Optimal Control Variables Research Articles

Combined Phase Shift and Frequency Modulation of a Dual Active Bridge AC-DC Converter with PFC

This paper presents a combined phase-shift and frequency modulation scheme of a dual–active-bridge (DAB) ac–dc converter with power factor correction (PFC) to achieve zero voltage switching (ZVS) over the full range of the ac mains voltage. The DAB consists of a half bridge with bidirectional switches on the ac side and a full bridge on the dc side of the isolation transformer to accomplish single-stage power conversion. The modulation scheme is described by means of analytical formulas, which are used in an optimization procedure to determine the optimal control variables for minimum switch commutation currents. Furthermore, an ac current controller suitable for the proposed modulation scheme is described. A loss model and measurements on a 3.3-kW electric vehicle battery charger to connect to the 230 $\text{V}_\text{rms}$ / 50-Hz mains considering a battery voltage range of 280–420 V validate the theoretical analysis.

Constrained H1-regularization schemes for diffeomorphic image registration.

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss-)Newton-Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient.

Optimizing real power loss and voltage stability limit of a large transmission network using firefly algorithm

This paper proposes a Firefly algorithm based technique to optimize the control variables for simultaneous optimization of real power loss and voltage stability limit of the transmission system. Mathematically, this issue can be formulated as nonlinear equality and inequality constrained optimization problem with an objective function integrating both real power loss and voltage stability limit. Transformers taps, unified power flow controller and its parameters have been included as control variables in the problem formulation. The effectiveness of the proposed algorithm has been tested on New England 39-bus system. Simulation results obtained with the proposed algorithm are compared with the real coded genetic algorithm for single objective of real power loss minimization and multi-objective of real power loss minimization and voltage stability limit maximization. Also, a classical optimization method known as interior point successive linear programming technique is considered here to compare the results of firefly algorithm for single objective of real power loss minimization. Simulation results confirm the potentiality of the proposed algorithm in solving optimization problems.

Variational formulation and optimal control of fractional diffusion equations with Caputo derivatives

In this paper we start by giving a new definition of weak Caputo derivative in the sense of distributions, and we give a variational formulation to a fractional diffusion equation with Caputo derivative. We prove the existence and uniqueness of the solution to this weak formulation and use it to obtain a result on optimal control.

Optimal Learning in Experimental Design Using the Knowledge Gradient Policy with Application to Characterizing Nanoemulsion Stability

We present a technique for adaptively choosing a sequence of experiments for materials design and optimization. Specifically, we consider the problem of identifying the choice of experimental control variables that optimize the kinetic stability of a nanoemulsion, which we formulate as a ranking and selection problem. We introduce an optimization algorithm called the knowledge gradient with discrete priors (KGDP) that sequentially and adaptively selects experiments and that maximizes the rate of learning the optimal control variables. This is done through a combination of a physical, kinetic model of nanoemulsion stability, Bayesian inference, and a decision policy. Prior knowledge from domain experts is incorporated into the algorithm as well. Through numerical experiments, we show that the KGDP algorithm outperforms the policies of both random exploration (in which an experiment is selected uniformly at random among all potential experiments) and exploitation (which selects the experiment that appears t...

Modeling of Singularly Perturbed multi-criterion Optimal Control Workflows

One-criterion problem of control the complex metallurgical process presented by variable parameters in vector notation was considered. In the implementation vector notation presentation transformed into canonical form by means of piecewise continuous functions optimizing control variables on a given interval [0, T]. Pontryagin's maximum principle is used to determine the optimal conditions for solving one-criterion problem, which is formulated as regular multi-criteria (maximum performance, minimum loss of ferrous and nonferrous metals and energy, etc.) optimization problem. Assumed that a piecewise continuous equations in the zone u ⊂ U, and their existence in space U ⊂ E as the main way to solve multi-criteria optimization problems of metallurgical processes is acceptable convolution of trajectory one-criterion optimum problem. In the modeling of singularly perturbed multi-criteria optimal control problems of metallurgical processes was used the method of Whitham or the search of controlled variable and control action carried out in the form of an asymptotic series in small parameter with the highest differential equations derivatives. It is shown that the expansion of control actions equations system in an asymptotic series in the small parameter allows a distributed optimal control problem for considered process to be transformed to recurrent sequence of simple regular tasks. Finding the coefficients of the asymptotic expansion of the optimal control actions for multi-criteria metallurgical process is the desired solution with given initial conditions and singular perturbations.

Introduction: variational analysis, optimization and optimal control

Introduction: variational analysis, optimization and optimal control

Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks

We first conceive a novel transmission protocol for a multi-relay multiple-input--multiple-output orthogonal frequency-division multiple-access (MIMO-OFDMA) cellular network based on joint transmit and receive beamforming. We then address the associated network-wide spectral efficiency (SE) and energy spectral efficiency (ESE) optimization problems. More specifically, the network's MIMO channels are mathematically decomposed into several effective multiple-input--single-output (MISO) channels, which are essentially spatially multiplexed for transmission. Hence, these effective MISO channels are referred to as spatial multiplexing components (SMCs). For the sake of improving the SE/ESE performance attained, the SMCs are grouped using a pair of proposed grouping algorithms. The first is optimal in the sense that it exhaustively evaluates all the possible combinations of SMCs satisfying both the semi-orthogonality criterion and other relevant system constraints, whereas the second is a lower-complexity alternative. Corresponding to each of the two grouping algorithms, the pair of SE and ESE maximization problems are formulated, thus the optimal SMC groups and optimal power control variables can be obtained for each subcarrier block. These optimization problems are proven to be concave, and the dual decomposition approach is employed for obtaining their solutions. Relying on these optimization solutions, the impact of various system parameters on both the attainable SE and ESE is characterized. In particular, we demonstrate that under certain conditions the lower-complexity SMC grouping algorithm achieves 90% of the SE/ESE attained by the exhaustive-search based optimal grouping algorithm, while imposing as little as 3.5% of the latter scheme's computational complexity.

Is isotropic turbulence decay governed by asymptotic behavior of large scales? An eddy-damped quasi-normal Markovian-based data assimilation study

The present paper deals with the identification of the scales and features of the initial kinetic energy spectrum that govern the decay regime of freely decaying homogeneous isotropic turbulence (HIT). To this end, a Data Assimilation (DA) study is performed, which is based on a variational optimal control problem with the eddy-damped quasi-normal Markovian (EDQNM) model whose adjoint equation is derived in the present work. The DA procedure consists in reconstructing the initial kinetic energy spectrum in order to minimize the error committed on some features of decaying turbulence with respect to a targeted EDQNM simulation. The present results show that the decay of HIT over finite time is governed by a finite range of large scales, i.e., the scales ranging from the initial to the final integral scales (or equivalently by wave numbers comprised between the initial and the final location of the peak of the energy spectrum). The important feature of the initial condition is the slope of the energy spectrum at these scales, if such a slope can be defined. This is coherent with previous findings dealing with decay of non-self-similar solutions, or with the key assumptions that underly the Comte-Bellot–Corrsin theory. A consequence is that the finite time decay of HIT is not driven by the asymptotic large-scale behavior of the energy spectrum E(k → 0, t = 0) or the velocity correlation function f(r → +∞, t = 0), or even scales such as kL ≪ 1 or L/r ≪ 1. Governing scales are such that kL(t) = O(1) for values of the integral scale L(t) observed during the finite time decay under consideration. As a matter of fact, a null sensitivity of finite time decay of turbulence with respect to the asymptotic large scale features of the initial condition is observed. Therefore, the asymptotic features of the initial condition should not be investigated defining an inverse problem based of features of turbulence decay observed over a finite time.

Constrained multi-scale turnover Lagrangian map for anisotropic synthetic turbulence: A priori tests

Synthetic turbulence has been useful in the modelling and simulation of turbulence, and as a surrogate to understand the dynamics of real hydrodynamic turbulence. In a recently proposed Multiscale Turnover Lagrangian Map (MTLM) method, an initial random field is transformed into a synthetic field after a series of simple mappings, with moderate computational cost. It has been shown that the resulted fields reproduce highly realistic statistics on many aspects of isotropic hydrodynamic turbulence, including small-scale intermittency, geometric statistics, and pressure statistics. Thus, it is of great interests to generalize the method to model inhomogeneous turbulence. In this paper, we formulate the problem as an optimization problem, where the initial random field is taken as the control variable, and the additional features presented in inhomogeneous turbulence are taken as a target function to be matched by the synthetic fields. The goal is to find the optimal control variable which minimizes the difference between the target function and the synthetic field. Using the adjoint formulation, we derive the optimality system of the problem, which formulates a procedure to generate inhomogeneous synthetic turbulence. The procedure, named the Constrained MTLM, is applied to synthesize two Kolmogorov flows where persistent large scale structures produce nontrivial mean flow statistics and local anisotropy in small scales. We compare the synthetic fields with direct numerical simulation data, and show that the former reproduces closely the mean flow statistics such as Reynolds stress distribution and mean turbulent kinetic energy balance. They also reproduce the effects of inhomogeneity on small scale structures, which is manifested in the distributions of mean subgrid-scale energy dissipation, and the alignment between the subgrid-scale stress tensor and the filtered strain rate tensor, among others. We conclude that the method is useful to further extend the applicability of synthetic turbulence.

Analysis and Experimental Setup of a Switched Reluctance Generator for Maximum Output Power

Output power of a switched reluctance generator (SRG) in single pulse mode operation depends on control variables which consist of dc bus voltage, shaft speed, and excitation angles (turn-on and turn-off angles).This paper presents a model using equations to express maximum output power in terms of the control variables. The proposed analytical model is applied from a nonlinear magnetization curve that is used to mathematically demonstrate relationship of the control variables and to find the optimal control variables of the SRG for maximum output power. The validity of the analytical model has been confirmed by experimental results

Optimal control of combined air conditioning system with variable refrigerant flow and variable air volume for energy saving

An optimal control strategy for minimizing the energy consumption of variable refrigerant flow (VRF) and variable air volume (VAV) combined air conditioning systems was presented. The combined system was proposed to take advantages of VAV systems to solve the ventilation problem of VRF systems. The VAV part consists of an outdoor air processing unit and air supply and distribution devices. To determine set-point of the optimal control variable, i.e. outdoor air supply temperature, this paper proposed an optimal control strategy based on adaptive predictive model and recursive least squares estimation technique. Typical days in summer and winter were selected to test the strategy. Results indicated that the optimal control strategy reduces energy consumption of the combined system by 32.17% in summer and 2.47% in winter. The overall energy efficiency is enlarged by 12.18% in summer and 3.37% in winter, compared with the benchmark operation strategy.

Water flooding optimization with adjoint model under control constraints

The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conventional solving method of the maximum principle requires two solutions of time series: the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelerates the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.

Delay differential model for tumour-immune response with chemoimmunotherapy and optimal control.

We present a delay differential model with optimal control that describes the interactions of the tumour cells and immune response cells with external therapy. The intracellular delay is incorporated into the model to justify the time required to stimulate the effector cells. The optimal control variables are incorporated to identify the best treatment strategy with minimum side effects by blocking the production of new tumour cells and keeping the number of normal cells above 75% of its carrying capacity. Existence of the optimal control pair and optimality system are established. Pontryagin's maximum principle is applicable to characterize the optimal controls. The model displays a tumour-free steady state and up to three coexisting steady states. The numerical results show that the optimal treatment strategies reduce the tumour cells load and increase the effector cells after a few days of therapy. The performance of combination therapy protocol of immunochemotherapy is better than the standard protocol of chemotherapy alone.

Multi Objective Optimization of Process Parameters in WEDM during Machining of SS304

Wire electrical discharge machining (WEDM) allowed success in the production of newer materials, especially for the aerospace and medical industries. Using WEDM technology, complicated cuts can be made through difficult-to-machine electrically conductive components. WEDM is valuable because of its fine surface finish and its high degree of accuracy. The process is so complex that using trial and error method it is very difficult to set the process parameters at the correct range. Hence there is a need to develop the method for finding the optimal process parameters or control variables, so that the desired surface finish and MRR can be attained. In general, the selection of machining parameters in any machining process significantly affects production rate, product quality and production cost of a finished component. WEDM is a complex process involved with more number of control variables or parameters that affect its performance. However, after conducting pilot experiments and the literature survey more influencing parameters are found out and five process variables, viz., pulse on time, pulse off time, wire tension, and water pressure are taken into consideration for the research. In the present work Response Surface Methodology (RSM) is used to develop the quantitative relationships between the input and the output responses for the experimental data collected as per the DOE. Also the effects of the input process parameters over the MRR and Ra were plotted and studied. Later it is formulated as a multi objective optimization problem and solved for pareto optimal set using NSGA algorithm.

Social Welfare Maximization of Multimodal Transportation

Multimodal urban transportation systems exhibit complex inter actions between components, including users, multimodal transportation facilities, supply side agencies, and operators. Although these interactions are obvious, rigorous quantitative methods for optimizing control variables across modes of transportation on real-world networks are deficient. A social welfare maximization model was established for joint optimization of bus fare, rail transit fare, and congestion tolls for private cars. The authors determined the optimality conditions and the second-order partial derivatives for this optimization problem. Because of the complexity of the multimodal urban transportation system, the objective function of social welfare has no closed form and is extremely expensive to evaluate. The authors therefore proposed a simulation-based framework for evaluation of the objective function and optimization of three decision variables across multiple travel modes. Several metamodels (i.e., mathematical functions that approximate the true shape of an unknown, nonlinear, and complex objective function) were adopted to approximate the highly nonlinear input–output mappings in the urban system. This is the first study to develop a simulation-based method for joint optimization of transit and road network operations. The case study applied the simulation-based optimization framework to the Sino–Singapore ecocity in Tianjin, China, by using VISSUM as the urban systems simulator. An “ecocity” is defined by the authors as “a thriving city that is socially harmonious, environmentally friendly, resource-efficient, and a model for sustainable development.” Results show that metamodels can accurately approximate the real objective function and produce good suboptimal and near-optimal solutions. The optimal combination of transit fares and congestion tolls significantly outperform those under two baseline scenarios. The optimal solutions also suggest that extreme transit fares (too high or too low) or congestion tolls are contrary to welfare-maximizing objectives. The proposed method can be applied for joint optimization of other multimodal planning and operational strategies, such as investment and operational decisions across various modes of transportation.

Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations

Consideration was given to the problems of variational calculus and optimal control admitting impulsive controls and, correspondingly, discontinuous solutions. The evolution of the notion of singular space-time transformation beginning from the problem of classical variational calculus and ending with the problems of optimal control at the phase of impact was shown.

Self-optimising control of sewer systems

Self-optimising control is a useful concept to select optimal controlled variables from a set of candidate measurements in a systematic manner. In this study, use self-optimizing control tools and apply them to the specific features of sewer systems, e.g. the continuously transient dynamics, the availability of a large number of measurements, the stochastic and unforeseeable character of the disturbances (rainfall). Using a subcatchment area in the Copenhagen sewer system as a case study we demonstrate, step by step, the formulation of the self-optimising control problem. The final result is an improved control structure aimed at optimizing the losses for a given control objective, here the minimization of the combined sewer overflows despite rainfall variations.

A study on automatic optimal operation of a pump for solar domestic hot water system

The objective of this research is to determine optimal control variables of a collector pump placed on a collector loop to improve the performance of a solar domestic hot water system. A mathematical model of the system is developed to predict its operating performance under real weather conditions at Jeju Island, South Korea. The optimum control variables of the collector loop are investigated based on the relationship between the useful heat gain of the solar collector and the electricity consumption of the collector pump. In addition, the effects of various parameters such as solar collector area, initial water temperature, and volume of storage tank are analyzed. The results of the simulation showed that the optimum variable flow rate was determined at m=0.05ΔTAc/60(kg/s) (Kv=0.05). At this value, the useful heat gain of the solar collector Qu increased by about 1.54% while the electricity consumption of the collector pump Ep sharply decreased to 65.6% when the constant flow was replaced by the variable flow for the collector loop. Furthermore, the system performance is significantly affected by the change of initial water temperature and volume of the storage tank, as well as the collector area.

Fuzzy-TLBO optimal reactive power control variables planning for energy loss minimization

This paper offers a new approach to the problem of optimal reactive power control variables planning (ORPVCP). The basic idea is division of Load Duration Curve (LDC) into several time intervals with constant active power demand in each interval and then solving the energy loss minimization (ELM) problem to obtain an optimal initial set of control variables of the system so that is valid for all time intervals and can be used as an initial operating condition of the system. In this paper, the ELM problem has been solved by the linear programming (LP) and fuzzy linear programming (Fuzzy-LP) and evolutionary algorithms i.e. MHBMO and TLBO and the results are compared with the proposed Fuzzy-TLBO method. In the proposed method both objective function and constraints are evaluated by membership functions. The inequality constraints are embedded into the fitness function by the membership function of the fuzzy decision and the problem is modeled by fuzzy set theory. The proposed Fuzzy-TLBO method is performed on the IEEE 30 bus test system by considering two different LDC; and it is shown that using this method has further minimized objective function than original TLBO and other optimization techniques and confirms its potential to solve the ORPCVP problem with considering ELM as the objective function.