Nonlinear state estimation with robust convergence

The trajectories of chaotic fluctuations in dilute micellar solutions, which typically occur during the creation and destruction of shear‐induced structures in the flow inception of a 0.4 wt % cetyltrimethylammonium tosilate aqueous solution and an aqueous solution of 3 mM cetyyltrimethylammonium bromide‐sodium salicylate, are predicted here with an improved Bautista–Manero–Puig model. To determine the constancy of the model parameters with time, we applied successfully an integro‐differential approach. This methodology revealed that all the model parameters, but the elastic modulus is constant. The nature of the predicted fluctuations was analyzed by employing the exponent of Lyapunov. This analysis demonstrates that the fluctuations are chaotic deterministic in Regimes I and IV, whereas they are random in Region II. We found that the predictions of the modified model follow the experimental data and reveal that these fluctuations are related to the creation of elastic structures at the inception of shear flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3735–3745, 2018

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“…and ) can be uniquely solved for the (possibly time varying) two‐entry vector ( G 0 , λ 0 )( t ) if the Jacobian matrix, given by:

\overset{\overset{false¯}{O_{1}}}{true} = ([], \begin{array}{c} \frac{\partial σ}{\partial G_{0}} & \frac{\partial σ}{\partial λ_{0}} \\ \frac{\partial}{\partial G_{0}} \frac{\partial σ}{\partial t} & \frac{\partial}{\partial λ_{0}} \frac{\partial σ}{\partial t} \end{array})

is nonsingular at each time t in T , that is,

italicdet \overset{\overset{false¯}{O_{1}}}{true} \neq 0

. This matrix is also referred to as the observability matrix and its nonsingularity condition signifies that the parameter vector

Φ ((),, σ, \frac{\partial σ}{\partial t})

is “instantaneously” observable …”

Section: The Original Bmp Modelmentioning

confidence: 95%

Predictions of flow instabilities in the shear‐thickening regime with an improved bautista–manero–puig model

et al. 2018

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“…Several linearization methods have been also proposed (see for example [ l]), but they have the drawback that only local behavior can be guaranteed with limited performance and stability properties. Other estimation schemes based on geometric theory have been shown to guarantee convergence with linear output error dynamics but apply to an extremely restrictive class of plants [2]. The high gain [3], adaptive [4] and sliding mode [5] approaches have been also devised to solve the state reconstruction problem since it guarantees stability but their design involve conditions that must be assumed a priori or that are usually hard to verify [ 6 ] .…”

Section: Introductionmentioning

confidence: 99%

Application of a Robust Interval Observer to an Anaerobic Digestion Process

Alcaraz-González

Steyer

Harmand

et al. 2005

Dev. Chem. Eng. Mineral Process.

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“…The observability of the system will be posed in terms of the concept of non-linear observability (Hermann and Krener, 1977;Alvarez, 2000). We depart of the assumed fickian description of the extraction process.…”

Section: A1 Observability Testmentioning

confidence: 99%