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     

Adaptive type-2 fuzzy logic control of a bioreactor

Two adaptive type-2 fuzzy logic controllers with minimum number of rules are developed and compared by simulation for control of a bioreactor in which aerobic alcoholic fermentation for the growth of Saccharomyces cerevisiae takes place. The bioreactor model is characterized by nonlinearity and parameter uncertainty. The first adaptive fuzzy controller is a type-2 fuzzy-neuro-predictive controller (T2FNPC) that combines the capability of type-2 fuzzy logic to handle uncertainties, with the ability of predictive control to predict future plant performance making use of a neural network model of the nonlinear system. The second adaptive fuzzy controller is instead a self-tuning type-2 PI controller, where the output scaling factor is adjusted online by fuzzy rules according to the current trend of the controlled process. The performance of a type-2 fuzzy logic controller with 49 rules is used as reference.     

混杂系统基于参数规划的状态反馈预测控制

In this article, state feedback predictive controller for hybrid system via parametric programming is proposed. First, mixed logic dynamic （MLD） modeling mechanism for hybrid system is analyzed, which has a distinguished advantage to deal with the logic rules and constraints of a plant. Model predictive control algorithm with moving horizon state estimator （MHE） is presented. The estimator is adopted to estimate the current state of the plant with process disturbance and measurement noise, and the state estimated are utilized in the predictive controller for both regulation and tracking problems of the hybrid system based on MLD model. Off-line parametric programming is adopted and then on-line mixed integer programming problem can be treated as the parameter programming with estimated state as the parameters. A three tank system is used for computer simulation, results show that the proposed MHE based predictive control via parametric programming is effective for hybrid system with model/olant mismatch, and has a potential for the engineering applications.     

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.     

Investigation of a Model-Based Deep Reinforcement Learning Controller Applied to an Air Separation Unit in a Production Environment

The need for load flexibility and increased efficiency of energy-intensive processes has become more and more important in recent years. Control of the process variables plays a decisive role in maximizing the efficiency of a plant. The widely used control models of linear model predictive controllers (LMPC) are only partly suitable for nonlinear processes. One possibility for improvement is machine learning. In this work, one approach for a purely data-driven controller based on reinforcement learning is explored at an air separation plant (ASU) in productive use. The approach combines the model predictive controller with a data-generated nonlinear control model. The resulting controller and its control performance are examined in more detail on an ASU in real operation and compared with the previous LMPC solution. During the tests, stable behavior of the new control concept could be observed for several weeks in productive operation.     

Identification and predictive control of a simulated moving bed process: Purity control

A model predictive control strategy for a simulated moving bed (SMB) chromatographic process is proposed. For this, the average purities over one switching period of target components in extract and raffinate ports are selected as output variables, while the flow rates in Sections 2 and 3 of the SMB unit are chosen as the input variables. With this arrangement a linear input-output prediction model is identified through subspace identification and used for dynamic control. The realization of this concept is discussed and the implementation on a virtual eight column SMB unit is assessed, in the case of the separation of enantiomers behaving according to the binary bi-Langmuir adsorption isotherm. The identified prediction model is proven to be in good agreement with the first principles model used to simulate the actual SMB process. For typical control objectives encountered in real operation, i.e., disturbance rejection or set-point tracking, it is shown that the proposed controller demonstrates satisfactory control performances in minimizing off-spec products.     

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network (NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.     

Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

Multi-objective nonlinear model predictive control through switching cost functions and its applications to chemical processes

This paper proposes a switching multi-objective model predictive control (MOMPC) algorithm for constrained nonlinear continuous-time process systems. Different cost functions to be minimized inMPC are switched to satisfy different performance criteria imposed at different sampling times. In order to ensure recursive feasibility of the switching MOMPC and stability of the resulted closed-loop system, the dual-mode control method is used to design the switching MOMPC controller. In this method, a local control law with some free-parameters is constructed using the control Lyapunov function technique to enlarge the terminal state set of MOMPC. The correction termis computed if the states are out of the terminal set and the free-parameters of the local control laware computed if the states are in the terminal set. The recursive feasibility of the MOMPC and stability of the resulted closed-loop system are established in the presence of constraints and arbitrary switches between cost functions. Finally, implementation of the switching MOMPC controller is demonstrated with a chemical process example for the continuous stirred tank reactor.     

Generic model controller tuning for chemical processes with input saturation

Control in the face of process input constraints is very common and of great practical importance in the processing industries. Generic Model Control (GMC) is a model‐based control framework for both linear and nonlinear systems. In this paper, a constrained GMC controller tuning approach using a nonlinear least squares technique is proposed. This tuning approach is simple to apply. For a SISO GMC control system with input saturation, the tracking performance is significantly improved by adding a simple heuristic switching strategy. The effectiveness of the proposed controller tuning approach is demonstrated using dynamic simulations and MIMO real‐time experiments.     

Limitations of the LDF/equimolar counterdiffusion assumption for mass transport within porous adsorbent pellets

Mass transfer resistance plays an important role in the performance of a periodic adsorption process under rapid cycling conditions. In this study, we examine the limitations of the Fick plus equimolar counterdiffusion (F+EC) and linear driving force (LDF) model for simulating the enrichment of oxygen from air in comparison to the dusty gas model (DGM) under rapid pressure swing adsorption (RPSA) conditions. A conservative, finite volume approach to the solution of the governing differential equations is developed and validated for an adsorbent pellet. Two variations on the RPSA boundary conditions at the pellet surface are investigated. The first considers the square-wave change in concentration from adsorption to desorption investigated with the RPSA-LDF model of Nakao and Suzuki (J. Chem. Eng. Jpn. 16(1983)114). The second considers the partial pressure variation as predicted from an adsorption simulator, representative of the true conditions experienced over a two-step RPSA cycle. From both cases, the impact of bulk gas motion within the pores (DGM) resulted in deviations exceeding 30% on the predicted working capacity of the sieve. This identifies the equimolar counterdiffusion assumption as a significant limitation for predicting performance with macro-mesoporous adsorbents. Along with bulk flow, an additional 10-50% deviation resulted from the RPSA-LDF model incorrectly predicting working capacity (in relation to the F+EC) for the case where boundary conditions do not follow a step change. To propose additional cycle-time-corrected correlations and/or intrapellet concentration profiles when approaching the RPSA limit appears futile given the range of operating conditions expected over a true cycle. The level of radial discretisation within the pellet also appears to be more sensitive for the F+EC as opposed to the DGM approach. These trends were observed for dimensionless cycle times exceeding the traditionally excepted critical value of 0.1, highlighting the importance of a DGM approach in describing mass transfer when approaching the RPSA limit.     

Optimization-based predictive control of a simulated moving bed process using an identified model

For optimization-based dynamic control of simulated moving bed (SMB) process, a novel control strategy based on process identification, which is an extension of the earlier work (Song et al., 2006a. Identification and predictive control of a simulated moving bed process: purity control. Chemical Engineering Science 61, 1973-1986), is proposed. A linear output prediction model is obtained by the method of subspace identification and used for the dynamic control. The controller is designed for optimizing the production cost while maintaining the specified product purities. For all of these, the average purities over one switching period of the target components in extract and raffinate streams, the reciprocal productivity and the solvent consumption are selected as output variables, while the flow rates in 1, 2, 3 and 4 are chosen as the manipulated variables. The realization of this concept is discussed and assessed on a virtual eight column SMB unit for a system following a bi-Langmuir isotherm. The identified prediction model is proven to be in good agreement with the first principles model considered as the actual SMB process. For typical control objectives encountered in actual operation, i.e., disturbance rejection and set-point tracking, it is shown that the proposed controller exhibits excellent performance, hence it is an effective tool for optimization-based control of SMB process.     

基于神经网络和多模型的非线性自适应PID控制及应用

针对一类未知的单输入单输出离散非线性系统,提出了基于神经网络和多模型的非线性自适应PID控制方法。该方法由线性自适应PID控制器、神经网络非线性自适应PID控制器以及切换机构组成。采用线性自适应PID控制器可保证闭环系统所有信号有界;采用神经网络非线性自适应PID控制器可改善系统性能;通过引入合理的切换机制,能够在保证闭环系统稳定的同时,提高系统性能。理论分析表明,该方法能够保证闭环系统所有信号有界,如果适当地选择神经网络的结构和参数,系统的跟踪误差将收敛于任意给定的紧集。将所提出的方法应用于连续搅拌反应釜,仿真结果验证了所提出方法的有效性。由于该方法基于增量式数字PID控制器,在工业过程中有着广阔的应用前景。     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

典型大时变时滞系统神经网络模糊PID控制及应用

针对典型大时变时滞系统,设计了一种基于神经网络的模糊PID控制器.该控制器综合模糊逻辑、神经网络与PID调节的各自优点,既具有模糊控制简单和有效的非线性控制作用,又具有神经网络的学习和适应能力,同时还具备PID控制的广泛适应性.该控制器能实现系统参数大范围失配情况下的闭环鲁棒稳定,并使闭环系统达到设定值无静差跟踪及满意的动态性能.     

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     

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.     

Explicit model predictive control of gas–liquid separation plant via orthogonal search tree partitioning

Solutions to constrained linear model predictive control (MPC) problems can be pre-computed off-line in an explicit form as a piecewise linear (PWL) state feedback defined on a polyhedral partition of the state space. This admits implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. Recently, algorithms that determine an approximate explicit PWL state feedback solution by imposing an orthogonal search tree structure on the partition, have been developed, and it has been shown that they may offer computational advantages. This paper considers the application of an approximate approach to the design of an explicit model predictive controller for a two-input two-output laboratory gas–liquid separation plant, including experimental evaluation. The approximate explicit MPC controller achieves performance close to that of the conventional MPC, but requires only a fraction of the real-time computational machinery, thus leading to fast and reliable computations.     

非线性Hammerstein模型预测控制策略及其在pH中和过程中的应用

所有实际工业过程都包含一定程度的非线性,如pH中和过程由于其本身的强非线性是工业过程控制中具有挑战性的难题,但至今为止仍缺乏有效的非线性控制方法。将基于差分方程模型的模型预测控制策略(model predictive control,MPC)推广到包含一个静态非线性多项式函数和一个线性差分方程动态环节的非线性Hammerstein系统,详细描述了基于静态非线性多项式函数的最优控制作用求解方法,提出了一套新的非线性Hammerstein MPC 控制策略(nonlinear Hammerstein predictive control,NLHPC)。pH中和过程控制仿真和控制实验表明,NLHPC的控制结果好于工业上常用的非线性 PID(nonlinear PID,NL-PID)控制器。     

基于2次核SVM的单步非线性模型预测控制

A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.