Computational Optimization and Applications

, Volume 38, Issue 1, pp 173–190 | Cite as

Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria

  • Hans D. MittelmannEmail author
  • Gautam Pendse
  • Daniel E. Rivera
  • Hyunjin Lee


System identification is an important means for obtaining dynamical models for process control applications; experimental testing represents the most time-consuming step in this task. The design of constrained, “plant-friendly” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear problem example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has great benefits compared to multisine signals that minimize crest factor. The constrained nonlinear optimization problems that are solved represent challenges even for high-performance optimization software.


System identification Process control Constrained optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bayard, D.: Statistical additive uncertainty bounds using Schroeder-phased input design. Appl. Math. Comput. 58, 169–198 (1993) zbMATHCrossRefGoogle Scholar
  2. 2.
    Byrd, R., Gilbert, J., Nocedal, J.: A trust region method based on interior point techniques for nonlinear programming. Math. Program. A 89, 149–185 (2000) zbMATHCrossRefGoogle Scholar
  3. 3.
    Byrd, R., Hribar, M., Nocedal, J.: An interior point method for large scale nonlinear programming. SIAM J. Optim. 9, 877–900 (1999) zbMATHCrossRefGoogle Scholar
  4. 4.
    Chien, I.-L., Ogunnaike, B.A.: Modeling and control of high-purity distillation columns. In: 1992 AIChE Annual Meeting, Miami Beach, FL, paper 2a, 1992 Google Scholar
  5. 5.
    Cybenko, G.: Just-in-time learning and estimation. In: Bittani, S., Picci, G. (eds.) Identification, Adaptation, Learning. NATO ASI, pp. 423–434. Springer, Berlin (1996) Google Scholar
  6. 6.
    Drud, A.S.: A large scale GRG code. ORSA J. Comput. 6, 207–216 (1994) zbMATHGoogle Scholar
  7. 7.
    Duym, S., Schoukens, J.: Design of excitation signals for the restoring force surface method. Mech. Syst. Signal Process. 9(2), 139–158 (1995) CrossRefGoogle Scholar
  8. 8.
    Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239–269 (2002) zbMATHCrossRefGoogle Scholar
  9. 9.
    Godfrey, K. (ed.): Perturbation Signals for System Identification. Prentice-Hall International, Hertfordshire (1993) zbMATHGoogle Scholar
  10. 10.
    Godfrey, K., Barker, H., Tucker, A.: Comparison of perturbation signal for linear system identification in the frequency domain. IEEE Proc. Control Theory Appl. 146, 535 (1999) CrossRefGoogle Scholar
  11. 11.
    Guillaume, P., Schoukens, J., Pintelon, R., Kollár, I.: Crest-factor minimization using nonlinear Chebyshev approximation methods. IEEE Trans. Inst. Meas. 40(6), 982–989 (1991) CrossRefGoogle Scholar
  12. 12.
    Hussain, M.: Review of the applications of neural networks in chemical process control-simulation and on-line implementation. Artif. Intell. Eng. 13(1), 55–68 (1999) CrossRefGoogle Scholar
  13. 13.
    Lee, H., Rivera, D., Mittelmann, H.: Constrained minimum crest factor multisine signals for plant-friendly identification of highly interactive systems. In: Proceedings of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, The Netherlands, pp. 947–952, 2003 Google Scholar
  14. 14.
    Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice-Hall, Englewood Cliffs (1999) Google Scholar
  15. 15.
    Matoušek, J.: Geometric Discrepancy: an Illustrated Guide. Springer, Berlin (1999) Google Scholar
  16. 16.
    Mittelmann, H.: 2004, Benchmarks for optimization software.
  17. 17.
    Morari, M., Zafiriou, E.: Robust Process Control. Prentice-Hall, Englewood Cliffs (1988) Google Scholar
  18. 18.
    Pendse, G.: Optimization-based formulations using the Weyl criterion for input signal design in system identification. Master’s thesis, Arizona State University, Tempe, AZ, USA (2004) Google Scholar
  19. 19.
    Rivera, D., Lee, H., Braun, M., Mittelmann, H.: Plant-friendly system identification: a challenge for the process industries. In: Proc. of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, Netherlands, pp. 917–922, 2003 Google Scholar
  20. 20.
    Sriniwas, G.R., Arkun, Y., Chien, I.-L., Ogunnaike, B.: Nonlinear identification and control of a high-purity distillation column: a case study. J. Proc. Control 5, 149 (1995) CrossRefGoogle Scholar
  21. 21.
    Stenman, A.: Model on demand: algorithms, analysis and applications. Ph.D. thesis, Department of Electrical Engineering, Linköping University, Sweden (1999) Google Scholar
  22. 22.
    Weischedel, K., McAvoy, T.: Feasibility of decoupling in conventionally controlled distillation column. Ind. Eng. Chem. Fund. 19, 379–384 (1980) CrossRefGoogle Scholar
  23. 23.
    Weyl, H.: Über die Gleichverteilung von Zahlen mod eins. Math. Ann. 77, 313–352 (1916) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hans D. Mittelmann
    • 1
    Email author
  • Gautam Pendse
    • 1
  • Daniel E. Rivera
    • 2
  • Hyunjin Lee
    • 2
  1. 1.Department of Mathematics and StatisticsArizona State UniversityTempeUSA
  2. 2.Control Systems Engineering Laboratory, Department of Chemical EngineeringArizona State UniversityTempeUSA

Personalised recommendations