Have you considered using back-emf observers for sensorless speed estimation?

Sensorless control is gaining in popularity for motor drive applications which don’t demand precise speed control. Fan or pump drives that operate within 20% to 100% speed range are the right candidates for sensorless control. Regardless of your motor type, you can likely eliminate the mechanical sensors mounted on rotor shaft .

If you are internet addict like me and have ever searched “sensorless control or sensorless vector control of BLDC/PMSM motor” you would have a plethora of material. In majority of these literatures, basic methodology of sensorless motor control revolves around back-emf. From basic laws of electromagnetic theory, we know that back-emf generated inside the any electric machine’s armature winding is proportional to rotor speed.

Therefore, sensorless speed and position estimation gets divided into two basic categories:

1. Sensing or measurement of back-emf from armature terminals  
2. Back-emf observer based mathematical equations describing motor behavior

A classical example of back-emf sensing based algorithm is 120 degree commutation or trapezoidal control of brushless DC (BLDC) motor in which back-emf of non-energized phase is measured for rotor position. This helps to efficiently commutate the motor. TI's Instaspin-BLDC solution is based on this principle. A similar, yet far less common, technique can be used for DC motors also. Please refer to a helpful blog by title, “Easy cruise control for brushed motors using BEMF” based on back-emf sensing to maintain constant speed.

Closed loop back-emf observers relie on back-emf calculation. These techniques have their own pro’s and con’s. Frankly, it is beyond the scope of this blog to explain them in details or bring out subtle difference between them; this blog is my attempt to explain one of the basic underlying concepts which is common in all these back-emf observer based methods. You might be familiar with observer based technique in this category including sliding mode observer and luenberger observer. 

Are you thrown off by my choice of a DC motor instead of directly utilizing BLDC or PMSM motor models for explaining the underlying concept? My reasoning is pretty simple in that DC motors are the most fundamental and once you understand all its characteristics and control principles then you can apply to others. The other fact is that its armature terminal equations are simple and straight-forward which makes it much easier on me to explain.

Let’s get started with DC motor equivalent circuit model as shown in figure 1, which can be represented by following two equations:

Where,

Va is applied voltage at motor armature terminal, in volts

i_a is armature current, in amp

Ra is armature resistance, in ohm

La is armature inductance, in henry

e_a is bace-emf induced in armature, in volt

Ke is motor back-emf constant, in volt per rad per sec

ω_m is motor speed in rad/sec

From equation 2, it is clear that if back-emf voltage e_a is known, speed can be calculated because ke is already known parameter. To calculate back-emf voltage e_a, motor equation 1 can be utilized.

Typically, DC motors are driven with pulse-width-modulated (PWM) switching power converter. There are lots of power circuit configurations which can be utilized. These range from the simple step down buck-converter consist of single MOSFET and a diode to most advanced H-bridge configuration consist of four MOSFETs and diodes.

In each case, average value of applied armature voltage Va can be very well determined based on DC link voltage and operating duty-cycle.

Now in equation 1, Ra and La is already known from the motor data sheet, Va can be determined as explained above, so if ia armature current is measured, the only unknown quantity, back-emf voltage e_a can be calculated simply by subtracting the resistive and inductive drops from applied voltage Va.

Splendid, isn’t it! But, this way of calculation of back-emf voltage e_a is only a mathematical possibility, it’s not a reliable solution in real world scenarios because it requires differentiation of measured current which is susceptible to measurement noise. Any induce noise in motor current measurement, such as PWM switching noise or external induced noise, will get amplified by differentiation. The result makes the back-emf calculation vulnerable to noise.

In order to avoid differentiation of measured current, closed loop observer base structure is used as shown in Figure 2 below. This shows s is Laplace variable and 1/s represent integration.

The back-emf voltage e_a, is calculated indirectly by passing the error between actual measured current and estimated current through PI controller. The idea is pretty straight forward, in order to make error between actual current and measured current to zero, the PI controller output has to become to actual back-emf e_a.

As true with any sensorless scheme, the presented back-emf observer scheme is also sensitive to motor parameter variation especially to armature resistance. You can use these simulation files to check the estimated back-emf deviates from the actual value.  

Will you consider this method the next time you have a sensorless control using DC motors?

Why not try out your own advance observer, such as a sliding mode observer, on your next project with a BLDC/PMSM motors?

TI supplies various motor control kits, which supports sliding mode observe based vector control project on C2000 based MCU. For more details, please visit control-suite.

Thanks for reading, and your comments are welcome below.