Modeling in the Frequency Domain

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Presentation transcript:

Modeling in the Frequency Domain System & Control Engineering Lab. School of Mechanical Engineering

CHAPTER OBJECTIVES Review the Laplace transform Learn how to find a mathematical model, called a transfer function, for linear, time-invariant electrical, mechanical, and electromechanical systems Learn how to linearize a nonlinear system in order to find the transfer function

Block Diagram

LAPLACE TRANSFORM REVIEW

LAPLACE TRANSFORM REVIEW

TRANSFER FUNCTIONS

TRANSFER FUNCTIONS OF PHYSICAL SYSTEMS ELECTRICAL NETWORK TRANSFER FUNCTIONS TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS ELECTROMECHANICAL SYSTEM TRANSFER FUNCTIONS ELECTRIC CIRCUIT ANALOGS

ELECTRICAL NETWORK TRANSFER FUNCTIONS

ELECTRICAL NETWORK TRANSFER FUNCTIONS Kirchhoff’s Voltage Law (KVL), Loop method

ELECTRICAL NETWORK TRANSFER FUNCTIONS

ELECTRICAL NETWORK TRANSFER FUNCTIONS Kirchhoff’s Current Law (KCL), Node method

ELECTRICAL NETWORK TRANSFER FUNCTIONS Impedance Method

Elements of Electrical System: Impedance Method Theorem 1. If there are n impedance in series Equivalent impedance for two impedances in series

Elements of Electrical System Impedance Method Theorem 2. If there are n impedance in parallel Equivalent impedance for two impedances in parallel

ELECTRICAL NETWORK TRANSFER FUNCTIONS Impedance Method

ELECTRICAL NETWORK TRANSFER FUNCTIONS Kirchhoff’s Current Law (KCL), Node method

ELECTRICAL NETWORK TRANSFER FUNCTIONS vA= vC

ELECTRICAL NETWORK TRANSFER FUNCTIONS

ELECTRICAL NETWORK TRANSFER FUNCTIONS Cramer’s rule

ELECTRICAL NETWORK TRANSFER FUNCTIONS Cramer’s rule where

OPERATIONAL AMPLIFIERS

OPERATIONAL AMPLIFIERS Inverting Op-Amp Non-inverting Op-Amp

INVERTING OPERATIONAL AMPLIFIERS

INVERTING OPERATIONAL AMPLIFIERS Transfer function

INVERTING OPERATIONAL AMPLIFIERS: PID Controller

INVERTING OPERATIONAL AMPLIFIERS: PID Controller

NON-INVERTING OPERATIONAL AMPLIFIERS

NON-INVERTING OPERATIONAL AMPLIFIERS Transfer function

TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS where

ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS