Background
Many people (myself included in my early 3D printing days) implicitly expect off-the-shelf near “perfection” of the heater performance of their printer. It takes time and practice to learn and appreciate that PID controller tuning is a largely empirical process without a one size fits all solution. Different printer firmware uses different implementations of the PID controllers and different methodologies to derive (approximate) the process PID constants. When this is combined with a practically infinite number of printer designs and configurations, corner cases exist where the predefined solutions can struggle or falter. The purpose of this post is to document a reasonably simple to follow approach that will allow people to experiment with manual tuning of the Klipper PID controller in those corner cases.
Basic Process Steps
- Establish typical average PWM drive value for the heater being characterized
- Reconfigure Klipper
printer.cfgto allow manual open-loop control of the heater - Perform an open-loop step response test of the ‘process’
- Use the data stored in
klippy.logto model key process parameters: process gain, process time constant, process dead time - Use the key process parameters to derive Klipper PID constants using one of the many available tuning techniques, such as Ziegler-Nichols, Cohen-Coon, etc.
- Verify heater response and stability using the manually derived PID constants
Detailed Procedure
The following summary outlines the steps that I took to manually derive the PID constants for my heavily modified CR-10S Pro heated bed.
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Establish typical average PWM value for heater when printing. For example, set bed to 70C, allow it to come up to temperature and stabilize, then note the average PWM value. This is your
<TARGET_PWM>value. In my example we will use 25% or<TARGET_PWM>value of 0.25, because this is roughly the average PWM value that my bed uses to control at around 70 degrees C. This will give process gain specific to your selected target temperature. -
Modify your Klipper printer configuration in
printer.cfgto comment out the[heater_bed]block. Define new[fan_generic]block using the same output pin. This will allow you to enter PWM drive values for the bed manually in an open-loop fashion. Define new[temperature_sensor]block. This will allow you to monitor and log the bed temperature. In my example using a Duet 3 Mini 5+ the configuration is as follows:#[heater_bed] #heater_pin: PB17 # OUT0 #sensor_type: EPCOS 100K B57560G104F #sensor_pin: vref_scaled:PC0 # TEMP0 #pullup_resistor: 2200 #control: pid #pid_Kp = 51.75 #pid_Ki = 0.823 #pid_Kd = 813.2 #min_temp: 0.0 #max_temp: 110.0 [fan_generic bed_power] # for manual open-loop PID testing only pin: PB17 # OUT0 [temperature_sensor Heater_Bed] # for manual open-loop PID testing only sensor_type: EPCOS 100K B57560G104F sensor_pin: vref_scaled:PC0 # TEMP0 pullup_resistor: 2200 min_temp: 0.0 max_temp: 110.0 -
Restart Klipper and home your printer - homing will activate the steppers and ensures that Klipper data logging remains active throughout this exercise. Then set initial bed PWM by entering the following Klipper console commands at the same time (web interfaces like Fluidd allow multi-line console commands to be sent at once):
SET_IDLE_TIMEOUT TIMEOUT=<MARKER> SET_FAN_SPEED FAN=bed_power SPEED=<START_PWM>where
<MARKER>is a unique number that’s easy to correlate later to the PWM value, and where<START_PWM>is 5% lower than<TARGET_PWM>, or<START_PWM>=<TARGET_PWM>- 0.05. In my example we will use the following commands:SET_IDLE_TIMEOUT TIMEOUT=10020 SET_FAN_SPEED FAN=bed_power SPEED=0.20Allow the bed temperature to completely stabilize, noting this may take a very long time (1/2 hour to an hour, or even longer).
!!! WARNING !!!
!!! DO NOT UNDER ANY CIRCUMSTANCES LEAVE THE PRINTER UNATTENDED !!!Normal closed-loop heater safety features of Klipper do not work in this configuration because Klipper is configured to power the heater as if it was a manually controlled fan!
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Once bed temperature is completely stable and no longer changes, increase the bed PWM by entering the following Klipper console commands at the same time:
SET_IDLE_TIMEOUT TIMEOUT=<MARKER> SET_FAN_SPEED FAN=bed_power SPEED=<TARGET_PWM>In my example we will use the following commands:
SET_IDLE_TIMEOUT TIMEOUT=10025 SET_FAN_SPEED FAN=bed_power SPEED=0.25Allow the bed temperature to increase and completely stabilize. Once again, this may take a very long time.
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Enter the following command:
SET_FAN_SPEED FAN=bed_power SPEED=0then restore your original Klipper printer configuration inprinter.cfg. -
Download
klippy.logand locate the heater_bed PWM drive commands and heater_bed temperature log. You will need to extract the following column entries from the log file:Stats 746372.8:this is the MCU time reference in seconds
Heater_Bed: temp=55.2this is our custom defined open-loop Heater_Bed temperatureYou will also need to locate and note the time markers when the PWM commands were issued, particularly the second command that introduced 5% PWM step input. These markers will look similar to this in
klippy.logand will be present in the log file at the appropriate MCU times:idle_timeout: Timeout set to 10025.00 sIn this case the
bed_powerPWM control was set to 0.25 per the<MARKER>value selected earlier. -
Create a spreadsheet with the data extracted above. The spreadsheet will need TIME, POWER and TEMP columns. For example, it may look like this:
MCU TIME TIME POWER TEMP [sec] [sec] [%] [deg.C] 234317.3 0.0 0.20 68.2 234318.3 1.0 0.20 68.2 234319.3 2.0 0.20 68.1 234320.3 3.0 0.20 68.2 234321.3 4.0 0.20 68.1 234322.3 5.0 0.20 68.1 234323.3 6.0 0.20 68.2 234324.3 7.0 0.20 68.1 234325.3 8.0 0.20 68.2 234326.3 9.0 0.20 68.1 234327.3 10.0 0.20 68.1 234328.3 11.0 0.20 68.2 234329.3 12.0 0.20 68.1 The POWER [%] column will need to be populated manually based on the power command time stamps extracted from
klippy.log. -
Open https://pidtuner.com/ in your browser and complete the initial three steps of the process:
(1) ‘Import Data’, noting that ‘Input’ is the manual PWM command (POWER [%]) and ‘Output’ is the temperature (TEMP [deg.C]).
(2) ‘Select Step’ to pick a subset of the recorded data that corresponds to good steady initial temperature and fully stabilized final temperature
(3) ‘Select Model’ 1st Order model type and confirm good fit between your collected data (blue) and the model prediction (orange). Record the model fit parameters highlighted below: k (process gain), tao (process time constant), theta (process dead time).
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Download the Control Specialists Loop Tuning Calculator spreadsheet from https://controlspecialists.co.uk/wp-content/uploads/2017/08/Control-Specialists-Ltd-Loop-Tuning-Calculations-V4.5.xlsx. Alternatively, if you would like to derive the PID constants by yourself, there are many references and papers available that describe how to obtain the PID constants from process parameters.
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Enter the process model parameters k, tao and theta into KP, TC and DT cells of the SELF REGULATING LOOP RULES spreadsheet as highlighted below. If desired, adjust the SAFETY FACTOR. Collect values of P (Gain), I (sec/rep) and D (secs) from the PID row of the chosen tuning technique (for example COHEN COON as highlighted below). NOTE: The calculated values of the PID constants are very sensitive to the value of the process dead time (theta or DT), because dead time is “the enemy” of closed loop control. It is therefore very important to establish the dead time as accurately as possible. The value can be confirmed manually by looking at the raw data - see Process Parameters section below.
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Calculate your PID constants to use in Klipper
printer.cfgas follows:pid_Kp = P (Gain) * 255 _______________ 0.83 * 255 = 211.7 in this example
pid_Ki = P (Gain) * 255 / I (sec/rep) _____ 211.7 / 13.5 = 15.68 in this example
pid_Kd = P (Gain) * 255 * D (secs) ________ 211.7 * 2 = 423.4 in this exampleNote that the derived PID constants must all be multiplied by 255, as shown above, in order to be entered in the
printer.cfgfile. Refer toPID_PARAM_BASEin Klipper source code for more information. -
Test your new PID constants by modifying
printer.cfgand heating the bead to a desired temperature. Note the behaviour of the temperature and especially PWM power commanded by the Klipper PID loop. Below is a comparison of the PID loop performance of my printer bed with Klipper auto-tuned PID constants and PID constants derived manually as described above:
// Klipper auto-tune PID parameters: pid_Kp = 70.14 pid_Ki = 1.218 pid_Kd = 1010.1
// Manual Cohen-Coon PID parameters: pid_Kp = 211.7 pid_Ki = 15.68 pid_Kd = 423.4
It is worth noting that the manually tuned PID constants result in substantially tighter control, as evidenced by virtually no temperature overshoot (0.1 deg.C in practice) and very aggressive power control. As shown above I obtained those using SAFETY FACTOR of 1. In some cases such aggressive loop could become unstable resulting in temperature and power oscillations. In those cases a higher safety factor value would be appropriate, for example 1.5. Feel free to experiment with your specific setup - the beauty here is that once you establish the thermal model of your setup, you can derive the PID constants using any technique of your preference and with your chosen safety factor (or effectively stability margin).
Process Parameters
The following graph illustrates the meaning of the three key process parameters: gain (change in process variable PV divided by change in controller output CO), time constant (time it takes PV to reach 0.63 of total PV change, shown as tau and calculated from the end of the dead time) and dead time (time it takes from the change in CO to the point where the maximum PV slope line intersects the original level of PV line, shown as td). Unfortunately I do not recall where I came across it, so I am unable to credit the source.
Additional Notes
I have not spent much time experimenting with the hot end PID constants because in my case the Klipper auto-tuned values work very well. In principle, identical approach can be used for the hot end but it will require some more creativity in editing printer.cfg because Klipper will not function without a defined & functional [extruder] block.
Revisions
2022-04-07: Revised content of steps 7 to 10 in order to fix my incorrect interpretation of PID_PARAM_BASE. The overall method and final results are not affected by this revision.
2022-04-11: I seem to have experienced a “senior moment” when compiling step 6. Despite copying the content of my own notes from several months ago, I am unable to reproduce the presence of Received 746305.064772: {"id": 1750268944, "method": "gcode/script", "params": {"script": "SET_FAN_SPEED FAN=bed_power SPEED=0.25"}} in the logs. Furthermore, I am not sure how my original logs included these stamps since they originate from webhooks.py I therefore revised steps 3 to 6 with a workaround that inserts time stamps in the logs using the SET_IDLE_TIMEOUT command.
2023-10-14: Included a note in step 10 to emphasize the high sensitivity of the calculated PID constants to the value of process dead time (theta / DT). Added an illustration visualizing the process parameters for those who wish to derive them manually, instead of using https://pidtuner.com/.
2024-01-14: Revised step 3 to include printer homing to keep data logging active.
