In this paper we consider the filter design problem for very high dimensional systems. Assuming the hypothesis on separability of the vertical and horizontal structure for the error covariance, the number of unknown e...
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In this paper we consider the filter design problem for very high dimensional systems. Assuming the hypothesis on separability of the vertical and horizontal structure for the error covariance, the number of unknown elements in the error covariance is reduced drastically and are estimated from generated error samples. A low-cost filtering algorithm is thus determined and parameterized up to some pertinent gain coefficients to be tuned to optimize the filter performance. Results from the experiment on assimilation of the sea surface height (SSH) into an oceanic numerical model demonstrate the high effectiveness of the proposed filtering approach.
Abstract In this paper, the problem of steady-state regulation of the magnetic flux profile in a tokamak plasma using the lower hybrid current drive as actuator is considered. Based on a simplified control-oriented mo...
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Abstract In this paper, the problem of steady-state regulation of the magnetic flux profile in a tokamak plasma using the lower hybrid current drive as actuator is considered. Based on a simplified control-oriented model of the magnetic flux dynamics in a tokamak plasma a polytopic control law was developed. Shape constraints on the actuator are considered and conditions to derive a polytopic linear parameter-varying controller that guarantees stability of the closed-loop system are given. Validation and implementation issues are discussed and numerical simulations are presented.
In this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain...
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In this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite dierence scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with dierent controls, the validity of the optimality of the obtained control is verified numerically.
This paper deals with the optimal and safe operation of jacketed tubular reactors. Despite the existence of advanced distributed controllers, optimal steady-state reference profiles to be tracked are often unknown. In...
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This paper deals with the optimal and safe operation of jacketed tubular reactors. Despite the existence of advanced distributed controllers, optimal steady-state reference profiles to be tracked are often unknown. In Logist et al. [2008], a procedure which combines analytical and numerical optimal control techniques, has been proposed for deriving optimal analytical (and thus generic) references, and it has been illustrated for plug flow reactors. The aim of this paper is to illustrate the general applicability of this procedure by allowing dispersion. As dispersion significantly complicates a possible solution process (due to second-order derivatives and split boundary conditions), hardly any generic results are known. Nevertheless, the dispersive plug flow reactor model is important for practice, since varying the dispersion level allows to mimic an entire reactor range, i.e., from plug flow to perfectly mixed reactors. As an example a jacketed tubular reactor in which an exothermic irreversible first-order reaction takes place is adopted. It is shown that the procedure yields generic reference solutions for ( i ) three different cost criteria, and ( ii ) different dispersion levels.
The fault detection problem for parabolic or biharmonic PDEs is solved. Additive and multiplicative actuator, sensor and process faults without knowing the signal form can be taken into account. In addition, disturban...
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The fault detection problem for parabolic or biharmonic PDEs is solved. Additive and multiplicative actuator, sensor and process faults without knowing the signal form can be taken into account. In addition, disturbances with a finite signal energy on a moving horizon can be present and are considered by a threshold. Integral transformations are used to derive a residual generator and the threshold. The corresponding integral kernels are determined by a flatness-based realization of a nontrivial setpoint change for a DPS. Moreover, a trade-off design based on L 2 norms is systematically achieved for the fault detection. The efficiency of this design approach is demonstrated with simulations of a faulty cantilever beam.
Abstract This paper introduces a method for synthesizing reduced-order nonlinear model-based predictive controllers that have support in an arbitrary open subset, for semilinear parabolic equations. The predictive con...
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Abstract This paper introduces a method for synthesizing reduced-order nonlinear model-based predictive controllers that have support in an arbitrary open subset, for semilinear parabolic equations. The predictive control law is computed based on reduced-order, nonlinear multi-step-ahead finite-element predictors, identified directly from experimental input-output data. An advantage of this approach is that it does not require knowledge of the partial differential equation (PDE) model of the process. The proposed approach is computationally efficient and suitable for real-time implementation as it does not involve solving a complex nonlinear programming problem. The design method can deal effectively with load disturbances and noise in a similar manner to that adopted in the classical Generalized Predictive Control framework. The method is used to design and evaluate numerically a nonlinear predictive controller for a one-dimensional nonlinear parabolic equation.
The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled syste...
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The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled system of transport processes and ordinary differential equations. These time-delay systems can be viewed as modules over a ring of entire functions. It is shown that spectral controllability and freeness of the module over an associated ring are necessary and sufficient for the module to be free. Using a module basis, a flatness-based tracking controller is derived that is infinite-dimensional, in general, due to the distributed delays. However, no (explicit) predictions are required to assign a finite spectrum to the delay system. Two examples illustrate the results, one of which being a neutral type system.
Model-based trajectory planning is addressed for the realization of desired temperature trajectories for a deep drawing tool. Based on the distributed-parameter system description of the tool a finite element approxim...
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Model-based trajectory planning is addressed for the realization of desired temperature trajectories for a deep drawing tool. Based on the distributed-parameter system description of the tool a finite element approximation is deduced which serves as basis for a systematic flatness-based design of a feedforward control. Trajectory assignment is considered by taking into account the minimization of a process-related objective function. Simulation and experimental data obtained from a fully equipped forming tool are presented for pure feedforward control and a two-degree-of-freedom control concept amending the feedforward part by an output error feedback controller. These confirm the applicability of the design technique and the tracking performance.
This paper is concerned with the modeling problems of dynamic consumption systems. In particular, the distribution effects of wealth across consumers on the aggregate demand are considered by using the modeling theory...
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This paper is concerned with the modeling problems of dynamic consumption systems. In particular, the distribution effects of wealth across consumers on the aggregate demand are considered by using the modeling theory of distributed-parameter systems. The resulting model is a Partial Differential Equation that describes evolution of the distribution density of consumers with respect to their wealth. A simple solution to the model is also derived under assumptions properly made according to practical background, which can be used in economic analysis readily. Finally the modeling method is illustrated by an application to the forecasting of household cars in China.
A new frequency domain technique is presented for modeling uncertainty of elastic vibrating systems whose eigenvalues and eigenvectors concerning higher order vibrating modes are unknown. First, a feasible set of syst...
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A new frequency domain technique is presented for modeling uncertainty of elastic vibrating systems whose eigenvalues and eigenvectors concerning higher order vibrating modes are unknown. First, a feasible set of systems is defined to be the set of all systems governed by a differential equation with certain noun bounds of unknown input and output operators and partially known eigenvalues and corresponding parameters. Then an unstructured uncertainty class is characterized in frequency domain so that it includes the feasible set and that the magnitude of additive perturbation bound be minimized. Significance of the characterization is illustrated by numerical study of finite dimensional controller desisn for an ideal flexible beam.
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