Infinite horizon model predictive control with no terminal constraint

This paper investigates the constrained infinite horizon linear quadratic regulator (CIHLQR). In particular, it is shown that the terminal set inclusion condition that is associated with this control law introduces limitations into the control system. By relaxing this condition, it is demonstrated that the resulting controller will in many cases remain equivalent to CIHLQR. It is further shown that CIHLQR with a relaxed terminal set inclusion condition offers significant benefits, in terms of computational expense and performance when compared with standard finite horizon model predictive control (MPC) approaches.     

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.     

Moving horizon approach of integrating scheduling and control for sequential batch processes

Online integration of scheduling and control is crucial to cope with process uncertainties. We propose a new online integrated method for sequential batch processes, where the integrated problem is solved to determine controller references rather than process inputs. Under a two‐level feedback loop structure, the integrated problem is solved in a frequency lower than that of the control loops. To achieve the goal of computational efficiency and rescheduling stability, a moving horizon approach is developed. A reduced integrated problem in a resolving horizon is formulated, which can be solved efficiently online. Solving the reduced problem only changes a small part of the initial solution, guaranteeing rescheduling stability. The integrated method is demonstrated in a simulated case study. Under uncertainties of the control system disruption and the processing unit breakdown, the integrated method prevents a large loss in the production profit compared with the simple shifted rescheduling solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1654–1671, 2014     

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     

Iterative learning model predictive control for constrained multivariable control of batch processes

In this paper, we propose a model predictive control (MPC) technique combined with iterative learning control (ILC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batch; thus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. The proposed ILMPC formulation is based on general MPC and incorporates an iterative learning function into MPC. Thus, it is easy to handle various issues for which the general MPC is suitable, such as constraints, time-varying systems, disturbances, and stochastic characteristics. Simulation examples are provided to show the effectiveness of the proposed ILMPC.     

Economic model predictive control of chemical processes with parameter uncertainty

This work proposes an EMPC (Economic Model Predictive Control) algorithm that integrates RTO (Real Time Optimization) and EMPC objectives within a single optimization calculation. Robust stability conditions are enforced on line through a set of constraints within the optimization problem.A particular feature of this algorithm is that it constantly calculates a set point with respect to which stability is ensured by the aforementioned constraints while searching for economic optimality over the horizon. In contrast to other algorithms reported in the literature, the proposed algorithm does not require terminal constraints or penalty terms on deviations from fixed set points that may lead to conservatism.Changes in model parameters over time are also compensated for through parameter updating. The latter is accomplished by including the parameters’ values as additional decision variables within the optimization problem.Several case studies are presented to demonstrate the algorithm’s performance.     

A multi-priority hierarchical optimization method for double-layer model predictive control

Considering the demand for the sequential regulation of manipulated variables in actual industrial process control, the conventional solution of double-layer model predictive control faces the problem that the weight coefficients are difficult to tune. This paper proposes an improved hierarchical optimization method for manipulated variables in the steady-state optimization layer of double-layer model predictive control. The proposed method can adjust the manipulated variables sequentially without an accurate weight coefficient to avoid difficulty in tuning the weight coefficients. The relation between the optimal solution and the feasible region of the steady-state optimization layer is analysed to describe the reoptimization of the key manipulated variables. The impact of the economic cost coefficient on the optimal solution with the sensitivity analysis method is studied, and the complexity of using the weight coefficient to solve the priority optimization problem of the manipulated variables is assessed. The steady-state optimization solution procedure is improved based on the theory of the multiobjective complete hierarchical method. The hierarchical and sequential optimization of the manipulated variables results in expanding the space and freedom of the key manipulated variables, increasing efficiency, reducing consumption, and improving economic performance. The improved hierarchical optimization method is direct and simple in achieving optimization sequentially and satisfies the need for adjusting the manipulated variables according to human intentions.     

High-order iterative learning model predictive control for batch chemical processes

In order to address two-dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high-order iterative learning model predictive control (HILMPC) method in this paper. A set of local state-space models are first constructed to represent the batch chemical processes by adopting the just-in-time learning (JITL) technique. Meanwhile, a pre-clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two-stage 2D controller is designed to achieve integrated control by combining high-order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed-loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013     

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.     

Explicit model predictive control through robust optimization

A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete-time uncertain linear systems is presented. We consider uncertain processes, affected by box-bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Closed-loop dynamic real-time optimization with stabilizing model predictive control

Dynamic real-time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set-point trajectories that are in turn passed on to the lower-level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed-loop DRTO (CL-DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper-level DRTO. The resulting CL-DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single-input single-output and multi-input multi-output continuous stirred tank reactor case studies.     

Explicit distributed model predictive control design for chemical processes under constraints and uncertainty

In multivariable industrial processes, the common distributed model predictive control strategy is usually unable to deal with complex large-scale systems efficiently, especially under system constraints and high control performance requirements. Based on this situation, we use the distributed idea to divide the large-scale system into multiple subsystems and transform them into the state space form. Combined with the output tracking error term, we build an extended non-minimal state space model that includes output error and measured output and input. When dealing with system constraints, the new constraint matrix is divided into range and kernel space by using the explicit model predictive control algorithm, which reduces the difficulty of solving constraints in the extended system and further improves the overall control performance of the system. Finally, taking the coke furnace pressure control system as an example, the proposed algorithm is compared with the conventional distributed model predictive control algorithm using non-minimal state space, and the simulation results show the feasibility and superiority of this method.     

基于多目标分层的预测控制定态优化技术

多目标分层优化要求是从复杂工业过程的现场实际应用背景出发而提出的.详细阐述了复杂工业过程的多目标分层优化要求的含义,在预测控制两级分层结构的基础上提出了基于二次规划的定态优化有效求解方法.通过Shell控制问题等仿真结果,说明所提出的定态优化技术具有良好的控制性能,能够适应生产过程的需要.     

Model predictive control for wastewater treatment process with feedforward compensation

Being an optimizing technology, model predictive control (MPC) can now be found in a wide variety of application fields. The main and most obvious control goal to be achieved in a wastewater treatment plant is to fulfill the effluent quality standards, while minimizing the operational costs. In order to maintain the effluent quality within regulation-specified limits, the MPC strategy has been applied to the Benchmark Simulation Model 1 (BSM1) simulation benchmark of wastewater treatment process. After the discussion of open loop responses of outputs to manipulated inputs and measured influent disturbances, the strategies of feedback by linear dynamic matrix control (DMC), quadratic dynamic matrix control (QDMC) and nonlinear model predictive control (NLMPC), and improvement by feedforward based on influent flow rate or ammonium concentration have been investigated. The simulation results indicate that good performance was achieved under steady influent characteristics, especially concerning the nitrogen-related species. Compared to DMC and QDMC, NLMPC with penalty function brings little improvement. Two measured disturbances have been used for feedforward control, the influent flow rate and ammonium concentration. It is shown that the performance of feedforward with respect to the influent ammonium concentration is much higher than for the feedforward with respect to the influent flow rate. However, this latter is slightly better than the DMC feedback. The best performance is obtained by combining both feedforward controllers with respect to the influent ammonium concentration and flow rate. In all cases, the improvement of performance is correlated with more aeration energy consumption.     

Dynamic recurrent radial basis function network model predictive control of unstable nonlinear processes

A multistep model predictive control (MPC) strategy based on dynamically recurrent radial basis function networks (RBFNs) is proposed for single-input single-output (SISO) control of uncertain nonlinear processes. The control system consists of two automatically configured RBFNs, a trained network representing the plant model and a network with on-line learning to function as controller. The automatic configuration and learning of the networks is carried out by using a hierarchically self-organizing learning algorithm. This control strategy is structurally simple and computationally efficient since a single output node of each RBFN is configured to provide multistep predictions for plant output and controller. The performance of the proposed RBFNMPC strategy is evaluated by applying to two unstable nonlinear chemical processes, a chemical reactor and a biochemical reactor, and also a stable polymerization reactor. Further, the results of the RBFNMPC is compared with similar RBFN model based control strategies and also with well tuned PID/PI controller. The results show the better performance of the proposed RBFNMPC for the control of open-loop unstable nonlinear processes that exhibit multiple steady-state behavior.     

Considerations on nonlinear model predictive control techniques

The nonlinear model predictive control (NMPC) is an on-line application based on nonlinear convolution models. It is an appealing control methodology, but it is difficult to implement and its solution is not so performing since it unavoidably means to solve a usually large-scale, constrained, and multidimensional optimization. To increase the difficulty, this optimization problem is subject to computationally heavy differential and algebraic constraints constituting the same convolution model and the least squares nature of the objective function easily leads to narrow valleys and multimodality issues.Beyond a short review of the state-of-the-art, the paper is aimed at highlighting the possibility to exploit at best the intrinsic features of the specific system one is going to control using the NMPC. The idea is to give the NMPC the possibility to automatically select the best combination of algorithms (differential solvers and optimizers) in accordance with the specific problem to be solved. From this perspective, the NMPC could be easily extended to many scientific fields traditionally far from process systems and computer-aided process engineering and the user has not to worry about which specific differential solvers and optimizers are needed to solve his/her problem.