PID¶
+PID control is a widely used control method in the 3D printing world. +It’s ubiquitous when it comes to temperature control, be it with heaters to +generate heat or fans to remove heat. This document aims to provide a +high-level overview of what PID is and how to use it best in Klipper.
+PID Calibration¶
+Preparing the Calibration¶
+When a calibration test is performed external influences should be minimized as +much as possible:
+-
+
- Turn off fans +
- Turn off chamber heaters +
- Turn off the extruder heater when calibrating the bed and vice versa +
- Avoid external disturbances like drafts etc +
Choosing the right PID Algorithm¶
+Klipper offers two different PID algorithms: Positional and Velocity
+-
+
- Positional (
pid) + * The standard algorithm + * Very robust against noisy temperature readings + * Can cause overshoots + * Insufficient target control in edge cases
+ - Velocity (
pid_v) + * No overshoot + * Better target control in certain scenarios + * More susceptible to noisy sensors + * Might require larger smoothing time constants
+
Refer to the control statement in the +Configuration Reference.
+Running the PID Calibration¶
+The PID calibration is invoked via the PID_CALIBRATE command. +This command will heat up the respective heater and let it cool down around +the target temperature in multiple cycles to determine the needed +parameters.
+Such a calibration cycles looks like the following snippet:
+3:12 PM PID_CALIBRATE HEATER=extruder TARGET=220 TOLERANCE=0.01 WRITE_FILE=1
+3:15 PM sample:1 pwm:1.0000 asymmetry:3.7519 tolerance:n/a
+3:15 PM sample:2 pwm:0.6229 asymmetry:0.3348 tolerance:n/a
+3:16 PM sample:3 pwm:0.5937 asymmetry:0.0840 tolerance:n/a
+3:17 PM sample:4 pwm:0.5866 asymmetry:0.0169 tolerance:0.4134
+3:18 PM sample:5 pwm:0.5852 asymmetry:0.0668 tolerance:0.0377
+3:18 PM sample:6 pwm:0.5794 asymmetry:0.0168 tolerance:0.0142
+3:19 PM sample:7 pwm:0.5780 asymmetry:-0.1169 tolerance:0.0086
+3:19 PM PID parameters: pid_Kp=16.538 pid_Ki=0.801 pid_Kd=85.375
+ The SAVE_CONFIG command will update the printer config file
+ with these parameters and restart the printer.
+Note the asymmetry information. It provides an indication if the heater's
+power is sufficient to ensure a symmetrical "heat up" versus "cool down /
+heat loss" behavior. It should start positive and converge to zero.
+A negative starting value indicates that the heat loss is faster than the heat
+up, this means the system is asymmetrical. The calibration will still be
+successful but reserves to counter disturbances might be low.
Advanced / Manual Calibration¶
+Many methods exist for calculating control parameters, such as Ziegler-Nichols, +Cohen-Coon, Kappa-Tau, Lambda, and many more. By default, classical +Ziegler-Nichols parameters are generated. If a user wants to experiment with +other flavors of Ziegler-Nichols, or Cohen-Coon parameters, they can extract the +constants from the log as seen below and enter them into this +spreadsheet.
+Ziegler-Nichols constants: Ku=0.103092 Tu=41.800000
+Cohen-Coon constants: Km=-17.734845 Theta=6.600000 Tau=-10.182680
+Classic Ziegler-Nichols parameters work in all scenarios. Cohen-Coon parameters +work better with systems that have a large amount of dead time/delay. For +example, if a printer has a bed with a large thermal mass that’s slow to heat +up and stabilize, the Cohen-Coon parameters will generally do a better job at +controlling it.
+Further Readings¶
+History¶
+The first rudimentary PID controller was developed by Elmer Sperry in 1911 to +automate the control of a ship's rudder. Engineer Nicolas Minorsky published the +first mathematical analysis of a PID controller in 1922. In 1942, John Ziegler & +Nathaniel Nichols published their seminal paper, "Optimum Settings for Automatic +Controllers," which described a trial-and-error method for tuning a PID +controller, now commonly referred to as the "Ziegler-Nichols method.
+In 1984, Karl Astrom and Tore Hagglund published their paper "Automatic Tuning +of Simple Regulators with Specifications on Phase and Amplitude Margins". In the +paper they introduced an automatic tuning method commonly referred to as the +"Astrom-Hagglund method" or the "relay method".
+In 2019 Brandon Taysom & Carl Sorensen published their paper "Adaptive Relay +Autotuning under Static and Non-static Disturbances with Application to +Friction Stir Welding", which laid out a method to generate more accurate +results from a relay test. This is the PID calibration method currently used by +Klipper.
+Details of the Relay Test¶
+As previously mentioned, Klipper uses a relay test for calibration purposes. A +standard relay test is conceptually simple. You turn the heater’s power on and +off to get it to oscillate about the target temperature, as seen in the +following graph.
+
The above graph shows a common issue with a standard relay test. If the system +being calibrated has too much or too little power for the chosen target +temperature, it will produce biased and asymmetric results. As can be seen +above, the system spends more time in the off state than on and has a larger +amplitude above the target temperature than below.
+In an ideal system, both the on and off times and the amplitude above and below +the target temperature would be the same. 3D printers don’t actively cool the +hot end or bed, so they can never reach the ideal state.
+The following graph is a relay test based on the methodology laid out by +Taysom & Sorensen. After each iteration, the data is analyzed and a new maximum +power setting is calculated. As can be seen, the system starts the test +asymmetric but ends very symmetric.
+
Asymmetry can be monitored in real time during a calibration run. It can also +provide insight into how suitable the heater is for the current calibration +parameters. When asymmetry starts off positive and converges to zero, the +heater has more than enough power to achieve symmetry for the calibration +parameters.
+3:12 PM PID_CALIBRATE HEATER=extruder TARGET=220 TOLERANCE=0.01 WRITE_FILE=1
+3:15 PM sample:1 pwm:1.0000 asymmetry:3.7519 tolerance:n/a
+3:15 PM sample:2 pwm:0.6229 asymmetry:0.3348 tolerance:n/a
+3:16 PM sample:3 pwm:0.5937 asymmetry:0.0840 tolerance:n/a
+3:17 PM sample:4 pwm:0.5866 asymmetry:0.0169 tolerance:0.4134
+3:18 PM sample:5 pwm:0.5852 asymmetry:0.0668 tolerance:0.0377
+3:18 PM sample:6 pwm:0.5794 asymmetry:0.0168 tolerance:0.0142
+3:19 PM sample:7 pwm:0.5780 asymmetry:-0.1169 tolerance:0.0086
+3:19 PM PID parameters: pid_Kp=16.538 pid_Ki=0.801 pid_Kd=85.375
+ The SAVE_CONFIG command will update the printer config file
+ with these parameters and restart the printer.
+When asymmetry starts off negative, It will not converge to zero. If Klipper +does not error out, the calibration run will complete and provide good PID +parameters, However the heater is less likely to handle disturbances as well +as a heater with power in reserve.
+3:36 PM PID_CALIBRATE HEATER=extruder TARGET=220 TOLERANCE=0.01 WRITE_FILE=1
+3:38 PM sample:1 pwm:1.0000 asymmetry:-2.1149 tolerance:n/a
+3:39 PM sample:2 pwm:1.0000 asymmetry:-2.0140 tolerance:n/a
+3:39 PM sample:3 pwm:1.0000 asymmetry:-1.8811 tolerance:n/a
+3:40 PM sample:4 pwm:1.0000 asymmetry:-1.8978 tolerance:0.0000
+3:40 PM PID parameters: pid_Kp=21.231 pid_Ki=1.227 pid_Kd=91.826
+ The SAVE_CONFIG command will update the printer config file
+ with these parameters and restart the printer.
+Pid Control Algorithms¶
+Klipper currently supports two control algorithms: Positional and Velocity. +The fundamental difference between the two algorithms is that the Positional +algorithm calculates what the PWM value should be for the current time +interval, and the Velocity algorithm calculates how much the previous PWM +setting should be changed to get the PWM value for the current time interval.
+Positional is the default algorithm, as it will work in every scenario. The +Velocity algorithm can provide superior results to the Positional algorithm but +requires lower noise sensor readings, or a larger smoothing time setting.
+The most noticeable difference between the two algorithms is that for the same +configuration parameters, velocity control will eliminate or drastically reduce +overshoot, as seen in the graphs below, as it isn’t susceptible to integral +wind-up.
+
In some scenarios Velocity control will also be better at holding the heater at +its target temperature, and rejecting disturbances. The primary reason for this +is that velocity control is more like a standard second order differential +equation. It takes into account position, velocity, and acceleration.
+ + +