15.5. Examples

Try these first

1. 1.

   State the Final Value Theorem.

   Hint

   Remember the left-hand side is what we want to find.

2. 2.

   What is the first step in applying FVT?

   Hint

   Look for the transformation rules you previously learned.

3. 3.

   What does FVT help determine?

   • Initial value
   • Steady-state value
   • Dynamic response

   Hint

   Recall the purpose of the theorem!

4. 4.

   True or False: FVT cannot be applied if any poles of sF(s) are in the right half-plane.

   • True
   • False

   Hint

   Think about the implications of system stability.

5. 5.

   For f(t) = e^(-3t), apply FVT to predict the long-term behavior. What is the final value?

   Hint

   Remember to look for potential limits as s approaches zero.

6. 6.

   Discuss the implications of applying FVT incorrectly on a control system's stability analysis.

   Hint

   Think about what happens if the assumptions for convergence are violated.