1. Vector Control of Induction Machines

2. Introduction
The traditional way to control the speed of induction motors is the V/Hz-control
Low dynamic performance
In applications like servo drives and rolling mills quick torque response is required.
Desire to replace dc drives led to vector control
Braunschweig, Leonhard, Blaschke, Hasse, late 70-ies

3. What is vector control?
Vector control implies that an ac motor is forced to behave dynamically as a dc motor by the use of feedback control.
Always consider the stator frequency to be a variable quantity.
Think in synchronous coordinates.

4. Basic blocks of a vector controlled drive

5. Addition of a block for calculation of the transformation angle

6. The current is controlled in the d- and q-directions
magnetization
torque production

7. Vector controller

8. Stator and rotor of an induction machine

9. Magnetization current from the stator

10. The flux

11. The rotation

12. View from the rotor

13. Induced voltage and current

14. Torque production

15. Ampere-turn balance

16. Rotor flux orientation
Difficult to find the transformation angle since the direction of the flux must be known
Flux measurement is required
Flux sensors (and fitting) are expensive and unreliable
Rotor position measurement does not tell the flux position
The solution is flux estimation

17. Rotor flux orientation using measured flux
Original method suggested by Blaschke
Requires flux sensors
Flux coordinates: aligned with the rotor flux linkage

18. Rotor flux orientation

19. From Chapter 4

20. Transformation to flux coordinates

21. The flux coordinate system is ”synchronous” only at steady-state
The flux coordinate system is ”synchronous” only at steady-state. During transients the speed of the rotor flux and the stator voltage may differ considerably.

22. The rotor equation (5.9)

23. Split into real and imaginary parts

24. Rotor flux dynamics are slow

25. Torque control

26. Rotor flux orientation using estimated flux
The rotor flux vector cannot be measured, only the airgap flux.
Flux sensors reduce the reliability
Flux sensors increase the cost
Therefore, it is better to estimate the rotor flux.

27. The "current model" in the stator reference frame (Direct Field Orientation)

28. The current model

29. The "current model" in synchronous coordinates (Indirect Field Orientation)

30. Transformation angle

31. Remarks on indirect field orientation
Does not directly involve flux estimation (superscript f dropped)
Not ”flux coordinates” but ”synchronous coordinates”
Since the slip relation is used instead of flux estimation, the method is called indirect field orientation

32. Indirect field orientation based on the current model

33. Feedforward rotor flux orientation
Significantly reduced noise in the transformation angle
Fast current control is assumed (ref.value=measured value)
No state feedback => completely linear

34. The voltage model
The current model needs accurate values of the rotor time constant and rotor speed
The trend is to remove sensors for cost and reliability reasons
Simulate the stator voltage equation instead of the rotor voltage equation

35. Solve for the rotor current and insert in

36. Multiplication by
yields
Solve for

37. Direct field orientation using the voltage model

38. Stator flux orientation
"Direct self-control" (DSC) schemes first suggested by Depenbrock, Takahashi, and Noguchi in the 1980s.
At low frequencies the current model can be used together with:

39. Field weakening

40. Current control

43. Transfer function and block diagram of a three-phase load

44. Review of methods for current control
Hysteresis control
Stator frame PI control
Synchronous frame PI control

45. Hysteresis control (Tolerance band control)
Measure each line current and subtract from the reference. The result is fed to a comparator with hysteresis.
Pulse width modulation is achieved directly by the current control
The switching frequency is chosen by means of the width of the tolerance band.
No tuning is required.
Very quick response

46. Drawbacks of hysteresis control
The switching frequency is not constant.
The actual tolerance band is twice the chosen one.
Sometimes a series of fast switchings occur.
Suitable for analog implementation. Digital implementation requires a very high sampling frequency.

47. Stator frame PI control
Two controllers: one for the real axis and one for the imaginary axis
Cannot achieve zero steady-state error
Tracking a sinusoid means that steady-state is never reached in a true sense
Integral action is useless except at zero frequency

48. Synchronous frame PI control
In a synchronous reference frame the current is a dc quantity at steady-state.
Zero steay state error is possible.
Coordinate transformations necessary
Easily implemented on a DSP
Usually the best choice!

49. Design of synchronous frame PI controllers
Remove cross-coupling

51. Desired closed-loop system

52. Choice of controller parameters

53. Speed control
Applications: pumps and fans in the process industry, paper and steel mills, robotics and packaging, electric vehicles
Very different dynamic requirements
Most drives have low to medium high requirements on dynamics. These drives are considered here.
Cascade control is sufficient

54. Block diagram of a speed-controlled drive system

55. The mechanical system

56. The speed controller
The task of the speed controller is to provide a reference value for the torque (or current) which makes the mechanical system respond to the speed reference with a specified rise time.

57. Block diagram with speed controller

59. Choice of controller parameters

60. Realistic choice of bandwidth
Care must be taken that the bandwidth of the speed controller is not unnecessarily high.
In fact this should be decided during the first steps in the design process of a drive system
The bandwidth is directly connected to the current rating of the inverter.

61. A change in the speed reference
How large steps should be foreseen?

62. Check if the current controller is sufficiently fast.
With
and
Check if the current controller
is sufficiently fast.