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Class Oct. 1 st ~ 8 th : Dynamics Modeling & SVM

Class Oct. 1 st ~ 8 th : Dynamics Modeling & SVM. HW #3 due 10/8 (Quiz #3 on 10/8): Ch2. P23, P25, P 26 (5 th ed. Problems & solutions are Posted! ) ODE  Laplace transform  Transfer Function Sec. 3.3 terminologies : fill in blanks

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Class Oct. 1 st ~ 8 th : Dynamics Modeling & SVM

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  1. Class Oct. 1st ~ 8th: Dynamics Modeling & SVM • HW #3 due 10/8 (Quiz #3 on 10/8): Ch2. P23, P25, P 26 (5th ed. Problems & solutions are Posted!) • ODE Laplace transform  Transfer Function • Sec. 3.3 terminologies: fill in blanks • The 2nd Report (team project) is due 10/15. The guideline is posted.  The last chance to change your project. • Today’s lecture: Mathematical background for the 2nd class subject, state-space variable modeling

  2. Next subjects • Modeling of Dynamic Systems, Ch. 2 • electrical & mechanical • Space-state Variable Modeling (SVM) • an nth-order system  n number of 1st-order DEs  one1st-order DE • Chapter 3 (main), 4, 5, 6 • Control Design based on SVM, Ch. 12 • Pole placement & Ackermann’s formula • Special Lecture

  3. State-space Variable Modeling (SVM) • EE4201: A systems (electrical & mechanical) • ODE (nth-order) • Laplace Function (nth-order)  Transfer Function T(s) • MTRE 4000: A systems (electrical & mechanical) • ODE (nth-order) • n number of 1st-order ODEs • one1st-order DE  solve it using Laplace (linear systems) or directly in time domain (n.l. systems) A spring board to advanced controls!

  4. Matrix & State-space Variable Modeling • Matrix for n # of linear equations with n # of variables:

  5. Matrix for n # of linear equations with n # of variables:

  6. Matrix & State-space Variable Modeling • Matrix for n # of linear equations with n # of unknown variables: • 2nd-order D.E. (system dynamics) can be written by 2of 1st-order D.E.  finally one1st-order D.E using matrices

  7. State-space Variable Modeling • 2nd-order D.E. (system dynamics) can be written by 2 of 1st-order D.E.  finally one1st-order D.E using matrices

  8. Modeling of Mechanical Dynamics: M, fv, K

  9. Modeling of Mechanical Dynamics Basic components: Mass, dynamic friction, & spring

  10. Ex.: SVM u(t) b

  11. State-space Variable Modeling (SVM) - Terminology  Fill in blanks for Quiz #3

  12. SVM The state variables describe the future response of a system given the present state, the excitation inputs, and the equations describing the dynamics.

  13. SVM • State variable provide information of the system behavior • Show dynamic internal characteristics & connection / relationship • nth-order D.E. (dynamics) can be written by n numberof 1st-order D.E.  finally one1st-order D.E using matrices • Matrix calculation using a computer

  14. State Variable Modeling (SVM) • Classical technique: • ODE (in time domain)  Laplace Function  Response in time domain • The state-space variable modeling (SVM): • Modern time-domain approach • Represent MIMO in SISO form • Computer simulation, and also can cover changes in system parameters. • A spring board to advanced controls!

  15. p1(t) P2.23, Y(s) = P1(s) p2(t) T(s) = P1(s)/F(s)

  16. p1(t) P2.23, Y(s) = P1(s) p2(t)

  17. SVM: P2.25, Y(s) = P2(s) p2(t) p3(t) p1(t)

  18. SVM: P2.25, Y(s) = P2(s) p2(t) p3(t) p1(t)

  19. Modeling of Electrical Dynamics: R, L, C

  20. Ex.: Fig. 3.2(Example 2.6)

  21. Ex.: Fig. 3.2(Example 2.6)

  22. Ex. 3.1

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