Suppose that we have a transfer function with delay like below:
G (s) = e-sL/(1+Ts)
T: Time Constant
L: Time Delay
Here is the question:
"Why is the control of this system; while L>T; difficult ", and What difficulties can be accured while designing a feedback (or something else) controller for this delayed system ?
The main difficulty is that the delay term creates a transcendental characteristic equation for the close loop system. This means the closed-loop-system has infinitely many characteristic roots, and guaranteeing that all of them are inside the left half of the complex plane is not easy.
Hi,
A big time-delay can be considered as a unstable-zero, which imposes huge limitation on the system stability. In other word, high gain control would be impossible.
read this:
Qing-Chang Zhong, Robust Control of Time-delay Systems, Springer-Verlag London Limited 2006
dear "Lio, Rudy and Ali" Thank you for sharing your useful ideas and your helps.
If you design the system, try to place sensors and actuators in a way that removes \exp{-sL} factor in the transfer function, so the system has some state variables that was delayed, but the input and output are not delayed. That is the best way to design a system.
If you are given a system to design a controller that has a pure delay in the transfer function like yours, there are method to deal with it. 1) Smith predictor. 2) H-infinity control. See the book by Başar and Bernhard.
Article H ∞ -optimal control and related minimax design problems. A ...
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