► The CSTR model of each zinc solution purification reactor is established. ► A time-delayed dynamic model for the purification process was constructed. ► We identify the unknown model parameters ...based on the real-life observed data. ► A numerical method is developed based on the control parameterization method. ► The optimal control problem for purification is solved using the proposed method.
In zinc solution purification process, zinc dust is used to remove impurity ions in several serial stirred tank reactors. It is modelled by using several interacting continuously stirred tank reactor (ICSTR) systems with multiple time delays. Some unknown parameters of the ICSTR model are identified based on experimental data collected from a zinc production factory in China. Then a time delayed optimal control problem with continuous inequality constraints is constructed for the zinc solution purification. A numerical computational algorithm is developed, based on the control parameterization method, to design an optimal control law to ensure that a sufficiently low level of effluent impurities is achieved with the least zinc dust consumption. Finally, numerical simulation is carried out. The results obtained indicate that the effect of the optimal control for zinc solution purification is highly satisfactory.
We develop a generalized numerical optimization algorithm for the rotationally invariant multi-orbital slave boson approach, which is applicable for arbitrary boundary constraints of high-dimensional ...objective function by combining several classical optimization techniques. After constructing the calculation architecture of rotationally invariant multi-orbital slave boson model, we apply this optimization algorithm to find the stable ground state and magnetic configuration of two-orbital Hubbard models. The numerical results are consistent with available solutions, confirming the correctness and accuracy of our present algorithm. Furthermore, we utilize it to explore the effects of the transverse Hund’s coupling terms on metal–insulator transition, orbital selective Mott phase and magnetism. These results show the quick convergency and robust stable character of our algorithm in searching the optimized solution of strongly correlated electron systems.
A mathematical model of the evaporation system in the form of a state space model with multiple time delays is constructed. On this basis, an optimal control of an industrial-scale alumina ...evaporation process is obtained, where the objective is to find a control such that the specific quality of the sodium aluminate solution control is met with the least energy usage and the constraints on the state and the control are satisfied. Then, a numerical algorithm is developed for solving this optimal control problem. It is applied to study the optimal control of a practical alumina evaporation process and the results obtained are highly satisfactory.
► We study an optimal control problem of an evaporation process for alumina production. ► The process model was a state space model with multiple time delays. ► The problem was a time-delayed optimal control problem with continuous constraints. ► Constraints were approximated by transcription method and smoothing technique. ► Optimal controls were in the form of the piecewise constant functions.
The digital wideband arrays with data converters and digital signal processing capability permit greater flexibility in the pattern synthesis than conventional time-delay steered wideband arrays, ...which provides an opportunity to solve the polarised pattern synthesis of wideband arrays by using numerical optimisation algorithms. A finite-impulse response (FIR) filter is placed at each element to directly optimise the synthesised polarisation and wideband power patterns. Both the optimisations of the sum and difference patterns are formulated as convex programming problems to obtain efficient solutions. The proposed synthesis method, which has no special requirement on the array geometry and element pattern, is flexible and applicable to arbitrary arrays. By optimising the complex coefficients of FIR filters, any state of polarisation can be synthesised in a given angle-frequency space with frequency-invariant main beams and arbitrary sidelobe upper bounds. Various design examples are presented to testify the potentiality of the proposed method.
In the development of measurement facilities, taking into account the diversity of signals and factors influencing error, the selection of a method of discrete wavelet filtering of measurement ...signals is a timely issue. Results are given of the development of an algorithm for the selection of a method of discrete wavelet filtering, taking into account the nature of the measurement signal. The three most widespread methods of discrete wavelet filtering were studied, with subsequent comparative analysis for twenty types of measurement signals. The following methods of wavelet filtering were analyzed: with a common threshold for all levels of decomposition; without a threshold, with simple resetting to zero of the detail coefficients until reaching the minimum rms error of filtering of measurement signals; and a universal threshold for detail coefficients at each level of decomposition. The measurement signals were studied for twenty types from the PyWavelets library, to which in addition, uncorrelated normally distributed noise with zero mean and specified standard deviation is added. The criteria for comparing methods were determined for noisy signals before filtering, and for the filtered signals. The signal-to-noise ratio, the difference of entropy errors, the rms error of filtering, and the function of the measurement signal were used as the criteria. For each method of filtering, the criteria for comparison were determined from the condition of the minimum rms error introduced by noise to the measurement signal of the given type. Both the energy and the informational characteristics of the signal were considered for selection of a method. A cyclical search determined the filtering parameters for reaching the minimum rms error of filtering. The proposed algorithm makes it possible to determine the most effective methods of discrete wavelet filtering, depending on the nature of the measurement signal. In this, the designer solves two problems at the same time: selection of the filtering method and determination of the filtering parameters.
Quasi-static ultrasound elastography is a promising imaging method that analyzes motions from ultrasound images acquired with and without quasi-static forces. Window length is a key parameter for ...displacement and strain estimation in ultrasound elastography. Traditional methods with fixed windows cannot estimate displacements accurately in areas with uniform and sharp motions simultaneously. In this study, a new ultrasound elastography method based on a variable windows-based numerical optimization algorithm (VW-NOA) is proposed and evaluated using simulated data generated by finite element analysis software (COMSOL3.3). Compared to traditional methods, this proposed approach allows variable windows size based on wavelet analysis on coarse strains calculated by NOA. Thus, it produces fewer errors, especially for areas near boundaries that cross different elastic tissues. We use simulation and phantom experiments to evaluate the method and data and statistical analysis indicate that accuracy or contrast-to-noise ratio (CNR) was improved for VW-NOA compared to original NOA.
Both the lack of the downward regulation capacity and the transmission capacity limit have led to considerable wind power curtailments in China. The battery energy storage system (BESS) provides a ...new solution to reduce the wind power curtailments due to its relatively high energy density and flexible installed location. In this paper, a new bi-level programming model is proposed to optimize the size and location of BESS for reducing the wind curtailments. The revenues of BESS, when it is located either at the wind farm or the load center, are considered comprehensively. Moreover, a numerical optimization algorithm is developed to solve the proposed model. Simulation results demonstrate the validity of the proposed model and developed algorithm. They also reveal that the BESS located at the load center offers more net profit compared to the one located at the wind farm. Subsequently, sensitivity analysis is performed to assess the effect of key parameters on the optimal values of BESS.
This paper deals with the problem of open-loop control design for a dynamic object which is described by a nonlinear system of differential equations. To solve this problem a direct method is used, ...in which the target functional is minimized by population-based algorithm. The method is applied to a test problem which consists of finding optimal control for spacial motion of maneuverable aircraft. Proposed technique is compared with two classical solutions to considered problem. One of them is based on equating to zero the partial control derivatives of the Hamilton function, wherease the other on the Hamilton function maximum over controls (Pontryagin maximum principle). The paper confirms high degree of similarity between solutions obtained by all considered methods of selecting target functional. However, classical algotithms show slightly worse accuracy and higher sensitivity to the quality of initial approximation. In addition, proposed direct method permits to evade the necessity to solve a two-point boundary value problem required in classical algorithms.
•A detailed modeling and optimization software tool is developed for HRES.•A fast and reliable Sequential Linear Programming algorithm is proposed and developed.•Object oriented programming is used ...to allow simpler extensions and additions.•Application to a real HRES located in Tuscany is presented.
Combining renewable energy sources, as photovoltaic arrays (PV), wind turbine (WT), biomass fuel generators (BM), with back-up units to form a Hybrid Renewable Energy System (HRES) can provide a more economic and reliable energy supply architecture compared to the separate usage of such units. In this work an optimization tool for a general HRES is developed: it generates an operating plan over a specified time horizon of the setpoints of each device to meet all electrical and thermal load requirements with possibly minimum operating costs. A large number of devices, such as conventional and renewable source generators, mandatory and deferrable/adjustable electrical loads, batteries, combined heat and power configurations are modeled with high fidelity. The optimization tool is based on a Sequential Linear Programming (SLP) algorithm, equipped with trust region, which is able to efficiently solve a general nonlinear program. A case study of a real HRES in Tuscany is presented to test the major functionalities of the developed optimization tool.
In this paper, we consider a new approach to optimization of nonlinear control systems based on the representation of optimality conditions and improvement of the control in the form of special ...fixed-point problems for control operators. We propose algorithms for approximate solution of optimal control problems based on iterative methods for finding fixed points. The effectiveness of the optimization methods proposed is illustrated by model and test problems.
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