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 System Impedance 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

19. ELECTRICAL NETWORK TRANSFER FUNCTIONS Cramer’s rule

20. ELECTRICAL NETWORK TRANSFER FUNCTIONS Cramer’s rule
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 SYSTEM TRANSFER FUNCTIONS

30. TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

31. TRANSLATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

32. ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

33. ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

34. ROTATIONAL MECHANICAL SYSTEM TRANSFER FUNCTIONS

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 SYSTEM TRANSFER FUNCTIONS