Problem

Develop a PLC program to prevent a machine operator from starting a motor that has tripped off more than $5$ times in an hour. The operation of the program can be summarized as follows:

$$ A start and stop push buttons are used to operate the motor.

$$ The normally open overload $($OL$)$ relay contact momentarily closes each time an overload current is sensed$.$

$$ Every time the motor stops due to an overload condition, the motor start circuit is locked out for $5$ min.

$$ If the motor trips off more than $5$ times in an hour, the motor start circuit is permanently locked out and cannot be started until the reset button is actuated.

$$ The lock$-$out pilot light is switched on whenever a permanent lock$-$out condition exists.