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Modeling in the Frequency Domain

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

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Modeling in the Frequency Domain

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

  2. 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

  3. Block Diagram

  4. LAPLACE TRANSFORM REVIEW

  5. LAPLACE TRANSFORM REVIEW

  6. TRANSFER FUNCTIONS

  7. 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

  8. ELECTRICAL NETWORK TRANSFER FUNCTIONS

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

  10. ELECTRICAL NETWORK TRANSFER FUNCTIONS

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

  12. ELECTRICAL NETWORK TRANSFER FUNCTIONS Impedance Method

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

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

  15. ELECTRICAL NETWORK TRANSFER FUNCTIONS Impedance Method

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

  17. ELECTRICAL NETWORK TRANSFER FUNCTIONS vA= vC

  18. ELECTRICAL NETWORK TRANSFER FUNCTIONS Transfer function

  19. ELECTRICAL NETWORK TRANSFER FUNCTIONSCramer’s rule

  20. ELECTRICAL NETWORK TRANSFER FUNCTIONSCramer’s rule Transfer function where

  21. OPERATIONAL AMPLIFIERS

  22. OPERATIONAL AMPLIFIERS • Inverting Op-Amp • Non-inverting Op-Amp

  23. INVERTING OPERATIONAL AMPLIFIERS

  24. INVERTING OPERATIONAL AMPLIFIERS Transfer function

  25. INVERTING OPERATIONAL AMPLIFIERS: PID Controller

  26. INVERTING OPERATIONAL AMPLIFIERS: PID Controller

  27. NON-INVERTING OPERATIONAL AMPLIFIERS

  28. NON-INVERTING OPERATIONAL AMPLIFIERS Transfer function

  29. TRANSLATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS

  30. TRANSLATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS

  31. TRANSLATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS Transfer function

  32. ROTATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS

  33. ROTATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS

  34. ROTATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS Transfer function

  35. TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

  36. TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

  37. TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS

  38. TRANSFER FUNCTIONS FOR SYSTEMS WITH GEARS where

  39. ROTATIONAL MECHANICAL SYSTEMTRANSFER FUNCTIONS

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