Adjusting Source Cell PID Values
For adjusting PID values on the Eurotherm
Make sure you're changing the right PID values! If there is gain scheduling set, you will need to go into full access mode of the Eurotherm to adjust PID2 values.
Monkey Patch Method
If the campaign has gone on long and you notice cell (base) instability, this may be due to the change of the thermal coupling coefficient between the cell heating zones due semi-depleted crucible. Before performing the Ziegler Nichols method on the base/tip (which takes forever), try reducing the tip to base delta (keep the approximately the same base temperature because that determines your BEP). Monitor the temp and if it seems quasi-stable, then monitor the Sorenson voltage/current as AMBER's update time is TOO SLOW to see the undulations we are concerned with for crystal growth. If that doesn't work, maybe increase the delta? Or do the ZN method and get ready to be bored out of your mind.
Closed Loop Cycling Method
By placing a Proportional-only controller (no Integral or Derivative terms in oscillation by setting the Proportional Band to a very small value, the control loop will cycle with a characteristic frequency (Figure 1). This characteristic frequency will be a very accurate representation of the system‚ Äôs responsiveness and therefore can be used to derive the controller time constants.
To outline procedure:
Eliminate Integral and Derivative action from the controller
Reduce the Proportional Band until the control loop oscillates. Measure the period of oscillation, T.
Widen the Proportional Band until the process is just slightly unstable. This value of Proportional Band, is referred to as the point of ultimate sensitivity.
Refer to the Table 1 for values of Pb, TI and TD.
Table 1: Closed-Loop Cycling Tunning Constants
Controller | Proportional Band Pb | Integral Time TI | Derivative Time TD |
Proportional Only (P) | 2P | NA | NA |
Proportional & Integral (P I) | 2.2P | 0.8T | NA |
Proportional, Integral, and Derivative (P I D) | 1.67P | 0.5T | 0.12T |
Again, the settings given in the chart establish control with a 4:1 decay ratio which may give too much overshoot for some processes. Table 2 gives guidelines for altering these values, when using Proportional, Integral and Derivative terms.
'Table 2: Varying Response - Tuning Constants !'
Controller | Proportional Band Pb | Integral Time TI | Derivative Time TD |
Under-damped | P | 0.5T | 0.125T |
Critically-damped | 1.5P | T | 0.167T |
Over-damped | 2P | 1.5T | 0.167T |