A new model reduction method, based on frequency fitting, is proposed for single-input discrete-time singular (non-causal) systems. The reduced-order models are obtained by minimising the least square frequency response error between the original system and the reduced-order model. Finally, the method is illustrated by a numerical example and is compared with other related techniques.
Inspec keywords: frequency response; reduced order systems; discrete time systems; least squares approximations
Other keywords:
Subjects: Discrete control systems; Control system analysis and synthesis methods; Simulation, modelling and identification
References
-
-
1)
- L.Q. Zhang , J. Lam , Q.L. Zhang . Optimal model reduction of discrete-time descriptor systems. Int. J. Syst. Sci. , 5 , 575 - 583
-
2)
- C. Sun , J. Hahn . Reduction of stable differential-algebraic equation systems via projections and system identification. J. Process Control , 639 - 650
-
3)
- S. Sunder , R.P. Ramachandran . A unified and efficient least-squares design of linear phase nonrecursive filters. Signal Process. , 41 - 53
-
4)
- W.Q. Liu , V. Sreeram . Model reduction of singular systems. Int. J. Syst. Sci. , 10 , 1205 - 1215
-
5)
- S. Xu , J. Lam . H∞ model reduction for discrete-time singular systems. Syst. Control Lett. , 121 - 133
-
6)
- F.L. Lewis , M.A. Christodoulou , B.G. Mertzios , K. Ozcaldiran . Chained aggregation of singular system. IEEE Trans. Autom. Control , 9 , 1007 - 1012
-
7)
- J. Wang , W.Q. Liu , Q.L. Zhang . Model reduction for singular systems via covariance approximation. Opt. Control Appl. Methods , 6 , 263 - 278
-
8)
- S. Gugercin , A.C. Antoulas . Model reduction of large-scale systems by least squares. Linear Algeb. Appl. , 290 - 321
-
9)
- J. Wang , Q.L. Zhang , Q.W. Liu . ℋ∞ Suboptimal Model Reduction for Singular Systems. Int. J. Control , 11 , 992 - 1000
-
10)
- Zhang, Q.L., Sreeram, V., Wang, G., Liu, W.Q.: `ℋ', Proc. Am. Control Conf., 2002, p. 1168–1173.
-
11)
- K. Perev , B. Shafai . Balanced realisation and model reduction of singular systems. Int. J. Syst. Sci. , 6 , 1039 - 1052
-
12)
- S. Xu , J. Lam , W.Q. Liu , Q.L. Zhang . ℋ∞ Model reduction for continuous time singular systems. IEE Proc. , 6 , 637 - 641
-
13)
- M. Jamshidi . (1983) Large scale systems: modeling and Control.
-
14)
- H. Löffler , W. Marquardt . Order reduction of non-linear differential algebraic process models. J. Process Control , 32 - 40
-
15)
- S. Sunder , R.P. Ramachandran . Design of nonrecursive filters satisfying arbitrary magnitude and phase specifications using a least-squares approach. IEEE Trans. Circuits Syst. - II , 11 , 711 - 716
-
16)
- Mohammad, A.A.: `Modeling issues and the Lyapunov equations in dynamical control systems', 1992, PhD, The University of Akron.
-
17)
- L. Petzold , L. Jay , J. Yen . Numerical solution of highly oscillatory ordinary differential equations. Acta Numerica , 437 - 484
-
18)
- L. Dai . (1989) Singular control systems.
-
1)
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