Control Engineering for BME

45 flashcards · Physics · by Kristóf Nagy

1. root locus steps

   poles zeros find x axis parts, RHS odd poles --> zeros, symmetric around x-axis # asymptotes angle intersection/centroid break away/in

2. RL: # asymptotes

   n_p - n_z

3. RL: intersection/centroid

   σa=\sigma_a = σa​= Σpi−Σzinp−nz\frac{\Sigma p_i - \Sigma z_i}{n_p - n_z}np​−nz​Σpi​−Σzi​​

4. RL: asymptotes angle

   θ=\theta = θ= ±(2k+1)πnp−nz\pm \frac{(2k+1)\pi}{n_p - n_z}±np​−nz​(2k+1)π​ k = 0, 1, 2, ... until enough for #asymp

5. RL: breakaway / break-in points

   N'd - d'N = 0

6. RL: block diagram / transfer function

7. RL: real axis rule

   number of all points (poles, zeros) must be ODD (páratlan) on the right-hand-side of any point of root-locus on the x-axis (real-axis)

8. bode: block diagram

   H(s) = transfer function of the system

9. bode: standard form

10. bode magnitude

    calculate this, and use the full as constant value in dB

11. bode magnitude

    -20 dB/dec. at 1, it's 0

12. bode magnitude

    +20 dB/dec. at 1, it's 0

13. bode magnitude

    before p_i --> 0 after p_i --> -20dB/dec.

14. bode magnitude

    before z_i --> 0 after z_i --> +20dB/dec.

15. (bode magnitude)

16. bode rules

    split: multiply the types calculate each, plot (sketch them together) sum

17. bode phase

    K>0: 0° (+) K<0: ±\pm± 180° (-)

18. bode phase

    -90° constant

19. bode phase

    +90° constant

20. bode phase

21. bode phase

22. ss TF

23. ss X(s) (or Y(s)?) output, Laplace transform solution method

24. making a ss

    normal ma=... all forces in t space define x1=y, x2=y' write x1'=... (usually just x2) & x2'=... (this will the most part) put them into the matrix form make the other y1=... & y2=... to describe how is y in x (can also have a U part)

25. ss: P(s), eigenvalues

    det(sI-A) (=0)

26. ss form

27. moving pick up point

    after: 1/G before: G

28. moving sum junction

    before: 1/G after: G

29. Nyquist sentence

30. gain margin

    ∠P(jωpc)=180°\angle P(j\omega_{pc})=180°∠P(jωpc​)=180° gm=1∣G(jωpc)∣g_m = \frac{1}{|G(j\omega_{pc})|}gm​=∣G(jωpc​)∣1​

31. phase margin

    ∣G(jωgc)∣=1|G(j\omega_{gc})|=1∣G(jωgc​)∣=1 ϕm=180°+∠G(jωgc)\phi_m = 180° + \angle G(j\omega_{gc})ϕm​=180°+∠G(jωgc​)

32. 2nd order system TF

33. 1st order system TF

    C(s)R(s)=as+a\frac{C(s)}{R(s)} = \frac{a}{s+a}R(s)C(s)​=s+aa​

34. R

35. L

36. C

    (integral till t)

37. k (spring)

38. B or C or D (damper)

39. F=ma

    F(s)=Ms2X(s)F(s)=Ms^2X(s)F(s)=Ms2X(s)

40. phase ϕ\phiϕ

    add when (...)*(...) subtract if divided

41. magnitude M

    multiply/divide normally when (...)*/(...)

42. steady state error analysis ess=e_{ss} = ess​=

    (for unity feedback)

43. names for input

44. RH criterion

    no sign change in the 1st column no sign change in the coeffs # of sign changes = poles on the RHS (bad) side, rest on the good rows of zeros: poles on the jωj\omegajω axis (# is the line above s^n), take derivative and make that the next n+1 line, and continue can still be marginally stable if all other stuff matches

45. RH oscillation

    s^1 = row of 0s = oscillation previous row: a*s^2+b=0 solution gives omega rad of resonance freq