When controlling a DC motor that is rated at 5V theoretically I can drive the motor in these ways:
Is there a difference between the two? Will using option 2/3 shorten the life of the motor? Would changing the PWM frequency improve the motor lifespan? The reason for doing this is that it is possible to drive the motor much slower with higher voltage.
Yes, this is very different. PWM drive and voltage drive separately don't really mean that much, but when combined in this way you will get significantly different performance.
Electrically, you can model a motor as an inductor (windings), resistor and a voltage source (the EMF, proportional to the motor speed). When you apply a lower voltage compared to a higher voltage, you will:
With PWM and a higher voltage, you will be able to achieve higher peak speeds and often much higher torque at equal speeds.
There is no real reason that a motor will damage when applying higher voltages. Motor damage is caused by:
Also, overheating or running a motor at very high currents will cause a (significant) reduction in torque because of magnetic saturation.
If you can guarantee that you keep your motor within speed, torque and force limits as well as properly cool it, there is no downside to running it at higher voltages with PWM.
A PWM driven motor is a buck converter. To the extent that your circuit and motor make a good buck converter, there is no difference between each of your options.
Some things to keep in mind:
At some much higher voltage, maybe around \$1000V\$, the insulation in the windings will fail. \$20V\$ is far too low for this to be a concern.
If your PWM frequency is too low for the winding inductance of the motor, the current over each PWM cycle will change significantly, you will have high torque ripple, and you no longer have a good buck converter. Performance and efficiency will suffer. In the extreme case, you may not even get the motor to spin.
Just as with a buck converter, a PWM drive involves transistors and other circuitry which is necessarily introduces additional losses. PWM drive is also more complex to design, harder to get working properly, is more expensive to implement, etc. Some of these losses (for example, hysteresis losses) are inside the motor, and will result in a higher motor temperature, which is usually the limiting parameter for motor performance, and a higher temperature will overall reduce the motor's lifetime. However, you would require a very poor design to make these losses approach losses you already have at DC, such as resistive losses in the windings, so the difference between PWM and DC drive efficiency is not much.
There are a couple things you need to watch out for when you use PWM.
First, the PWM voltage that your motor will see will have high frequency harmonics. These harmonics will introduce losses in your motor that wouldn't be there if you were using DC voltage. What this means is that your motor will get hotter when with PWM vs. DC (all other things being equal). How this affects the life of your motor depends on a lot of things. There is a very crude rule of thumb in the motor world that says for every 10 °C increase in motor coil temperature, you reduce the life of the motor's insulation by half. You would have to do a ratings test on the motor with the PWM drive you are using to either derate the motor or to tell you how much hotter it would get using PWM at the nameplate rating. Most people are really equipped to do this test, though.
Second, assuming you are talking about low voltages like your example (5V-20V), the increased voltage itself probably won't have much of an effect on insulation life. Obviously it depends on the motor, but generally the insulation in motors can withstand voltages up to at least 1000 V for short periods of time. Given voltage spikes due to the PWM, this means you don't really have to worry about reduction in insulation life until you are talking about motors that are rated ~ 400V-600V or above. The higher voltages with PWM could have an effect on brush life but its really hard to say without testing.
