Question

The positioning system of a printer can be modelled as

Y(s) = (2(s+40))/(s² + 32s + 80) *R(s)

where the input R(s) represents the desired position and Y(s) is the output position. If the input is a unit step input, the final value of the output is (in the time domain):

Answer 1

The positioning system of a printer can be modeled using a mathematical equation. To find the final value of the output in the time domain, we need to perform partial fraction decomposition and find the inverse Laplace transform of the expression.

Step-by-step explanation:

The positioning system of a printer can be modeled using the equation Y(s) = (2(s+40))/(s² + 32s + 80) * R(s), where Y(s) represents the output position and R(s) represents the desired position. If the input is a unit step input, we can determine the final value of the output in the time domain.

To find the final value of the output in the time domain, we need to find the inverse Laplace transform of Y(s). However, before we do that, we need to perform partial fraction decomposition on the expression for Y(s). Once we have the inverse Laplace transform, we can substitute t = ∞ to find the final value of the output in the time domain.

Let's go step-by-step to solve the problem:

1. Perform partial fraction decomposition on the expression for Y(s).
2. Find the inverse Laplace transform of the decomposed fractions.
3. Substitute t = ∞ in the inverse Laplace transform to find the final value of the output in the time domain.