Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC

Heat and mass transfer effects of ice growth mechanisms in pure water and aqueous solutions

Interactions between heat and mass diffusion determine growth mechanisms during ice crystallization. The effects of heat and mass transfer on ice growth in pure water and magnesium sulfate solution were investigated by studying the evolution of the gradient of the refractive index using color Schlieren deflectometry. For pure water, the gradient of the refractive index of water was used to calculate the temperature and therefore the local supersaturation. Its effect on the ice crystal growth rate and morphology was studied. It was found that, for local supersaturations greater than 2.8, the morphology was dendritic ice, with a growth rate 2 orders of magnitude higher than that for layered growth. During dendritic growth, 3−16% of the heat of crystallization diffused to the liquid side, which is counter to current understanding. At the transition (between the time of partial melting of the dendritic ice and the beginning of the layered ice growth), a higher supersaturation than that responsible for layered growth was observed. For ice growth from an aqueous salt solution, a mass and thermal diffusion boundary layer in front of the growing ice was created by diffusion of the solutes from the ice and by the release of heat of crystallization

Extensions and corollaries of the thermodynamic solvate difference rule

The ever-growing requirement to develop new materials for highly specific applications is making major demands for thermodynamic data which have not, to date, been measured. This, in turn, means that, increasingly, estimated values are required to make thermodynamic interpretations and feasibility studies of reactions involving these materials. In this vein, four further extensions of, and insights into, the Thermodynamic Solvate Difference Rule, are presented here and tested. The result is the provision of valuable, albeit approximate, rules useful for many areas of organic/inorganic chemisty to predict thermodynamic data in cases where experimental data have not yet been determined. These extended rules take the form P{MpXq.jL,p} + P{M-p'X-q''.kL,p} approximate to P{MpXq.dL,p} + P{M-p'X-q''.sL,p} where j + k = d + s and the salt M-p'X-q' can be the same as MpXq. P represents any of the individual thermodynamic properties: Delta H-f degrees, Delta(f)G degrees, Delta S-f degrees, etc. Also P{MpXq.jL,p} + P{M-p'X-q''.kL,p} approximate to P{MpXq.kL,p} + P {M-p'X-q''.jL,p} For salts MpXq, M-p'X-q', and M-r'X-s' and then for multiple salts compounded from these, where one salt is considered to be the "solvent" of the other, and vice-versa, then P{MpXq.jM(r)'X-s',s} approximate to P{MpXq,s} + j.Theta(P){M-r'X-s',s - s} P{M-r',X-s'.dM(p)X(q),s} approximate to P{M-r'X's,s} + d.Theta(P){MpXq,s - s} where Theta(P){M-r'X-s', s-s} and Theta(P){MpXq,s-s} are constants, independent of the nature of MpXq and M-r'X-s', respectively. Thus, salts may e permuted as being regarded as solvent and solvate. A cascading rule can be established as follows P{MpXq.M-p'X-q'.jM(r)'X-s',s} approximate to P{MpXq.M-p'X-q',s} + j.Theta(P){M-r'X-s',s-s} approximate to P {MpXq's} + Theta(P){M-p'X-q',s-s} + j.Theta(P){M-r'X-s',s-s} and permutationps Lreon. Developed and applied initially for inorganic compounds, the rule is shown to extend into the arena of organic thermochernistry