For batch performance optimization of seeded cooling crystallization processes with respect to multiple production objectives, a multi-objective optimization (MOO) based nonlinear model predictive control (NMPC) design is proposed in this paper. By taking into account three important production objectives related to the target crystal size, yield, and batch time, respectively, an MOO program is established with respect to the important operation conditions of seed loading ratio, initial solution supersaturation and cooling temperature profile. To find a good trade-off between these cross-coupled objectives, an enhanced goal attainment method (EGAM) is adopted to acquire the Pareto solution set for the above MOO program, by taking a piece-wise linear cooling profile for implementation. Then a hybrid decision making (HDM) strategy is developed to determine the optimal compromise solution. Based on the optimized objectives and operation conditions, a NMPC scheme is established for batch run of the seeded cooling crystallization process. Meanwhile, a receding-horizon nonlinear Kalman filter (RNKF) is designed to estimate the zero- and third-order moments of crystal population (related to the total number and volume of crystals) during crystallization for control implementation. Moreover, the kinetic model parameters with higher impact on the NMPC scheme are timely updated by moment estimation to improve system performance under time-varying uncertainties. Simulation results and experiments on the seeded cooling crystallization of beta form L-glutamic acid (beta-LGA) are shown to demonstrate the effectiveness and advantage of the proposed optimization and control scheme.

In this paper, an in-situ measurement method is proposed for detecting needle- or rod-shape particle length distribution (PLD) during a crystallization process, by using the instrument named focused beam reflectance measurement (FBRM). A data pretreatment strategy is firstly presented to modify the measured chord length distribution (CLD) of particles by FBRM for proper analysis, which could guarantee measurement accuracy when the particle length are smaller than 150 μm. Based on the pretreated CLD, a moment conversion algorithm is established for estimating the moments of particle population density, so as to further improve the measurement accuracy for particles possessing larger sizes. Correspondingly, the particle growth-nucleation model parameters are efficiently estimated by using the interior point method (IPM) in combination with the homotopy analysis method (HAM). Then the PLD is reconstructed based on these estimated low-order moments, through a modified cubic-spline interpolation algorithm with variable interpolation grids. Experimental results on the seeded cooling crystallization process of β form L-glutamic acid (LGA) well demonstrate the effectiveness of the proposed method for in-situ measurement.

To overcome the influence from time-varying process uncertainties of seeded batch cooling crystallization in engineering practice, an adaptive receding-horizon nonlinear Kalman filter (ARNKF) is proposed in this paper for the moment estimation and prediction of the product crystal size distribution (CSD). The proposed ARNKF consists of two parts: one is an adaptive algorithm constructed to estimate the initial values of the process and measurement noise covariances before taking a moving time window for state estimation, and the other is an adaptive fading factor strategy conducted inside the moving time window to timely adjust the noise covariances for computation, so that the estimation accuracy on moments related to the total number and mass of crystal population could be effectively improved along the cooling crystallization process. Based on the estimated moments in real time, a prediction algorithm of product CSD is established by using the updated kinetic model parameters such that the prediction accuracy could be substantially improved along the crystallization process. Simulation study and experimental results on the seeded batch cooling crystallization process of beta form l-glutamic acid well demonstrate the effectiveness and advantage of the proposed method.

In this paper, an extended sectional quadrature method of moments (ESQMOM) is proposed to describe the kinetics of crystal growth and nucleation process, since the existing SQMOM could only be used for crystal aggregation and breakage process. A modified expression of particle number density is established with respect to the boundary nodes of all sections divided in the particle size range, and meanwhile, an interval merging strategy is developed to tackle the problem arising from particle flux flow between sections due to the crystal growth mechanism, such that moments could be predicted more precisely compared to the existing methods. Correspondingly, improved prediction of crystal size distribution (CSD) could be obtained. Based on these estimated moments, a multi-objective optimization algorithm is given to further improve estimation on the kinetic parameters of 0 form L-glutamic acid (0-LGA) cooling crystallization process. Simulation results on benchmark examples and experiments on seeded cooling crystallization of 0-LGA are given to illustrate the effectiveness and merits of the proposed method. (c) 2022 Elsevier Ltd. All rights reserved.

In this paper, a process optimization method is proposed for cooling crystallization process of β form L-glutamic acid, based on the moving horizon estimation (MHE) of the moment information of crystal growth kinetics. By transforming the population balance equations (PBEs) of the process kinetic model into differential algebraic equations using the quadrature method of moments (QMOM), a modified MHE estimation algorithm with variable horizon is developed to estimate low-order moments reflecting the fundamental characteristics of cooling crystallization process. Based on these estimated moments, an optimization program is established to solve the optimal operation profile of cooling temperature, by imposing the constraints of moment and cooling rate for numerical computation. An illustrative example of seeded cooling crystallization process of β-LGA is studied, which demonstrates that the proposed MHE algorithm could obtain better accuracy compared to the classical state estimation methods of extended Kalman filter (EKF) and MHE. Moreover, the optimized result of target crystal size distribution (CSD) by the proposed method is significantly better than those of the conventional linear or programming cooling strategies in practice.

In this paper, a novel data-driven model building method is proposed for predicting one-dimensional product crystal size distribution (CSD) or chord length distribution (CLD) of batch cooling crystallization processes, based on only batch run data. The proposed model relating the manipulated variable of cooling rate to the product CSD are constructed by two classes of basis functions, one is the wavelet basis function for reshaping the CSD and the other is the polynomial basis function for weighting the chosen wavelet basis functions to reflect the nonlinear relationship between the input and the density of individual crystal size among the product crystals. Correspondingly, a double-layer least-squares algorithm is established to estimate the model parameters, along with an adaptive strategy to determine the location and number of wavelet basis functions. By introducing an objective function that combines the information entropy of product CSD and the sample deviation of product crystals in each batch with respect to the target crystal size, the optimal input design of cooling rate for the desired product CSD is carried out by using a particle swarm optimization (PSO) algorithm to solve the non-convex optimization problem with the established CSD model. Simulation tests on the hen-egg-white lysozyme crystallization process along with experiments on the L-glutamic acid cooling crystallization process are performed to demonstrate the effectiveness and advantage of the proposed method.

In this paper, a cell average technique(CAT) based parameter estimation method is proposed for cooling crystallization involved with particle growth, aggregation and breakage, by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD) algorithm. To overcome the deficiency of CAT that demands high computation cost for implementation, a set of ordinary differential equations(ODEs) entailed from CAT based discretized population balance equation(PBE) are solved by using the AD based high-order Taylor expansion. Moreover, an AD based trust-region reflective(TRR) algorithm and another interior-point(IP) algorithm are established for estimating the kinetic parameters associated with particle growth, aggregation and breakage. As a result, the estimation accuracy can be further improved while the computation cost can be significantly reduced, compared to the existing algorithms. Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT, TRR and IP algorithms in comparison with the existing algorithms. Moreover, seeded batch cooling crystallization experiments of β form L-glutamic acid are performed to validate the proposed method.

Quadrature method of moments (QMOM) is a promising method to solve population balance models of industrial crystallization processes. The existing techniques for solving the differential algebraic equations (DAEs) arising in the QMOM formulation suffer from poor numerical robustness. In this paper, the fundamental formulation of QMOM is revisited by using automatic differentiation (AD) for computation to improve its performance. A closed-form solution to the algebraic equations resulting from the quadrature approximation of moments is derived by augmenting the original variable set with an extra set of variables. Based on this closed-form solution, two algorithms, namely, the augmented ODE and augmented AD-QMOM, are proposed. Numerical case studies show that both of the proposed approaches can effectively improve numerical robustness such that a much higher number of moments can be solved compared to the existing approaches. Moreover, the augmented AD-QMOM approach is shown to be computationally more efficient than the augmented ODE approach.

Dual-inverter drive of open-end winding ac machine is equivalent to the conventional three-level inverter system from the point of view of voltage vector count, but is simpler in the structure. Decoupled PWM strategy is usually used in the dual- inverter drive. In this paper, it is proposed that a three-phase open-end winding permanent magnet synchronous motor (PMSM) is driven with a five-leg inverter so as to simplify the power electronic circuit and to reduce the hardware cost, whilst the decoupled PWM strategy is evolved accordingly. Simulation and experiments show that the evolved drive system can achieve a similar control performance to the traditional system.

Compared with a traditional single inverter-fed permanent magnet synchronous motor( PMSM), the 3-phase open-end winding PMSM driven by single DC supply and dual inverters is benefited from more applicable voltage vectors,more flexible control method,as well as better drive performance,but suffers from the larger number of inverter legs and more complicated hardware structure. Therefore,in this paper,the drive topology of single-supply dual-inverter,i. e. six-leg inverter,with common-mode-voltage-free( CMVF)space vector pulse width modulation( SVPWM)is evolved so as to eliminate some of the inverter legs,whilst the motor performance with each evolved topology is comparatively analyzed. It is seen that the evolved topologies induce extra paths for the zero-sequence current which,however,is not actually generated due to the absence of the zero-sequence voltage under the CMVF SVPWM control. Thus,the motor performance is hardly deteriorated by the topology evolution. The proposed topology evolution not only provides a reference for the selection and design of the inverter and motor windings,but also reveals the innate character of the CMVF SVPWM.

On the basis of the characteristics of the switched reluctance motor and the calculation principles of transient torque , the measurement of the transient torque of the switched reluctance motor is investigated . Meanwhile , a measuring system of the transient torque of the switched reluctance motor is developed using the virtual instrument technology and the multifunctional data acquisition card PCI-6250 .Based on the data acquisition as well as the related calculation principles , combined with LabVIEW and data configuration program MAX ,and by means of the PCI card to acquise the data of the switched reluctance motor ,the transient characteristics of the motor ,such as torque ,rotate speed ,phase voltage ,phase current can be instantaneously measured by the system .In addition ,the synchronous waveform and numerical value can be displayed and relatively configured on the terminal client .Meanwhile the data of real-time measurement can be saved by the users .

The inherent nonlinearity of the switched reluctance motor （SRM） makes it impossible to eliminate torque ripple for conventional average torque control method, which also restricts its application in high performance servo. The direct instantaneous torque control strategy was adopted. In order to track the reference torque accurately, the instantaneous torque was directly controlled by hysteresis and PWM control with torque sharing function during the phase commutation. The control strategy was applied to a prototype motor control. Finally, the experiment verified the effectiveness of the strategy.

The inherent highly nonlinearity of switched reluctance motor not only makes it difficult to eliminate torque ripple with conventional average torque control techniques, but also restricts its application in the high-performance servo systems. A novel control strategy combing direct instantaneous torque control with the torque sharing function control is proposed in this paper. In order to track the reference torque accurately, the instantaneous torque is directly controlled by a hysteresis and PWM controller with torque sharing function. The control strategy is applied to a prototype motor control system, and is verified by the experiment results.

In this paper, a transient characteristic measuring system for switched reluctance motor (SRM) based on virtual instrument technology and the multi-function data acquisition card PCI-6250 is developed. Firstly, the system hardware is built up. The transient data including phase current and voltage, rotor angle position are collected by the data acquisition card, and transmitted to a computer by PCIBUS. Secondly, the system software is designed on the bases of LabVIEW and the data configuration program MAX. The software of system deals with the collected data and calculates the instantaneous torque. The transient characteristics of SRM including torque, speed, phase voltage, and phase current can be measured in real time, and displayed and saved simultaneously. Finally, the measurement system is applied to the testing of a prototype motor, and the results are helpful to the analysis and improvement of the SRM control system.

Direct instantaneous torque control (DITC) method of the switched reluctance motor (SRM) is studied in this paper. Modeling and simulations of the DITC system have been conducted with MATLAB/Simulink. The simulation results accurately reflect the actual operation states of SRM. It is verified that DITC method can effectively reduce the torque ripple of SRM.

Rosen piezoelectric transformer has its unique advantages in portable high-voltage applications. Model parameters of Rosen piezoelectric transformer are important for simulation and analysis of piezoelectric transformer's electrical characteristics. Usually, these model parameters are obtained with expensive impedance analyzer. Based on the measured voltage gain-frequency response characteristics, a practical approach for model parameters measurement of piezoelectric transformer was proposed. Firstly, the voltage gain-frequency response was measured and then transformed into optimization function which matches voltage gain expression. Secondly, L, C and N was obtained using MATLAB simulation with fminsearch minimization cost function. MPT3006A50L0 multilayer piezoelectric transformer samples were measured and analyzed using this method. The comparisons show that the measured results agree well with the test data provided by Agilent 4294A impedance analyzer.