Power Electronics

# Sensorless Control For PMDC Motors

A technique for controlling motor speed without Hall sensors or other signal-generating devices saves wear on bearings and brushes, decreases motor noise, and reduces no-load current.

The use of permanent magnet direct current (PMDC) motors has greatly increased over the years as more products are being made portable and free to use away from mains power sockets. Generally speaking, PMDC motors are more efficient and more readily controlled than the ac motors they replace. This is advantageous when using rechargeable batteries that do not require frequent recharging.

As more PMDC motors were used to replace ac motors on cordless appliances, they also were designated to replace ac motors where more controllability was desirable. High-voltage PMDC motors have found their way into more domestic appliances, including “white goods.”

### The PMDC Motor

The graph shown in Fig. 1 illustrates many of the performance characteristics of a typical PMDC motor. The blue line, which shows the speed of the motor as a function of torque or load, is straight and descends from the high no-load speed to the stall-torque at zero speed. The black line shows the current increasing from the small no-load value to the highest value at stall torque loads. This also is a straight line, and for PMDC motors, the current and torque are related by a constant known as the “motor constant,” which is a function of the magnetic field strength and the number of winding turns in the motor.

The red line shows the efficiency of the motor, which is the relationship between the motor's power output divided by the power input. The green line shows the motor's power output and is a product of speed and torque. For the straight-line relationship, the maximum power output will always occur at the point of half no-load speed and half stall current.

Motor performance is described by the following basic equation:

V= WK + IR (1)

where V is the applied voltage, I is the load current, R is the motor circuit resistance, K is the motor constant, and W is the motor speed. Equation 1 can be rewritten as:

V - IR = WK (2)

and

V - IR/K = W. (3)

But I is a function of the load and motor constant from which it can be seen that the motor speed W varies with the applied voltage and the load or load current. If the voltage applied to the motor is increased, then the speed at any given load will increase and, if the voltage applied is reduced, then the speed for any given load will decrease.

Most motor applications have more than one working point and vary in speed, as a table saw might from the load of a heavy cut to the load of a light cut to no-load at all. At a fixed input voltage, the motor speed will change, increasing as load is reduced. For greatest efficiency, most motors are designed so that the maximum working load lies at a point somewhere between maximum efficiency and maximum power.

Under those circumstances, the motor speed rises rapidly to no-load speed when the load is off, as it often is for an application such as drilling or sanding or carpet beating. These increases in motor speed lead to increased wear from friction and a high no-load current demand that consumes stored energy in batteries.

Typically, motor speeds can be controlled by using control circuits with feedback devices such as Hall sensors or frequency generators added to the motor. However, Johnson Electric has developed a method of controlling motor speed without the need for Hall sensors or other signal-generating devices integrated into the motor.

This sensorless control technique is based on several principles. First, it is assumed that the motor speed varies linearly with motor load at a given applied voltage. A second assumption is that the motor current varies proportionally to the motor load. Finally, it is understood that the motor speed at any particular motor load (current) can be varied by varying the applied voltage.

Therefore, if a way can be devised to vary the voltage applied to the motor in a ratio with the load current, which varies with the load itself, then it would be possible to ensure that the motor does not accelerate as the load is reduced. For example, the current at a load of 300 mNM is about 65 A, and the speed with 12 V applied is 10,200 rpm. If the load was reduced to 100 mNM, then a current of 20 A would be demanded and the speed would be increased to 17,500 rpm. However, if the applied voltage was simultaneously reduced to 7 V, then the speed would be held to 10,200 rpm. This is the result of simple ratios between the voltage drop in circuit and the applied voltages.

The curves in Fig. 2. show the performance of the same motor as shown before but with a controller acting to hold the speed to the same as the load speed. The blue speed/torque line can be seen to flatten after the load point 300 mNM is decreased, saving both wear on bearings and brushes, decreasing motor noise and decreasing the no-load current to save stored energy.

### The Controller

A small and known resistance (marked in red in Fig. 3) is placed in the circuit feeding the motor. As current is demanded by the load on the motor, it passes through this fixed resistance and develops a voltage drop across the resistance.

This voltage drop, proportional to the load, can then be compared within a digital circuit so that the controller can determine the desired pulse width on the input voltage to create an average input voltage that will drive the motor to a particular and predetermined speed.

Appliances provide some typical applications for this control technique. In vacuum cleaners using brush/roller configurations, it is as desirable to prevent the brush/roller from running at high speeds when the cleaning load is reduced as it would be when moving from carpet to hard floors. Furthermore, in power tool applications such as drilling or sawing, the motor often idles between holes or cuts as the craftsman moves positions. During this idle time, the motor would accelerate to higher speeds than the working speed causing a loss of stored energy and shorter life.

Using a Johnson Electric PMDC motor with the described velocity control provides an opportunity to control the motor speed without complicating the motor construction with feedback devices. Having a regulator that controls the motor velocity within 5% of a desired speed prevents the motor from increasing its speed as the loads applied decrease. This reduces the noise of operation and prolongs the life of bearings, brushes and the commutator, and for battery-driven applications, reduces the waste of stored energy.