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Pwm Based Speed Control of Dc Motor Drive

Introduction When the switch is closed, the motor sees 12 Volts, and when it is open it sees 0 Volts. If the switch is open for the same amount of time as it is closed, the motor will see an average of 6 Volts, and will run more slowly accordingly. As the amount of time that the voltage is on increases compared with the amount of time that it is off, the average speed of the motor increases. This on-off switching is performed by power MOSFETs. A MOSFET is a device that can turn very large currents on and off under the control of a low signal level voltage. The time that it takes a motor to speed up and slow down under switching conditions is dependant on the inertia of the rotor , and how much friction and load torque there is. The graph below shows the speed of a motor that is being turned on and off fairly slowly: We can see that the average speed is around 150, although it varies quite a bit. If the supply voltage is switched fast enough, it wonтЂ™t have time to change speed much, and the speed will be quite steady. This is the principle of switch mode speed control. Thus the speed is set by PWM. Inductors Before we go on to discuss the circuits, we must first learn something about the action of inductive loads, and inductors. Inductors do not allow the current flowing through them to change instantly (in the same way capacitors do not allow the voltage across them to change instantly). The voltage dropped across an inductor carrying a current i is given by the equation Where di/dt is the rate of change of the current. If the current is suddenly changed by opening a switch, or turning a transistor off, the inductor will generate a very high voltage across it. For example, turning off 100 Amps in 1 microsecond through a 100 microHenry inductor generates 10kV! PWM frequency The frequency of the resulting PWM signal is dependant on the frequency of the ramp waveform. Frequencies between 20Hz and 18kHz may produce audible screaming from the speed controller and motors. Each switching on and off of the speed controller MOSFETs results in a little power loss. Therefore the greater the time spent switching compared with the static on and off times, the greater will be the resulting "switching loss" in the MOSFETs. The higher the switching frequency, the more stable is the current waveform in the motors. This waveform will be a spiky switching waveform at low frequencies, but at high frequencies the inductance of the motor will smooth this out to an average DC current level proportional to the PWM demand. This spikiness will cause greater power loss in the resistances of the wires, MOSFETs, and motor windings than a steady DC current waveform. It can be seen from the following two graphs. One shows the worst case on-off current waveform, the other the best case steady DC current waveform Both waveforms have the same average current. However, when we work out the power dissipation in the stray resistances in our motor and speed controller, for the DC case: and for the switching case, the average power is So in the switching waveform, twice as much power is lost in the stray resistances. In practice the current waveform will not be square wave like this, but it always remains true that there will be more power loss in a non-DC waveform. Choosing a frequency based on motor characteristics Then we can work out mathematically the minimum frequency to attain this goal. This section is a bit mathematical so you may wish to miss it out and just use the final equation. The following shows the equivalent circuit of the motor, and the current waveform as the PWM signal switches on and off. This shows the worst case, at 50:50 PWM ratio, and the current rise is shown for a stationary or stalled motor, which is also worst case. T is the switching period, which is the reciprocal of the switching frequency. Just taking the falling edge of the current waveform, this is given by the equation ? is the time constant of the circuit, which is L / R. So the current at time t = T/2 (i1) must be no less than P% lower than at t = 0 (i0). This means

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