The Laplace Transform The Laplace Transform table Transfer

The Laplace Transform

The Laplace Transform table

Transfer Function

Transfer function • Transfer function The transfer function of a linear, time-invariant , differential equation system is defined as the ratio of the Laplace transform of the output (response function) to the Laplace transform of the input (driving function) under the assumption that all initial conditions are zero. Consider the linear time-invariant system defined by the following differential equation: Transfer function=

To find the transfer function To derive the transfer function, we proceed according to the following steps. 1. Write the differential equation for the system. 2. Take the Laplace transform of the differential equation, assuming all initial conditions are zero. 3. Take the ratio of the output to the input. This ratio is the transfer function. Now consider some simple cases of finding transfer function

Differential Equation of Physical Systems Electrical Inductance Translational Spring Rotational Spring Fluid Inertia Describing Equation Energy or Power

Differential Equation of Physical Systems Electrical Capacitance Translational Mass Rotational Mass Fluid Capacitance Thermal Capacitance

Differential Equation of Physical Systems

Differential Equation of Physical Systems

Block Diagrams. A block diagram of a system is a pictorial representation of the functions performed by each component and of the flow of signals. The functional block or simply block is a symbol for the mathematical operation on the input signal to the block that produces the output. The transfer functions of the components are usually entered in the corresponding blocks.