A Novel Model Order Reduction Technique for Linear Continuous-Time Systems Using PSO-DV Algorithm
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A Novel Model Order Reduction Technique for Linear Continuous-Time Systems Using PSO-DV Algorithm Vasu Ganji1 · Sivakumar Mangipudi2
· Ramalingaraju Manyala3
Received: 30 May 2016 / Revised: 1 September 2016 / Accepted: 3 October 2016 © Brazilian Society for Automatics–SBA 2016
Abstract In this paper a new frequency-domain model order reduction method is proposed for the reduction of higher-order linear continuous-time single input single output systems using a recent hybrid evolutionary algorithm. The hybrid evolutionary algorithm is developed from the mutual synergism of particle swarm optimization and differential evolution algorithm. The objective of the proposed method is to determine an optimal reduced-order model for the given original higher-order linear continuous-time system by minimizing the integral square error (ISE) between their step responses. The method has significant features like easy implementation, good performance, numerically stable and fast convergence. Applicability and efficacy of the method are shown by illustrating an IEEE type-1 DC excitation system, and by a typical ninth-order system taken from the literature. The results obtained from the proposed algorithm are compared with many familiar and recent reduction techniques that are available in the literature, in terms of step ISE values and impulse response energies of the models. Furthermore step and frequency responses are also plotted. Keywords Model order reduction · PSO-DV algorithm · Error minimization · Linear-time invariant systems · Step integral square error
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Sivakumar Mangipudi [email protected]
1
Department of EEE, S.V.P Engineering College, Vizag, India
2
E.E.E Department, Gudlavalleru Engineering College, Gudlavalleru, India
3
Foreign Universities and Relations, JNTUK, Kakinada, India
1 Introduction Scientists and Engineers are usually facing a problem with the analysis, design and synthesis of complex physical systems. The first step in studying such complex system is to develop a mathematical model which would act as a representative of the physical system. The mathematical model empowers for virtual experimentation when the physical experimentation on the system is too expensive, tedious, infeasible, or even impossible to conduct. Besides that, the mathematical modelling of such complex physical systems leads to either higher-order differential equations, (or) transfer functions, (or) state-space formulations. These higher-order mathematical models are difficult to use either for analysis and controller design. Hence, the model order reduction methods are necessary to find an appropriate reduced-order model and that which will reflect the dominant characteristics of the original higherorder system under consideration. The reduced-order model (ROM) will help in better understanding of the original system, lower the computational complexities, and simplifies the control design. Several model order reduction methods for linear continuous-time SISO systems are available in the literature, in time-doma
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