A method for optimisation of proportional–integral–derivative controller parameters and measurement filter time constant is presented. The method differs from the traditional approach in that the controller and filter parameters are simultaneously optimised, as opposed to standard, sequential, design. Control performance is maximised through minimisation of the integrated absolute error caused by a unit step load disturbance. Robustness is achieved through $H ∞$ constraints on sensitivity and complementary sensitivity. At the same time, noise attenuation is enforced by limiting either the $H 2$ or $H ∞$ norm of the transfer function from measurement noise to control signal. The use of exact gradients makes the synthesis method faster and more numerically robust than previously proposed alternatives.

References

1. 1)
  - 10. Balchen, J.G.: ‘A performance index for feedback control systems based on the fourier transform of the control deviation’, Acta Polytechn. Scandinavica, 1958, 247, pp. 1–18.
2. 2)
  - 19. Garpingar, O., Hägglund, T.: ‘A software tool for robust PID design’. 17th IFAC-World Congress, Seoul, Korea, July 2008.
3. 3)
  - 1. Hast, M., Hägglund, T.: ‘Optimal proportional–integral–derivative set-point weighting and tuning rules for proportional set-point weights’, IET Control Theory Appl., 2015, 9, (15), pp. 2266–2272.
4. 4)
  - 20. Åström, K.J., Panagopoulos, H., Hägglund, T.: ‘Design of PI controllers based on non-convex optimization’, Automatica, 1998, 34, (5), pp. 585–601.
5. 5)
  - 3. Larsson, P.-O., Hägglund, T.: ‘Comparison between robust PID and predictive PI controllers with constrained control signal noise sensitivity’. Conf. on Advances in PID Control. IFAC, Brescia, Italy, 2012.
6. 6)
  - 9. Kristiansson, B., Lennartson, B.: ‘Evaluation of simple tuning of PID controllers with high-frequency robustness’, J. Process Control, 2006, 16, (2), pp. 91–102.
7. 7)
  - 12. Leva, A., Maggio, M.: ‘A systematic way to extend ideal PID tuning rules to the real structure’, J. Process Control, 2011, 21, (1), pp. 130–136.
8. 8)
  - 11. Lennartson, B.: ‘Multi criteria hinf optimal PID controllers from an undergraduate perspective’. IFAC Conf. on Advances in PID Control, Brescia, Italy, March 2012.
9. 9)
  - 4. Šekara, T.B., Mataušek, M.R.: ‘Optimization of PID controller based on maximization of the proportional gain under constraints on robustness and sensitivity to measurement noise’, IEEE Trans. Autom. Control, 2009, 54, (1), pp. 184–189.
10. 10)
  - 2. Åström, K.J., Hägglund, T.: ‘Advanced PID control’ (ISA - The Instrumentation, Systems, and Automation Society, Research Triangle Park, NC 27709, 2006).
11. 11)
  - 26. Hast, M., Åström, K.J., Bernhardsson, B., et al: ‘Pid design by convex-concave optimization’. 2013 European Control Conf., Zürich, Switzerland, July 2013.
12. 12)
  - 24. Esch, J., Knings, T., Ding, S.X.: ‘Optimal performance tuning of a PI-controller for an integrator plant with uncertain parameters as a convex optimisation problem’. 52nd Conf. on Decision and Control, 2013, pp. 1977–1982.
13. 13)
  - 16. Micić, A.D., Mataušek, M.R.: ‘Optimization of PID controller with higher-order noise filter’, J. Process Control, 2014, 24, (5), pp. 694–700.
14. 14)
  - 14. Skogestad, S.: ‘Simple analytic rules for model reduction and PID controller tuning’, J. Process Control, 2003, 13, (4), pp. 291–309.
15. 15)
  - 25. Gerry, J.P.: ‘Conditionally stable tuning of PI and PID controllers on common processes’. American Control Conf., 1984, pp. 512–517.
16. 16)
  - 23. Hara, S., Iwasaki, T., Shiokata, D.: ‘Robust PID control using generalized KYP synthesis: direct open-loop shaping in multiple frequency ranges’, IEEE Control Syst., 2006, 26, (1), pp. 80–91.
17. 17)
  - 18. Grimholt, C., Skogestad, S.: ‘Improved optimization-based design of PID controllers using exact gradients’. European Symp. on Computer Aided Process Engineering, Copenhagen, Denmark, June 2015.
18. 18)
  - 7. Romero Segovia, V., Hägglund, T.: ‘Measurement noise filtering for PID controllers’, J. Process Control, 2014, 24, (4), pp. 299–313.
19. 19)
  - 5. Panagopoulos, H., Åström, K.J., Hägglund, T.: ‘Design of PID controllers based on constrained optimisation’, IEEE Proc. Control Theory Appl., 2002, 149, (1), pp. 32–40.
20. 20)
  - 13. Romero Segovia, V., Hägglund, T., Åström, K.J.: ‘Measurement noise filtering for common PID tuning rules’, Control Eng. Pract., 2014, 32, pp. 43–63.
21. 21)
  - 22. Lipp, T., Boyd, S.: ‘Variations and extension of the convex–concave procedure’, Optim. Eng., 2014, 17, (2), pp. 1–25.
22. 22)
  - 6. Garpinger, O., Hägglund, T.: ‘Software-based optimal PID design with robustness and noise sensitivity constraints’, J. Process Control, 2015, 33, pp. 90–101.
23. 23)
  - 8. Kristiansson, B., Lennartson, B.: ‘Robust and optimal tuning of PI and PID controllers’, IEEE Proc. Control Theory Appl., 2002, 149, (1), pp. 17–25.
24. 24)
  - 15. Åström, K.J., Hägglund, T.: ‘Revisiting the Ziegler–Nichols step response method for PID control’, J. Process Control, 2004, 14, pp. 635–650.
25. 25)
  - 17. Larsson, P.-O., Hägglund, T.: ‘Control signal constraints and filter order selection for PID controllers’. Proc. of American Control Conf., San Francisco, California, USA, 2011.
26. 26)
  - 21. Garpinger, O.‘Optimal PI and PID parameters for a batch of benchmark process models representative for the process industry’. Dept. Automatic Control, Lund University, Sweden, Technical Report 7645, 2015.

Simultaneous design of proportional–integral–derivative controller and measurement filter by optimisation

References

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