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Pid Auto Tuning In Simulink Tutorial

05.08.2020
Pid Auto Tuning In Simulink Tutorial Average ratng: 6,1/10 7633 votes

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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.

Jul 01, 2019  Auto-tuning: the tuning is done by a software. I implemented Auto-tuning library for position and speed of DC motor (see the source code) using Relay On/Off method. This code is written for PHPoC platform. PID gain from auto-tuning is not the best gain. You can manually fine-tune based on PID gain from auto-tuning. Thing used in this project. PID for Dummies 'I personally have a few hundred dollars worth of books on controllers, PID algorithms, and PID tuning. Since I am an engineer, I stand a chance of understanding some of it. But where do you go if you want to understand PID without a PhD? Finn Peacock has written some very good material about PID which simplifies understanding. Most quadcopter software including Betaflight and KISS allows users to adjust PID values to improve flight performance. In this post I will try to explain what PID is, how it affects stability and handling of a drone, and also share some tips on how to tune PID. The Art of Quadcopter PID Tuning. Quadcopter PID tuning really is an art form.

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:

Parameters of the PID controller and the tuning concept were included in this chapter. Chapter 4 gives a detail result and analysis on the design aspects for the system, which consist of SIMULINK of DC motor and PID controller using MATLAB SIMULINK. Chapter 5 presents the overall conclusion of development of the project. However, PID controller tuning is considered as an obstacle towards having an efficient and stable control system, where most of the PID controllers in practice are tuned by traditional techniques.

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.

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

Tuning

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.

Pid

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.

Temp DutyCycle Thermistor R Commercial PID Kp,Ki,Kd
60.0 6.0 31630
100.0 15.7 10108 1.1%/C, 35.5s, 8.8s 2.81, 0.08, 3.13
120.0 22.5 5802 1.0%/C, 32.0s, 8.0s 2.55, 0.08, 3.14
135.0 26.5 3967
150.0 28.5 2840 1.2%/C, 29.0s, 7.2s 3.06, 0.10, 2.35
170.0 34.0 1829
185.0 43.7 1347 0.8%/C, 27s, 6.7s 2.04, 0.08, 3.28
190.0 45.9 1200 0.8%/C, 26s, 6.5s 2.04, 0.08, 3.18
200.0 51.0 977
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From the series: Getting Started with Simulink

Pid Tuning Methods

Michael Carone, MathWorks
Priyanka Gotika, MathWorks

Pid Auto Tuning

Learn how to quickly change PID gain values using the PID controller block in Simulink®. Update the gain coefficients in your block by adjusting sliders or using the PID automatic tuning tool in Simulink Control Design™, and then instantly see the results of your changes.

Product Focus

Pid Tuning Software

Series: Getting Started with Simulink

Pid Loop Tuning Basics

    Part 1: Building and Simulating a Simple Simulink Model Learn how to get started with Simulink. Explore the Simulink start page and learn how to use some of the basic blocks and modeling components.

    Part 2: Adding a Controller and Plant to the Simulink Model Explore how to create a plant control model using Simulink. The example walks you through how to create both open- and closed-loop systems.

    Part 3: Viewing Simulation Results Visualize simulation results using tools such as the Simulation Data Inspector to view and compare signal data from multiple simulations, or the Dashboard Scope to see your results directly in the Simulink editor.

    Part 4: Tuning a PID Controller Automatically tune PID gain values using the PID controller block and instantly see the results of your changes in Simulink.

    Part 5: Comparing and Saving Simulation Data Use the Simulation Data Inspector in Simulink to compare the results of multiple simulation runs. Open the results in MATLAB Figures to further annotate and add information to your figures.

    Part 6: Managing Your Simulink Model Cooking academy. Use Simulink Projects to manage all the models and documents related to your project. Easily track and work with your files, and allow team members to access all documents.

    Part 7: Adding Components to Your Simulink Model Create subsystems and components in your Simulink model. Create model references so you or your team can work on components independently from the top-level model.

    Part 8: Modeling Continuous and Discrete Systems in One Simulink Model Switch between continuous and discrete domains. This example shows how to update a Simulink PID controller block in order to easily move between the two domains.

    Part 9: Using Templates and Examples Save and share your model as a template so team members can access it right from the Simulink start page. In addition, explore examples that help get you started with models for many applications.