0/1 or OFF/ON controllers still very widely used in power plants,process control and automation. Unlike Fuzzy Logic Controllers where memebership function values will take the values between 0 to 1.In this worksheet I will discuss how to design Relay Logic Controller RLC) and the flexibilty behind the design of such RLC. Example: Suppose that we have a Pressure Sensor (PS), Level Sensor (LS) and temperature Sensor (TS), all are Normally Open contacts and each is connected to a control relay. It is required to design a Relay Controller to give a certain functions for the outputs. 1- For the 3 sensors, we need to make a state table as shown below:

Now, what about the Outputs? OK, 1- Let us say that for the Normal operations (0,0,0) a Green Light is ON, else will be OFF. 2- If any logic 1 in PS, LS or TS, we have a corresponding Red Light, namely PRed, TRed and LRed will be ON. In addition, for every any 2 sensors are ON, we have the Red light ON and a Buzzer or Alarm ON at the same time. 3- The highest priority is, when the 3 sensors are ON, then a siren will be ON. Output Table: The below Output table shows the Output requirement

Writing and simplifying the Output equations: ------------------------------------------------------- From the output table above, we look in each column and search for Logic 1 and writing the corresponding equation from the input table. For mutiple Logic 1 in any one of the columns, we need to ORing all equations. For example, Green Light= (NOT PS) And (NOT LS) And (NOT TS).Keep in mind Logic 0 is NOT. For the Siren, Siren= PS And LS And TS. For PRed=(PS And NOT LS And NOT TS) OR (PS And LS And NOT TS) OR (PS And NOT LS And TS). The same for the remaining functions. We need to simplify, if possible, the equations either by using Boolean Algebra or Karnaugh map, as Mathcad does not have a logical simplification. The full programme as hereunder and all the possible inputs were taken to obtain the Outputs. Compare the results. Please note that, all the statements in the Output equations are infact either Normally open or Normally closed contacts coming from the Relays PS, LS and TS which are controlled by the Normally open Sensors PS, LS and TS.

Enter the data for PS, LS and TS in single column matrix to match the table above:

Use Boolean operators following the description specified above:

Which match the output table.