Analog Compensator Vs digital Compensator in Power electronics Converter

Question

I was working on designing a feedback compensator for my buck converter. I decided to use the compensator circuit in the feedback and give its output to Arduino which gives the duty cycle as shown below. The Arduino senses the voltage and directly generates a duty cycle without any other calculations. I have figured out my transfer functions and is of the form shown below. :

An example of how my compensator equation will look like.

This compensator will give me some analog circuit based on OP-amps, capacitors and resistors.

I have seen some people implementing PID controllers in other applications, but I want to ask if an Arduino would be sufficient implementing the transfer function of this type. Also, which one should be preferred in this case...should I go for the analog hardware or the digital one in this case.

Finally, I want to ask that if I want to implement the given transfer function is a microcontroller than do I have to process it in the time domain i.e. converting this complete equation in time domain and then performing the calculations like integrations derivative etc.???

I need some suggestions as I am new into this.

Answer 1

Arduino Uno will be able to close the control loop if the switching frequency is around mains frequency (50-60Hz). Hopefully. Even then you may end up coding some math in assembly for things to be fast enough. So, if you want to run a switcher with the secondary winding of a mains transformer used as the inductor - go for it. It doesn't need to be practical, you are learning, and it will be way, way easier to debug such a relatively slow switching converter, with affordable instrumentation (low end oscilloscopes, home-made current sense amplifiers, etc.).

For a typical converter running at 100kHz, the innermost control loop must be updated at a rate >10MHz, so you'll need a much faster MCU, and ideally a core dedicated just to controlling the converter. A 12-bit 25Ms/s ADC would be a reasonable starting point. To close the loop I'd suggest a hard-realtime processor core or an FPGA. Parallax Propeller II would have plenty enough processing power to close the control loop at 100kHz, but it may require more than one core working in parallel. Prop II also has high-bandwidth 8-bit DACs (one per each GPIO pin!) - should you need those.

Otherwise, you'll have to learn basics of VHDL or Verilog and get yourself an FPGA development board. Prop II has a bit more on-board analog hardware than most FPGAs, so it is more versatile when doing digital control loops that aren't too complex to implement on it. FPGAs - even fairly small ones - have lots of DSP resources, and that's relatively hard to beat on a microcontroller. Prop II can do 8 16x16 multiplications in parallel at 100MHz instruction rate. A $5 Efinity FPGA chip can do these multiplications at a higher rate. But FPGAs don't come with the analog goodies that Prop II has.

Answer 2

This will work in principle, but it requires that the ADC conversion and the PID computation be completed with negligible delay. Any delay adds (linear) phase to the PID loop and tends to make the system unstable.

If your PWM is at (say) 100 kHz (== 10 us), and your ADC + computation takes 2 us, you add 360*2u/10u = 72 degrees of phase at 100 kHz, and 7.2 degrees at 10 kHz.

In addition, there is noise from ADC resolution; PID computation and resolution of the PWM generator. This doesn't affect accuracy, but may make the output noisier.

Another way of thinking about it: Consider when (in the current cycle), the next PWM is calculated. A conventional PWM loop (comparing a linear ramp with an error amplifier signal) has what is called 'natural sampling' which doesn't introduce excessive delays. Think of it having the computation repeating at a very high frequency (>> PWM rate) and at each instant deciding if the current PWM cycle should be terminated. An MCU approach generally computes the next PWM width once during the current cycle. It doesn't 'update' this info based on even more recent ADC data. Because of this delay (net PWM computed during current PWM), the phase delay is quite significant.

To make this work, you will need to have a relatively low BW for your loop. It will work, but load (and line) response will be poorer.