Inverse self-regulation

Notice that as ti approaches zero, P approaches infinity. This is much worse than having no capacity at all, i.e., dead time alone. The reason is that this expression holds only for a non-self-regulating process whose gain varies inversely with the time constant without limit. Fortunately, non-self-regulating processes dominated by dead time are virtually nonexistent. 

Loops containing two integrations are capable of a limit cycle, however. An example would be a non-self-regulating process such as liquid level, with a proportional-plus-reset controller. The gain product of the two integrating elements will vary as the square of the period, more than can be offset by the gain of hysteresis. Under these conditions, loop gain varies inversely with amplitude. 

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