Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

Abstract

To control and observe spatially distributed thermal flow systems, the controllable field and observable field around the actuator and sensor are of interest, respectively. For spatially distributed systems, the classical systems theoretical concepts of controllability and observability are, in general, difficult to apply. In this study, sensitivity fields were used to analyse the behaviour from input to state and from initial state to output. For the analysis of controllability and observability, a large-scale, bulk storage facility with coupled thermal flow of air and agro-products was used. Analysis of this system using the classical systems theory results in controllability and observability results that are dependent on the step size of the spatially discretised system. Due to matrix multiplications, inaccurate results are calculated if the step size is too small. Our findings indicate that input-state and initial-state output sensitivity fields provide sufficient information about the controllability and observability of large coupled spatially distributed systems, using finite-dimensional state space representation with small discretisation steps.

Optimal Sensor Placement in Hydraulic Conduit Networks: A State-Space Approach

“…A system that is observable allows a full reconstruction of the states over time from given input-output data. However, for large networks, the observability matrix O may be ill-conditioned, which would lead to an observability analysis that does not lead to accurate conclusions [33]. If the eigenvalues of matrix A all have negative real parts, the system is called (asymptotically) stable.…”

“…For linear, time-invariant systems, such as given by Equations ( 7) and ( 8), the sensitivity of the output y with respect to the initial state x(0) is given by Ce At [33]. Therefore, the observability Gramian W O from Equation ( 10) can be interpreted as a Fisher Information Matrix, and it can thus be understood as a measure of information content.…”

Smart detection and real-time learning in water distribution: an integrated data-model approach

“…A system that is observable allows a full reconstruction of the states over time from given input-output data. However, for large networks, the observability matrix 𝒪𝒪 may be illconditioned, which would lead to an observability analysis that does not lead to accurate conclusions (Grubben and Keesman 2018). If the eigenvalues of matrix 𝑪𝑪 all have negative real parts, the system is called (asymptotically) stable.…”

“…For linear, time-invariant systems, such as given by Eqs. (4.7, 4,8), the sensitivity of the output 𝑦𝑦 with respect to the initial state 𝑥𝑥(0) is given by 𝑪𝑪𝑒𝑒 𝑪𝑪𝑨𝑨 (Grubben and Keesman 2018). Therefore, the observability Gramian 𝑊𝑊 𝒪𝒪 from Eq (4.10) can be interpreted as a Fisher Information Matrix, and can thus be understood as a measure of information content.…”

“…Originally observability analysis investigates whether network flows and pressures can or cannot be inferred from measurements from a selected number of sensors (Kalman and Buey 1961;Kwakernaak and Sivan 1972). Nowadays, observability analysis also focusses on the numerical aspects, and therefore observability becomes a measure of how well states can be reconstructed from input-output measurements (Grubben and Keesman 2018). Traditional sensitivity-based optimal sensor placement solely focuses on maximizing burst detectability by placement of additional pressure sensors (Steffelbauer and Fuchs-Hanusch 2016;Cugueró-Escofet et al 2017;Boatwright et al 2018;Qi et al 2018;Quiñones-Grueiro et al 2018).…”