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.     

Nonlinear model predictive control: current status and future directions

Linear model predictive control (LMPC) is well established as the industry standard for controlling constrained multivariable processes. A major limitation of LMPC is that plant behavior is described by linear dynamic models. As a result, LMPC is inadequate for highly nonlinear processes and moderately nonlinear processes which have large operating regimes. This shortcoming coupled with increasingly stringent demands on throughput and product quality has spurred the development of nonlinear model predictive control (NMPC). NMPC is conceptually similar to its linear counterpart except that nonlinear dynamic models are used for process prediction and optimization. The purpose of this paper is to provide an overview of current NMPC technology and applications, as well as to propose topics for future research and development. The review demonstrates that NMPC is well suited for controlling multivariable nonlinear processes with constraints, but several theoretical and practical issues must be resolved before widespread industrial acceptance is achieved.     

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.     

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.     

Koopman Lyapunov-based model predictive control of nonlinear chemical process systems

In this work, we propose the integration of Koopman operator methodology with Lyapunov-based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed-loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed-loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.     

Modeling and predictive control using fuzzy logic: Application for a polymerization system

In this study, a predictive control system based on type Takagi‐Sugeno fuzzy models was developed for a polymerization process. Such processes typically have a highly nonlinear dynamic behavior causing the performance of controllers based on conventional internal models to be poor or to require considerable effort in controller tuning. The copolymerization of methyl methacrylate with vinyl acetate was considered for analysis of the performance of the proposed control system. A nonlinear mathematical model which describes the reaction plant was used for data generation and implementation of the controller. The modeling using the fuzzy approach showed an excellent capacity for output prediction as a function of dynamic data input. The performance of the projected control system and dynamic matrix control for regulatory and servo problems were compared and the obtained results showed that the control system design is robust, of simple implementation and provides a better response than conventional predictive control. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

内部重整固体氧化物燃料电池发电系统的非线性预测控制

固体氧化物燃料电池（SOFC）发电系统运行除了电堆本体外还需要包含诸多其他辅助组件以期获得系统输出的最大效率,为了使SOFC电堆能够对纯氢以外的燃料具有更好的适用性,加入了燃料内部重整装置和燃烧室两个重要辅助组件。文中在对系统展开建模的基础上提出了采用非线性模型预测控制策略,能够更有效地使输出燃料气体的组分、温度、压力、浓度和流率满足燃料电池堆正常运行的需要,通过仿真分别论证了线性模型预测控制和非线性模型预测控制两种不同控制方案的有效性和适用性。     

Distributed lyapunov‐based model predictive control with neighbor‐to‐neighbor communication

This work considers distributed predictive control of large‐scale nonlinear systems with neighbor‐to‐neighbor communication. It fulfills the gap between the existing centralized Lyapunov‐based model predictive control (LMPC) and the cooperative distributed LMPC and provides a balanced solution in terms of implementation complexity and achievable performance. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. For each subsystem, an LMPC is designed based on the subsystem model and the LMPC only communicates with its neighbors. At a sampling time, a subsystem LMPC optimizes its future control input trajectory assuming that the states of its upstream neighbors remain the same as (or close to) their predicted state trajectories obtained at the previous sampling time. Both noniterative and iterative implementation algorithms are considered. The performance of the proposed designs is illustrated via a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J 60: 4124–4133, 2014     

一类连续/间歇过程的迭代学习模型预测控制

An iterative learning model predictive control (ILMPC) technique is applied to a class of continuous/batch processes. Such processes are characterized by the operations of batch processes generating periodic strong disturbances to the continuous processes and traditional regulatory controllers are unable to eliminate these periodic disturbances. ILMPC integrates the feature of iterative learning control (ILC) handling repetitive signal and the flexibility of model predictive control (MPC). By on-line monitoring the operation status of batch processes, an event-driven iterative learning algorithm for batch repetitive disturbances is initiated and the soft constraints are adjusted timely as the feasible region is away from the desired operating zone. The results of an industrial appli-cation show that the proposed ILMPC method is effective for a class of continuous/batch processes.     

An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system

Advanced model-based control strategies,e.g.,model predictive control,can offer superior control of key process variables for multiple-input multiple-output systems.The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization.This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control.To showcase this approach,five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system.This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges.These controllers also had reasonable per-iteration times of ca.0.1 s.This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which,in the face of process uncertainties or modelling limitations,allow rapid and stable control over wider operating ranges.     

基于T-S模糊模型的间歇过程的迭代学习容错控制

间歇过程不仅具有强非线性,同时还会受到诸如执行器等故障影响,研究非线性间歇过程在具有故障的情况下依然稳定运行至关重要。针对执行器增益故障及系统所具有的强非线性,提出一种新的基于间歇过程的T-S模糊模型的复合迭代学习容错控制方法。首先根据间歇过程的非线性模型,利用扇区非线性方法建立其T-S模糊故障模型,再利用间歇过程的二维特性与重复特性,在2D系统理论框架内,设计2D复合ILC容错控制器,进而构建此T-S模糊模型的等价二维Rosser模型,接着利用Lyapunov方法给出系统稳定充分条件并求解控制器增益。针对强非线性的连续搅拌釜进行仿真,结果表明所提出方法具有可行性与有效性。     

Differential recurrent neural network based predictive control

In this paper an efficient algorithm to train general differential recurrent neural network (DRNN) is developed. The trained network can be directly used in the nonlinear model predictive control (NMPC) context. The neural network is represented in a general nonlinear state-space form and used to predict the future dynamic behavior of the nonlinear process in real time. In the new training algorithms, the ODEs of the model and the dynamic sensitivity are solved simultaneously using Taylor series expansion and automatic differentiation (AD) techniques. The same approach is also used to solve the online optimization problem in the predictive controller. The efficiency and effectiveness of the DRNN training algorithm and the NMPC approach are demonstrated through a two-CSTR case study. A good model fitting for the nonlinear plant at different sampling rates is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The DRNN based NMPC approach results in good control performance under different operating conditions.     

A novel two-dimensional PID controller design using two-dimensional model predictive iterative learning control optimization for batch processes

It is known that the key indicators of batch processes are controlled by conventional proportional–integral–derivative (PID) strategies from the view of one-dimensional (1D) framework. Under such conditions, the information among batches cannot be used sufficiently; meanwhile, the repetitive disturbances also cannot be handled well. In order to deal with such situations, a novel two-dimensional PID controller optimized by two-dimensional model predictive iterative learning control (2D-PID-MPILC) is proposed. The contributions of this paper can be summarized as follows. First, a novel two-dimensional PID (2D-PID) controller is developed by combining the advantages of a PID-type iterative learning control (PIDILC) strategy and the conventional PID method. This novel 2D-PID controller overcomes the aforementioned disadvantages and extends the conventional PID algorithm from one-dimension to two-dimensions. Second, the tuning guidelines of the presented 2D-PID controller are obtained from the two-dimensional model predictive control iterative control (2D-MPILC) method. Thus, the proposed approach inherits the advantages of both PID control, PIDILC strategy, and 2D-MPILC scheme. The superiority of the proposed method is verified by the case study on the injection modelling process.     

APPLICATION OF FUZZY ADAPTIVE CONTROLLER IN NONLINEAR PROCESS CONTROL

In general, physical processes are usually nonlinear and control system design based on the linearization technique cannot control the process well for a wide range of operation. Use of the variable transformation method may not always solve the problem. In this paper, a fuzzy adaptive controller is proposed to control the nonlinear process. The CSTR control problem has also been considered. The results are compared with the method of nonlinear model predictive control (NMPC) with constrained and unconstrained control variables. A fuzzy model-following control system scheme is also proposed. The results show that the proposed controller is a feasible control structure for a nonlinear or parameter-variations process control.     

Fuzzy multi‐model based adaptive predictive control and its application to thermoplastic injection molding

Many chemical processes are inherently nonlinear. A single linear model is ineffective for these processes. Several local linear models may be developed for different operating conditions. A combination of these local models, through a fuzzy logic representation, results in an overall model for a wider operation range. In this paper, on‐line improvements and a fuzzy multi‐model have been proposed for predictive control implementation. Firstly, assuming that the premises of the fuzzy rules keep their original structures, the linear parameters in the rule consequents are on‐line updated by a weighted recursive least squares algorithm at each sample interval. Secondly, a batch learning algorithm is proposed to tune the fuzzy rule premises using a competitive learning algorithm. The effectiveness of the proposed improvements is demonstrated with experimental applications to the filling velocity control of thermoplastic injection molding     

Aeration control of a wastewater treatment plant using hybrid NMPC

In the operation of wastewater treatment plants a key variable is dissolved oxygen (DO) content in the bioreactors. As oxygen is consumed by the microorganisms, more oxygen has to be added to the water in order to comply with the required minimum dissolved oxygen concentration. This is done using a set of aerators working on/off that represents most of the plant energy consumption. In this paper a hybrid nonlinear predictive control algorithm is proposed, based on economic and control aims. Specifically, the controller minimizes the energy use while satisfying the time-varying oxygen demand of the plant and considering several operation constraints. A parameterization of the binary control signals in terms of occurrence time of events allows the optimization problem to be re-formulated as an nonlinear programming (NLP) problem at every sampling time. Realistic simulation results considering real perturbations data sets for the inlet variables are presented.     

Proactive fault‐tolerant model predictive control

Fault‐tolerant control methods have been extensively researched over the last 10 years in the context of chemical process control applications, and provide a natural framework for integrating process monitoring and control aspects in a way that not only fault detection and isolation but also control system reconfiguration is achieved in the event of a process or actuator fault. But almost all the efforts are focused on the reactive fault‐tolerant control. As another way for fault‐tolerant control, proactive fault‐tolerant control has been a popular topic in the communication systems and aerospace control systems communities for the last 10 years. At this point, no work has been done on proactive fault‐tolerant control within the context of chemical process control. Motivated by this, a proactive fault‐tolerant Lyapunov‐based model predictive controller (LMPC) that can effectively deal with an incipient control actuator fault is proposed. This approach to proactive fault‐tolerant control combines the unique stability and robustness properties of LMPC as well as explicitly accounting for incipient control actuator faults in the formulation of the MPC. Our theoretical results are applied to a chemical process example, and different scenaria were simulated to demonstrate that the proposed proactive fault‐tolerant model predictive control method can achieve practical stability and efficiently deal with a control actuator fault. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2810–2820, 2013     

Neurocontrol of a multi-effect batch distillation pilot plant based on evolutionary reinforcement learning

The time cost of first-principles dynamic modelling and the complexity of nonlinear control strategies may limit successful implementation of advanced process control. The maximum return on fixed capital within the processing industries is thus compromised. This study introduces a neurocontrol methodology that uses partial system identification and symbiotic memetic neuro-evolution (SMNE) for the development of neurocontrollers. Partial system identification is achieved using singular spectrum analysis (SSA) to extract state variables from time series data. The SMNE algorithm uses a symbiotic evolutionary algorithm and particle swarm optimisation to learn optimal neurocontroller weights from the partially identified system within a reinforcement learning framework. A multi-effect batch distillation (MEBAD) pilot plant was constructed to demonstrate the real world application of the neurocontrol methodology, motivated by the nonsteady state operation and nonlinear process interaction between multiple distillation columns. Multi-loop proportional integral (PI) control was implemented as a reduced model, reflecting an approach involving no modelling or significant controller tuning. Rapid multiple input multiple out nonlinear controller development was achieved using SSA and the SMNE algorithm, demonstrating comparable time and cost to implementation in relation to the reduced model. The optimal neurocontroller reduced the batch time and therefore the energy consumption by 45% compared to conventional multi-loop SISO PI control.