1. DCmotors and their representation:
The basic principle of a DC motor is the production of a torque as a result of the flux interaction between a “field” produced on the STATOR (either produced by a permanent magnet, or a field winding) and the current circulating in the “armature” windings on the ROTOR.

4. In order to produce a torque of constant sign, the armature winding loops are connected to a set of “brushes” which commutate the current appropriately in each loop according to their geometric position. The commutator is a MECHANICAL RECTIFIER.

5. Basic Equations of a DC Machine
field winding
counter emf
armature voltage
electrical torque
developed power

6. Speed control:
For control problems, one assumes that the back emf’s magnetizing characteristic, E(If) is linear

7. Va “Voltage Control”
If “Field Control”
Ia (with If fixed) “Demand Torque”

8. In practice, for speeds less than the base speed (rated), the armature current and field currents are maintained at fixed values (hence constant torque operation), and the armature voltage controls the speed.
For speeds higher than the base speed, the armature voltage is maintained at rated value, and the field current is varied to control the speed. However, this way the power developed Pd is maintained constant. This mode is referred to as “field weakening” operation.

10. Case of Series Motor (or Universal Motor)
If and Ia are equal

11. Operating Modes of DC Motors:
Motoring:
The back emf E < Va both Ia and If are positive. The motor develops a torque to meet the load torque

12. Dynamic Breaking:
The voltage source is removed, and the armature is shorted. The kinetic energy stored in the rotor of the motor is dissipated in the armature resistance since the machine now works as a generator.

13. Note here that theoretically, since the armature voltage is proportional to the speed, the motor would never stop... (windage

14. Regenerative Breaking:
The back emf E > Va , the machine acts as a generator, and the armature current flows towards the source, hence energy stored in the machine rotor is fed back to the source. Note however that this will cause the machine to slow down usually until E=Va and then revert to mode 1.

16. Plugging:
Plugging is when the field current is reversed, hence the back emf changes sign, and the equation of the machine becomes:
a very high torque generated in the opposite direction of rotation

17. Two Transistor control of regenerative operation
When the main switch opens, the armature current I(a1) has to be dissipated through the freewheeling diode.

18. Then if one closes switch T1, the machine behaves as a generator with the energy stored in its inertia. Therefore the armature current I(a2)will start flowing and follows I(1).
After a certain time one opens the switch T1, and the current I(a2) has to be redirected via diode D2 back to the source with I(2).

19. The chopping rate of switch T1 can be set in order to control the average current (Ia2), usually 1.5 times rated value.
This is possible only if the speed is fast enough to provide terminal voltage.
When the emf E reaches E=Ra.I(rated), the switch T1 remains closed for
maximum breaking possible with the given emf.

20. Four Quadrant Operation:

21. CONTROL FEEDBACK LOOPS
Assume that the source is a rectifier. We are controlling the DC motor with the voltage control of the armature (separate excitation).

22. The rectifier can be considered as a power amplifier controlled by the firing angle . The open loop system can be pictured as

23. If one uses a tacho-generator to monitor the speed a closed loop controller can be built:

24. The difference between input setting and the feedback signal is the error signal.
However, with SCR drives, any change in motor speed will immediately give rise to excessive motor and thyristor currents. Hence a current limiter must be added to the control loop.
This is obtained by a second feedback loop.

26. Induction Motor Control
Induction machines are the “workhorse” in industry

27. The squirrel cage machine is of rugged construction, low production cost, low maintenance and environmental properties (for example explosion proof).
The advent of power electronics have made it possible to match the induction machine performance to that of DC machines, in fact practically supplanting DC machines in industries, since the price of a single DC machine is much higher than the equivalent induction machine with full control.

28. Adjustable Speed Drives are used in process control for fans, compressors, pumps, blowers etc... Servo drives are becoming more and more common using very sophisticated control schemes, for instance in computer peripherals, machine tools and robotics applications. These are usually lower power ratings though.

29. Example: Centrifugal Pump
The induction motor driving the centrifugal pump will work at quasi constant speed
there is energy loss through the throttle

30. Setting the speed which will provide the desired flow rate
Setting the speed which will provide the desired flow rate. Hence considerable energy savings. In this case, the pump performance is

31. Induction Motor Principle

32. The simplified equivalent circuit is:
It can be shown that the power developed by the shaft is equal to the power that would be dissipated in the equivalent resistance

33. Hence the POWER DEVELOPED in a 3 phase motor is:
developed torque is

35. STATOR VOLTAGE CONTROL

36. Constant Voltage Inverter Drive
Note that the source capacitor maintains a constant voltage

39. Constant Current Inverter Drive:

41. Speed Control with Rotor Resistance

43. The only inconvenience here is of course the loss of power in the external resistance.
Automatic control can be achieved by using a chopper in the rotor circuit.

44. Kramer Drive

45. Frequency Control of the Drive
Intuitively one can see that the rotor will rotate at speed slightly lower than the stator frequency (slip), hence a speed control is achieved when the stator frequency is changed.

46. If we want to have both speed control and still maintain a high torque, the maximum torque at base speed (synchronous rated) is given by:

47. This is equivalent to the DC machine. Tmax-base remains constant
This is equivalent to the DC machine. Tmax-base remains constant. In this region
the control is done by the Voltage, maintaining the flux at its maximum.
Then the region called the “field weakening” as for the DC machine.
In order to maintain the flux constant, the ratio V/f must be maintained constant. However, due to losses in the machine, at low speeds, one must have a boost voltage at low speeds to compensate for losses.

48. VECTOR CONTROL of INDUCTION MOTORS
The production of torque in a d.c. or cage induction motor is a function of the position or vector relationship in space of the air-gap magnetic flux to the rotor current. The flux and armature current are always ideally positioned by virtue of the switching action of the commutator; hence control of the armature current gives immediate control of the torque, a feature which makes both the steady state and transient control of the torque in a d.c. motor relatively easy.

50. The torque developed is related to the in-phase component of I2 shown as Iq, and the flux is related to the current Im modified by the reactive component of I2 to give the component shown as Id.

51. The object of vector control, sometimes referred to as “field orientation control”, is to separately control the magnitude of the two components Id and Iq, such that the flux is proportional to Id and the torque is proportional to Iq. This is referred to as DECOUPLING the control (we need 2 degrees of freedom).

52. In the d.c. motor the flux is stationary, with the armature current fixed in space by the commutator action, but in the induction motor both the flux and rotor currents rotate together. We have only 1 degree of freedom in the 3 phase source currents.
The instantaneous values of the three-phase currents in the stator determine the angle of the flux in space and that of the rotor current, so we must have a shaft encoder (2nd degree of freedom) which measures the rotor angular mechanical position relative to the instantaneous stator currents.

53. To implement vector control the motor parameters must be known and values put into a highly complex set of mathematical equations developed from generalized machine theory.

54. The basic tools used in calculations is the use of “Parker’s Model” which allows to transform a 3 phase rotating vector system into a 2 phase rotating vector system (which is the same as of a DC machine with a direct; in line with the flux, and quadrature axis; perpendicular to it).
The phase command currents (*) are triggering the inverter to produce the real line currents (a,b,c). An acquisition system must sample the line currents, filter and condition these quantities and presents them to an ABC to DQ transformation block. The calculated (c) direct and quadrature quantities must now be positioned in such a way that the direct axis aligns with the stator axis. Hence the block which computes this alignment must also receive the absolute position of the rotor using the rotor angle q. We now obtain the (D-Q) components aligned with the real rotor position, and feed this into the Model Block.

55. The components (*DQ) have to be realigned to the stator axis (e), and fed to an inverse transformation module which calculates the line control vector currents (ABC*) feeding the inverter, and the loop is closed.

56. The main difficulty here is that the stator frame reference is used in calculations of the model, and that I(ds) must be aligned with the rotor flux. However this rotor flux depends upon the SLIP, and of course varies in time (this is why it is called Asynchronous!). The trick in the method is to establish the rotor flux axis at each sample.

57. INDIRECT VECTOR CONTROL
The flux vectors are computed from the terminal quantities of the motor (stator currents, voltages and measured air gap flux). It uses the motor slip frequency to compute the desired flux vector.
The amount of DECOUPLING is dependant upon the motor parameters in the indirect method. Without a good knowledge of the motor parameters an ideal decoupling is not possible.

58. DIRECT VECTOR CONTROL
determine directly the air gap flux by measurement, and from there derive the rotor flux and stator flux linkages.
excellent low-speed performance

59. Indirect Vector Control (indirect field oriented control) or IFOC
In this method the feedback uses the rotor slip.
The first equation tries to make sure that we have a constant flux
(magnitude of ), while controls the torque.

60. The speed is integrated in order to obtain the position and hence obtain the unit vectors for the transformation
If the motor parameters change during operating conditions, the model is not accurate and the model predictions will not align exactly the rotor flux with the direct axis, and the control is not adequately decoupled.

61. (Indirect field oriented control )