Disturbance rejection of ball mill grinding circuits using DOB and MPC

Ball mill grinding circuit is essentially a multivariable system with couplings, time delays and strong disturbances. Many advanced control schemes, including model predictive control (MPC), adaptive control, neuro-control, robust control, optimal control, etc., have been reported in the field of grinding process. However, these control schemes including the MPC scheme usually cannot achieve satisfying effects in the presence of strong disturbances. In this paper, disturbance observer (DOB), which is widely used in motion control applications, is introduced to estimate the disturbances in grinding circuit. A compound control scheme, consisting of a feedforward compensation part based on DOB and a feedback regulation part based on MPC (DOB-MPC), is thus developed. A rigorous analysis of disturbance rejection performance is given with the considerations of both model mismatches and external disturbances. Simulation results demonstrate that when controlling the ball mill grinding circuit, the DOB-MPC method possesses a better performance in disturbance rejection than that of the MPC method.     

ROBUST NONLINEAR PREDICTIVE CONTROL USING A DISTURBANCE ESTIMATOR

A robust nonlinear predictive control strategy using a disturbance estimator is presented. The disturbance estimator is comprised of two parts: one is the disturbance model parameter adaptation and the other is future disturbance prediction. A linear discrete model is proposed as a disturbance model which is formulated by using process inputs and available process measurements. The recursive least square (RLS) method with exponential forgetting is used to determine the uncertain disturbance model parameters and for the future disturbance prediction, future disturbances projected by the future process inputs are used. Two illustrative examples: a jacketed CSTR as a SISO system: an adiabatic CSTR as a MIMO system, and experimental results of the distillation column control are presented. The results indicate that a substantial improvement in nonlinear predictive control performance is possible using the disturbance estimator.     

NONLINEAR MODEL PREDICTIVE CONTROL

Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers designed using (1) nonlinear variable transformations, (2) a linear controller tuned using the internal model control approach, and (3) open-loop optimal control. NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Unlike the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control. NMPC also demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to its set-point without steady-state offset.     

Disturbance rejection of dead-time processes using disturbance observer and model predictive control

This article mainly focuses on disturbance rejection of dead-time processes by integrating a modified disturbance observer (MDOB) with a model predictive controller (MPC). The effect caused by model mismatches is regarded as a part of the lumped disturbances. This means that the disturbances considered here include not only external disturbances, but also internal disturbances caused by model mismatches. Control structure of the proposed method includes two parts which can be designed separately. The MPC which acts as a prefilter, is employed to generate appropriate control actions such that a desired setpoint tracking response is achieved. The MDOB is employed to estimate the disturbances of the closed-loop system, and the estimation is used for feedforward compensation design to reject disturbances. Rigorous analysis of setpoint tracking and disturbance rejection properties of the closed-loop system are given in the presence of both model mismatches and external disturbances. The proposed scheme is applied to control the temperature of a simplified jacketed stirred tank heater (JSTH). Simulation results demonstrate that the proposed method possesses a better disturbance rejection performance than those of the MDOB-PI, MPC and PI methods in controlling such dead-time processes.     

Recent developments in the control of constrained hybrid systems

We review recently developed schemes for the constrained control of systems integrating logic and continuous dynamics. The control paradigm we focus on is model predictive control (MPC) and its derivatives, with the emphasis on explicit solution. The exposition of the basic theory is supplemented by a number of application case studies showing the effectiveness as well as the limitations of the deployed algorithms. Current and future lines of research are briefly discussed.     

ADAPTIVE FUZZY MODEL BASED PREDICTIVE CONTROL OF AN EXOTHERMIC BATCH CHEMICAL REACTOR*

An adaptive fuzzy model based predictive control (AFMBPC) approach is presented to track the desired temperature trajectories in an exothermic batch chemical reactor. The AFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. This approach has the flexibility to cope with different fuzzy model structures whose choice also lead to improve the controller performance. In this approach, adaptation of fuzzy models using dynamic process information is carried out to build a predictive controller, thus eliminating the determination of a predefined fixed fuzzy model based on various sets of known input-output relations. The performance of the AFMBPC is evaluated by comparing to a fixed fuzzy model based predictive controller (FFMBPC) and a conventional PID controller. The results show the better suitability of AFMBPC for the control of highly nonlinear and time varying batch chemical reactors.     

Model predictive control relevant identification and validation

The role of data prefiltering in model identification and validation is presented in this paper. A model predictive control relevant data prefilter, namely the multistep ahead prediction filter for optimal predictions over every step within a finite horizon, is presented. It is shown that models that minimize the multistep prediction errors can be identified or verified by filtering the data using certain data prefilters and then applying the prediction error method to the filtered data. Based on these identification results, a predictive control relevant model validation scheme using the local approach is proposed. The developed algorithms are verified through simulations as well as industrial applications.     

Identification of models for control of wet granulation

The modeling work in this paper provides insight on improved control and design (including measurement selection) of a granulation process. Two different control strategies (MPC and PID) are evaluated on an experimentally validated granulation model. This model is based on earlier work done at The University of Sheffield, UK and Organon, The Netherlands [C.F.W. Sanders, W. Oostra, A.D. Salman, M.J. Hounslow, Development of a predictive high-shear granulation model; experimental and modeling results, 7th World Congress of Chemical Engineering, Glasgow (2005), C11-002]. The granulation kinetics were measured in a 10 liter batch granulator with an experimental design that included four process variables. The aggregation rates were extracted with a Discretized Population Balance (DPB) model. Knowledge of the process kinetics was used to model a continuous (well mixed) granulator. The controller model for the Model Predictive Controller is a linearized state space model, derived from the nonlinear DPB model. It has the four process variables from the experimental design and a feed ratio as input variables. Since the DPB model describes the whole Granule Size Distribution (GSD), candidate sets of lumped output variables were evaluated. When measuring controller performance based on the full granule size distribution, it is shown that a PID controller can actually produce results that fluctuate more than the open-loop response. An MPC controller improves stability on both process outputs and the full granule size distribution. The work shows that measuring and controlling specific number based lumped outputs result in a more stable process than when mass based lumped outputs are used. The paper describes a general strategy of using lab scale batch experiments to design and control (small or large scale) continuous granulators. The continuous experiments in this paper are based on simulation, therefore future experimental validation will elucidate further the link between batch and continuous granulation.     

Stability of model predictive control with time-varying weights

In this paper, we show that the stability of constrained Model Predictive Control (MPC) systems can be guaranteed by using time-varying weights. It unifies two popular MPC algorithms with guaranteed stability - Infinite Horizon MPC and MPC with End Constraint. Use of time-varying weights may also be useful in analyzing stability properties of MPC for linear time-varying systems as well as uncertain linear systems.     

Modeling and control of film porosity in thin film deposition

Systematic methodologies are developed for modeling and control of film porosity in thin film deposition. The deposition process is modeled via kinetic Monte Carlo (kMC) simulation on a triangular lattice. The microscopic events involve atom adsorption and migration and allow for vacancies and overhangs to develop. Appropriate definitions of film site occupancy ratio (SOR), i.e., fraction of film sites occupied by particles over total number of film sites, and its fluctuations are introduced to describe film porosity. Deterministic and stochastic ordinary differential equation (ODE) models are also derived to describe the time evolution of film SOR and its fluctuation. The coefficients of the ODE models are estimated on the basis of data obtained from the kMC simulator of the deposition process using least-square methods and their dependence on substrate temperature is determined. The developed ODE models are used as the basis for the design of model predictive control (MPC) algorithms that include penalty on the film SOR and its variance to regulate the expected value of film SOR at a desired level and reduce run-to-run fluctuations. Simulation results demonstrate the applicability and effectiveness of the proposed film porosity modeling and control methods in the context of the deposition process under consideration.     

MODEL PREDICTIVE CONTROL (MPC) AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING

Model predictive control (MPC) is one of the main process control techniques explored in the recent past; it is the amalgamation of different technologies used to predict future control action and future control trajectories knowing the current input and output variables and the future control signals. It can be said that the MPC scheme is based on the explicit use of a process model and process measurements to generate values for process input as a solution of an on-line (real-time) optimization problem to predict future process behavior. There have been a number of contributions in the field of nonlinear model–based predictive control dealing with issues like stability, efficient computation, optimization, constraints, and others. New developments in nonlinear MPC (NMPC) approaches come from resolving various issues, from faster optimization methods to different process models. This article specifically deals with chemical engineering systems ranging from reactors to distillation columns where MPC plays a role in the enhancement of the systems’ performance.     

基于模型预测控制的反应再生工艺控制实现

介绍了先进控制系统中的模型预测控制技术。具体阐述了模型预测控制中的动态矩阵控制算法（DMC）,包括预测模型、滚动优化、反馈校正。以炼油厂催化裂化装氍的反应再生工艺为例,分析了反应再生工艺控制的多变量、多耦合特性,指出了控制的难点。最后,采用动态矩阵控制算法对反应再生工艺的一再、二再温度进行了优化控制,最终实现了控制目标。     

Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞-norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.     

Economically efficient operation of CO2 capturing process part I: Self-optimizing procedure for selecting the best controlled variables

We study optimal operation of a post-combustion CO₂ capturing process where optimality is defined in terms of a cost function that includes energy consumption and penalty for released CO₂ to the air. Three different operational regions are considered.In region I, with a nominal flue gas flowrate, there are two optimally unconstrained degrees of freedom (DOFs) and the corresponding best self-optimizing controlled variables (CVs) are found to be the CO₂ recovery in the absorber and the temperature at tray no. 16 in the stripper. In the region II, with an increased flue gas flowrate, the heat input is saturated and there is one unconstrained DOF left. The best CV is temperature at tray no. 13 in the stripper. In region III, when the flue gas flowrate is further increased, the process reaches the minimum allowable CO₂ recovery of 80% and there is no unconstrained DOF. We have then reached the bottleneck and a controller is needed to adjust the feed flowrate to avoid violating this minimum.The exact local method and the maximum gain rule are applied to find the best CVs in each region.