential equations. In: Joint Meeting of the Northern and Southern California Sections of the MAA, San Luis Obispo (1995)Google Scholar