Bilinear model predictive control of grade change operations in paper production plants

In this work the bilinear model predictive control method is applied to control the grade change operations in paper production plants. Because of the high nonlinearity of the grade change processes, control of the grade change operations has been performed manually by experienced engineers in the plants. In some cases the bilinear model can be very effective to represent nonlinear processes. In this study a bilinear model for paper plants is identified first. It is found that the bilinear model tracks the plant without significant discrepancy. Based on the multivariable bilinear plant model the optimal input variables are computed using the one-step ahead prediction method. Even for frequent changes in paper grades the bilinear model predictive control scheme exhibits good control performance.     

Dynamics of the wet-end section in paper mills

A model representing the wet-end section of a paper mill has been developed to characterize its dynamic behavior during the grade change. The model is based on the mass balance relationships written for the simplified wetend white water network. From the linearization of the dynamic model, higher-order Laplace transfer functions were obtained followed by the reduction procedure to give simple lower-order models in the form of 1^st-order or 2^nd-order plus dead times. The dynamic response of the wet-end is influenced both by the white water volume and by the level of wire retention. Effects of key manipulated variables such as the thick stock flow rate, the ash flow rate and the retention aid flow rate on the major controlled variables were analyzed by numerical simulations. The simple dynamic model developed in the present study can be effectively used in the operation and control. This paper is dedicated to Professor Se Ki Moon on the occasion of his retirement from Hanyang University.     

Prediction and quality control of the melt index during production of high-density polyethylene

In polyolefin processes the melt index (MI) is the most important control variable indicating product quality. Because of the difficulty in the on-line measurement of MI, a lot of MI estimation and correlation methods have been proposed. In this work a new dynamic MI estimation scheme is developed based on system identification techniques. The empirical MI estimation equation proposed in the present study is derived from the 1 ^st -order dynamic models. Effectiveness of the present estimation scheme was illustrated by numerical simulations based on plant operation data including grade change operations in high density polyethylene (HDPE) processes. From the comparisons with other estimation methods it was found that the proposed estimation scheme showed better performance in MI predictions. The virtual sensor model developed based on the estimation scheme was combined with the virtual on-line analyzer (VOA) to give a quality control system to be implemented in the actual HDPE plant. From the application of the present control system, significant reduction of transition time and the amount of off-spec during grade changes was achieved     

Modeling and control of the melt index in HDPE process

We investigate the model for an industrial isothermal HDPE slurry reactor. The model, consisting of several nonlinear equations, can be linearized to give sets of linear time invariant state space model. The effectiveness of the linearized model is verified by the numerical simulations. A simple model predictive control scheme is constructed based on the linear state space model. The value of the melt index is obtained from the values of the manipulated and controlled variables generated from the control scheme. The control performance can be evaluated from the comparison between the computed melt index values and measured melt index values. The control scheme shows good tracking performance in the numerical simulations. We believe that the model developed in the present study can be effectively used to predict process variables as well as to control the melt index.     

Modeling and simulation of wet-end white water system in the paper mill

A dynamic model representing the wet-end of a paper mill is developed to characterize its dynamic behavior. The model is based on the mass balance relationships written for the simplified wet-end white water network. The dynamic response of the wet-end is influenced both by the white water volume and by the level of wire retention. Effects of key manipulated variables such as the thick stock flow rate, the ash flow rate and the retention aid rate on the major controlled variables are analyzed by numerical simulations. It can be said that the consistency of the model with plant data seems to be reasonably good and can be used as a tool for plant analysis and control.     

Time-optimal control of mmama copolymerization in a CSTR for grade change

The time-optimal control of MMA-MA copolymerization in a CSTR is treated for a grade-change operation. The control objective is to bring system specifications, such as polymer production rate and polymer composition, to desired values in minimum time. The initiator concentration is chosen as a manipulated variable. Two cases are considered: One is to get the time optimal control for both a desired polymer production rate and a desired weight composition of MA in dead copolymer; the other is only for a desired polymer production rate. In numerical calculation, the final t(ⁱ)_f is chosen at each iteration as the time at which the system reached steady-state. This allows us to use a more easily manipulatable form of the performance index and at the same time not directly use the free final time boundary condition.     

Modeling of the drying process in paper plants

In this study a model for the drying process in paper production plants was developed based on the mass and heat balances around drying cycles. Relationships for the heat transfer coefficients between the web and the air as well as between the drying cylinder and the web were extracted from the closed-loop plant operation data. It was found that the heat transfer coefficients could be represented effectively in terms of moisture content, basis weight and reel velocity. The effectiveness of the proposed model was illustrated through numerical simulations. From the comparison with the operation data, the proposed model represents the paper plant being considered with sufficient accuracy.     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

Model predictive control of a fixed-bed reactor with nonlinear quality inference

A generic model predictive control framework has been proposed for a fixed-bed reactor with exothermic reaction. The proposed framework can conduct nonlinear inferential control of a product concentration together with linear multivariable control of bed temperatures. In addition, the framework can accommodate the multi-rate sampling and analysis delay caused by the product measurement. Performance of the proposed technique has been demonstrated with a non-adiabatic fixed bed reactor model producing maleic anhydride under various operating scenarios.     

A recursive PLS-based soft sensor for prediction of the melt index during grade change operations in HDPE plant

An empirical model has been developed for the successful prediction of the melt index (MI) during grade change operations in a high density polyethylene plant. To efficiently capture the nonlinearity and grade-changing characteristics of the polymerization process, the plant operation data is treated with the recursive partial least square (RPLS) scheme combined with model output bias updating. In this work two different schemes have been proposed. The first scheme makes use of an arbitrary threshold value which selects one of the two updating methods according to the process requirement so as to minimize the root mean square error (RMSE). In the second scheme, the number of RPLS updating runs is minimized to make the soft sensor time efficient, while reducing, maintaining or normally increasing the RMSE obtained from first scheme up to some extent. These schemes are compared with other techniques to exhibit their superiority. This paper is dedicated to Professor Chang Kyun Choi to celebrate his retirement from the school of chemical and biological engineering of Seoul National University.     

Grinding time for control of the size fraction of products in the attrition milling

Grinding tests for garnet were carried out by using an attrition mill under wet processes. Effects of feed filling ratios and a chemical agent (sodium hexametaphosphate, SHP) were investigated on the grinding time of the garnet. The progeny particles obtained were screened into various particle size intervals, which were 100 mesh over, 100/400 mesh and 400 mesh under. In order to estimate the mass fraction of the particles in a given particle size interval, mathematical models were derived from the first-order reaction model, then compared to experimental data. It was observed that variation of the feed filling ratio did not show a significant effect on the mass fraction of the product. The chemical agent was, however, effective so that the mass fraction could be controlled by adjusting the content of SHP.     

Model predictive control of condensate recycle process in a cogeneration power station: Controller design and numerical application

A model predictive control (MPC) system has been developed for application to the condensate recycle process of a 300 MW cogeneration power station of the East-West Power Plant, Gyeonggido, Korea. Unlike other industrial processes where MPC has been predominantly applied, the operation mode of the cogeneration power station changes continuously with weather and seasonal conditions. Such characteristic makes it difficult to find the process model for controller design through identification. To overcome the difficulty, process models for MPC design were derived for each operation mode from the material balance applied to the pipeline network around the concerned process. The MPC algorithm has been developed so that the controller tuning is easy with one tuning knob for each output and the constrained optimization is solved by an interior-point method. For verification of the MPC system before process implementation, a process simulator was also developed. Performance of the MPC was investigated first with a process simulator against various disturbance scenarios.     

Model parameter estimation and feedback control of surface roughness in a sputtering process

This work focuses on model parameter estimation and model-based output feedback control of surface roughness in a sputtering process which involves two surface micro-processes: atom erosion and surface diffusion. This sputtering process is simulated using a kinetic Monte Carlo (kMC) simulation method and its surface height evolution can be adequately described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation (PDE). First, we estimate the four parameters of the stochastic KSE so that the expected surface roughness profile predicted by the stochastic KSE is close (in a least-square sense) to the profile of the kMC simulation of the same process. To perform this model parameter estimation task, we initially formulate the nonlinear stochastic KSE into a system of infinite nonlinear stochastic ordinary differential equations (ODEs). A finite-dimensional approximation of the stochastic KSE is then constructed that captures the dominant mode contribution to the state and the evolution of the state covariance of the stochastic ODE system is derived. Then, a kMC simulator is used to generate representative surface snapshots during process evolution to obtain values of the state vector of the stochastic ODE system. Subsequently, the state covariance of the stochastic ODE system that corresponds to the sputtering process is computed based on the kMC simulation results. Finally, the model parameters of the nonlinear stochastic KSE are obtained by using least-squares fitting so that the state covariance computed from the stochastic KSE process model matches that computed from kMC simulations. Subsequently, we use appropriate finite-dimensional approximations of the identified stochastic KSE model to design state and output feedback controllers, which are applied to the kMC model of the sputtering process. Extensive closed-loop system simulations demonstrate that the controllers reduce the expected surface roughness by 55% compared to the corresponding values under open-loop operation.     

On the dynamics and control of through-plane water distributions in PEM fuel cells

We provide a semi-analytic solution to simplify an experimentally validated numeric realization of a two-phase, reaction-diffusion, distributed parameter model of the through-plane water distributions as they evolve inside polymer electrolyte membrane (PEM) fuel cell gas diffusion layers. The semi-analytic solution is then analyzed for stability and to gain insight into the dynamics of the equilibrium (steady-state) water distributions. Candidate distributions for vapor and liquid water are then identified which allow maximum membrane hydration while simultaneously avoiding voltage degradation that results from anode liquid water accumulation (flooding). The desired anode water distributions could be maintained via control of the anode channel conditions (boundary value control) with the ultimate goal to maximize the hydrogen utilization and prolong fuel cell life.     

Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues

This paper describes a procedure to find the best controlled variables in an economic sense for the activated sludge process in a wastewater treatment plant, despite the large load disturbances. A novel dynamic analysis of the closed loop control of these variables has been performed, considering a nonlinear model predictive controller (NMPC) and a particular distributed NMPC-PI control structure where the PI is devoted to control the process active constraints and the NMPC the self-optimizing variables. The well-known self-optimizing control methodology has been applied, considering the most important measurements of the process. This methodology provides the optimum combination of measurements to keep constant with minimum economic loss. In order to avoid nonfeasible dynamic operation, a preselection of the measurements has been performed, based on the nonlinear model of the process and evaluating the possibility of keeping their values constant in the presence of typical disturbances.