===== Ziegler-Nichols Loop Tuning =====
The Ziegler-Nichols loop tuning protocol(([[https://staff.guilan.ac.ir/staff/users/chaibakhsh/fckeditor_repo/file/documents/Optimum%20Settings%20for%20Automatic%20Controllers%20(Ziegler%20and%20Nichols,%201942).pdf|Optimum Settings for Automatic Controllers, by J.G. Zieger and N. B. Nichols]] and\\
[[https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method|Wikipedia]])) is a simple method to establishing the loop parameter values for a PI or PID control loop. This protocol is designed to optimize the loop for disturbance rejection.\\ 
==== Links ====
Click here for the [[slice:qt|SLICE-QTC Manual]].\\
Click here for the [[slice:quick_start_qt|SLICE-QTC Quick Start Guide]].\\
Click here for the [[slice:qt:API|SLICE-QTC API]].\\
Click here for the [[https://www.vescent.com/products/electronics/slice/slice-qt-four-channel-temperature-controller/|SLICE-QTC web page]].\\
Click here for the [[https://github.com/Vescent|Github page for SLICE-QTC GUI]].\\
Click here for the [[https://github.com/Vescent/SLICE-QT-Firmware-Upgrade|Github page for SLICE-QTC firmware revisions]].\\
Click here for a [[https://youtu.be/jCuHNOW5q8c|Video Tutorial]].\\
==== Instructions ====
<WRAP center round box 60%>
| {{ :warning-sign.png?50&nolink }}  | There is the possibility for the loop to go unstable at too high gain.  Use caution as gain is increased.  |
</WRAP>

  - From the Home Screen, touch the Channel icon for the loop to be tuned
  - Touch Settings > PID Params
  - Choose a Set Point temperature
  - Set Proportional Gain (K<sub>P</sub>) to 0
  - Turn off Integral and Differential portions of the loop (T<sub>I</sub> & T<sub>D</sub>, respectively)
  - While monitoring the error in temperature on rolling graph on the SLICE-QTC display or an  [[slice:qt#front-panel_inputs_outputs|external oscilloscope]], **slowly** increase (~10% per increment) K<sub>P</sub> until the error begins to oscillate
  - Use the {{slice:graph_scale_x.gif}} and {{slice:graph_scale_y.gif}} icons, to scale displayed response appropriately
  - Use the {{slice:graph_pause.gif}} icon to pause the graph
    - Note: the pause icon only pauses the graph, not the servo control
  - Note K<sub>P</sub> where oscillations of increasing amplitude begin; this is K<sub>P, cr</sub>, the critical proportional gain.
  - Use the Cursors enabled by touching the {{slice:cursors.gif}} icon to measure the period of oscillation, T<sub>cr</sub>
        - You can use the two rotary knobs or touch & drag the cursors on the touch screen
  - Use the following table to set the values of K<sub>P</sub>, T<sub>I</sub>, and T<sub>D</sub>

<WRAP center round box 60%><tabcaption Z-N |Ziegler-Nichols loop values>
| **Type of Control Loop**  |  K<sub>P</sub>           | T<sub>I</sub>         | T<sub>D</sub>          |
| **PI**                    |  0.45•K<sub>P, cr</sub>  |  0.83•T<sub>cr</sub>  | 0                      |
| **PID**                   |  0.6•K<sub>P, cr</sub>   |  0.5•T<sub>cr</sub>   |  0.125•T<sub>cr</sub>  |
</tabcaption></WRAP>