Block J - Power MOSFET Control of a DC Permanent Magnet Motor

Objectives

1. Determine speed range of DC permanent magnet (PM) motor with a power MOSFET drive.

2. Determine speed regulation with load.

3. Determine current waveforms in MOSFET, motor, and bypass diode.

Background

In a recent experiment we examined the performance of a DC motor. We saw that speed could be controlled by either increasing the armature voltage or by decreasing the field voltage (and thus the field current). We also saw that the speed could get dangerously high if the field voltage was lost, an obvious disadvantage. A second disadvantage is that we had to have two separate supplies, one for the field and one for the armature, which increases the system cost. A third disadvantage is that changing the speed by mechanically adjusting a variable autotransformer is not suitable for frequent use or automatic control.

The first two disadvantages are eliminated by using a permanent magnet (PM) dc motor, where the field is supplied by permanent magnets rather than by coils of copper wire. This can reduce the cost of the motor, and can also increase the efficiency of the motor, since no input power is necessary to supply the field.

One way of dealing with the third disadvantage is to apply voltage to the motor in pulses rather than continuously, using a solid state switch such as a power MOSFET. The process is sometimes called Pulse Width Modulation (PWM).

Suppose we have a permanent magnet DC motor rated at 90 V and 1800 rpm. If we apply 60 V, we will find the speed to be approximately (60/90)(1800) = 1200 rpm. This can be done by connecting the motor to a 90 V source for, say, 2 ms, and disconnecting it for 1 ms, such that the average voltage is 60 V, as shown in Fig. 1. If we modulate the pulse width such that the motor is on for 1 ms and off for 2 ms, then the average terminal voltage is 30 V and the speed is approximately 600 rpm.

At first glance, this seems like a cruel and unusual punishment for a motor, being turned on and off so rapidly. Indeed, it can cause mechanical problems in a poorly designed motor, but the technique works rather well in a properly designed motor. The inertia of the motor helps it to maintain a nearly constant speed. If the pulse train frequency is too low, however, the motor will speed up and slow down noticeably during the on and off times. It appears to be hunting for the correct or average speed, so the phenomenon is called "hunting". Certainly the pulse frequency needs to be high enough that hunting is not a problem.

On the other hand, switching losses in the power MOSFET are directly proportional to the pulse frequency. Other problems such as radiated noise also get worse at higher frequencies. One therefore needs to stay within the appropriate frequency range. A good range would be 2 kHz to 20 kHz, although satisfactory performance may extend throughout the 200 Hz to 200 kHz range. The trend in some other solid state devices, such as switching power supplies, is toward pulse frequencies higher than 200 kHz, but there appears to be little incentive to move toward such high frequencies for DC motor drives.

Let us now examine circuit operation in more detail. Fig. 2 shows a simple model for the DC motor in a switching circuit. The motor has resistance R and inductance L due to the copper windings. There is also an induced voltage E_a given by

where n is the rotational speed in rpm and K is a constant for each motor, including the flux produced by the permanent magnets. The motor must be paralleled by a diode which can carry the motor current when the switch is open. Otherwise the rapid change in current will cause the inductor voltage v_L = L di/dt to get very large, and probably damage either the switch or the motor. When the switch is closed, the diode will be reversed biased so i_d = 0.

The voltage drop across the forward biased diode will be about 0.7 V. We will ignore this relatively small voltage in our analysis and assume that the motor is shorted when the switch is open and motor current is still flowing. The circuit has two different states which need to be analyzed separately. These states are shown in Fig. 3. The solution is simplified if we assume E_a to be a constant during either the on or the off period so we will do so.

Kirchhoff's voltage law around the loop of Fig. 3a is

This can be written as a first order differential equation.

..........(3)

If we assume the current to be zero when t = 0, the solution to this equation is

..........(4)

The differential equation for Fig. 3b is similar.

..........(5)

The boundary conditions are different, however, in that the inductor current i_L is always some finite value I_o when the switch opens. If we start over with a new time origin in Fig. 3b, so i_L = I_o at t = 0, the solution to the differential equation is

..........(6)

Typical current waveforms are given in Fig. 4. When the switch closes, the motor current rises along an exponential curve, reaching the value I_o just as the switch opens. The motor current then flows through the diode according to the exponential curve of (6) until i_L = 0. E_a then causes the diode to be reversed biased, so the motor is actually open circuited and coasting until the switch is turned on again. The time of diode conduction is determined by setting i_L = 0 in (6) and solving for t.

It should be noted that the switch can be turned on before the diode current has had time to return to zero. The voltage source V_B quickly takes over from the diode so the diode current appears to drop to zero instantly. This does not hurt anything, but (4) is no longer valid since the initial current is not zero.

Discussion and Calculations

1. Assume in Fig. 2 that R = 2 , L = 16 mH, and V_B = 90 V. By another test, it is found that E_a = 90 V when the speed is 1800 rpm and a constant voltage is applied. Assume the switch is on for 0.55 ms and off for 0.55 ms, there is no load, and the motor speed is 1440 rpm. Calculate the new value of E_a for this speed, using (1). If the current is zero at t = 0, what value of current would you expect at t = 0.55 ms?

2. Use the value of current calculated in the previous step as the initial current in the inductor when the switch is turned off, and estimate the time required for the current to go to zero, using (6).

3. Sketch the voltage across the switch from 0 to 1.1 ms. Do not spend a great deal of time doing accurate plotting. We really want to know if you understand Kirchhoff's law and can apply it in this case. (Hint. The case of the switch being in the on state should be easy. The off state is tricky, however. When the diode is conducting, the voltage across it is approximately 0.7 V, positive on the bottom. The voltage across the switch is most easily determined by applying Kirchhoff's law around the outside of the circuit where there are just three components, the battery, the switch, and the diode. When the diode is not conducting, however, it acts like an open circuit and we only have the left window or mesh of Fig. 2 to consider. The switch is open and the diode is not conducting, so i_t = 0 and i_d = 0, which requires i_L to be zero also. If i_L = 0, then v_R and v_L are zero also, leaving only E_a to consider. But E_a does not depend on current, but only on speed, as indicated in (1). If the switching frequency is high enough that speed does not change much during a cycle, then E_a is essentially constant. The voltage across the switch is then the difference between V_B and E_a.)

4. What is the frequency of the applied pulse train?

Instructional Activity in Class

1. Locate the 0.5 hp permanent magnet DC motor and the dynamometer. Mount them on the baseplate in the same orientation as in the DC motor experiment. Make sure the DC breaker is off (in the down position). Connect the bench mounted 0-150 V DC voltmeter to + and - under the DC breaker. Turn on the dc breaker. If the voltmeter is reading downscale, reverse the leads. The voltmeter should indicate between 85 and 95 V. Record this value in your notebook. Turn the DC breaker off.

2. Locate several components that need to be connected into a circuit. The bypass diode is mounted on a separate fixture and is physically larger than the diodes used in the rectifier experiment. The power MOSFET should have a rating of at least 200 V and 10 A, and should be mounted on a fixture with a heat sink and three banana jacks clearly labeled G, D, and S. Measure the resistance between D and S, and between G and S, with your Fluke Digital Multimeter. If this resistance is low (say less than 1000 ), the MOSFET is probably burned out. If so, call your instructor. The resistance should be very high, well above 1 M. If the MOSFET tests ok, then locate the Global 4001 Pulse Generator (should be on top of the bench). Make sure the square wave button is out. Attach a BNC to twin banana adapter to the far right BNC connector. Note that the Pulse Generator has separate pulse width and pulse spacing controls, each with an outer knob for range selection and an inner knob for variation within a range. Set both outer knobs at 100 µs. Set pulse width inner knob full clockwise (x1 position) and the pulse spacing inner knob full counterclockwise (x10 position).

3. We now want to connect up the circuit shown in Figures 5 and 6. Fig. 5 is a standard wiring diagram while Fig. 6 is a pictorial view of the bench with components sitting on it. Experience indicates that fewer wiring errors will be made if Fig. 6 is used rather than Fig. 5. Arrange the components as shown in Fig. 6 and insert the banana leads exactly as shown.

4. Turn pulse generator amplitude full clockwise. With the DC breaker still off, turn the pulse generator on and observe v_GS on CH1. Record actual peak values of v_GS (should be about 10 V). Record t_on and t_off from the scope. If these are significantly different from 0.1 ms and 1 ms, check with your instructor. Turn the pulse generator off.

5. We are now ready to carefully turn on the DC breaker. Watch the meters. If they show a short pulse, with both the voltage and current reading zero with the DC breaker switch on, turn the DC breaker switch off immediately and call the instructor. There are two possibilities. You have wired the circuit incorrectly or the power MOSFET has failed in a shorted condition. There is an internal DC circuit breaker behind the bench panel which should limit the current flow to 5 A. It is reset by turning the DC breaker switch off and back on. Fix your circuit so that the voltmeter shows about 90 V and the ammeter shows zero with the DC breaker switch on. Once your circuit passes this test, turn the DC breaker switch off, the pulse generator on, and the dynamometer control full counterclockwise.

6. In a moment we will turn on the DC breaker switch again. If all is well, a small current will flow and the motor will start to turn. If the bypass diode is reversed or shorted, the motor will not start and the internal dc circuit breaker will trip. Now turn on the DC breaker switch. If current is small and the motor is turning, try turning the pulse width inner knob counterclockwise (increasing the duty cycle). The motor should speed up while the frequency of the sound the motor is making should decrease. Turn the single phase AC breaker on and turn the dynamometer load control up. Torque should increase and the motor should slow down. The dynamometer should rotate in a direction so the torque scale reads correctly. If everything is working correctly except that the direction of rotation is backwards, turn off the DC breaker switch and call your instructor to check your circuit. Once it appears that your circuit is operating correctly, fill in the gaps in the following table in your notebook. Note that very low speeds are sometimes easier to estimate by counting revolutions in a 15 or 30 second interval than by using the Strobotac.
   

   Leave the motor running for the next two activities.

7. Use the clamp-on ammeter to examine the currents i_t, i_L, and i_d for the cases 7 and 8 in the above table. You may have to turn the ammeter over to get the current readings upscale as shown in Fig. 4. Sketch the current waveforms, recording the peak current. Turn the dynamometer control to get minimum torque and sketch again.

8. Replace the clamp-on ammeter with a x10 voltage probe connected to D of the MOSFET. For the same two conditions as the previous activity, sketch the drain to source voltage. Note voltage values where appropriate. Turn the single-phase AC breaker off.

9. Now we want to see the effect of a lower switching frequency. Hold the inner knob with one hand to prevent its rotation and rotate the outer knob all the way counterclockwise, to the 100 ms position. Repeat for the other set of knobs. Estimate t_on and t_off from the knob positions. Describe the motor operation.

10. Next we want to see the effect of a higher switching frequency. Holding the inner knobs fixed, move the outer knobs to the 1 µs positions. Estimate t_on and t_off from the knob positions. Describe the motor operation. Compare the gate on and off times with the drain to source on and off times. Turn the DC breaker off, and then the pulse generator.

Conclusion

1. Calculate the speed regulation (defined in Block H) with load for the case where t_on = 10 ms and t_off = 0.1 ms.

2. You should have observed a condition where the drain to source voltage with the MOSFET off was significantly less than 90 V. Where is the rest of the voltage necessary to satisfy Kirchhoff's voltage law? Explain.

3. Do you think noise might be a problem with this type of drive? If someone complained about the noise, what would you do?

4. Give your impressions as to general performance and ease of control of the PM motor as compared with the DC shunt or separately excited motor.