Abstract
The modal injection mechanism ensures the exponential convergence of an observer in a continuous tubular reactor in dependence with the system parameters, the sensor location, and the observer gains. In this paper, it is shown that by simple considerations in the boundary conditions, the observer convergence is improved regardless of the presence of perturbations, the sensor locations acquire a meaningful physical meaning, and by simple numerical manipulations, the perturbations in the inflow can be numerically estimated.
Highlights
Tubular reactors are of great importance in chemical and biochemical processes, specially those with non-monotonic kinetics [1], e.g., catalytic reactors with Langmuir–Hinshelwood kinetics [2,3] or bioreactors with Haldane kinetics [4]
The tubular reactors are continuous systems where the mass concentration in some inner point depends on the spatial and temporal coordinates. In this kind of reactors, it is almost impossible to measure the concentration along the reactor; it is usually found that only a finite set of points can be measured, and the system states must be reconstructed from this information
The necessity to measure or estimate the system states has motivated the design of observers for this distributed parameter system, including absolute stability results [5], adaptive switching observers [6], Lyapunov-based approaches [7], backstepping designs [8], sliding modes observers [9], kalman schemes [10,11], interval observers [12], and dissipative approaches [13]
Summary
Tubular reactors are of great importance in chemical and biochemical processes, specially those with non-monotonic kinetics [1], e.g., catalytic reactors with Langmuir–Hinshelwood kinetics [2,3] or bioreactors with Haldane kinetics [4]. The tubular reactors are continuous systems where the mass concentration in some inner point depends on the spatial and temporal coordinates (see Figure 1). In this kind of reactors, it is almost impossible to measure the concentration along the reactor; it is usually found that only a finite set of points can be measured, and the system states must be reconstructed from this information. In the non-linear dissipative observer [17], three measurements of the concentration are made in the reactor: In some inner point and in both boundaries. This paper is organised as follows: In Section 2, the previous results and inconvenience of neglecting the effects of the boundary gains are described; in Section 3, the advantages of a correct selection of the boundary gains are proposed; in Section 4, the numerical results are shown; and in Section 5, the conclusions are presented
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