Research On Partial Least Square Aided Predictive Control With Its Application Verification

With the rapid development of modern production process,the scale of production is increasing,and the physical and chemical reactions are becoming more and more complex.It is therefore too difficult to establish accurate models of these production equipments.For some production equipment in cutting-edge science,such as plasma experimental device,we can hardly even establish their models.On the other hand,although many of the production equipment are open-loop stable,there exists unknown nonlinear characteristics generally.Tracking control of the open-loop stable non-linear system with unknown model has become the new challenge in controller design.For this reason,this paper takes the open-loop stable non-linear system with unknown model as the controlled object,and studies the predictive control strategy in partial least squares framework.First of all,the development history and research status of model predictive control,partial least squares regression and data-driven control methods are summarised in this paper,after which we point out the shortcomings of the existing partial least squares regression algorithm and predictive control strategy under the partial least squares regression framework:1)the traditional partial least square algorithms do not completely decompose the data space,resulting in the insufficient precision of the regression model.Besides,the partial least squares adopt the iterative calculation method,so that the model cannot be updated online.Therefore the predictive control in partial least squares framework cannot be applied to the control of nonlinear systems;2)most of the existing nonlinear partial least squares do not have the ability of online learning based on process data,and the predictive control under the nonlinear partial least squares framework will project the linear constraint of the original data space into the nonlinear constraint of the latent variable space,which leads to difficulties in solving the control signal;3)in order to avoid the solvability problem,the existing predictive control in nonlinear partial least squares framework usually operate linear approximation of nonlinear regression model to construct the predictive model.It therefore lost the original prediction precision of the original nonlinear regression model.Besides the predictive controlin nonlinear partial least squares framework usually requires constraints on control signals,which leads to slow convergence speed of control signal.Considering the problems above,this thesis will present solutions to solve them step by step.First,in view of the traditional method of partial least squares(PLS)regression's model precision is not enough,the calculation of the regression model requires complex iterative computation,and the predictive control strategy in partial least squares framework of control strategy could not handle the nonlinear system,this thesis put forward the predictive control in modified PLS(MPLS)framework.The model precision is improved due to the complete decomposition of the input and output space,at the same time the complex iterative calculation is avoid.By train the MPLS online using a sliding time window,the predictive control in MPLS framework is proposed which is applicable for nonlinear system.Second,aiming at soling the problem that most of the existing predictive control in nonlinear PLS framework can not update the model parameters online,and it is difficult to solve the control signal because the original linear constraints are mapped to nonlinear constraints,a locally weighted projection regression(LWPR)algorithm with on-line incremental learning ability together with predictive control in LWPR framework is proposed.On this basis,predictive control strategy in LWPR framework avoids the nonlinear mapping of the original space linear constraints.Third,in review of these problems,the predictive control in recursive partial least squares framework is studied.First of all,the proposed MPLS is improved,and the recursive MPLS(RMPLS)regression method is proposed.Then,the parameters of the RMPLS regression model are predicted by using the algorithm of LWPR,and the multi-step prediction model is constructed on the premise of no loss in accuracy.The predictive control in RMPLS-LWPR framework is finally proposed.Benchmark studied in the typical nonlinear benchmark process is proposed,in which the three proposed data-driven predictive control strategies are compared and studied.It is verified that the predictive control strategy in RMPLS-LWPR framework has the highest multi-step prediction accuracy and the best tracking control performance.Fourth,aiming at the tracking control of the plasma experimental device,which is a typical open-loop stable non-linear system with unknown model,the experimental verification of the predictive control algorithm proposed in this paper is proposed.The plasma experimental device of Xidian university is taken as the background in this paper.Considering that the device is still under construction and here is no online testing environment for the control algorithm,there is no online testing environment for the control algorithm.We first use the currently available measured data of the plasma experimental device to test the proposed RMPLS-LWPR based multi-step predictive algorithm.At the same time,the finite element simulation of the experimental device is carried out under the condition of low temperature and low speed plasma.After comparing the results of the finite element simulation with the measurable data,the effectiveness of the finite element simulation on the device is verified.Then the finite element simulation model is encapsulated as a black box controlled object,and the three predictive control algorithms proposed in this paper are verified and discussed through the black box model,which lays the foundation for the final deployment of the control algorithm in the device after the plasma experimental device is built.