Control of plastic melt temperature: A multiple input multiple output model predictive approach

Good control of plastic melt temperature for injection molding is very important in reducing operator setup time, ensuring product quality, and preventing thermal degradation of the melt. The controllability and setpoints of other process parameters also depend on the precise monitoring and control of plastic melt temperatures. We experimentally investigated the thermal interactions between the barrel zones of an instrumented plastic injection molding machine (IMM). These interactions result from the zone temperature differences that are used in normal machine operations. From these experimental interactions, multiple-input-multiple-output (MIMO) and single-input-single-output (SISO) models were derived for controlling these zone temperatures using a Model Predictive Control (MPC) strategy. An experimental comparison was made between MIMO MPC and SISO MPC of plastic melt temperature, which showed that the MIMO MPC scheme is more energy efficient, having zero overshoot.     

Temperature control of injection molding. Part I: Modeling and identification

This paper develops a mathematical model for the dynamics of a plastic injection molding machine (IMM) that may be used for the design of a temperature‐control system. The research in this paper is novel in comparison to others since the derived models explicitly include the effects of zone interaction and backpressure, and do not lump these into an arbitrary disturbance signal. A series of experiments were conducted on a 150‐tonne IMM to identify the parameters of the proposed model using measurements of zone temperatures, percentage heater input, backpressure and screw speed. The identified model was validated using a series of blind tests that compared the model output with the measured barrel temperatures of the IMM. Polym. Eng. Sci. 44:2308–2317, 2004. © 2004 Society of Plastics Engineers.     

从区间模型预测控制到双层结构模型预测控制

模型预测控制算法（MPC）存在设定点控制与区间控制两种策略,区间预测控制较之设定点控制在技术上具有先进性。目前,主流的预测控制软件技术均采用双层结构,即上层稳态优化计算最优设定点,下层动态控制负责动态跟踪最优设定点。从过程稳态的角度出发,分别对区间预测控制和双层结构预测控制进行了机理分析,从定性与定量两个方面比较了这两者的异同点,提出并证明了两者的一致性条件。论述了双层结构预测控制较之单层结构下的区间控制更具先进性。     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Distributed model predictive control based on dissipativity

A noncooperative approach to plant‐wide distributed model predictive control based on dissipativity conditions is developed. The plant‐wide process and distributed control system are represented as two interacting process and controller networks, with interaction effects captured by the dissipativity properties of subsystems and network topologies. The plant‐wide stability and performance conditions are developed based on global dissipativity conditions, which in turn are translated into the dissipative trajectory conditions that each local model predictive control MPC must satisfy. This approach is enabled by the use of dynamic supply rates in quadratic difference forms, which capture detailed dynamic system information. A case study is presented to illustrate the results. © 2012 American Institute of Chemical Engineers AIChE J, 59: 787–804, 2013     

Reference Trajectory Optimization Under Constrained Predictive Control

Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.     

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Development of a novel control strategy for a highly segmented injection mold tempering for inline part warpage control

The demand of precise injection-molded parts is steadily increasing and is today one of the most relevant challenges, due to local variations in temperature and pressure during the production of the part. These variations can lead to a significant change of the local specific volume, shrinkage potential, and inner stress, which ultimately results in part warpage. By homogenizing the local specific volume over the part according to the specific pvT-behavior of the polymer, warpage is expected to be reduced. The following work describes a new approach to control the local specific volume by a newly developed segmented and highly dynamic mold temperature control based on rapid heating ceramics and CO₂ evaporation chambers. Since injection molding is a dynamic process and heat transfer inside the mold is comparably slow, a special control strategy is necessary to activate the heating and cooling elements in advance. For this, a novel prediction strategy based on a discretization of the one-dimensional heat equation has been developed. Experimental trials including a classical PID controller and a model predictive control approach (MPC) show that the MPC is superior regarding the process stability.     

A robustly stabilizing fault-tolerant MPC: A performance improvement-based approach

In terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost-contracting formulation-based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision-making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.     

Demand reduction in building energy systems based on economic model predictive control

This paper proposes and demonstrates the effectiveness of an economic model predictive control (MPC) technique in reducing energy and demand costs for building heating, ventilating, and air conditioning (HVAC) systems. A simulated multi-zone commercial building equipped with of variable air volume (VAV) cooling system is built in Energyplus. With the introduced Building Controls Virtual Test Bed (BCVTB) as middleware, real-time data exchange between Energyplus and a Matlab controller is realized by sending and receiving sockets. System identification is performed to obtain zone temperature and power models, which are used in the MPC framework. The economic objective function in MPC accounts for the daily electricity costs, which include time-of-use (TOU) energy charge and demand charge. In each time step, a min–max optimization is formulated and converted into a linear programming problem and solved. In a weekly simulation, a pre-cooling effect during off-peak period and a cooling discharge from the building thermal mass during on-peak period can be observed. Cost savings by MPC are estimated by comparing with the baseline and other open-loop control strategies. The effect of several experimental factors in the MPC configuration is investigated and the best scenario is selected for future practical tests.     

A Comparative Study of Combined Feedforward/Feedback Model Predictive Control for Nonlinear Systems

Model predictive control (MPC) provides a natural framework to realize feedforward and feedback control for nonlinear systems where the effect of disturbances (DVs) cannot be separated from that of manipulated variables (MVs). This study examines the performance of MPC with measured DVs as partial inputs of the model used, which is termed as combined feedforward/feedback MPC (CMPC) in contrast to conventional MPC using a model without input of any measured DV. In the simulation of a pH process, we demonstrate the clear superiority of CMPC over MPC. In the experiment with a bench‐scale ethanol and water distillation column, CMPC and MPC using artificial neural network (ANN) models are applied to the dual temperature control problem. External recurrent neural networks (ERNs) with and without a measured DV (feed rate of the column) as their partial input are built and employed in the experiment, with a result that inclusion of the measured DV in the model makes CMPC perform significantly better than MPC. To strengthen practical experience in applying ANN‐based MPC, a detailed procedure of the experiment is also documented.     

Lexicographic optimization based MPC: Simulation and experimental study

Multi-variable prioritized control study is carried out using model predictive control (MPC) algorithms. The conventional MPC algorithm implements multi-variable control through one augmented objective function and requires weights adjustment for required performance. In order to implement explicit prioritization in multiple control objectives, we have used lexicographic MPC. To achieve better tracking performance, we have used a new MPC algorithm, by modifying the lexicographic constraint, referred to as MLMPC, where tuning of weights is not required. The effectiveness of MLMPC algorithm is demonstrated on a PMMA reactor for controlling the number average molecular weight and the reactor temperature. We have also verified the benefits of proposed algorithm on an experimental single board heater system (SBHS) for controlling temperature of a thin metal plate. These simulation and experimental studies demonstrate the superiority of the proposed method over conventional MPC and lexicographic MPC. Finally, we have presented generalized mathematical solutions to the optimization problem in MLMPC.     

Model-based control strategies for a chemical batch reactor with exothermic reactions

Batch reactor control provides a very challenging problem for the process control engineer. This is because a characteristic of its dynamic behavior shows a high nonlinearity. Since applicability of the batch reactor is quite limited to the effectiveness of an applied control strategy, the use of advanced control techniques is often beneficial. This work presents the implementation and comparison of two advanced nonlinear control strategies, model predictive control (MPC) and generic model control (GMC), for controlling the temperature of a batch reactor involving a complex exothermic reaction scheme. An extended Kalman filter is incorporated in both controllers as an on-line estimator. Simulation studies demonstrate that the performance of the MPC is slightly better than that of the GMC control in nominal case. For model mismatch cases, the MPC still gives better control performance than the GMC does in the presence of plant/model mismatch in reaction rate and heat transfer coefficient.     

Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor

This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open-loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection.     

Energy efficient model predictive building temperature control

Many systems used in buildings for heating, ventilating, and air-conditioning waste energy because of the way they are operated or controlled. This paper explores the application of model predictive control (MPC) to air-conditioning units and demonstrates that the closed-loop performance and energy efficiency can be improved over conventional approaches. This work focuses on the problem of controlling the vapor compression cycle (VCC) in an air-conditioning system, containing refrigerant which is used to provide cooling. The VCC considered in this work has two manipulated variables that affect operation: compressor speed and the position of an electronic expansion valve. The system is subject to constraints, such as the range of permissible superheat, and also needs to regulate temperature variables to set points. An MPC strategy is developed for this type of system based on linear models identified from data obtained from a first-principles model of the VCC. The MPC strategy incorporates economic measures in the objective function as well as control objectives. Tests are carried out on a simulated VCC system that is linked to a simulation of a realistic building that is developed in the U.S. Department of Energy Computer Simulation Program, EnergyPlus. The MPC demonstrated significantly better tracking control relative to conventional approaches (a reduction of 70% in terms of the integral of squared error for step changes in the temperature set-point), while reducing the VCC energy requirements by 16%. The paper describes the control approach in detail and presents results from the tests.     

Repetitive model predictive control of a reverse flow reactor

This paper deals with the control of a catalytic reverse flow reactor (RFR) used for methane combustion. The periodic flow reversals effected on the system makes it both continuous and discrete in nature (i.e., a hybrid system). Control of this system is challenging due to the unsteady state behavior of the process along with its mixed discrete and continuous behavior. Although model predictive control (MPC) is proven to be a powerful technique for several processes it becomes less effective in systems such as the RFR where the model prediction errors and the effect of disturbances on the plant output repeat from time to time. In such cases, control can be improved if the repetitive error pattern is exploited. A novel repetitive model predictive control (RMPC) strategy, that combines the basic concepts of iterative learning control (ILC) and repetitive control (RC) along with the concepts of MPC, is proposed for such systems. In the proposed strategy, the state variables of the model are reset periodically along with predictive control action such that the process follows the reference trajectory as closely as possible. The results obtained prove that the RMPC approach provides an excellent performance for the control of the RFR.     

Identification and control of a riser‐type FCC unit

This paper addresses the use of feedforward neural networks for the steady‐state and dynamic identification and control of a riser type fluid catalytic cracking unit (FCCU). The results are compared with a conventional PI controller and a model predictive control (MPC) using a state space subspace identification algorithm. A back propagation algorithm with momentum term and adaptive learning rate is used for training the identification networks. The back propagation algorithm is also used for the neuro‐control of the process. It is shown that for a noise‐free system the adaptive neuro‐controller and the MPC are capable of maintaining the riser temperature, the pressure difference between the reactor vessel and the regenerator, and the catalyst bed level in the reactor vessel, in the presence of set‐point and disturbance changes. The MPC performs better than the neuro controller that in turn is superior to the conventional multi‐loop diagonal PI controller.     

基于模型预测残差闭环潜能指标的MPC控制器实时性能监控

由于模型预测控制器对模型失配等不确定因素具有较强的鲁棒性,因此现有的多步预测误差方法不能及时显著地检测到由模型失配导致的MPC控制器性能潜能的变化。针对上述问题,提出一种改进的多步预测误差方法和实时性能监控策略。考虑到MPC控制器的模型预测残差能有效反映模型失配等信息,利用预测残差对现有多步预测误差方法进行改进,改进的方法能够更好地检测由模型失配引起的MPC控制器性能潜能的改变。在连续搅拌槽加热器(continuous stirred tank heater,CSTH)系统上的仿真实验验证了该方法的可行性与有效性。     

Actuator stiction compensation via model predictive control for nonlinear processes

The problem of valve stiction is addressed, which is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. A model predictive control (MPC) stiction compensation formulation is developed including detailed dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions due to stiction. Although developed with a focus on stiction, the MPC‐based compensation method presented is general and has potential to compensate for other nonlinear valve dynamics which have some similarities to those caused by stiction. Feasibility and closed‐loop stability of the proposed MPC formulation are proven for a sufficiently small sampling period when Lyapunov‐based constraints are incorporated. Using a chemical process example with an economic model predictive controller (EMPC), the selection of appropriate constraints for the proposed method is demonstrated. The example verified the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC causes it to select set‐points that the valve output can reach and causes the operating constraints to be met. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2004–2023, 2016