The equivalent dead time
D of a meromorphic function G(s) in |s| < ∞ is defined as an integral_??_dt, where
u (t) is the unit step function,
i (t) the indicial response of
G (s), andK the final value of
i (t). It is shown that
G (s) can be written in the form K(1+a
1s+a
2s
2+ ……)/(1+b
1s+b
2s
2+……) and D is equal to b
1-a
1 if
D exists. It is also shown that
D corresponds to thecenter of gravity of the impulse response of
G (s).
Then, the author proposes to use
D as a new measures of delay. Using
D, the delay is explicitly defined in a sense. Relations between the pole-zero configuration of
G (s) and the delay areinvestigated.
It is shown that the equivalent dead time of a unity feedback system is equal to that of theopen loop multiplied by the steady-state positional error for input
u (t) in the case of a type0 system, to the steady-state velocity error for input
tu (t) in the case of a type 1 system, and to 0 in the cases of type 2, 3, … systems. Consequently, if the type of system is other than 0, we canobtain the steady-state velocity error by calculating D from the result of the indicial responseexperiment.
To approximate a dead time by a delay with distortion or vice versa, it is proposed to make theequivalent dead time of the approximate transfer function equal to that of the true transfer function.As an example, it is shown that such a method gives much better approximation than the usualone in the case where the transfer function of a process is approximated by a lst-order delay and adead time.
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