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.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

LMI-based robust model predictive control for a continuous MMA polymerization reactor

A linear matrix inequality (LMI)-based robust model predictive control (MPC) is applied to a continuous stirred-tank reactor for the polymerization of methyl methacrylate (MMA). The polytopic model is constructed to predict the responses to various control input sequences by using Jacobians of uncertain nonlinear model at several operating points and the controller design is characterized as the problem of minimizing an upper bound on the ‘worst-case’ infinite horizon objective function subject to constraints on the control input and plant output. Simulation studies under different conditions are conducted to validate the feasibility of the optimization problem and evaluate the applicability of such a control scheme. Simulation results show that, despite the model uncertainty, the LMI-based robust model predictive controller performs quite satisfactorily for the property control of the continuous polymerization reactor and guarantees the robust stability.     

Some manifold learning considerations toward explicit model predictive control

Model predictive control (MPC) is a de facto standard control algorithm across the process industries. There remain, however, applications where MPC is impractical because an optimization problem is solved at each time step. We present a link between explicit MPC formulations and manifold learning to enable facilitated prediction of the MPC policy. Our method uses a similarity measure informed by control policies and system state variables, to “learn” an intrinsic parametrization of the MPC controller using a diffusion maps algorithm, which will also discover a low-dimensional control law when it exists as a smooth, nonlinear combination of the state variables. We use function approximation algorithms to project points from state space to the intrinsic space, and from the intrinsic space to policy space. The approach is illustrated first by “learning” the intrinsic variables for MPC control of constrained linear systems, and then by designing controllers for an unstable nonlinear reactor.     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network,AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

Soft-constrained model predictive control based on data-driven distributionally robust optimization

This article proposes a novel distributionally robust optimization (DRO)-based soft-constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state-space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first-order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO-based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi-stage scenario based stochastic MPC.     

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.     

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.     

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.     

改进的模糊预测控制算法及其在CSTR过程中的应用

A finite horizon predictive control algorithm,which applies a saturated feedback control law as its local control law,is presented for nonlinear systems with time-delay subject to input constraints.In the algorithm,N free control moves,a saturated local control law and the terminal weighting matrices are solved by a minimization problem based on linear matrix inequality(LMI) constraints online.Compared with the algorithm with a nonsaturated local law,the presented algorithm improves the performances of the closed-loop systems such as feasibility and optimality.This model predictive control(MPC) algorithm is applied to an industrial continuous stirred tank reactor(CSTR) with explicit input constraint.The simulation results demonstrate that the presented algorithm is effective.     

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     

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     

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.     

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.     

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.     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

Multivariable model predictive control of a novel rapid pressure swing adsorption system

A multivariable model predictive control (MPC) algorithm is developed for the control and operation of a rapid pressure swing adsorption (RPSA)‐based medical oxygen concentrator. The novelty of the approach is the use of all four step durations in the RPSA cycle as independent manipulated variables in a truly multivariable context. The RPSA has a complex, cyclic, nonlinear multivariable operation that requires feedback control, and MPC provides a suitable framework for controlling such a multivariable system. The multivariable MPC presented here uses a quadratic optimization program with integral action and a linear model identified using subspace system identification techniques. The controller was designed and tested in simulation using a complex, highly coupled, nonlinear RPSA process model. The model was developed with the least restrictive assumptions compared to those reported in the literature, thereby providing a more realistic representation of the underlying physical phenomena. The resulting MPC effectively tracks set points, rejects realistic process disturbances and is shown to outperform conventional PID control. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1234–1245, 2018     

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) (Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.