On the Design of Integral Observers for Unbiased Output Estimation in the Presence of Uncertainty

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

Oxygen Control for an Industrial Pilot-Scale Fed-Batch Filamentous Fungal Fermentation

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

Optimal grade transition for polyethylene reactors via NCO tracking

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

Run-to-run Optimization of Filamentous Fungal Fermentation

Improving the productivity of fed-batch filamentous fungal fermentations can be formulated as a dynamic optimization problem. However, numerical optimization based on a nominal process model is typically insufficient when uncertainty in the form of model mismatch and process disturbances is present. This paper considers a measurement-based approach that consists of tracking the necessary conditions of optimality (NCO tracking). For this, the nominal input profiles are dissected into time functions and constant parameters that are assigned to the various parts of the NCO. These input elements are then adapted using appropriate measurements. NCO tracking is used here to maximize enzyme production in the case of parametric uncertainty. Upon parameterization of the feed rate input, only point constraints need to be met for optimality, which can be achieved on a run-to-run basis. The approach is illustrated in simulation and compared to open-loop application of the nominal optimal solution

Preferential Estimation for Uncertain Linear Systems at Steady State: Application to Filamentous Fungal Fermentation

State estimation is a widely used concept in the control community, and the literature mostly concentrates on the estimation of all states. However, in soft sensor problems, the emphasis is on estimating a few soft outputs as accurately as possible. The concept of preferential estimation consists of estimating these soft outputs with an accuracy higher than those with which the other states are estimated. The main question is whether or not the accuracy along the soft outputs can be improved at the detriment of others. This papers shows that, though preferential estimation is not possible for ideal linear systems, it is indeed possible for linear systems with model uncertainty. The theoretical concepts are illustrated on a filamentous fungal fermentation

Parameter identification to enforce practical observability of nonlinear systems

info:eu-repo/semantics/publishe