Hierarchical mathematical models of complex plants on the basis of power boiler example

• Autorzy: Stanisławski W. , Rydel M.
• Języki publikacji: EN

Abstrakty

EN

The methodology of hierarchical linearized mathematical models construction of complex plants to control purposes is presented in the paper. Thanks to the methodology, the one high order model (flat, one level model), is replaced by a collection of models, which are placed at different hierarchy levels. The models represent dynamic processes typical for each hierarchy level, and omit fast dynamic processes significant at lower levels. The higher is hierarchy level, the slower dynamic processes is described by the model and the lower is order of the models. Multi-level model structure gives possibility of dynamic properties analysis by application of aggregation procedure. One of the principal aggregation procedure is reduction of models at individual levels of hierarchical structure. Such approach enables creating a reduced hierarchical model including a collection of models at every level of hierarchy, characterized by various adequacy scopes and accuracy of the plant features approximation. The paper presents methodology of hierarchical complex plants models creation on the example of evaporator of the BP-1150 boiler. Each of the subsystem at individual level of model hierarchy is a multi-input and multi-output causal systems.

Słowa kluczowe

EN

once-through steam boiler; reduced hierarchical model; complex model reduction

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2010
• Tom: Vol. 20, no. 4
• Strony: 381--416
• Opis fizyczny: Bibliogr. 36 poz., rys., wzory

Twórcy

autor

Stanisławski W.

autor

Rydel M.

• Control and Computer Engineering, Opole University of Technology, Sosnkowskiego 31, 45-272 Opole, Poland

Bibliografia

• [1] A. ANTOULAS: Approximation of Large-Scale Dynamical System. Society for Industrial and Applied Mathematics, Philadelphia, 2005.
• [2] A. ANTOULAS and D. SORENSEN: Approximation of large-scale dynamical system: An overview. Int. J. of Applied Mathematics and Computer Science, 11(5), (2001), 1093-1121.
• [3] A. ANTOULAS, D. SORENSEN and S. GUGERCIN: A modified low-rank smith method for large-scale lyapunov equations. Numerical Algorithms, 32(1), (2003), 27-55.
• [4] P. BENNER, E. QUINTANA-ORTI and G. QUINTANA-ORTI: Efficient numerical algorithms for balanced stochastic truncation. Int. J. of Applied Mathematics and Computer Science, 11(5), (2001), 1123-1150.
• [5] D. BOLEY: Krylov space methods on state-space control models. Circuits, Systems and Signal Processing, 13(6), (1994), 733-758.
• [6] T.Y. CHIU: Model reduction by the low-frequency approximation balancing method for unstable systems. IEEE Trans. on Automatic Control, 41(7), (1996), 995-997.
• [7] D. ENNS: Model reduction with balanced realizations: An error bound and frequency weighted generalization. In 23rd IEEE Conf. on Decision and Control, (1984), 127-132.
• [8] P. FELDMANN and R.W. FREUND: Efficient linear circuit analysis by pade approximation via the lanczos process. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, 14(5), (1995), 639-649.
• [9] W. GAWRONSKI and J. JUANG: Model reduction in limited time and frequency intervals. Int. J. of Systems Science, 21(2), (1990), 349-376.
• [10] K. GLOVER: All optimal hankel-norm approximations of linear multivariable systems and their l, error bounds. Int. J. of Control, 39(6), (1984), 1115-1193.
• [11] T. GUDMUNDSSON and A. LAUB: Approximate solution of large sparse lyapunov equations. IEEE Trans. on Automatic Control, 39(5), (1994), 1110-1114.
• [12] S. GUGERCIN: An iterative svd-krylov based method for model reduction of largescale dynamical systems. In 44th IEEE Conf. on Decision and Control, (2005), 5905-5910.
• [13] S. GUGERCIN and A. ANTOULAS: A comparative study of 7 algorithms for model reduction. In 39th IEEE Conf. on Decision and Control, 3 (2000), 2367-2372.
• [14] S. GUGERCIN and A. ANTOULAS: A survey of model reduction by balanced truncation and some new results. Int. J. of Control, 77(8), (2004), 748-766.
• [15] M. ILAK and C. ROWLEY: Reduced-order modeling of channel flow using traveling pod and balanced pod. In 3rd AIAA Flow Control Conference, (2006).
• [16] D. IMAEV, M. RYDEL and W. STANISŁAWSKI: Reduction of flow boiler proper models as control objects. In XVI National Automation Conference, (2008), 198-207. (in Polish).
• [17] A. LAUB, M. HEATH, C. PAIGE and R. WARD: Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Trans. on Automatic Control, 32(2), (1987), 115-122.
• [18] J. R. LI and J. WHITE: Reduction of large circuit models via low rank approximate gramians. Int. J. of Applied Mathematics and Computer Science, 11(5), (2001), 1151-1171.
• [19] Y. LIU and B. ANDERSON: Singular perturbation approximation of balanced system. In 28th IEEE Conf. on Decision and Control, 2 (1989), 1355-1360.
• [20] B. MOORE: Principal component analysis in linear systems: Controllability, observability and model reduction. IEEE Trans. on Automatic Control, 26(1), (1981), 17-32.
• [21] G. OBINATA and B. ANDERSON: Model Reduction for Control System Design. Springer-Verlag, London, 2001.
• [22] G. PAPPAS: Hierarchically consistent control systems. IEEE Trans. on Automatic Control, 45(6), (2000), 1144-1160.
• [23] T. PENZL: Algorithms for model reduction of large dynamical systems. Linear Algebra and its Applications, 415 (2006), 322-343.
• [24] L. T. PILLAGE and R.A. ROHRER: Asymptotic waveform evaluation for timing analysis. IEEE Trans on Computer-Aided Design of Integrated Circuits and Systems, 9(4), (1990), 352-366.
• [25] M. RYDEL: Reduction of hierarchical complex objects models based on steram boiler. PhD thesis, Opole University of Technology, Opole, 2008. (in Polish).
• [26] M. RYDEL and W. STANISŁAWSKI: Problems of a complex plant models reduction. Measurement Automation and Monitoring, 2 (2010), 197-200. (in Polish).
• [27] M. G. SAFONOV and R.Y. CHIANG: A schur method for balanced-truncation model reduction. IEEE Trans. on Automatic Control, 34(7), (1989), 729-733.
• [28] W. STANISŁAWSKI: Modelling and Computer simulation of Power Boilers flow boilers. Monograph Studies, 124 Opole, 2001, (in Polish).
• [29] W. STANISŁAWSKI and D. IMAEV: Hierarchical approach to the steam boiler modelling and simulation. In 12th European Simulation Multiconference, (1998), 171-175.
• [30] W. STANISŁAWSKI and W. MINKINA: Verification of mathematic model of steam boiler of bp-1150 boiler, for control purposes. Measurements Automation Robotics, 3 (1999), 7-10, (in Polish).
• [31] W. STANISŁAWSKI and M. RYDEL: Aggregation of hierarchial models of complex control objects based on a power plant. In 11th Int. Conf. on Methods and Models in Automation and Robotics, (2005), 985-990.
• [32] W. STANISŁAWSKI and M. RYDEL: Hierarchical models of complex control objects. In XV National Automation Conference, (2005), 149-154, (in Polish).
• [33] A. VARGA: Balancing-free square-root algorithm for computing singular perturbation approximations. In 30th IEEE Conf. on Decision and Control, 2 (1991), 1062-1065.
• [34] G. WANG, V. SREERAM and W. Q. LIU: A new frequency-weighted balanced truncation method and an error bound. IEEE Trans. on Automatic Control, 44(9), (1999), 1734-1737.
• [35] K. WILLCOX and J. PERAIRE: Balanced model reduction via the proper orthogonal decomposition. AIAA Journal, 40(11), (2002), 2323-2330.
• [36] P. WORTELBOER and O. BOSGRA: Generalized frequency weighted balanced reduction. In 31st IEEE Conf. on Decision and Control, 3 (1992), 2848-2849.