Determination of the transfer-function matrix from the two-dimensional Fornasini-Marchesini state-space model

Author(s):  
H. Luo ◽  
W.-S. Lu ◽  
A. Antoniou
2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.


2018 ◽  
Vol 13 (2) ◽  
pp. 326-337
Author(s):  
Yosuke Kawasaki ◽  
Yusuke Hara ◽  
Masao Kuwahara ◽  
◽  
◽  
...  

This study proposes a real-time monitoring method for two-dimensional (2D) networks via the fusion of probe data and a traffic flow model. In the Great East Japan Earthquake occurring on March 11, 2011, there was major traffic congestion as evacuees concentrated in cities on the Sanriku Coast. A tragedy occurred when a tsunami overtook the stuck vehicles. To evacuate safely and efficiently, the state of traffic must be monitored in real time on a 2D network, where all networks are linked. Generally, the traffic state is monitored only at observation points. However, observation data presents the risk of errors. Additionally, in the estimated traffic state of the 2D network, unlike non-intersecting road sections (i.e., one-dimensional), it is necessary to model user route choice behavior and origin/destination (OD) demand to input in the model. Therefore, in this study, we develop a state-space model that assimilates vehicle density and divergence ratio data obtained from probe vehicles in a traffic flow model that considers route choice. Our state-space model considers observational errors in the probe data and can simultaneously estimate traffic state and destination component ratio of OD demand. The result of simulated traffic model verification shows that the proposed model has good congestion estimation precision in a small-scale test network.


2013 ◽  
Vol 791-793 ◽  
pp. 818-821
Author(s):  
Shi Li ◽  
Xi Ju Zong ◽  
Yan Hu

This paper is concerns with the study of modeling and control of biochemical reactor. Firstly, a mathematical model is established for a typical biochemical reactor, the mass balance equations are established individually for substrate concentration and biomass concentration. Then, the model is linearized at the steady-state point, two linear models are derived: state space model and transfer function model. The transfer function model is used in internal model control (IMC), where the filter parameter is selected and discussed. The state space model is applied in model predictive control (MPC), where controller parameters of control prediction horizon length and constraint of control variable variation are discussed.


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