Research and Development Trend of Shape Control for Cold Rolling Strip

Shape is an important quality index of cold rolling strip. Up to now, many problems in the shape control domain have not been solved satisfactorily, and a review on the research progress in the shape control domain can help to seek new breakthrough directions. In the past 10 years, researches and applications of shape control models, shape control means, shape detection technology, and shape con- trol system have achieved significant progress. In the aspect of shape control models, the researches in the past improve the accuracy, speed and robustness of the models. The intelligentization of shape control models should be strengthened in the future. In the aspect of the shape control means, the researches in the past focus on the roll opti- mization, mill type selection, process optimization, local strip shape control, edge drop control, and so on. In the future, more attention should be paid to the coordination control of both strip shape and other quality indexes, and the refinement of control objective should be strengthened. In the aspects of shape detection technology and shape control system, some new types of shape detection meters and shape control systems are developed and have successfully indus- trial applications. In the future, the standardization of shape detection technology and shape control system should be promoted to solve the problem of compatibility. In general,the four expected development trends of shape control for cold roiling strip in the future are intelligentization, coordi- nation, refinement, and standardization. The proposed research provides new breakthrough directions for improv- ing shape quality.

Application of Smith Predictor Based on Single Neural Network in Cold Rolling Shape Control

Flatness is one of the most important criterion factors to evaluate the quality of the steel strip. To improve the strip＇ s flatness quality, the most frequently used methodology is to employ the closed-loop automatic shape control system. However, in the shape control system, the shape-meter is always installed at the down way of the exit of the cold rolling mill and can not sense the changes of the strip flatness in the rolling gap directly. This kind of installation results in the delay of the feedback in the control system. Therefore, the stability and response performance of the system are strongly affected by the delay. At present, there is still no mature way to design controllers for systems with time delay. Although the conventional PID controller used in most practical applications has the capability to compensate the delay, the effect of the compensation is limited, especially for the systems with long time delay. Smith predictor, as a compensator for solving this problem, is now widely used in industry systems. However, the request of highly precise model of the system and the poor adaptive performance to the changes of related parameters limit the application of the Smith predictor in practice. In order to overcome the drawbacks of the Smith predictor, a new Smith predictor based on single neural network PID （SNN-PID） is proposed. Because the single neural network is employed into the Smith predictor to improve the controller＇s self-adaptability, the adaptive capability to the varying parameters of the system is improved. Meanwhile, for the purpose of solving the problems such as time-consuming and complicated calculation of the neural networks in real time, the learning coefficient of neural network is divided into several stages as usually done in expert control system. Therefore, the control system can obtain fast response due to the improved calculation speed of the neural networks. In order to validate the performance of the proposed controller, the experiment is conducted on the shape control system in a 300 mm four-high reversing cold rolling mill. The experimental results show that the SNN-PID with Smith predictor controller can effectively compensate the delay effects and achieve better control performance than the conventional PID controller.

Simulation of type selection for 6-high cold tandem mill based on shape control ability

A theoretical method for selecting strip rolling mill type that considered shape control ability was established using the figure alteration range that was worked by the alteration track of vector expressing strip's cross section (crown) to express the shape control ability of rolling mill. With the mathematical models and simulation software that were developed by the authors' own models, four types of mills were aimed, including HCM (6-high middle rolls shift type HC (high crown) -mill), HCMW (6-high middle rolls and work rolls shift type HC-mill), UCM (6-high middle rolls shift type HC-mill with middle roll bender) and UCMW (6-high middle rolls and work rolls shift type HC-mill with middle roll bender), and the shape and crown control ability of every mill type was analyzed and compared. An appropriate arrangement mode of tandem mill was brought forward. The results show that UCMW mill is a perfect choice for controlling shape and crown, and the area of control characteristics curve of UCMW (or UCM) is twice than that of HCM, but UCM mill is also a good choice for its simple frame. In other word, the shape and crown controlling ability of UCMW mill is better than that of UCM mill, but the frame of UCM mill is simpler than that of UCMW mill. As for the final type of mill, should be synthetically decided by thinking over fund and equipment technology.

Fuzzy Shape Control Based on El man Dynamic Recursion Network Prediction Model

In the strip rolling process, shape control system possesses the characteristics of nonlinearity, strong coupling, time delay and time variation. Based on self adapting Elman dynamic recursion network prediction model, the fuzzy control method was used to control the shape on four-high cold mill. The simulation results showed that the system can be applied to real time on line control of the shape.

Shape control on probability density function in stochastic systems

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

Shape control technology during electrochemical synthesis of gold nanoparticles

Gold nanoparticles with different shapes and sizes were prepared by adding gold precursor （HAuC14） to an electrolyzed aqueous solution of poly（N-vinylpyrrolidone） （PVP） and KN03, which indicates the good reducing capacity of the PVP-containing solution after being treated by electrolysis. Using a catholyte and an anolyte as the reducing agents for HAuC14,＇ respectively, most gold nanoparticles were spherical particles in the former case but plate-like particles in the latter case. The change in the pH value of electrolytes caused by the electrolysis of water would be the origin of the differences in shape and morphology of gold nanoparticles. A hypothesis of the H＋ or OH- catalyzed PVP degradation mechanism was proposed to interpret why the pH value played a key role in determining the shape or morphology of gold nanoparticles. These experiments open up a new method for effectively controlling the shape and morphology of metal nanoparticles by using electrochemical methods.

Adaptive Shape Control for Thermal Deformation of Membrane Mirror with In-plane PVDF Actuators

Optical membrane mirrors are promising key components for future space telescopes. Due to their ultra-thin and high flexible properties, the surfaces of these membrane mirrors are susceptible to temperature variations. Therefore adaptive shape control of the mirror is essential to maintain the surface precision and to ensure its working performance. However, researches on modeling and control of membrane mirrors under thermal loads are sparse in open literatures. A 0.2 m diameter scale model of a polyimide membrane mirror is developed in this study. Three Polyvinylidene fluoride(PVDF) patches are laminated on the non-reflective side of the membrane mirror to serve as in-plane actuators. A new mathematical model of the piezoelectric actuated membrane mirror in multiple fields,(i.e., thermal,mechanical, and electrical field) is established, with which dynamic and static behaviors of the mirror can be analyzed.A closed-loop membrane mirror shape control system is set up and a surface shape control method based on an influence function matrix of the mirror is then investigated. Several experiments including surface displacement tracking and thermal deformation alleviation are performed. The deviations range from 15 μm to 20 μm are eliminated within 0.1 s and the residual deformation is controlled to micron level, which demonstrates the effectiveness of the proposed membrane shape control strategy and shows a satisfactory real-time performance. The proposed research provides a technological support and instruction for shape control of optical membrane mirrors.

Finite element analysis of shape control for continuous hot rolling mills of super wide strip steel

The efficacy of shape control is the core of this technology and the main basis of automatic shape control system model designing. This passage constructs the three-dimensional elastic deformation model of CVCplus roll system in 2250 mm hot rolling mill. Comparing and analyzing different influence of working factors on control characteristic, the shape control characteristic of CVCplus roll system in its whole work time is studied, and the cause is analyzed and the difference of the roll gap curve and crown adjustable area in early and latter work time is compared. The outcome has crucial meaning in both theory and production.

Static shape control of a flat shell structure

The eight-node and forty-DOF piezoelectric shell element were applied to shape control of a flat shell structure. By the direct and converse effects, a distributed piezoelectric sensor layer was used to monitor the shape deformation and a distributed actuator layer was used to suppresse the deflection. A finite element model was for static response of laminated shell with piezoelectric sensors/actuators was derived. The model was verified by calculating piezoelectric polymeric PVDF bimorph beam. The results are in good agreement with those obtained by theoretical analysis of Tzou and Hwang . A case study of the static shape control of a flat shell structure is presented.

Shape Control,Crystalline Conversion and Pseudocapacitance Properties of Mn3O4:Effects of Yb3+Doping

We report a facile method for the synthesis of manganese oxide（Mn3O4） nanorods via the direct reaction of MnCl2 and H2 O2 by doping Yb3＋ ions at room temperature and air atmosphere. The Mn3O4：Yb3＋ samples were characterized by X-ray diffraction（XRD）, scanning electron microscopy（SEM）, cyclic voltammetry（CVs）, electrochemical impedance spectroscopy（EIS）, and charging-discharging test（CD）. The results show that trace Yb3＋ doping（6 at%） could effectively induce crystalline transformation of Mn3O4 from cubic system（space group Fd-3 m） to tetragonal system（space group I41/amd） and incite the morphology changing from irregular particles to uniform nanorods. When Yb3＋ doping amount is 3%, the capacitance of Mn3O4 reaches the maximum, 246 F/g, which is related to the morphology change and the corresponding decrease of impedance.

Shape Control and Vibration Analysis of Pi-ezolaminated Plates Subjected to Electro-Mechanical Loading

Shape control and free vibration analysis of piezolaminated plates subjected to electro mechanical loading are evaluated using finite element method. First order shear deformation theory is employed in the analysis. Both extensions as well as shear actuators are considered for piezolaminated plates. Rectangular four node isoparametric element is used in the finite element formulation. Variation of temperature is neglected for the orthotropic layers of the laminate and for piezolayer. Annular circular plates and rectangular plates with piezoelectric layers mounted and/or integrated are analysed for various parameters. Numerical results are presented for varying the actuator voltage for annular plates with different thicknesses of piezo patches. In case of rectangular plate shear actuator is considered for vibration analysis.

STATIC SHAPE CONTROL OF LAMINATED PLATE CONTAINING PIEZOELECTRIC PATCHES

By applying the Heaviside function, the equations governinglaminated plates possess- ing spatially distributed piezoelectricpatches have been established. Based on these equations, static shapecontrol of laminated plates is discussed. BY using a genetic andcollocation algorithm, the opti- mal locations and scales of thesepiezoelectric patches have been selected. Numerical examples are pre-sented to illustrate the efficiency of the algorithm and thepiezoelectric actuators.

Shape Control and Modification of Rational Cubic B-Spline Curves

This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented.

Size and shape control of LiFePO4 nanocrystals for better lithium ion battery cathode materials

Lithium iron phosphate （LiFePO4） is a potential high efficiency cathode material for lithium ion batteries, but the low electronic conductivity and single diffusion channel for lithium ions require good particle size and shape control during the synthesis of this material. In this paper, six LiFePO4 nanocrystals with different size and shape have been successfully synthesized in ethylene glycol. The addition sequence Fe-PO4-Li helps to form LiFePO4 nanocrystals with mostly {010} faces exposed, and increasing the amount of LiOH leads to a decrease in particle size. The electrochemical performance of the six distinct LiFePO4 particles show that the most promising LiFePO4 nanocrystals either have predominant {010} face exposure or high specific area, with little iron（II） oxidation.

Shape Control of Doped Semiconductor Nanocrystals (d-Dots)

Formation of Mn2+-doped ZnSe quantum dots(Mn:ZnSe d-dots)with both branched and nearly spherical shapes has been studied.Structure analysis indicates that the Mn2+dopants were localized in the core of a branched nanocrystal.The growth of branched d-dots,rather than spherical ones,was achieved by simply varying the concentration of two organic additives,fatty acids,and fatty amines.The photoluminescence properties of the branched nanocrystals were explored and compared with those of the nearly spherical particles.

Head and Tail Shape Control in Vertical-Horizontal Rolling Process by FEM

Using 3D rigid-plastic finite element method （FEM）, a numerical simulation model for nonsteady state vertical-horizontal rolling process in roughing trains was built and was validated by comparing the simulated values with experimental ones of width and shape of the stock ends. According to certain 2050 roughing processing technologies, the short shape control （SSC） of the stock ends was investigated using the model. Based on the simulated results, a new SSC model was developed. The analyzed results showed that the new SSC model is effective in improving the shape of the stock ends.

Shape control of spacecraft formation using a virtual spring-damper mesh

This paper derives a distance-based formation control method to maintain the desired formation shape for spacecraft in a gravitational potential field. The method is an analogy of a virtual spring-damper mesh. Spacecraft are connected virtually by spring-damper pairs. Convergence analysis is performed using the energy method. Approximate expressions for the distance errors and control accelerations at steady state are derived by using algebraic graph representations and results of graph rigidity. Analytical results indicate that if the underlying graph of the mesh is rigid, the convergence to a static shape is assured, and higher formation control precision can be achieved by increasing the elastic coefficient without increasing the control accelerations. A numerical example of spacecraft formation in low Earth orbit confirms the theoretical analysis and shows that the desired formation shape can be well achieved using the presented method, whereas the orientation of the formation can be kept pointing to the center of the Earth by the gravity gradient. The method is decentralized, and uses only relative measurement information. Constructing a distributed virtual structure in space can be the general application area. The proposed method can serve as an active shape control law for the spacecraft formations using propellantless internal forces.

Boundary Shape Control of the Navier-Stokes Equations and Applications

In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

Technique of Probability Density Function Shape Control for Nonlinear Stochastic Systems

The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.

Catalyst-Free Synthesis and Shape Control of CdTe Nanowires

The procedure reported here allows for the size and shape control of CdTe nanowires by means of colloidal chemistry. Thus, ultrathin, straight, saw-tooth-like and one-sided branched nanowires with zinc blende structures could be synthesized. Their formation does not require any catalyst and is most likely due to the oriented attachment of nanoparticles formed in the beginning of the reaction. The use of oleylamine as a solvent turned out to be crucial in order to achieve CdTe nanowires. The reaction between oleic acid and oleylamine in the presence of CdO proved to be essential, not only to activate the Cd precursor but also to provide reaction conditions facilitating nanowire formation by oriented attachment.