## How do you solve Laplace problems?

The solution is accomplished in four steps:

- Take the Laplace Transform of the differential equation. We use the derivative property as necessary (and in this case we also need the time delay property)
- Put initial conditions into the resulting equation.
- Solve for Y(s)
- Get result from the Laplace Transform tables. (

### What is the Laplace transform of constant?

In general, if a function of time is multiplied by some constant, then the Laplace transform of that function is multiplied by the same constant. Thus, if we have a step input of size 5 at time t=0 then the Laplace transform is five times the transform of a unit step and so is 5/s.

**Why do we use partial fraction expansion in control systems?**

Why perform partial fraction expansion? Partial fraction expansion (also called partial fraction decomposition) is performed whenever we want to represent a complicated fraction as a sum of simpler fractions.

**What is partial fraction method?**

Partial Fractions are used to decompose a complex rational expression into two or more simpler fractions. Generally, fractions with algebraic expressions are difficult to solve and hence we use the concepts of partial fractions to split the fractions into numerous subfractions.

## How do you solve a difficult partial fraction?

Summary

- Start with a Proper Rational Expressions (if not, do division first)
- Factor the bottom into: linear factors.
- Write out a partial fraction for each factor (and every exponent of each)
- Multiply the whole equation by the bottom.
- Solve for the coefficients by. substituting zeros of the bottom.
- Write out your answer!

### What is inverse Laplace transform by partial fraction expansion?

Exponentials in the numerator Inverse Laplace Transform by Partial Fraction Expansion This technique uses Partial Fraction Expansionto split up a complicated fraction into forms that are in the Laplace Transform table.

**What is partial fraction expansion?**

This technique uses Partial Fraction Expansionto split up a complicated fraction into forms that are in the Laplace Transform table. As you read through this section, you may find it helpful to refer to the review section on partial fraction expansion techniques.

**Are two partial fraction representations equivalent to each other?**

The second technique is easy to do by hand, but is conceptually a bit more difficult. It is easy to show that the two resulting partial fraction representations are equivalent to each other. Let’s first examine the result from Method 1 (using two techniques). We start with Method 1 with no particular simplifications.

## What if the Laplace domain function is not strictly proper?

When the Laplace Domain Function is not strictly proper (i.e., the order of the numerator is different than that of the denominator) we can not immediatley apply the techniques described above. Example: Order of Numerator Equals Order of Denominator