transfer functions
DESCRIPTION
A presentation about Transfer Functions.TRANSCRIPT
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THE TRANSFER FUNCTION
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Linear, time-invariant differential equation:
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Example:
Find the transfer function represented by
Solution:
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Examples:1. Find the transfer function corresponding to
the differential equation
2. Find the differential equation correspondingto the transfer function
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Answers:
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
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Electric Network Transferfunctions We now combine electrical components into
circuits, decide on the input and output, andfind the transfer function. Our guidingprinciples are Kirchhoff’s laws.
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Table 2.3Voltage-current, voltage-charge, andimpedance relationships for capacitors,resistors, and inductors
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Example:Find the transfer function relating the capacitorvoltage to the input voltage.
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Example:Given the network,find the transferfunction I2(s) / V(s)
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Operational Amplifiers
Is an electronic amplifier used as a basicbuilding block to implement transferfunctions
Differential input High input impedance Low output impedance High constant gain amplification
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Inverting operationalamplifier
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Example:Find the transfer function Vo(s) / Vi(s)
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Noninverting Operational Amplifier
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Example:Find the transferfunction Vo(s) /Vi(s) for the givencircuit
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Translational MechanicalSystem Transfer Functions Mechanical systems, like electrical networks,
have three passive, linear components. Twoof them, the spring and the mass, are energy-storage elements; one of them the viscousdamper, dissipates energy.
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Force-velocity, force-displacement, andimpedance translational relationshipsfor springs, viscous dampers, and mass
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Example:Find the transfer function X(s) / F(s) for thesystem.
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Example:Write the equations of motion for the mechanicalnetwork
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a. Forces on M1 due only to motion of M1b. forces on M1 due only to motion of M2c. all forces on M1
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a. Forces on M2 due only to motion of M2;b. forces on M2 due only to motionof M1;c. all forces on M2
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Example:Write, but do not solve, the equations of motion forthe mechanical network
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Example:Find the transfer function G(s) = X2(s) / F(s)for the translational mechanical system