Closed Loop Method

Note: This text is meant to be used with a flow loop simulator.  If you do not see a flow controller above, please click here.

Our goal is to determine the control loop's Ultimate Gain (Ku) and Ultimate Period (Pu), and use them to calculate the tuning parameters.  The Ultimate Gain is the controller gain at which the process variable cycles at a constant amplitude, as shown below in figure C.  The Ultimate Period is the time it takes the process variable to complete one cycle.  To practice, and to get a feel for how this method works, follow the steps below to tune the flow loop above.  Notice the P term is implemented as gain (Kc); the I term, integral,  is in repeats per minute (Ri), and derivative, D, is in minutes (Td).  The controller is reverse acting; the flow control valve is "air to open."  That is, the flow control valve is closed when the controller output is at zero percent.

1. Document the controller's current P, I, and D settings.  Of course, this step is irrelevant in this demonstration but should be observed in the real world.
2. If the controller is in automatic, switch it to manual.
3. Set the controller's integral (Ri) and derivative (Td) parameters to their minimum settings.  Remember, if integral is implemented as "minutes per repeat," its minimum setting is a very large number.  In this case, however, integral is implemented as "repeats per minute," so zero is ideal.  Zero is ideal for derivative also.
4. Set the controller's gain (Kc) to a relatively small value.  When the technician or engineer is tuning an existing control loop, the controller gain as found is usually a good initial value.  This process loop is very responsive, so a gain of one should be a good starting point.
5. With the controller in manual, set the controller's output (OP) to a value that maintains the process variable (PV) close to its normal operating point.  In this case, manipulate the controller output (OP) to achieve a flow rate (PV) of about fifty.  The astute technician or engineer may notice a deficiency here.  Do you?  After you accomplish this step, click here (future) for the answer.
6. When the process variable  is stable, switch the controller to automatic.
7. Step change the controller set point (SP) ten percent and observe the process variable.  The process variable may be easier to observe if the output trace is switched off.  To do so, remove the check mark beside the OP label.
8. Analyze the process  variable:
   • If the process variable does not cycle or cycles with decreasing amplitude, as with figure A, switch the controller to manual, increase the controller's gain, and return to step five.  (Use the initial gain setting, one in this case, as the initial gain step size.  Otherwise, increase gain by one half the previous increase or decrease in gain.  In other words, if in the previous step you decreased the gain by .5, increase the gain by .25 in this step.) 
   • If the process variable cycles with increasing amplitude, as with figure B, switch the controller to manual, decrease the controller's gain, and return to step five.  (Decrease the gain by one half the previous increase or decrease in gain.  In other words, if in the previous step you increased the gain by 1, decrease the gain by .5 in this step.) 
   • Otherwise, the process variable should be cycling with a constant amplitude, similar to figure C, which is the goal.  Document the controller's gain as Ku.  Determine the period of the cycling process variable and document it as Pu.  The engineer or technician may simply time one cycle to determine Pu; however, it is usually easier and more accurate to time several cycles and calculate Pu.  Pu equals elapsed time, in minutes, divided by number of cycles.  For instance, the distance between each gray vertical line on the chart above represents one minute, so if the process variable cycles seven time between two successive vertical lines, the period, Pu, is 1 minute divided by 7 cycles, which equals .1429 minutes.  Switch the controller to manual and stabilize the process.  Since this is a flow loop, and derivative should never be implemented in a flow loop, we will implement gain and integral only.  From the tables below, use the formula Kc = 0.45 * Ku to calculate the controller's gain setting, and Ri = 1.2 / Pu to calculate the controller's integral setting.  Input the new settings and test the loop.  See the bottom of this page for one individual's results.

Clabberhead used the Ultimate Method to determine the following PID settings for the above flow controller:
Kc = .844
Ri = 8.4
Td = 0