Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Publications

3 Conventional and PSO Based Approaches for Model Reduction of SISO Discrete Systems

Authors: C. Ardil, S. Panda, R. Prasad, S. K. Tomar

Abstract:

Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the 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, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO 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.

Keywords: Particle Swarm Optimization, discrete system, Integral Squared Error, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation

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2 Model Reduction of Linear Systems by Conventional and Evolutionary Techniques

Authors: C. Ardil, S. Panda, R. Prasad, S. K. Tomar

Abstract:

Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO 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.

Keywords: Stability, Particle Swarm Optimization, Integral Squared Error, Reduced Order Modeling, Continued Fraction Expansions, Mihailov Stability Criterion

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1 Reduction of Linear Time-Invariant Systems Using Routh-Approximation and PSO

Authors: C. Ardil, S. Panda, R. Prasad, S. K. Tomar

Abstract:

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO 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 examples.

Keywords: Particle Swarm Optimization, model order reduction, Markov parameters, Integral Squared Error, Routh Approximation, Steady State Stability

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