A stepwise method for tuning PI controllers using ITAE criteria

Christober Vinoth Raj, Honeywell

July 25, 2012

Christober Vinoth Raj, Honeywell

How to get open loop step response in FOC
The previous steps in the process I am describing are related to field oriented control as follows:

1) Set point1(SP1) is made equal to the controller variable (CV1) (i.e.) SP1 = CV1

2) Id and Iq (Output of FwPark transform) is left open.

3) Setpoint1 is given a step value of 0.1 and the process variable (PV) [Speed] is monitored until a steady state is reached

4) Step the SP1 value to 0.4 and wait for the process to stabilize

5) Step the process again, the same magnitude as step 2 (0.1), but this time in a reverse direction.

6) Repeat the above steps for Setpoint2 also.

7) Open loop response to step input 0.4 (Step 4) is shown in Figure 4 below.

Click on image to enlarge.

Figure 4. Open loop step response
Open Loop Step #5. Open loop analysis of the obtained step response is summarized as follows:

1) Measure Δ PV as per Figure 3. This is the amount that the PV changed when we stepped the CV for the second time.

2) Measure ΔCV from the CV trace as per Figure 3. This is the size of the second step of the controller output.

3) Calculate the process gain (PG). This is calculated as PG = ΔPV/ΔCV

4) Look at the CV trace and determine the "time of step". We'll label this T0. This is the time value on the x axis where your step input to the controller begins as per Figure 5 below.

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Figure 5. Tracing the curve to a noisy response
5) Determine the time at which the PV is at 25% of its max value. It is denoted as Td25.

6) Determine the time at which the PV is at 75% of its max value. It is denoted as Td75.

7) Calculate the process time constant, TC where TC = 0.9*(T75 – T25)

8) Calculate the dead time, DT where DT = (TC75 – T0) – (1.4 * TC) + Controller’s Update time

9) Real time signal might look like the blue color response as in Figure 5 above. Draw a curve of best fit as shown in red color.

10) Stop the analysis if negative dead time is observed. It may be due to the unusual step response obtained through experiments as seen in Figure 6 below[9].

Click on image to enlarge.

Figure 6. Unusual Step Response