A stepwise method for tuning PI controllers using ITAE criteria
Mapping ITAE into an FOC
The generic control loop as depicted in Figure 1 is translated to FOC control loop as shown in Figure 2 below.
Click on image to enlarge.
Process + sensor: It includes motor, inverter board and the FOC algorithms other than the PI controller.
Process variable: The speed at which the motor rotates is defined as the process variable
Set Point 1(SP1), Controller variable 3(CV3): SP1 is the desired value of Iq. From Speed PI controller perspective this value is called as controller variable 3.
Set Point 2(SP2): SP2 is the desired value of Id
Set Point 3(SP3): SP3 is the desired speed at which the motor rotates
Controller variable 1(CV1): It is the output of Current q PI controller
Controller variable 2(CV2): It is the output of Current d PI controller
A stepwise approach to ITAE PI tuning
Open Loop Step #1. If the system has more than one PI loop, decide on the tuning sequence.
1 - Tune the fastest acting loop first (i.e. the fastest loops are the ones where the PV changes fastest in response to a SP change)
2 - With cascade loops: tune the inner loop first, then the outer loop.
In FOC, tune the Current PI controllers (Id, Iq) first and then the speed PI controller.
Open Loop Step #2. Identify the type of PI algorithm used in the system. This document explains the tuning method for standard or Non Interacting PI algorithm.
Classical Notation:
Laplace Notation:
(Note: For other types of PI algorithms and tuning methods refer to Reference[2])
Open Loop Step #3. Determine the speed of the loop. For every 50 microseconds (Sample time) the controller updates the PI algorithm in the experimental FOC setup.
Open Loop Step #4. This test gives the tuning constants Kp and KI. We will be manipulating the open loop set point and measure selected few open-loop characteristics of the loop. We will then use these characteristics to mathematically calculate the best tuning constants.
To complete this test we need to continue recording both the CV (controller variable) and the PV (process variable).
Procedure to get open loop response is briefly summarized as follows:
1) Wait until the process reaches steady state (i.e. PV is relatively horizontal)
2) Step the SP as much as feasible in a positive direction.
3) Wait for the process to stabilize
4) Step the process again, the same magnitude as step 2, but this time in a reverse direction.
5) Wait for the process to stabilize.
Figure 3 below shows the CV trace and also explains how the process should respond.
Click on image to enlarge.
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