[vc_empty_space][vc_empty_space]
Reduced-order model based on H∞-balancing for infinite-dimensional systems
Fatmawatia, Saragih R.b, Soeharyadi Y.b
a Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]This paper presents a model reduction for unstable infinite dimen-sional system (A;B;C) using H∞-balancing. To construct H∞-balanced realization, we find a Lyapunov-balanced realizationof a normalized left-coprime factorization (NLCF) of the scaled system (A; βB;C). Next, we apply the new coordinate transformation to obtain yet another re-alization of NLCF system. This result is then translated to have the new scaled system (At; βBt;Ct) whichsimilar with (A; βB;C). Fur-thermore, it can be verified that the solutions of a control and ffilter H∞-Riccati operator equations of the system (At;Bt;Ct) are equal and diagonal. This implies that the system (At;Bt;Ct) is H∞-balanced re-alization of the system (A;B;C). Based on the small H∞-characteristic values, the state variables of the system (At;Bt;Ct) is truncated, to yield a reduced-order model of the system (A;B;C). To demonstrate the effectiveness of the proposed method, numerical simulations are ap-plied to Euler-Bernoulli beam equation.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Coprime factorization,H∞-balancing,infinite-dimensional systems,Reduced-order model,Riccati equations[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]