Research On Shape Model Predictive Control Algorithm For Distribution Profile Process

The product performance requirements in many industrial fields,including polymers,papermaking and aircraft,continue to improve.So there is a need of distribution profile control,where the controlled variable is one distribution profile rather than one point in n-dimensional space.The shape of the distribution profile is changeable and easily deformed in the form of shifting and scaling.The traditional performance indexes based on Euclidean distance do not have the ability to correctly measure the shape similarity of the distribution profiles.It is difficult to achieve high-quality shape control of the distribution profile process.Therefore,combined with the shape similarity,this paper studies the shape model predictive control algorithms for the distribution profile process.The main contributions of this paper are as follows:(1)The traditional integral squared error index is based on Euclidean distance and mainly focuses on the absolute difference between the numerical information.Due to the lack of shift-invariance property,ISE is difficult to make correct similarity measurements for shifting along the numerical axis.A gradient feature-based shape model predictive control algorithm is developed.The algorithm quantifies the shape similarity between the distribution profiles based on gradient features.The rolling optimization proposition contains numerical and gradient features and is discretized by the composite trapezoidal rule.Finally,the optimization proposition is solved to get the optimal solution.Simulations show the effectiveness of the algorithm.(2)The shape of the distribution profile is complex and exhibits multi-scale characteristics.It is difficult to measure shape similarity with features of a single scale.A multiscale feature-based shape model predictive control algorithm is proposed for the distribution profile process.The algorithm uses discrete orthogonal wavelet transform to extract features of the distribution profile at different scales.Then the optimization proposition is constructed based on a multiscale similarity index of the distribution profiles.By setting the weighting coefficients corresponding to features of different scales,this algorithm can control the shape similarity of different scales.In particular,the scaling coefficients obtained by Haar wavelet transform can reflect the mean values of the distribution profile.On this basis,the algorithm can perform multiscale feedback correction according to the mean values to improve the robustness of the control system.(3)Aiming at the distribution profile shifting and scaling along the distribution axis,this paper proposes a DTW-based shape model predictive control algorithm for the distribution profile process.The algorithm uses the DTW to construct the optimal mapping between the distribution profiles,which can effectively measure the shape similarity when the distribution profiles are deformed along the distribution axis.The optimal control strategy is obtained by solving the rolling optimization proposition based on the optimal mapping.The simulation shows that this algorithm can identify and utilize the similar shape features to achieve the control of the overall shape of the distribution profile.