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ENTC 395

ENTC 395. Lecture 1b Overview of Dynamic Systems. R. W. Bolton Thompson 120D 845-0588 bbolton@tamu.edu. Today. 1st order systems Examples Response 2nd order systems Examples Response. 1st order system. Placing a thermometer in a water bath. 100 80 60 40 20.

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ENTC 395

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  1. ENTC 395 Lecture 1bOverview of Dynamic Systems R. W. Bolton Thompson 120D 845-0588 bbolton@tamu.edu

  2. Today • 1st order systems • Examples • Response • 2nd order systems • Examples • Response

  3. 1st order system Placing a thermometer in a water bath. 100 80 60 40 20 The following equilibrium equation can be written for this system T T bath

  4. 1st order system Temperature response of the system. 100 80 60 40 20 T Step Response 1st Order System 12 10 T bath 8 Response 6 4 2 0 0 2 4 6 8 10 tau

  5. Step Response 1st Order System 0 -2 -4 -6 Response -8 -10 -12 0 2 4 6 8 10 tau 1st order system Temperature response of the system. 100 80 60 40 20 T T amb

  6. R Vin C Vout 1st order system Voltage across a capacitor

  7. Step Response 1st Order System R 12 10 8 Vin C Vout Response 6 4 2 0 0 2 4 6 8 10 tau 1st order system Voltage across a capacitor

  8. Step Response 1st Order System 12 10 8 Response 6 4 2 0 0 2 4 6 8 10 tau Other1st order systems All have a similar response:

  9. 2nd order systems The cart is a second order mechanical system

  10. 5 Position 0 -5 0 2 4 6 8 10 Time 2nd order mechanical system Possible solution for a simple mechanical system

  11. 5 5 Position Position 0 0 -5 -5 0 2 4 6 8 10 0 2 4 6 8 10 Time Time 5 5 Position 0 0 Position -5 -5 0 2 4 6 8 10 0 2 4 6 8 10 Time Time 2nd Order system responses Possible responses of a system like the cart:

  12. 5 4 3 Position 2 1 0 0 2 4 6 8 10 Time Step response Step response of a damped system: • Transient zone • Steady-state zone • Final offset • Overshoot

  13. 2nd order electrical system Electrical components have similar mathematical relations.

  14. Electrical System The governing equation in this electrical system is the sum of voltages around a closed loop.

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