2. دانشگاه صنعتي اميركبير دانشكده مهندسي پزشكي State-space Models with Embedded Integrator استاد درس دكتر فرزاد توحيدخواه آبان 1388 کنترل پيش بين-دکتر توحيدخواه

3. Taking a difference operation on both sides:

5. New state variable vector:

6. Example 1:

8. Characteristic equation:

9. Prediction of State and Output Variables

10. The future control trajectory: Future state variables:

14. Optimization

17. Example 2:

23. We can verify this by increasing Nc to 9, while maintaining r ω = 10 First four parameters in U are slightly different from the previous case

24. Receding Horizon Control

25. Example 4:

28. Receding horizon control

29. Closed-loop Control System

31. Standard form of linear time-invariant state feedback

33. Example 5 closed-loop feedback gain matrices in Ex. 2

36. State Estimation

37. Basic Ideas About an Observer

41. Example 7: Linearized equation of motion of a simple pendulum

42. (a) Estimation without observer

44. Model alone is not sufficient to predict the angle of the pendulum

45. (b) Estimation with observer

47. Example 8DC motor

48. Discrete-time model is observable ?

49. Second pole at λ = 1 cannot be moved no matter what choice we make for j 2

50. Kalman Filter

53. State Estimate Predictive Control

55. Closed-loop state-space equation:

58. Example 9. The augmented model for a double integrated plant (see Example 1) is given by