Abstract
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.
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References
Bayard, D.: Statistical additive uncertainty bounds using Schroeder-phased input design. Appl. Math. Comput. 58, 169–198 (1993)
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)
Byrd, R., Hribar, M., Nocedal, J.: An interior point method for large scale nonlinear programming. SIAM J. Optim. 9, 877–900 (1999)
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
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)
Drud, A.S.: A large scale GRG code. ORSA J. Comput. 6, 207–216 (1994)
Duym, S., Schoukens, J.: Design of excitation signals for the restoring force surface method. Mech. Syst. Signal Process. 9(2), 139–158 (1995)
Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239–269 (2002)
Godfrey, K. (ed.): Perturbation Signals for System Identification. Prentice-Hall International, Hertfordshire (1993)
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)
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)
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)
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
Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice-Hall, Englewood Cliffs (1999)
Matoušek, J.: Geometric Discrepancy: an Illustrated Guide. Springer, Berlin (1999)
Mittelmann, H.: 2004, Benchmarks for optimization software. http://plato.asu.edu/bench.html
Morari, M., Zafiriou, E.: Robust Process Control. Prentice-Hall, Englewood Cliffs (1988)
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)
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
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)
Stenman, A.: Model on demand: algorithms, analysis and applications. Ph.D. thesis, Department of Electrical Engineering, Linköping University, Sweden (1999)
Weischedel, K., McAvoy, T.: Feasibility of decoupling in conventionally controlled distillation column. Ind. Eng. Chem. Fund. 19, 379–384 (1980)
Weyl, H.: Über die Gleichverteilung von Zahlen mod eins. Math. Ann. 77, 313–352 (1916)
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Mittelmann, H.D., Pendse, G., Rivera, D.E. et al. Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria. Comput Optim Appl 38, 173–190 (2007). https://doi.org/10.1007/s10589-007-9033-0
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DOI: https://doi.org/10.1007/s10589-007-9033-0