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Transfer Function andTheir Response
Student: Nguyen Tien D
ID: 20100908
Class: Mechatronic - K
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Content
Introduction of transfer function(TF)
Block Diagram(BD)
MATLAB representation of Transfer Func
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The Laplace Transform
Definition
L f t( )( )
0
tf t( ) e s t
d = F(s)
Here the complex frequency is s j w
The Laplace Transf orm exists w hen
0
tf t( ) e s t
d this means that the integral converges
The Laplace Transform
the Laplace transfo rmconverts integral and differential
equations into algebraic equations
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Transfer functions (TF) are frequently used to characterize
relationships or systems that can be described by Linear differential equations.
Transfer Function (TF): The transfer function (TF) of a LTI diffsystem is defined as the ratio of the Laplace transform (L(response function) to the Laplace transform (LT) of the inputunder the assumption that all initial conditions are zero.
Introduction of transfer function(TF)4
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Assume that our model is linear differential equation have the f
where D denotes the differential operator d/dt . A(D) and B(D) are polyno
Di= , the I th derivative, u(t) is the model input and y(t) its output.
write
Introduction of transfer function(TF)
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Transfer Function (TF): G(s)
() =()
()=
()
()
Introduction of transfer function(TF)
G(s)U(s) Y(s)
InputOutput
Transfer Function
Block diagram representation of a transfer function
U(s)
Laplace transform of the output variableY(s) Laplace transform of the input variableG(s) transfer function
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7 Impulse Response Function
Introduction of transfer function(TF)
Now, consider the output (response) of the system to a unit-impulse
when all the I.Cs are zero. Since
the LT of the output of the system is
is called the impulse response function of the system. The impulse-r
thus the response of a linear system to a unit impulse input when the
The LT of g(t ) gives the TF.
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8Block Diagrams
Block Diagrams of Dynamic Systems
A Block Diagram (BD) of a dynamic system is a graphic representafunctions performed by each component of the system and of th
within the system
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Summing Point
Block Diagrams
Figure shows a circle with a cross, the symbol that stands for a summ(+) or (-) sign at each arrowhead indicates whether the associaadded or subtracted.
It is important that the quantities being added or subtracted have thand the same units.
Summing point
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10Block Diagrams
Block Diagram of a closed-loop system
The output C(s) is fed back to the summing point, where it is coinput R(s). The closed loop nature of the system is indicatedfigure. The output C(s) is obtained by multiplying the TF G(s) the block, E(s).
Block Diagram of a closed loop-system with feedback elem
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11MATLAB representation of Transfer Functions
The transfer function of a system is represented by two arrays ofFor example, consider a system defined by
This system is represented as two arrays, each containing thethe polynomials in descending powers of s as follows
MATLAB will automatically respond with the display
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12MATLAB representation of Transfer Functions
Partial-Fraction Expansion with MATLAB
MATLAB allows us to obtain the partial-fraction expansion of theratio of two polynomials
The command
The partial fraction expansion of B(s) A(s) is given by
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MATLAB representation of Transfer Functions
Example 1:
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MATLAB representation of Transfer Functions
Example 1:
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MATLAB representation of Transfer Functions
Example 2: G(s)=
G(s)=
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Thanks for listening
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