Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

A batch-to-batch optimal iterative learning control （ILC） strategy for the tracking control of product quality in batch processes is presented. The linear time-varying perturbation （LTVP） model is built for product quality around the nominal trajectories. To address problems of model-plant mismatches, model prediction errors in the previous batch run are added to the model predictions for the current batch run. Then tracking error transition models can be built, and the ILC law with direct error feedback is explicitly obtained, A rigorous theorem is proposed, to prove the convergence of tracking error under ILC, The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

A HIGH ACCURACY DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.

UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.

Size Effect on Onset and Subsequent Evolution of Adiabatic Shear Band:Theoretical and Numerical Analysis

The adiabatic shear instability of ductile materials has attracted more and more attentions of researchers and groups,who have been sparing no effort in further understanding of the underlying mechanism since the first experimental depiction of adiabatic shear instability by Zener and Hollomon.As for the adiabatic shear instability,many factors account for its occurrence,including heat conduction,inertia effect,microstructure effect and so on.However,lots of experimental evidence has shown that metal materials display a strong size effect when the characteristic length scale is in the order of microns.The size effect has also been observed in the analysis of shear band in the ductile materials because the order of the bandwidth stays within the microscale range.However,a comprehensive understanding of the whole process of adiabatic shear banding(ASB),including the early onset and the subsequent evolution,is still lacking.In this work,a gradient plasticity model based on the Taylor-based nonlocal theory feasible for the linear perturbation analysis and convenient for numerical calculation is proposed to investigate the strain gradient on the onset of ASB and the coupling effect of heat conduction,inertia effect and strain gradient at the early stage,as well as on the subsequent evolution process at later stages.As for the onset of ASB,the linear perturbation method is used to consider the effect on the initial formation of ASB.After the investigation of the onset of ASB.the characteristic line method is applied to describe the subsequent nonlinear evolution process of ASB.Three stages of ASB evolution are clearly depicted during the evolution process,and the significance of size effect on the ASB nonlinear evolution process of ASB at different stages is analyzed.With the help of linear perturbation analysis and characteristic line method,a comprehensive description of the role of strain gradient in the ASB from the early onset to the end of the evolution is provided.