1.3 Vector Control Summary

The indirect vector control process can be summarized as follows:

1. The three-phase stator currents are measured. For currents in a motor with balanced three phase windings, these measurements provide values i_a and i_b. i_c is calculated by the following equation: i_a + i_b + i_c = 0.

2. The three-phase currents are converted to a stationary two-axis system. This conversion provides the variables i_α and i_β from the measured i_a and i_b and the calculated i_c values. The values i_α and i_β are time-varying quadrature current values as viewed from the perspective of the stator.

3. The stationary two-axis coordinate system is rotated to align with the rotor flux using a transformation angle calculated at the last iteration of the control loop. This conversion provides the i_d and i_q variables from i_α and i_β. The values i_d and i_q are the quadrature currents transformed to the rotating coordinate system. For steady state conditions, i_d and i_q are constant.

4. Error signals are formed using i_d, i_q and reference values for each are shown below.

1. The i_d reference, controls rotor magnetizing flux.
2. The i_q reference, controls the torque output of the motor.
3. The error signals are input to PI controllers.
4. The output of the controllers provide v_d and v_q, which are voltage vector that will be applied to the motor.

5. A new transformation angle is estimated from the position estimation observer using v_α, v_β, i_α and i_β. This new angle guides the FOC algorithm as to where to place the next voltage vector.

6. The v_d and v_q output values from the PI controllers are rotated back to the stationary reference frame using the new angle. This calculation provides the next quadrature voltage values v_α and v_β.

7. The v_α and _vβ values are transformed back to three-phase values v_a, v_b and v_c. The three-phase voltage values are used to calculate new PWM duty cycle values that generate the desired voltage vector.

The entire process of transforming to a rotating frame, PI iteration, transforming back to stationary frame and generating PWM is illustrated in the following figure.

The next sections of this application note describe these steps in greater detail.