Industrial filamentous fungal fermentations are typically operated in fed-batch mode. Oxygen control represents an important operational challenge due to the varying biomass concentration. In this study, oxygen control is implemented by manipulating the substrate feed rate, i.e. the rate of oxygen consumption. It turns out that the setpoint for dissolved oxygen represents a trade-off since a low dissolved oxygen value favors productivity but can also induce oxygen limitation. This paper addresses the regulation of dissolved oxygen using a cascade control scheme that incorporates auxiliary measurements to improve the control performance. The computation of an appropriate setpoint profile for dissolved oxygen is solved via process optimization. For that purpose, an existing morphologically structured model is extended to include the effects of both low levels of oxygen on growth and medium rheological properties on oxygen transfer. Experimental results obtained at the industrial pilot-scale level confirm the efficiency of the proposed control strategy but also illustrate the shortcomings of the process model at hand for optimizing the dissolved oxygen setpoints.
In fluidized-bed gas-phase polymerization reactors, several grades of polyethylene are produced in the same equipment by changing the operating conditions. Transitions between the different grades are rather slow and result in the production of a considerable amount of off-specification polymer. Grade transition improvement is viewed here as a dynamic optimization problem, for which numerous approaches exist. Numerical optimization based on a nominal process model is typically insufficient due to the presence of uncertainty in the form of model mismatch and process disturbances. This paper proposes to implement optimal grade transition using a measurement-based approach instead. It is based on tracking the necessary conditions of optimality (NCO tracking) using a decentralized control scheme. For this, the nominal input profiles are dissected into arcs and switching times that are assigned to the various parts of the NCO. These input elements are then adapted using appropriate measurements. NCO tracking is used to determine optimal grade transition in polyethylene reactors. The problem of minimizing the transition time from a steady state of low melt index to that of high melt index is studied, with the feeds of hydrogen and inert and the output flow rate considered as manipulated variables. In the optimal solution, all arcs are determined by path constraints, and all switching times are determined by path and terminal constraints, which significantly eases the adaptation. The on-line and run-to-run adaptation of these parameters is illustrated in simulation.
Estimation problems have been traditionally formulated so as to minimize the estimation error of the full state vector. However, in applications that involve the tracking of only a few unmeasured variables, it is sufficient to limit the attention along certain directions in state space. This way, it is hoped that better accuracy can be obtained along the desired directions, possibly at the cost of poorer estimates along the other directions. This problem, termed preferential estimation, is formally formulated in this paper as a least-squares minimization problem. Using calibration measurements of the preferred variables, the above mentioned problem is solved numerically via tuning of the Kalman filter. The approach is illustrated in simulation on the optimization of a penicillin fermentation process, where preferential estimation is used successfully to reduce the error in tracking a single unmeasured variable, the substrate concentration.
Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given that as many independent measurements are available as there are independent sources of disturbance. In the most general case, the dimensionality of the disturbance vector affecting the plant states corresponds to the order of the system and thus all states need to be measured. This condition, which is termed integral observability in the literature, represents a fairly restrictive situation. This study focuses on the more realistic case, where only the output variables are measured. Accordingly, the objective reduces to the unbiased estimation of the output variables. It is shown that both stability and asymptotically unbiased output estimation can be achieved if the system is observable, regardless of the dimensionality of the disturbance vector. Furthermore, a condition is provided under which, using output measurements, the errors in all states can be pushed to zero. It is also proposed to use off-line output measurements to tune the observer using a calibration-like approach. Integral observers and integral Kalman filters are evaluated via the simulation of a fourth-order linear system perturbed by unknown non-vanishing disturbances.
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