Differential Evolution algorithm for model reduction of SISO discrete systems

Reduction of Single Input Single Output (SISO) discrete systems into Reduced Order Model (ROM), using a conventional and a bio-inspired evolutionary technique is presented in this paper. In the conventional technique, mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method, the original discrete system is first converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively and the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. Finally, the reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Differential Evolution (DE) optimization technique is employed to reduce the higher order model. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

[1]  R. Parthasarathy,et al.  System reduction using Cauer continued fraction expansion about s = 0 and s = ∞ alternately , 1978 .

[2]  Sidhartha Panda,et al.  Evolutionary Techniques for Model Order Reduction of Large Scale Linear Systems , 2009 .

[3]  A. Davies,et al.  Bilinear transformation of polynomials , 1974 .

[4]  M. Milanese,et al.  A note on the derivation and use of reduced-order models , 1976 .

[5]  Sidhartha Panda,et al.  A Combined Conventional and Differential Evolution Method for Model Order Reduction , 2009 .

[6]  Sidhartha Panda,et al.  Model Reduction of Linear Systems by Conventional and Evolutionary Techniques , 2009 .

[7]  Sidhartha Panda,et al.  Differential evolutionary algorithm for TCSC-based controller design , 2009, Simul. Model. Pract. Theory.

[8]  Cemal Ardil,et al.  Reduction of Linear Time-Invariant Systems Using Routh-Approximation and PSO , 2009 .

[9]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[10]  C. Therapos,et al.  A Direct Method for Model Reduction of Discrete systems , 1984 .

[11]  Y. Shamash.  Continued fraction methods for the reduction of discrete-time dynamic systems , 1974 .

[12]  P. Gutman,et al.  Contributions to the model reduction problem , 1982 .

[13]  R. Parthasarathy,et al.  Bilinear transformation by synthetic division , 1984 .

[14]  Ching‐Shieh Hsieh,et al.  Model reduction of linear discrete-time systems using bilinear Schwarz approximation , 1990 .

[15]  R. Parthasarathy,et al.  System reduction by Routh approximation and modified Cauer continued fraction , 1979 .

[16]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[17]  B. G. Bosch,et al.  Influence of second-harmonic frequency termination on Gunn-oscillator performance , 1969 .