A new approach to order reduction using stability equation and big bang big crunch optimization

Abstract

A new method of model order reduction is introduced by combining the merits of big bang big crunch (BBBC) optimization technique and stability equation (SE) method. A linear-continuous single-input single-output system of higher order is considered and reduced to a lower order system. The denominator polynomial of the reduced system is obtained by SE method, whereas the numerator terms are generated using BBBC optimization. Furthermore, step and frequency responses of the original reduced system are plotted. The superiority of the proposed method is justified by solving numerical examples from the available literature and comparing the reduced systems in terms of error indices.

Adaptive Finite-Time Control for a Flexible Hypersonic Vehicle with Actuator Fault

“…Air-breathing hypersonic vehicles (AHVs) are intended to be a reliable and cost-effective technology for access to space. Because the slender geometries and light structures cause significant flexible effects and strong coupling between propulsive and aerodynamic forces resulting from the integration of the scramjet engine, AHVs are confronting many complex problems and challenges, involving many different research areas, such as aerodynamics, thermal protection, and communication, and many problems of these fields have been reported [1][2][3]. Meanwhile, flight control design for AHVs is a hot topic and a challenging task [4,5].…”

Distributed state estimation for uncertain sensor networks with mixed time delays subject to sensor saturations

“…The numerical example has further demonstrated the effectiveness of the theoretical results. To utilize effectively the distributed algorithms proposed in this paper, the methods such as the cloud computing and the reduced-order technique (Desai and Prasad 2013;Mehrsai, Karimi, and Thoben 2013) should also be considered which will be one of our main concerns in the future.…”

Routh--type $L_2$ model reduction revisited

“…whose poles are −1, −1 ± , −1 ± 2, −1 ± 3, −1 ± 4. The same original system has been used in [11] to find a third-order approximating model by means of a "biased stability-equation" technique. Fig.…”

“…1. Impulse responses of: (i) the original model (32) (bold solid line), (ii) the third-order approximation (33) obtained using Algorithm A (bold dashed line), (iii) the third-order approximation (34) obtained using Algorithm B (thin solid line), (iv) the third-order model derived in [11] (dotted line), and (v) the third-order model obtained via balanced truncation (dashdotted line). Step responses of: (i) the original model (32) (bold solid line), (ii) the third-order approximation (33) obtained using Algorithm A (bold dashed line), (iii) the third-order approximation (34) obtained using Algorithm B (thin solid line), (iv) the third-order model derived in [11] (dotted line), and (v) the third-order model obtained via balanced truncation (dashdotted line).…”

“…The model reduction problem has aroused a continual interest in the engineering community since the dawn of control and system theory [40,71], its importance being evident not only in system simulation and controller synthesis but also in many problems related to robustness and uncertainty issues. Indeed, despite the dramatic increase of computing capabilities that make the need for simplified models less compelling, the new challenges facing the control engineer have led to a revival of studies on this topic with particular emphasis on optimisation and algorithmic efficiency (see, e. g., [1,2,4,7,11,12], [14]- [59], [61,65,69,70]).…”