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1. Ni Auto Tune Pid Codes
2. Pid Tune G Code

The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Ziegler and Nathaniel B. Nichols. It is performed by setting the I (integral) and D (derivative) gains to zero. The 'P' (proportional) gain, ${\displaystyle K_p}$ is then increased (from zero) until it reaches the ultimate gain${\displaystyle K_u}$, which is the largest gain at which the output of the control loop has stable and consistent oscillations; higher gains than the ultimate gain ${\displaystyle K_u}$ have diverging oscillation. ${\displaystyle K_u}$ and the oscillation period ${\displaystyle T_u}$ are then used to set the P, I, and D gains depending on the type of controller used and behaviour desired:

The ultimate gain ${\displaystyle (K_u)}$ is defined as 1/M, where M = the amplitude ratio, ${\displaystyle K_i=K_p/T_i}$ and ${\displaystyle K_d=K_p{T}_d}$.

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“PID auto-tuning” or “PID self-tuning” controllers are designed to simplify matters by choosing their own PID tuning parameters based on some sort of automated analysis of the controlled process’s behavior. Theoretically, the most basic PID auto-tuners simply automate the manual PID tuning procedures: force a change in the controller effort (bump or step tests), observe. Mar 17, 2020  The PID Autotuning VI helps in refining the PID parameters of a control system. Once an educated guess about the values of P, I and D have been made, the PID Autotuning VI helps in refining the PID parameters to obtain better response from the control system. Jul 20, 2017  The gcode for the PID autotuning is the M303 command. After that you will have to define the heating element you want to do the tuning for. The S behind that stands for the temperature you want to do the PID tuning. The c stands for the cycles you want to do. The more cycles, the better the PID values. I usualy take 8 cycles.

These 3 parameters are used to establish the correction ${\displaystyle u(t)}$ from the error ${\displaystyle e(t)}$ via the equation:

${\displaystyle u(t)=K_p\left(e(t)+\frac{1}{T_i}{\int }_0^{t}e(\tau )d\tau +T_d\frac{de(t)}{dt}\right)}$

which has the following transfer function relationship between error and controller output:

${\displaystyle u(s)=K_p\left(1+\frac{1}{T_{i}s}+T_{d}s\right)e(s)=K_p\left(\frac{T_d{T}_i{s}^2+T_{i}s+1}{T_{i}s}\right)e(s)}$

Evaluation[edit]

The Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a 'quarter wave decay'. This is an acceptable result for some purposes, but not optimal for all applications.

This tuning rule is meant to give PID loops best disturbance rejection.^[2]

It yields an aggressive gain and overshoot^[2] – some applications wish to instead minimize or eliminate overshoot, and for these this method is inappropriate. In this case, the equations from the row labelled 'no overshoot' can be used to compute appropriate controller gains.

References[edit]

1. ^Ziegler, J.G & Nichols, N. B. (1942). 'Optimum settings for automatic controllers'(PDF). Transactions of the ASME. 64: 759–768.Cite journal requires journal= (help)
2. ^ ^abcdefZiegler–Nichols Tuning Rules for PID, Microstar Laboratories

• Bequette, B. Wayne. Process Control: Modeling, Design, and Simulation. Prentice Hall PTR, 2010. [1]
• Co, Tomas; Michigan Technological University (February 13, 2004). 'Ziegler–Nichols Closed Loop Tuning'. Retrieved 2007-06-24.

Ni Auto Tune Pid Codes

External links[edit]

PID tuning refers to the parameters adjustment of a proportional-integral-derivative control algorithm used in most repraps for hot ends and heated beds.

PID needs to have a P, I and D value defined to control the nozzle temperature. If the temperature ramps up quickly and slows as it approaches the target temperature, or if it swings by a few degrees either side of the target temperature, then the values are incorrect.

To run PID Autotune in Marlin and other firmwares, run the following G-code with the nozzle cold:

This will heat the first nozzle (E0), and cycle around the target temperature 8 times (C8) at the given temperature (S200) and return values for P I and D. An example from http://www.soliwiki.com/PID_tuning is:

For Marlin, these values indicate the counts of the soft-PWM power control (0 to PID_MAX) for each element of the control equation. The softPWM value regulates the duty cycle of the f=(FCPU/16/64/256/2) control signal for the associated heater. The proportional (P) constant Kp is in counts/C, representing the change in the softPWM output per each degree of error. The integral (I) constant Ki in counts/(C*s) represents the change per each unit of time-integrated error. The derivative (D) constant Kd in counts/(C/s) represents the change in output expected due to the current rate of change of the temperature. In the above example, the autotune routine has determined that to control for a temperature of 200C, the soft PWM should be biased to 92 + 19.56*error + 0.71 * (sum of errors*time) -134.26 * dError/dT. The 'sum of errors*time' value is limited to the range +/-PID_INTEGRAL_DRIVE_MAX as set in Configuration.h. Commercial PID controllers typically use time-based parameters, Ti=Kp/Ki and Td=Kd/Kp, to specify the integral and derivative parameters. In the example above: Ti=19.56/0.71=27.54s, meaning an adjustment to compensate for integrated error over about 28 seconds; Td=134.26/19.56=6.86s, meaning an adjustment to compensate for the projected temperature about 7 seconds in the future.

The Kp, Ki, and Kd values can be entered with:

In the case of multiple extruders (E0, E1, E2) these PID values are shared between the extruders, although the extruders may be controlled separately. If the EEPROM is enabled, save with M500. If it is not enabled, save these settings in Configuration.h.

For the bed, use:

and save bed settings with:

For manual adjustments:

• if it overshoots a lot and oscillates, either the integral gain needs to be increased or all gains should be reduced
• Too much overshoot? Increase D, decrease P.
• Response too damped? Increase P.
• Ramps up quickly to a value below target temperature (0-160 fast) and then slows down as it approaches target (160-170 slow, 170-180 really slow, etc) temperature? Try increasing the I constant.

See also Wikipedia's PID_controller and Zeigler-Nichols tuning method. Marlin autotuning (2014-01-20, https://github.com/ErikZalm/Marlin/blob/Marlin_v1/Marlin/temperature.cpp#L250 ) uses the Ziegler-Nichols 'Classic' method, which first finds a gain which maximizes the oscillations around the setpoint, and uses the amplitude and period of these oscillations to set the proportional, integral, and derivative terms.

Saving PID settings

You will need to commit your changes to EEPROM or your configuration.h file for them to be permanent.

To save to EEPROM use:M500

Modifying Marlin Autotune parameters

The default Marlin M303 calculates a set of Ziegler-Nichols 'Classic' parameters based on the Ku (Ultimate Gain) and the Pu (Ultimate Period), where the Ku and Pu are determined by searching for a biased BANG-BANG oscillation around an average power level that produces oscillations centered on the setpoint. (See https://github.com/ErikZalm/Marlin/blob/Marlin_v1/Marlin/temperature.cpp#L238 )

You can transform these 'Classic' parameters into the Zeigler-Nichols 'Some Overshoot' set with:

Or the Z-N 'No Overshoot' set:

Note that the multipliers for the autotuning parameters each have only one significant digit (implying 10% maximum precision), and that the other schemes differ by factors of 2 or 3. PID autotuning and tuning isn't terribly precise, and changes in the parameters by factors of 5 to 50% are perfectly reasonable.

Pid Tune G Code

In Marlin, the parameters that control and limit the PID controller can have more significant effects than the popular PID parameters. For example, PID_MAX and PID_FUNCTIONAL_RANGE, and PID_INTEGRAL_DRIVE_MAX can each have dramatic, unexpected effects on PID behavior. For instance, a too-large PID_MAX on a high-power heater can make autotuning impossible; a too-small PID_FUNCTIONAL_RANGE can cause odd reset behavior; a too large PID_FUNCTIONAL_RANGE can guarantee overshoot; and a too-small PID_INTEGRAL_DRIVE_MAX can cause droop.

PID Tuning by Commercial PID

If you have access to a PID controller unit and a compatible thermal probe that fits down into your hotend, you can use them to tune your PID and calibrate your thermistor.

Connection of the output of the PID to your heater varies depending on your electronics. (I used a 1K2:4K7 voltage divider to drop the 22V output of the PID to 5V for my bread-boarded VNP4904)

After the PID is connected you can use it to measure the nozzle temperature and correlate it with the thermistor readings and resistances.

Conversion from the commercial PID values of kP in %fullscale, Ti in seconds, and Td in seconds is as follows:

As an example, a $30 MYPIN TD4-SNR 1/16 DIN PID temperature controller and $10 type-K probe can hold a particular Wildseyed hotend with a 6.8ohm resistor at 185.0C+/-0.1C using 12V with about a 43.7% duty cycle, or 0.437*12*12/6.8=9.25W. Invoking the autotuning on the controller produces these parameters: P=0.8%/C, I=27s, D=6.7s. Converting these to Marlin PID values:

Differences between the results can be caused by physical differences in the systems, (e.g: the thermocouple is closer to the heater than the thermistor,) or by different choices of autotuning parameters (e.g.: the MYPIN TD4 autotuning process is a proprietary black box, while Marlin uses Zeigler-Nichols 'Classic' method.)

The Temperature/resistance table below was developed by using the PID+thermocouple system to set temperatures on a sample hotend by controlling the heater while measuring the thermistor resistance. These values can be used with Nophead's http://hydraraptor.blogspot.com/2012/11/more-accurate-thermistor-tables.html or Marlin's https://github.com/ErikZalm/Marlin/blob/Marlin_v1/Marlin/createTemperatureLookupMarlin.py to create calibrated thermistor tables. The PID column collects the autotuning values produced by the PID controller for the indicated temperature. The kP,Ki,Kd lists the converted parameters.