Analyzing the natural color system's color-order system by using a nonlinear color-appearance model

The Natural Color System (NCS) is analyzed by using a nonlinear color-appearance model. Perceptual uniformity was examined for each of the NCS attributes of blackness (s), chromaticness (Cr), and hue. Some nonuniformities were found in chromaticness and hue spacing, which were probably the result of the assessing and scaling method used in developing the system. In addition, a colorimetric interpretation is given to a principal plane in the NCS consisting of the colors with (s,Cr) = (50,0) and (0,100). The colors with (0,100) have different values of Y for different hues. Based on the analysis, a method is developed to predict the NCS attributes from the values x, y, Y of an object color by using the nonlinear color-appearance model. The present analysis clarifies the importance of the NCS system in studying the color appearance of object colors.     

Whiteness-blackness and brightness response in a nonlinear color-appearance model

The achromatic response of the nonlinear color-appearance model is developed to predict the perceptions of whiteness-blackness, brightness, and lightness of object colors. The distinction between whiteness-blackness and brightness perceptions of achromatic colors is especially important in an adapting condition with nonuniform illumination or in a haploscopic match between different adapting fields. In the whiteness–blackness response, the reference gray is introduced from the viewpoint of opponency of achromatic response, and the whiteness–blackness response is divided into whiteness–grayness and grayness–blackness responses. By giving different weights for the whiteness–grayness and grayness–blackness responses, the metric lightness in the nonlinear color-appearance model agrees very closely with the CIE 1976 L* function without any alteration to the model formulation.     

Revision of the chroma and hue scales of a nonlinear color-appearance model

The following questions were raised to chroma and hue scales of the nonlinear color-appearance model: 1) significant nonuniformities of the chroma scales for different hues, and 2) deviations of hue scale between the model and the Munsell and the NCS schemes. It was suggested that the problems were caused by the use of the coefficient e_s(0) proposed by Hunt. Instead of e_s(0), a new coefficient E_s(0) was proposed, which corresponds to the chromatic strengths of spectral colors (including colors on the redpurple locus). By using E_s(0), the nonlinear color-appearance model could predict the hue and chroma scales of the Munsell and the NCS schemes quite nicely. the method in the present study is generally applicable for determining hue and chroma perceptions of object colors irrespective of the color-appearance model used.     

Lightness dependency of chroma scales of a nonlinear color-appearance model and its latest formulation

It has been noticed that the lightness dependency of equal chroma loci of the nonlinear color-appearance model already reported deviates markedly from that of equal Chroma loci of the Munsell scheme. to solve this problem, the new chroma C_N of the model is proposed by applying the correction of lightness L_A to the chroma C previously used. the chroma C is now used to predict the saturation of the newly revised model. the introduction of C_N improves significantly the agreement of lightness dependency between the model chroma, the Munsell Chroma, and the NCS chromaticness at various lightness levels. the formulation for the revised nonlinear colorappearance model is given in the Appendix.     

Colour matching using LEDs as primaries

In our metameric experiment, the colour of a filtered incandescent lamp was matched with the additive mixture of three LEDs in a Lummer–Brodhun‐type visual photometer. Two sets of primaries were used, one had their dominant wavelengths at 467, 533, and 600 nm; the other set had dominant wavelengths at 478, 552, and 635 nm. These values correspond approximately to the characteristic wavelengths of the Prime and Non‐Prime Colour spectral regions defined by W. A. Thornton. 1 Both the light of the incandescent lamp and that of the LED clusters were seen monocularly in a centrally divided bipartite field at a visual angle of 2°. The luminance of the matching fields was in the order of 20 cd/m² to provide sufficient gamut for the LED mixture. Ten young observers with normal colour vision participated in the experiment. The emission spectra of the viewing fields were measured with an array‐type spectroradiometer, and two sets of colour‐matching functions were used to calculate the chromaticity of the matching stimuli: the CIE 1931 standard colorimetric observer and the Judd–Vos modification of the colour‐matching functions. We found that the Judd–Vos modification of the CIE 1931 standard observer represents more accurately the real observers in the evaluation of our results. No systematic differences between the use of the two sets of LEDs were detected in contradiction to Thornton's findings. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 360–364, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20044     

Transformation of primaries using four chromaticity points and their maps

This note describes several approaches to transforming primaries using four chromaticity points and their maps. The motivation is an exercise described by Wold (Die Farbe 1999/2000;45:99–117). Whereas, several approaches to the problem depend on the points corresponding to the primaries themselves, and on whether the old primaries are specified in the new system or vice versa. This note presents an approach that will work for a general (nonsingular) set of four reference chromaticity points and their maps. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 506–509, 2008     

A nonlinear mechanical model for solid-filled rubbers

A nonlinear mechanical model has been proposed for application to nonlinear viscoelastic elastomers. The model consists of four nonlinear elements similar to the Burgers model. Based on the theory of reaction rate proposed by Eyring and the statistic concept of entropy-spring developed in rubber elasticity, four relevant nonlinear elements are used to construct the model. The deformation, or the time rate of deformation of each element is described by a nonlinear stretch parameter A. According to the model and the parameter A, two groups of equations are derived to describe the creep or relaxation behavior of solid-filled and pure rubbers, respectively. In order to examine the applicability of the model as well as the nonlinear stretch parameter, a series of experiments for solid-filled polybutadiene rubbers has been carried out, which include constant rate of tensile tests, creep and relaxation tests with and without aging effects. It is found that the nonlinear stretch parameter satisfies the Eyring equation and that the model agrees the experiments extremely well.     

A multiple model approach to nonlinear internal model control design

A nonlinear internal model control (NIMC) design using multiple model is proposed. In this design approach, the process model is described via validity functions as the weighted sum of a set of local models. Subsequently, an approximate inverse of the process model is constructed in order to design NIMC controller. It is shown that the validity functions can be treated as time-varying uncertainties in the resultant NIMC structure, and a structured singular value test for mixed time-varying and time-invariant perturbations is used to assess the performance limitation of the proposed NIMC design. Simulation results of a continuous stirred tank reactor illustrate that the proposed NIMC design method is superior to the conventional IMC design.     

Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Discrete-time contraction constrained nonlinear model predictive control using graph-based geodesic computation

Modern chemical processes need to operate around time-varying operating conditions to optimize plant economy, in response to dynamic supply chains (e.g., time-varying specifications of product and energy costs). As such, the process control system needs to handle a wide range of operating conditions whilst optimizing system performance and ensuring stability during transitions. This article presents a reference-flexible nonlinear model predictive control approach using contraction based constraints. Firstly, a contraction condition that ensures convergence to any feasible state trajectories or setpoints is constructed. This condition is then imposed as a constraint on the optimization problem for model predictive control with a general (typically economic) cost function, utilizing Riemannian weighted graphs and shortest path techniques. The result is a reference flexible and fast optimal controller that can trade-off between the rate of target trajectory convergence and economic benefit (away from the desired process objective). The proposed approach is illustrated by a simulation study on a CSTR control problem.     

Evaluate the nonlinear viscoelasticity of polyolefin melts using the Larson model

Nonlinear rheological properties of polyolefins have long been studied and predicted by using the Larson model with the damping function generally obtained from the stress relaxation measurements. In this study, we investigate the nonlinear rheological properties of high density polyethylene (HDPE) and polypropylene (PP) using the Larson model with damping functions obtained from either the dynamic frequency sweep or the stress relaxation test. Experimental measurements and their corresponding model predictions for the rheological parameters were then compared to evaluate the applicability of the Larson model to the nonlinear rheology, and the following conclusions could be achieved. The steady shear viscosity could be satisfactorily described by the Larson model with the damping functions obtained from the two different methods, except at shear rates higher than 10³ s^?1. The predicted first normal stresses also account for the measured data, except for those using the stress relaxation data showing a little deviation for the PP sample. In addition, the predictions for elongation viscosity are also in good agreement with the experimental results within the short range of elongation rate achieved in this work. POLYM. ENG. SCI., 54:2354–2361, 2014. © 2013 Society of Plastics Engineers     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A two‐phase model for variable‐density fluidized bed reactors with generalized nonlinear kinetics

A model based on the classical two‐phase concept is developed for the simulation of variable‐density reaction with generalized nonlinear kinetics in a bubbling fluidized bed. The influence of reaction density parameter on the fluidodynamics and performance of the reactor for four general types of reactions was explored. The results show that the expansion factor has a significant effect on both fluidodynamic characteristics and reaction conversion. In all types of reactions, higher values of hydro‐dynamic variables were obtained when ? ≥ 0. Reaction conversion, however, dropped as the expansion factor increased. This trend was more pronounced for reaction orders higher than unity. This suggests that bubbling fluidized operations are probably not optimal and applicable for certain types of reactions. Comparative analysis between reaction type and implications for optimum fluidized bed reactor are discussed.     

基于内部热耦合精馏塔非线性wave模型的高纯控制

首先建立内部热耦合精馏塔（ITCDIC）的非线性波动降阶模型,并将非线性波动理论（wave）应用到ITCDIC控制问题中,实现一般模型控制（GMC）方案.与传统控制方案相比,基于波动理论的一般模型控制（waveGMC）不再采用ITCDIC的近似线性模型,更好地解决了高纯控制过程中的非线性问题,通过对波形的速度和位置控制能够在短时间内使系统达到稳定.苯-甲苯物系的实例研究表明,ITCDIC波动模型在高纯控制过程中能够精确反映ITCDIC的动态特征,waveGMC控制方案较传统控制方案更加稳定可靠.     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers