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An improvement of Gamma approximation for reduction of continuous interval systems

Bokam Jagadish Kumar, Singh Vinay Pratap, Devarapalli Ramesh, García Márquez Fausto Pedro

Archives of Control Sciences

2021

Vol. 31, No. 2

347--373

In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-inputsingle-output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.

Reduction of linear discrete time systems in frequency domain using continued fraction expansions

Prasad R., Devi S.

Systems Science

2004

Vol. 30, no 1

65-76

The continued fraction expansions (CFE) approach coupled with several powerful stable reduction methods is proposed for the reduction of high order z-transfer functions. These methods include the advantages of stability preservation methods (SPM), such as Routh approximation, Routh Hurwitz array and stability equation method etc., with those of the method based on continued fraction expansions. The high order z-transfer functions are transformed in w-domain using bilinear transformation and the denominator of the reduced models are found in w-domain. The numerators of reduced order models are determined by matching the quotients of continued fraction expansions in w-domain. Finally, the reduced z-transfer functions are determined using reverse bilinear transformation. In this paper, combined features of SPM and CFE have been utilised to reduce the linear discrete time systems. To match the initial value of the original step response the bilinear transformation is applied in the high order z transfer function in such a way that the numerator and denominator polynomials of original system are separately expressed in w domain. And, to remove any steady error between the system and model responses, steady state values of original, and reduced systems are matched. The method proposed preserves the time domain and frequency domain characteristics and gives stable models for stable systems. An example illustrates the method.