THE TRANSFER FUNCTION
Linear, time-invariant differential equation:
Example:
Find the transfer function represented by
Solution:
Examples:1. Find the transfer function corresponding to
the differential equation
2. Find the differential equation correspondingto the transfer function
Answers:
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
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.
Table 2.3Voltage-current, voltage-charge, andimpedance relationships for capacitors,resistors, and inductors
Example:Find the transfer function relating the capacitorvoltage to the input voltage.
Example:Given the network,find the transferfunction I2(s) / V(s)
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
Inverting operationalamplifier
Example:Find the transfer function Vo(s) / Vi(s)
Noninverting Operational Amplifier
Example:Find the transferfunction Vo(s) /Vi(s) for the givencircuit
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.
Force-velocity, force-displacement, andimpedance translational relationshipsfor springs, viscous dampers, and mass
Example:Find the transfer function X(s) / F(s) for thesystem.
Example:Write the equations of motion for the mechanicalnetwork
a. Forces on M1 due only to motion of M1b. forces on M1 due only to motion of M2c. all forces on M1
a. Forces on M2 due only to motion of M2;b. forces on M2 due only to motionof M1;c. all forces on M2
Example:Write, but do not solve, the equations of motion forthe mechanical network
Example:Find the transfer function G(s) = X2(s) / F(s)for the translational mechanical system
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