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1. PRESENTATION
SUBMITTED BY: SHAHMIR AHMED
SUBMITTED TO: ENG. ALI ASGHR
ROLL NO: 21013322-014
COURSE: CONTROL TECHNOLOGY
DEPARTMENT OF ELECTRICAL
ENGINEERING & TECHNOLOGY

2.  Title
laplace transform in control technology
The Laplace transform is a mathematical tool that converts differential
equations from the time domain (t) to the frequency domain (s). This
transformation simplifies the analysis and design of control systems.

3.  What is the laplace transform.
The Laplace transform of a function f(t) is denoted by F(s) and is defined
as:F(s) = ∫[from 0 to infinity] e^(-st) f(t) dtThis integral transforms a function
of time (t) into a function of a complex variable (s)

4.  Properties of the laplace transform.
• Linearity: L [af(t) + bf(t)] = aF(s) + bF(s)
• Time shifting: L [f(t - a)] = e^(-as) F(s)
• Differentiation: L [df(t)/dt] = sF(s) - f(0)
• Integration: L [∫f(t) dt] = F(s)/s

5.  Laplace transform and differential equation.
• The Laplace transform can be used to solve differential equations.
• By applying the Laplace transform to both sides of a differential equation,
we can convert it into an algebraic equation in the s domain.
• This algebraic equation is often easier to solve than the original differential
equation in the time domain.
• Once we solve for F(s), we can use the inverse Laplace transform to find
f(t).

6.  Transfer system in control system.
• A transfer function is a mathematical model that relates the output of a
system to its input in the frequency domain.
• It is expressed as the ratio of the Laplace transform of the output (C(s)) to
the Laplace transform of the input (R(s)).
• Transfer function = G(s) = C(s) / R(s)