Estimating Pure Diffusion Contributions in Alkaline Pulping Processes

A model that predicts isothermal alkali diffusion and reaction with acetyl groups in moist wood chips was derived and approximated. System parameters were estimated from unsteady-state experimental data. Simulation results reinforce the idea that the diffusion effect is not fully exploited in pulping processes. Traditionally, digestion is conducted at high temperature, where delignification reaction kinetics is enhanced and the reaction effect is predominant. This approach is being reviewed by modern industry since energy and environmental savings associated with low temperature operation might compensate for high-yield productivity. The concentration of alkali at the center of the chip is a measure of the completeness of wood deacetylation, which translates into the aptitude of the final product for pulping purposes. This concentration is predicted here from the solution to a pair of coupled ODE’s. Since alternatives combining both low and high-temperature processes are being studied, the results in this paper provide basic data for optimization analysis.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Costanza, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

A differentiable trajectory approximation to turbulent diffusion

The problem of turbulent diffusion is posed as determining the time evolution of the probability density of the concentration given those for the fluid velocity components, sources, and the initial concentration. At each time, all variables are elements of the Hilbert space L^2_R(R^3), and a finite-dimensional approximation based on expansions in orthonormal basis functions is developed. An expression for the joint probability density of all the Fourier coefficients is derived, the evaluation of which is shown to be particularly straightforward. Diffusion of material from a single source in an unbounded mildly turbulent fluid is considered as an application

Regular Optimal Control Problems with Quadratic Final Penalties

Hamilton’s canonical equations (HCEs) have played a central role in Mechanicsafter (i) their equivalence with the principle of least action, and (ii) the variationalcalculus leading to the Euler-Lagrange equation, were established and applied (see[1]). Also, since the foundational work of Pontryagin [22], HCEs have been atthe core of modern optimal control theory. When the problem concerning ann-dimensional control system and an additive cost objective is regular [19], i.e.when the Hamiltonian H(t, x, lambda, u) of the problem is smooth enough and can beuniquely optimized with respect to u at a control value u0(t, x, lambda) (depending onthe remaining variables), then HCEs appear as a set of 2n ordinary differentialequations whose solutions are optimal state-costate time trajectories.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico Para la Industria Química; Argentin

On-line costate integration for nonlinear control

The optimal feedback control of nonlinear chemical processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary-value situation for the coupled state-costate system is transformed into an initial-value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on-line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical nonlinear chemical reactor model, and compared against standard MPC and previous versions of bilinear-quadratic strategies based on power series expansions.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Neuman, C.. Universidad Nacional del Litoral; Argentin

Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem

New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Neuman, C. E.. Universidad Nacional del Litoral; Argentin

La ecuación generalizada de Riccati en derivadas parciales. Aplicación al control de reacciones electroquímicas

Se proponen y comparan soluciones al problema de mantener un sistema no lineal en equilibrio mediante una acción de control que optimiza un costo cuadrático durante un período de tiempo especificado. Se aplican los resultados al control de las llamadas “reacciones electroquímicas del hidr ógeno”(HER). Se resuelve el problema bilineal-cuadrático con horizonte finito apelando a diversos métodos que conducen a la formulación de ecuaciones diferenciales en derivadas parciales (EDP) y sistemas de ecuaciones diferenciales ordinarias cuyas soluciones se aproximan numéricamente. Una soluci ón aproximada de la EDP de Hamilton-Jacobi-Bellmann (HJB) asociada a este problema se obtiene mediante la expansión en serie de potencias de la función de valor. Se desarrolla un nuevo método para reducir considerablemente el almacenamiento de información y facilitar su complejo procesamiento en tiempo real. Este método se basa en la integración de una EDP de primer orden (RPDE) para la matriz generalizada de Riccati, que depende no solo del tiempo como en el problema clásico lineal-cuadrático, sino también del estado en que se encuentra el sistema. Este último método tiene algunas ventajas respecto del anterior, por ejemplo: (a) la RPDE provee la condición inicial para el coestado del sistema, o sea que transforma el problema de resolver las ecuaciones Hamiltonianas (HE), originalmente con condiciones de contorno, en otro de condiciones iniciales, lo que permite la integración de las HE en línea con el proceso; (b) el grado de aproximación al control óptimo depende del método utilizado para integrar la RPDE, y no de la cantidad de coeficientes guardados en la serie de potencia, en principio de infinitos términos, necesarios para la solución de la HJB; (c) permite utilizar toda la solución de la RPDE para tratar perturbaciones de distinta norma y duración, en reemplazo de la integración de las HE, reconocidamente inestables dada su estructura simpléctica. En el trabajo se comparan las siguientes tres alternativas para la regulación: (i) series de potencias para HJB; (ii) RPDE fuera de línea y HE en línea; (iii) RPDE fuera de línea y optimización en línea. Para alguno de los métodos se han desarrollado algoritmos numéricos especializados, que se comparan con la utilización de software matemático de uso corriente. También se ilustra el comportamiento de las soluciones frente a variaciones en los parámetros de dise˜no del costo cuadrático, especialmente de la penalización final.Fil: Bergallo, Marta. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Neuman, Carlos. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentin

Online suboptimal control of linearized models

A novel approach to approximately solving the restricted-control LQR problem online is substantiated and applied in two case-studies.  The first example is a one-dimensional system whose exact solution is known.  The other one refers to the temperature control of a metallic strip at the exit of a multi-stand rolling mill.  The new (online-feedback) strategy employs a convenient version of the gradient method, where partial derivatives of the cost are taken with respect to the final penalization matrix coefficients and to the switching times where the control (de)saturates.  The calculations are based on exact algebraic formula, which do not involve trajectory simulations, and so reducing in principle the computational effort associated with receding horizon or nonlinear programming methods.   Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

Approximating the Solution to LQR Problems with Bounded Controls

New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems.  Illustrations of numerical results are provided and checked against analytical solutions of  ´the cheapest stop of a train´ problem.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

Stochastic sensitivity analysis in chemical kinetics

The stochastic sensitivity analysis problem in chemical kinetics is defined as determining the probability density function (pdf) of the concentrations given probability density functions for the parameters and initial conditions. The joint concentration parameter pdf is found to satisfy the equation ([partial-derivative]p/[partial-derivative]t)+div(Fp) = 0, where the system dynamics are given by ? = F(x). The properties of the solution of this equation are studied, and the approach is applied to analyze the sensitivity of the kinetics of the photolysis of a mixture of carbon monoxide, nitrogen dioxide, nitric oxide, and water in air to uncertainties in the initial concentrations of the nitrogen oxides and in the values of two photolysis rate constants. Comparisons to other sensitivity analysis approaches are discussed

Optimizing thymic recovery in HIV patients through multidrug therapies

A control-theoretic approach to the problem of designing `low-side-effects´ therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side-effects during treatment is modelled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones.  The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient, and on the evolution of the viral load detected by periodical blood analyses.  The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral malignancies caused by the medication.  The problem is solved by a hybrid Dynamic Programming scheme that adhere to discrete-time observation and control actions, but maintaining the continuous-time setup for predicting states and side-effects.  The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months.  If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterwards, causing a desirable stabilization of the main variables.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Biafore, Federico Leonardo. Universidad Favaloro; ArgentinaFil: D'attellis, C. E.. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Universidad Favaloro; Argentin