1. In The Name of Allah The Most Beneficent The Most Merciful 1

2. ECE4545: Control Systems Tutorial: Mathematical Modeling- Frequency Domain Engr. Ijlal Haider UoL, Lahore 2

3. Figure 2.3 RLC network 3

4. Figure 2.15 a. Mass, spring, and damper system; b. block diagram 4

5. A Gear System 5

6. Laws Governing a Gear System a. angular displacement in lossless gears and b. torque in lossless gears 6

7. TF between I 2 and V 7

8. TF between X 2 and F s 8

9. Hydraulic System Flow is proportional to Level (for Laminar) (for Turbulent) Flow rate is analogous to Current Level difference is analogous to Potential difference 9

10. Hydraulic System Resistors: are used to model pressure drop due to an orifice, friction, leakage, etc. Hydraulic resistors are often nonlinear Capacitors: are used to model the compressibility of a hydraulic fluid. 10

11. Hydraulic System with Interaction 11

12. DC Motor 12

13. Thank You! 13