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Nasiri Soloklo, H., Bigdeli, N.. (1401). Improved Bilinear Balanced Truncation for Order Reduction of the ‎High-Order Bilinear System Based on Linear Matrix Inequalities ‎. فناوری آموزش, 11(1), 129-140. doi: 10.22061/jecei.2022.8812.554
H. Nasiri Soloklo; N. Bigdeli. "Improved Bilinear Balanced Truncation for Order Reduction of the ‎High-Order Bilinear System Based on Linear Matrix Inequalities ‎". فناوری آموزش, 11, 1, 1401, 129-140. doi: 10.22061/jecei.2022.8812.554
Nasiri Soloklo, H., Bigdeli, N.. (1401). 'Improved Bilinear Balanced Truncation for Order Reduction of the ‎High-Order Bilinear System Based on Linear Matrix Inequalities ‎', فناوری آموزش, 11(1), pp. 129-140. doi: 10.22061/jecei.2022.8812.554
Nasiri Soloklo, H., Bigdeli, N.. Improved Bilinear Balanced Truncation for Order Reduction of the ‎High-Order Bilinear System Based on Linear Matrix Inequalities ‎. فناوری آموزش, 1401; 11(1): 129-140. doi: 10.22061/jecei.2022.8812.554

Improved Bilinear Balanced Truncation for Order Reduction of the ‎High-Order Bilinear System Based on Linear Matrix Inequalities ‎

Journal of Electrical and Computer Engineering Innovations (JECEI)
دوره 11، شماره 1، فروردین 2023، صفحه 129-140    اصل مقاله (835.99 K)
نوع مقاله: Original Research Paper
شناسه دیجیتال (DOI): 10.22061/jecei.2022.8812.554
نویسندگان
H. Nasiri Soloklo؛ N. Bigdeli*
Control Engineering Department, Faculty of Technical and Engineering, Imam Khomeini International University, Qazvin, Iran.
تاریخ دریافت: 16 فروردین 1401،  تاریخ بازنگری: 25 خرداد 1401،  تاریخ پذیرش: 08 شهریور 1401 
چکیده
Background and Objectives: This paper proposes a new Model Order ‎Reduction (MOR) method based on the Bilinear Balanced Truncation ‎‎(BBT) approach. In the BBT method, solving the generalized Lyapunov ‎equations is necessary to determine the bilinear system's controllability ‎and observability Gramians. Since the bilinear systems are generally of ‎high order, the computation of the Gramians of controllability and ‎observability have huge computational volumes. In addition, the accuracy ‎of reduced-order model obtained by BT is relatively low. In fact, the ‎balanced truncation method is only available for local energy bands due ‎to the use of type I Gramians. In this paper, BBT based on type II ‎controllability and observability Gramians would be considered to fix ‎these drawbacks.‎
Methods: At first, a new iterative method is proposed for determining ‎the proper order for the reduced-order bilinear model, which is related to ‎the number of Hankel singular values of the bilinear system whose real ‎parts are closest to origin and have the most significant amount of ‎energy. Then, the problem of determining of type II controllability and ‎observability Gramians of the high-order bilinear system have been ‎formulated as a constrained optimization problem with some Linear ‎Matrix Inequality (LMI) constraints for an intermediate middle-order ‎system. Then, the achieved Gramians are applied to the BBT method to ‎determine the reduced-order model of the bilinear system. Next, the ‎steady state accuracy of the reduced model would be improved via ‎employing a tuning factor.‎
Results: Using the concept of type II Gramians and via the proposed ‎method, the accuracy of the proposed bilinear BT method is increased. ‎For validation of the proposed method, three high-order bilinear models ‎are approximated. The achieved results are compared with some well-‎known MOR approaches such as bilinear BT, bilinear Proper Orthogonal ‎Decomposition (POD) and Bilinear Iterative Rational Krylov subspace ‎Algorithm (BIRKA) methods.‎
Conclusion: According to the obtained results, the proposed MOR ‎method is superior to classical bilinear MOR methods, but is almost ‎equivalent to BIRKA. It is out-performance respecting to BIRKA is its ‎guaranteed stability and convergence. ‎
کلیدواژه‌ها
Model Order Reduction؛ ‎Bilinear System؛ Linear Matrix ‎Inequality؛ Generalized ‎Lyapunov equations؛ Balanced ‎Truncation
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