Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties. (c) 2005 Elsevier Ltd. All rights reserved.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Optimal control of affine connection control systems from the point of view of Lie algebroids

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.

Development of a numerical platform for the modeling and optimal control of liquid metal flows

The main purpose of this work is to develop a numerical platform for the turbulence modeling and optimal control of liquid metal flows. Thanks to their interesting thermal properties, liquid metals are widely studied as coolants for heat transfer applications in the nuclear context. However, due to their low Prandtl numbers, the standard turbulence models commonly used for coolants as air or water are inadequate. Advanced turbulence models able to capture the anisotropy in the flow and heat transfer are then necessary. In this thesis, a new anisotropic four-parameter turbulence model is presented and validated. The proposed model is based on explicit algebraic models and solves four additional transport equations for dynamical and thermal turbulent variables. For the validation of the model, several flow configurations are considered for different Reynolds and Prandtl numbers, namely fully developed flows in a plane channel and cylindrical pipe, and forced and mixed convection in a backward-facing step geometry. Since buoyancy effects cannot be neglected in liquid metals-cooled fast reactors, the second aim of this work is to provide mathematical and numerical tools for the simulation and optimization of liquid metals in mixed and natural convection. Optimal control problems for turbulent buoyant flows are studied and analyzed with the Lagrange multipliers method. Numerical algorithms for optimal control problems are integrated into the numerical platform and several simulations are performed to show the robustness, consistency, and feasibility of the method.