explain the need for laplace operator methods when solving control engineering problems?

Answer 1

The Laplace operator, or Laplace transforms, turn the sort of differential equations you get in control problems into simple algebraic equations. Ideal for engineers!

Answer 2

Laplace transforms make the solution of differential equations much simpler. Since control problems are often well modeled by differential equations, it makes sense that Laplace transforms would be used in their solution.