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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)