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Contact 99 is used to turn on coil 100. Contact 99 is also used to increment the UCTR counter. Register 40100 (in the UCTR) is used to count the number of times the coil has been turned on.
If the count reaches 3 then output coil 101 is turned on.
Timer T1 is used to count from 0 to 60 seconds. The current value of the count is stored in register 40101. Once the limit of 60 is reached, output coil 50 is used to reset the timer.
Output coil 50 is also used to reset the UCTR counter. The result of this is such that if the timer is reset prior to the counter reaching its limit (3) then the counter's output will never turn on.
The counter's output will only turn on if the counter reaches its limit prior to the timer reaching its limit.
Rungs 6 & 7 comprise the coil disable latch logic. Once the counter's output coil (101) goes true, this turns on coil 60 which acts as the disable to coil 100. (Note: contact 51 must be in the OFF position in order for coil 60 to "latch" ON.)
Rung 8 contains both the coil turn on switch (contact 99) as well as the coil disable latch (contact 60). With contact 60 in the ON state, coil 100 will be disabled, preventing it from being turned on until contact 60 is turned OFF.
Contact 51 (on rung 6) is used to turn off the latching logic and return coil 100 to an operational state.