Model Predictive Control In The PLS Latent Variable Space

With the rapid development of information and computer technology, data flow become more and more important in the industry. The data-driven modeling methods and control schemes have attracted attention in both academia and industry. Nevertheless, a high degree of correlation is often observed in the big data. Many principle component extraction based methods are widely developed to deal with this problem. Among them, partial least squares (PLS) regression is not only able to extract principal component from both input and output data, but also able to determine the direction on which input and output data has the largest covariance. Due to the combining property of dimensionality reduction and regression, PLS has also been successfully applied to fault diagnosis and process monitoring. With the benefits of automatic decoupling, loop pairing, and dimensionality reduction, model identification and model predictive control (MPC) in PLS latent variable space are studied in this paper. Model predictive control relevant identification (MRI), generalized predictive control (GPC), two kinds of robustification GPC method, a multiple model predictive control strategy, TS model based fuzzy GPC, reduced dimension control are involved in this paper.(1) To deal with collinearity between process variables, PLS model is introduced. In Chapter 2, a generalized predictive control (GPC) scheme under a dynamic partial least squares (PLS) framework is proposed. At the modeling stage, a model predictive control relevant identification (MRI) approach is used to improve the identification of the model. For each subsystem, MRI is implemented and GPC is designed independently. With the advantage of MRI and PLS framework, fewer parameters are needed to be estimated in the identification stage, nonsquare and ill-conditioned system can be handled naturally, control parameters tuning is easier and better control performance can be obtained. Furthermore, the computing time of control action which is very crucial for GPC on-line application decreases since each GPC is running in SISO subsystem in parallel.(2) In Chapter 3, a theoretical analysis about latent space GPC is presented including the analysis of sensitivity functions, robustness, and stability. In order to reject noise in high frequency, two modified latent space GPC are proposed. One is the C-filter method which can modify sensitivity to parameter or signal uncertainty without any impact on the nominal tracking, however, this method does not lend itself to systematic design. Hence, borrow the idea of Internal Model Control, the second modified method is proposed. In the predictive model, the process outputs is replaced by the model outputs, and an error term is used to compensate for any bias. In this way, the impact of noise and disturbance in high frequency can be reduced. Theoretically, the robustness is improved without any impact on the nominal tracking as well.(3) For dynamic nonlinear processes, linear model based MPC is acceptable only when the process is working in the neighborhood of the operating point. To deal with this problem, a switched multiple model predictive control (MMPC) strategy in the PLS framework is proposed in Chapter 4. Based on the identified PLS models, companion controllers are designed to form the MMPC strategy. A novel switching criterion based on Hotelling’s T2 statistic of the measured outputs is proposed to assure each model/control pair works in its operating region spanned by the identification data sets. Moreover, the control action is obtained by solving a QP problem, so this MMPC strategy is more suitable for practical process applications than other nonlinear MPC methods.(4) For dynamic nonlinear processes, a GPC based on nonlinear models directly is considered in Chapter 5. In the PLS inner model, a TS fuzzy model is used to describe the dynamics and nonlinearity between t and u. Based on the model and the idea of instant linearized, a fuzzy GPC scheme in the PLS latent space is designed. When the nonlinearity of process is very strong, this method should outperform the switching MMPC scheme.(5) In Chapter 6, two problems arose when latent space MPC plays the role of reduced dimension control are analyzed. For forced dimension reduction problem, a discussion of why offset appeared is presented from the view of space projection. For reduced dimension control, we pointed out that not all the setpoints are feasible. The choice of setpoints should be in accordance with the correlation in the identification data. When there exists nonlinear dependence, the choice of setpoints should coincide with the characteristic of the process.