A stepwise method for tuning PI controllers using ITAE criteria

Christober Vinoth Raj, Honeywell

July 25, 2012

Christober Vinoth Raj, Honeywell

Analysis for unusual step response
1) To find Process time constant (TC): Draw a line parallel to the initial gradient and the TC is where that crosses the steady state value of the response

Click on image to enlarge.

Figure 7. Analysis of unusual step response
Calculation of tuning constants
The tuning constants are calculated differently depending on whether P, PI or PID is used in the control.

The values of the constants A and B are different (Table 1 below) depending on whether P only, PI or PID control is used, and also whether it is desired to respond better to set point changes or load changes.

Table 1. Constants A and B for P, PI, PID control [8][9]
Open loop analysis in an FOC
1) Steps mentioned in Open Loop Step #5 are followed to get the open loop response

2) Controller Sample time : 50 Micro seconds

3) Figure 7 is the zoomed in plot of open loop response [experimental setup]

4) Process gain = ΔPV /ΔCV = 2711/ (0.4 – 0.1) = 9036

5) Measure the time of 25% Max value [ Td25 = 0.25 * 169 = 42.25] = 42.25 * 50 microseconds = 2.11 ms

6) Measure the time of 75% Max value [ Td75 = 0.75 * 169 = 126.75] = 126.75 * 50 microseconds = 6.33 ms

7) Calculate the time constant, TC where TC = 0.9*(6.33 – 2.11) = 3.798

8) Calculate the dead time, DT = (6.33 ms – 50 microseconds) – (1.4 * 3.798) + 50 microseconds = -5.31087

9) Dead time is a negative value. Stop the analysis and proceed as per earlier in analysis for unusual step response.

10) TC = 130 * 50 microseconds (Shown in Figure 8 below) = 6.5 ms,

11) DT = 6.5 * 0.1 = 0.65 ms

12) Now we are ready to calculate the tuning constants as per section 4.5.4

13) P = 0.000527 and I = 0.004315, after substituting the tuning constants, TC and DC values (Set Point change).

Click on image to enlarge.

Figure 8. Calculate TC as per time constraints calculation
The ITAE empirical method described here can be applied to any field oriented control application. Optimal controller gains are obtained through this method even for a high inductive BLDC motor.

Christober Venoth Raj works as a lead research engineer in automation and control solutions business unit at Honeywell, Bangalore. His current activity involves designing condition monitoring for machines and conveyor belts. Prior to joining Honeywell, worked at Infineon Technologies as an embedded software engineer.

References
[1] F.Y.Thomasson, Tuning Guide for basic control loops, 1997 Process control, Electrical & Info. Conf. Proceedings.
[2] Bela G.Leptak, Process control and optimization, Volume 2, 4th edition.
[3] Karl J.Astrom and Tore Hagglund, PID Controllers, 2nd edition.
[4] http://www.automationworld.com/operations-management/pid-tuning; accessed as on 21/12/2011
[5] Cecil L.Smith, Practical Process Control: Tuning and Troubleshooting.
[6] Dale E.Seborb, Thomas F.Edgar, Duncan A.Meelichamp; Process dynamics and control.
[7] Aidan O’Dwyer, PI and PID controller tuning rules for time delay processes: A summary
[8] P.W.Murril, Automatic control of processes, International Textbook Co., 1967.
[9] Rovlra, A.A., Murril P.W and smith, C.L., Tuning controllers for setpoint changes; Instruments and control systems, pp 67-69, 1969