Another method worth considering in any discussion of motor control is vector control. The detailed formulation of this method to control the torque and flux in PMSM was originally achieved by Jahns, Kliman, and Neumann [1] in the mid-1980s.

Additional work has been done by many authors, and you will find more information and explanation in references [2,3,4]. Here we will simply summarize the concept and compare it to the 180-degree V/f open-loop and closed-loop scalar control methods previously discussed.

When we examine the torque equation for a brushless DC motor, we realize that the equation is really a vector formulation with the vector product of the current and magnetic fields shown on the right-hand side:

If we formulate a rotor frame that has a d-axis parallel to the north-south line and a q-axis perpendicular to the d-axis, as illustrated in Figure 47 below, we can actually convert the stator currents in the rotor frame.

Figure 47. Stator frame to rotor frame transformation for vector control.

We then realize that the current along the d-axis creates pure flux, whereas the current along the q-axis creates pure torque. Denoting these two currents as Id and Iq, we can say that our control algorithm must control both these currents to maintain proper flux and proper torque in the system. We know that speed is directly related to torque, and torque is related to the q-axis current.

Therefore, we must create a reference q-axis current to maintain the speed. Then we can control the q-axis current through transformation of our axes. In this way we convert the single-variable speed control into control with more variables - speed, d-axis current, and q-axis current - and we use a vector formulation to compute the quantities that we need to control. Hence we call this method "vector control."

Now let's take a look at the detailed steps necessary for vector control. As Figure 48 below shows, a profile module gives the speed command to the control algorithm at some point in time.

On the right hand side, a control function outputs commands for the inverter, which is connected to the motor. This configuration has two current sensors to measure the phase U and phase W currents. The sensors are connected to the ADC on the MCU. The motor also has an encoder mounted on its rotor to give the quadrature pulses A, B and also the zero synch pulse Z. All three signals are sent to the input-capture and timer/counter peripheral for speed measurement.

Figure 48. Vector control flow diagram.

At every carrier-frequency interrupt, three PWM signals are generated. While all three PWM signals are applied, the system measures two currents by triggering the ADC channels.

During the next interrupt execution, these currents are then transformed from stator U, V, and W axes to d-q axes using matrix multiplications that involve the rotor angle q at that time. The rotor angle is measured by reading the A,B pulses and converting this reading into a proper angle. The control system's firmware is greatly helped if the MCU has a hardware timer with input capture and continuous counting of A,B pulses.

Based on the rotor position theta, stator currents are transformed in d-q axes currents as we have noted. The speed measurement is fed into the auto speed regulator (ASR), shown in Figure 48 above, which generates the reference q-axis current required to maintain the commanded speed.

This reference q-axis current and measured q-axis currents are fed into the auto current regulator (ACR) to create q-axis voltage to be applied to the next PWM. The reference current in the d-axis is maintained at constant level to maintain proper flux in the stator.

This reference d-axis current and the measured d-axis currents are fed into a second ACR to create the d-axis voltage. Corrections are made to the voltage calculations according to the number of pole pairs and the reference currents in the d and q axes.

When the final values Vd and Vq are computed, they are transformed from the rotor frame to the stator frame using inverse transformation and that rotor angle value. Three voltages in the stator frame - Vu, Vv and Vw - are converted into the PWM values that are to be output by the three-phase timer unit.

Current measurements and auto current regulators are executed at every carrier frequency. This process, which is known as "inner loop," uses the fastest control algorithm. In contrast, encoder measurements, and especially speed measurements, are performed at a lower rate. Therefore, the auto speed regulator and related computations are performed using a slower process called "outer loop."

A typical carrier-frequency or inner loop rate is about 4kHz or more, and the encoder-based speed computation or outer loop rate is about 500Hz or so. Occasionally the outer loop rate can drop as low as 50Hz.

Experts agree that vector control method controls the torque and flux very well, and it maintains the desired speed accurately. Vector control requires one position sensor and two current sensors to perform the necessary tasks. It also requires an MCU with high computing power so that the inner-loop and outer-loop processes can be executed properly. Additionally, the MCU must be capable of measuring two currents simultaneously, so it must have two sample-and-hold circuits in its ADC peripheral.

The vector-control method provides dynamic torque control based on exact speed measurements and current measurements. Consider an example in which the load changes during rotation. Since speed is measured several times (typically at a 500Hz rate), any load changes that affects the speed will be detected and for the next rotation, the q-axis current will be adjusted properly to maintain the same speed.

If higher current is required, it will be provided. Control and system experts generally regard vector control as the reference against which the performance of other methods are compared and evaluated.

The vector-control method does have some drawbacks. It requires sensors and thus adds cost to the final implementation. Also, it mandates an MCU with high computing power, which may add cost.

In Table 6, below, we see a comparison of the features, accuracy, and required MCU resources for the three control methods we have covered thus far: V/f open-loop, scalar, and vector control.

Table 6. Comparison of V/f open loop, scalar and vector control.

Sensorless control
Since the vector control method we have just examined requires one position sensor and two current sensors, the final system configuration may be costly.

Consumer applications, especially white goods, are very cost-sensitive and thus cannot afford this type of implementation. At the same time, these applications do not require the same performance accuracy for speed, as do industrial applications.

Therefore, two other control techniques have been developed that provide adequate performance for the system, yet keep cost down. These techniques are called sensorless because they do not require any position sensors. Both methods use the same 180-degree modulation and vector control algorithm.

The first of these methods eliminates the position sensor but keeps the two current sensors. It is known as "DCCT-based sensorless vector control" and is shown in Figure 49, below. Because this method uses no position sensor, angle and speed are estimated using the current measurements and voltages applied the previous PWM cycle.

Figure 49. Position sensorless control with 2 DCCT current sensors.

The method employs a Kalman-filter approach based on principles of modern control theory, an observer-based model, and a state transition matrix. Estimated angle and speed are used together in the same vector control algorithm to control the current in the q-axis.

Such an implementation requires many matrix calculations, and thus an MCU with high computing capability is a requirement. In fact, the CPU bandwidth needed is nearly double that of vector control method. Gain adjustment in the auto speed regulator and auto current regulator is very difficult. Exact motor parameters must be known, particularly the q-axis and d-axis inductance parameters, which are difficult to measure. Despite the challenges, such control is a reality and has been implemented in several applications.

In a second method, the position sensor and two DCCT sensors are eliminated. Currents are measured using the shunt resistance installed on the low side of the inverter, as shown in Figure 50, below. This shunt resistance is a precision resistor capable of measuring the full current range of the motor. Using one shunt, we measure two currents; thus this method is known as "one shunt current detection vector control" or simply "OSCD vector control."

Figure 50. One shunt current detection method that eliminates DCCT and position sensor.

The implementation shown in Figure 51, below,  is similar to that of the DCCT method, but it adds one more computing block, Current Meas. To understand why this addition is necessary, we'll look at how the current is measured.

Figure 51. OCSD implementation flow with current measurement module.

First, remember that our setup has only one shunt resistor. To measure individual phase currents, we must be careful. Figure 52 shows us how the three PWM outputs are applied. In this figure, the W phase has largest PWM time, V has next smaller, and U has the smallest.

If we measure the shunt current between the rising edge of W and the rising edge of V, we know that only the W phase (that is, only the Wp -upper W phase IGBT) is on at that time. So, we measure W phase current. Next, if we measure the current between the rising edge of V and the rising edge of U, then we are measuring the W and V phase current together.

Figure 52. One shunt current measurement technique using a additional timers to trigger ADC.

This also means that we are measuring the U phase current, because the sum of all currents in a star-winding motor is zero. Thus, we must make 2 current measurements at precise time during our interrupt processing. We need two other timer channels that can help us trigger the ADC at a precise time.

An example is the Renesas M16C 3-phase timer unit. This unit has a link with timer channels TB0 and TB1, such that it will trigger the ADC channels AN0 and AN1 at a precise time. All we have to do is load the appropriate register values.

As part of this process, we must compare the PWM values of all three phases and determine exactly how much time we need to load channels TB0 and TB1. It is important to note that the three PWM values continue to change constantly, so that W is not the largest.

Thus, we need to test the largest value every time and set the proper flags for the current we are measuring. All the comparisons, settings, and identifications required by this method make for complex processing task, one that requires significantly more code and more CPU time. The requirements for CPU bandwidth are generally more than double those of other vector-control schemes. The more complex software and higher computing power requirements keep many designers from using this method.

Performance by both sensorless methods is adequate and useful for applications that don't have tight accuracy requirements for speed. Cost is less than full vector methods and response is good -definitely better than that provided by scalar control.

Figure 53. Comparison of CPU bandwidth and code for six speed control algorithms

All six control algorithms we have examined, from 120-degree modulation through OSCD control, have been implemented in the Renesas M16C/28 series MCU with a prototype motor control platform. Measured performance, CPU bandwidth and code size are shown in Figure 53, above.

As we see, vector control with position and current sensors requires about 40% of the CPU bandwidth, while DCCT sensorless control requires about 74% or nearly double the bandwidth. Moreover, OSCD vector control without position and current sensors requires nearly 90% of CPU bandwidth, which is more than double the bandwidth used by vector control with sensors.