Question about PID control loop timing

Question

For my project I am creating a RISC processing architecture on an FPGA that can perform various basic instructions like adding, multiplying, subtracting, storing and fetching from memory etc. To prove my architecture I am using these instructions to control the speed of a motor using a PID control loop.

So the system has a potentiometer to set a speed setpoint, a direction and start/stop inputs, a motor driver to drive the motor with PWM, and an encoder to read the speed back. Its pretty simple.

I at the stage where everything has been tested individually and can now start controlling the motor speed with the PID loop. I am new to PID loops but have been reading up on them.

I read the speed setpoint from potentiometer and rotational speed from the encoder every 1ms. However in my program that I write with instructions that is ran at 100MHz, I keep calculating the speeds as they are refreshed every 1ms. So I calculate the same answer a lot of times before it is refreshed. This is no problem currently as it is only for display on 7 segments.

From my PID loop understanding, you need a fixed scan time as the integral and derivative accumulations will be skewed. Currently I have no means to do this as my processor will be calculating at 100MHz but the variables are only refreshing at 1ms.

I have two questions:

1. Should I add an interrupt capability to my processor to only run the PID code every 1ms as the speeds are refreshed?

2. Also in your opinions, is every 1ms too fast or too slow to refresh the values? This is a motor and encoder on a bench with no load so it probably doesn't even matter, I am just unsure.

If there is anything unclear, please ask :)

EDIT

Some additional process information:

Motor speed: Approx 1000 to 4000 rpm max

Motor no load, full speed current: 200mA

Motor load: Virtually nothing, just an encoder

Motor driver: L298n (PWM is created in FPGA logic)

Encoder type: Rotary incremental encoder, 2 12V channels 90 degree phase shifted, 1000ppr (doubled to 2000ppr)

Answer 1

1st write a spec with the Current vs acceleration vs RPM then repeat with an inertial load as the optimal PID parameters will change especially with reverse. Create an algorithm for it.

Also determine the power dissipation for such duty cycles of acceleration and create an algorithm for that. You ought to know that no-load = kV or RPM/V is a constant and current is proportional to force of acceleration which depends on load and there is a stall stiction start current.

You those two feedbacks with your encoder velocity and current feedback to create two loops and determine the error with your target profile and use PID feedback to optimize stability and minimize 1 or more parameter choices. Eg. Max/rated current, seek time, etc. So the signal bandwidth changes and the error tolerance on each control variable including overshoot and settling time are your specs. The lighter the load, the more bandwidth from faster response and samples per second you will need to support the dynamic range of speed control and tolerance error.

BW=0.35/Tr 10~90z handles only 3dB of BW but your step changes might span from 3 dB to 20 dB or more, thus depending on your goal to make the fastest settling (Tbd BW) time with minimal TBD overshoot determines your sampling rate.

car wheel magnetic speed sensors for example using Infineon IC measures velocity from 0.5 to over 150 kph for smart cornering and braking with something like 100 magnets per rev as the wheel encoder which is excessive at high RPM but this is how it measure speed. So the LSB’s are truncated at low speed and DSP interpolates with a Biphase digital output in addition with the ~ 100ish pulses per rev. the ECU handles all the PID etc.

You might want to be more ambitious in Your project.

p.. don’t use a BJT driver, use a Full bridge NCh driver that can handle your motor. Like an Arduino CNC shield. Look for PMIC software.

Answer 2

Should I add an interrupt capability to my processor to only run the PID code every 1ms as the speeds are refreshed?

Yes.

Also in your opinions, is every 1ms too fast or too slow to refresh the values? This is a motor and encoder on a bench with no load so it probably doesn't even matter, I am just unsure.

That sounds about right for a motor control. Unless it's an absolutely awesome motor, it will limit the loop closure frequency to no more than 20Hz or so -- that's well below the \$f_s \ge 10 B_w\$ rule that I go by.

You say you'll be sampling the loop at 1000Hz, and you've got a 1000 count encoder, yet you expect many samples without change -- that implies a pretty slow-moving motor.

Answer 3

Re: 2.: This is a question that control theory and the properties of your system will have to define. We can't tell you that!

Re: 1.: Yeah, that sounds like the standard way of doing that: add a timer unit, give it a couple easy registers (or memory-mapped registers) to control it, and an interrupt controller.

That thing doesn't have to be fancy, honestly - if you add a "SUSPEND" instruction you can simply stall your CPU until the interrupt generator fires. That's not really an interrupt controller (you can't interrupt anything while your CPU is actually doing anything), but for your single use case, it would certainly be easier than thinking about how to save and restore CPU state upon entering and leaving interrupt routines!

Answer 4

There is a rule of thumb for digital control loops : $$ f_s >= 20 B_w $$ Basically, the sampling rate should be at least 20 times the desired closed-loop bandwidth.

So in your case, the closed-loop bandwidth should be less than 50 Hz. For example, if you want a stabilization time of 1 ms, you need more bandwidth. It's up to you to determine what your requirements. From these requirements, you should be able to estimate a desired bandwidth.

Edit :

As @TimWescott mentionned the, rule of thumb $$ f_s >= 10 B_w $$ usually works well, so my rule of thumb is a bit conservative. However, the closer you get to the Nyquist frequency, the more you need to model accurately your plant, you need to consider all delays (computation delays, actuator delays, sampling delays). You need to make sure all your dynamics are properly modeled in the 0 to f_s/2 range, etc.