A wind turbine has a safety system which uses three inputs to a logic circuit. When the value of X = 1, the wind turbine is shut down. The following table shows which parameters ar... A wind turbine has a safety system which uses three inputs to a logic circuit. When the value of X = 1, the wind turbine is shut down. The following table shows which parameters are being monitored and form the three inputs to the logic circuit. The output, X, will have a value of 1 if any of the following combination of conditions occur: either the turbine speed <=1000rpm and bearing temperature >80°C or turbine speed >1000rpm and bearing temperature <80°C and wind velocity >120kph. Create the truth table based on these conditions.
Understand the Problem
The question involves a logic circuit for a wind turbine safety system. It describes how certain parameters (turbine speed, bearing temperature, and wind velocity) relate to a binary output, and requires forming inputs based on specified conditions.
Answer
The expression for output \( X \) is \( X = (\neg S \land T) \lor (S \land W) \lor T \).
Answer for screen readers
The logic for the output ( X ) is defined by the expression: $$ X = (\neg S \land T) \lor (S \land W) \lor T $$
Steps to Solve
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Identify the Conditions
Based on the problem description, the output X will be 1 if any of the following combinations of conditions are met:- The turbine speed (S) is less than or equal to 1000 rpm or the bearing temperature (T) is greater than 80°C.
- The turbine speed (S) is greater than 1000 rpm and the wind velocity (W) is greater than 120 kph.
- The bearing temperature (T) is greater than 80°C.
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Set Up the Logic Variables
Assign binary values to the conditions:- Let ( S = 0 ) if turbine speed ( \leq 1000 , \text{rpm} ); ( S = 1 ) if turbine speed ( > 1000 , \text{rpm} )
- Let ( T = 0 ) if bearing temperature ( \leq 80 , \text{°C} ); ( T = 1 ) if bearing temperature ( > 80 , \text{°C} )
- Let ( W = 0 ) if wind velocity ( \leq 120 , \text{kph} ); ( W = 1 ) if wind velocity ( > 120 , \text{kph} )
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Determine the Output X Logic
Using the conditions:- ( X = \text{(NOT S AND T)} \lor (S AND W) \lor (T) )
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Construct the Truth Table
Using the combinations of S, T, and W, you can derive the output ( X ):- Complete the truth table based on the conditions and corresponding binary values.
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Create the Logic Circuit
Based on the truth table, create the logic circuit using AND, OR, and NOT gates.
The logic for the output ( X ) is defined by the expression: $$ X = (\neg S \land T) \lor (S \land W) \lor T $$
More Information
This expression can be simplified to meet the requirements for a wind turbine safety system. The system shuts down the turbine to prevent damage based on the monitored parameters. Understanding logic conditions is essential in designing safety systems.
Tips
- Misinterpreting Conditions: Confusing the parameters can lead to incorrect outputs. Ensure you understand the thresholds for speed, temperature, and wind velocity.
- Incorrectly Filling the Truth Table: Double-check combinations to ensure all conditions are correctly applied. Each combination of S, T, and W should result in an accurate X.
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