The steps to take from a truth table to the final circuit are so unambiguous and direct that it requires little, if any, creativity or other original thought to execute them.Correspondingly, whereas a Sum-Of-Products expression could be implemented as a parallel collection of series-connected relay contacts, a Product-Of-Sums expression can be implemented as a series collection of parallel-connected relay contacts:Unfortunately, both of these circuits are quite complex, and could benefit from simplification. Such a Boolean expression would require many steps to simplify, with a large potential for making algebraic errors:Finally, we join these four Boolean product expressions together by addition, to create a single Boolean expression describing the truth table as a whole:Sum-Of-Products expressions are easy to generate from truth tables. If 2 have to fail for a spurious shutdown, this is reduced to once every 25 years.Our task, now, is to design the circuitry of the logic system to open the waste valve if and only if there is good flame proven by the sensors. Suppose that one of the three sensors were to fail in such a way that it indicated no flame when there really was a good flame in the incinerator’s combustion chamber. That single failure would shut off the waste valve unnecessarily, resulting in lost production time and wasted fuel (feeding a fire that wasn’t being used to incinerate waste).As a result of the simplification, we can now build much simpler logic circuits performing the same function, in either gate or relay form:In terms of unwanted shutdowns, each instrument has a given probability of failure (once every 5 years is a pretty good number as a rule of thumb).
Each sensor comes equipped with a normally-open contact (open if no flame, closed if flame detected) which we will use to activate the inputs of a logic system:Now that we have a Boolean Sum-Of-Products expression for the truth table’s function, we can easily design a logic gate or relay logic circuit based on that expression:The first step in designing this “sensor disagreement” detection circuit is to write a truth table describing its behavior. The PLC which provokes instrumented emergency action has to be an FSC, a fail safe controller. If only one has to fail to produce the unwanted shutdown you will have a spurious shutdown every five years or so. Also, if the incinerator is shut down (no flame), and one or more of the sensors still indicates flame (001, 010, 011, 100, 101, or 110) while the other(s) indicate(s) no flame, it will be known that a definite sensor problem exists.If all three sensors are operating properly, they should detect flame with equal accuracy. First, though, we must decide what the logical behavior of this control system should be. In other words, a computer could be programmed to design a custom logic circuit from a truth table specification! Do we want the valve to be opened if only one out of the three sensors detects flame? that means that if its not sure what the situation is, it will shut the system down.To illustrate this procedural method, we should begin with a realistic design problem. All we have to do is examine the truth table for any rows where the output is “high” (1), and write a Boolean product term that would equal a value of 1 given those input conditions. 【正解】を知っている方だけお願いします。これからネットで調べて「～だと思います」の方は、ご親切ありがたく思いますがご遠慮くださいませ。2 from 2、 3 out of 32回のうち2回とも、3回のうち3回とも、のような意味になるのでしょう It has to be said that most of the applications I personally know are for increasing plant reliability rather than increasing intrinsic safety. Probably not, because this would defeat the purpose of having multiple sensors.The best system is with three instruments that are continuously measuring the variable, are checked regularly in the field and are set up with deviation alarms.Whoever is monitoring the incinerator would then exercise judgment in either continuing to operate with a possible failed sensor (inputs: 011, 101, or 110), or shut the incinerator down to be absolutely safe. / … Suppose we were given the task of designing a flame detection circuit for a toxic waste incinerator.