Nonlinear state estimation and control of a batch reactive distillation

This paper deals with the advanced adaptive control of a batch reactive distillation (RD) column for the production of ethyl acetate. The nonlinear adaptive control law consists of the generic model controller (GMC) and an adaptive state estimator (ASE). In the first part of the present work, the design approach of the ASE scheme in two different forms, namely ASE1 and ASE2, has been addressed for a batch reactive rectifier. The predictor model of both the ASE estimators includes only a component mole balance equation around the condenser-reflux drum system and an extra state equation having no dynamics, and therefore, there is a large process/predictor mismatch. In presence of this structural discrepancy, the adaptive estimation schemes compute the imprecisely known parameters quite accurately based on the measured distillate composition under initialization error, disturbance and uncertainty. In the subsequent part, the adaptive GMC–ASE1 control structure has been formulated for the sample reactive column. This nonlinear control strategy shows comparatively better closed-loop performance than the gain-scheduled proportional integral (GSPI) controller due to the exponential error convergence capability of the estimation scheme and the high-quality control of the GMC law.     

Observer-based control algorithms for a distillation column

This paper studies the synthesis of nonlinear observer-based globally linearizing control (GLC) algorithms for a multivariable distillation column. Two closed-loop observers/estimators, namely extended Kalman filter (EKF) and adaptive state observer (ASO), have been designed within the GLC framework to estimate the state variables along with the poorly known parameters. Exactly same basic model structure was used for developing the observers. The model structure is so simple that the estimator design was performed based on only two component balance equations around the condenser-reflux drum and the reboiler-column base systems of the distillation column. To construct these observers, the poorly known parameters, namely component vapor flow rate leaving top tray, component liquid flow rate leaving bottom tray and distribution coefficient in the reboiler, were considered as extra states with no dynamics. The comparative study has been carried out between the proposed GLC in conjunction with ASO (GLC-ASO) and that coupled with EKF (GLC-EKF). The GLC-ASO control scheme showed comparatively better performance in terms of set point tracking and disturbance as well as noise rejections. The control performance of GLC-ASO and a dual-loop proportional integral derivative (PID) controller was also compared under set point step changes and modeling uncertainty. The proposed GLC-ASO structure provided better closed-loop response than the PID controller.     

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.     

ADAPTIVE MULTIVARIABLE PID CONTROLOF A DISTILLATION COLUMN WITH UNKNOWN AND VARYING DEAD TIME

A new, reliable, and easy-to-use adaptive control strategy has been developed to overcome the long-existing difficulties in adaptive control practice caused by unknown and varying process dead time. A self-tuning PID control algorithm is adopted to control a distillation column possessing second-order-plus-dead-time dynamics. The self-tuning strategy is based on recursive least-squares estimation of process parameters. U-D factorization is applied to stabilize the parameter estimation calculations. A variable forgetting factor is used to alleviate wind-up in the estimator. A simulation study and an experimental evaluation demonstrate the capability of the adaptive algorithm.     

Adaptive Generic Model Control of Multivariable Processes: Application to Semi-Batch Reactors with Different Relative Degrees

In this study, a multivariable Generic Model Control (GMC) approach is proposed based on input-output linear-in-parameters time series data-driven models. Adaptation of the model parameters is carried out at every sampling instant. For higher relative degree systems, two different definitions are used for output derivatives, yielding two versions of adaptive GMC for multivariable processes. The performance of the proposed control algorithms is illustrated by application to multivariable semi-batch reactors without and with coolant dynamics for control of temperature and one of the reactant concentrations. The study indicated that the adaptive GMC (AGMC) algorithms for higher relative degree multiple-input and multiple-output (MIMO) systems with a different relative degree have exhibited performance comparable to or better than the phenomenological model-based GMC with respect to both set point tracking and smooth input profiles, and also that the predictive version of AGMC (AGMC-II) has exhibited slightly lower integral square error (ISE) values compared to AGMC-I in case of multivariable semi-batch reactor with coolant dynamics.     

GENERIC MODEL ADAPTIVE CONTROL

Generic Model Control (GMC) is a process model based control algorithm incorporating a process model directly within the control structure. It has been shown to produce excellent control, despite reasonable modelling errors. In this paper an algorithm is developed within a GMC framework which reduces the effect of larger modelling errors by regularly updating the model parameters. This new adaptive algorithm is capable of adapting model parameters in a nonlinear model, where the parameters appear in a nonlinear manner. Several examples are presented to illustrate the principles of the technique.     

A novel online affine model identification of multivariable processes using adaptive neuro-fuzzy networks

This paper presents a novel systematic identification methodology for online affine modeling of multivariable processes using adaptive neuro-fuzzy networks. The proposed approach introduces an integrated procedure to simultaneously estimate a number of adaptive neuro-fuzzy networks with simple and compact dynamic structures to realize a multivariable affine model identification in real-time. A new fuzzy rule significance concept, based on a generic time-weighted rule activation record (WRAR), together with a measure of time-weighted root mean square (WRMS) error are incorporated to maintain efficient structural and parametric mechanisms for proper adaptation of the resulting neuro-fuzzy networks. An extended Kalman filter (EKF) algorithm is developed to adaptively adjust the neuro-fuzzy free parameters corresponding to the nearest created fuzzy rules. Extensive simulation test studies will be conducted to explore the capabilities of the proposed identification approach to adaptively develop online multivariable affine dynamic models for a highly nonlinear and time-varying continues stirred tank reactor (CSTR) and a highly nonlinear binary distillation column as two challenging benchmark problems.     

基于一般模型控制的高纯内部热耦合精馏策略

内部热耦合精馏塔（ITCDIC）是精馏节能控制的一个前沿。本文提出了一种基于一般模型控制（GMC）的内部热耦合精馏塔的先控策略,以解决导致传统线性控制策略难以得到较好控制效果的高纯下内部热耦合精馏塔的非线性。以苯-甲苯物系作为研究实例,对所提出的高纯ITCDIC控制策略进行了详细研究。设定值改变和过程扰动下的控制品质表明了所提出的高纯ITCDIC的GMC控制策略的切实有效性。     

APPLICATION OF MIMO ADAPTIVE CONTROL TO A BINARY DISTILLATION PROCESS

An adaptive controller developed from a generalized cost function is studied in this work. Theoretical derivation is considered first. Application of such controller to a multiple-input multiple-output (MIMO) system—a binary distillation column is examined. Practical issues in the implementation of adaptive regulators to control chemical engineering processes are discussed in detail.     

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.     

ADAPTIVE POLE-PLACEMENT CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR

A simulation of the polymerization of methylmethacrylate in a CSTR is adaptively controlled by two types of pole-placement algorithms. The strongly nonlinear polymerization process, exhibiting multiple steady states, presents difficult control problems for conventional feedback controllers. The performance of an adaptive explicit SISO controller and that of an adaptive implicit multivariable controller are compared and evaluated as applied to this process. The plant is identified by a recursive least squares estimator. Modifications made to the estimation algorithm help to maintain adequate closed-loop results. A simple warm-up procedure is introduced that successfully initializes the controller and estimator during plant start-up. Good servo and regulatory control are achieved by both pole-placement schemes.     

Composition estimation of multicomponent reactive batch distillation with optimal sensor configuration

An inferential state estimation scheme based on extended Kalman filter (EKF) with optimal selection of sensor locations using principal component analysis (PCA) is presented for composition estimation in multicomponent reactive batch distillation. The properties of PCA are exploited to provide the most sensitive dynamic temperature measurement information of the process to the estimator for accurate estimation of compositions. The state estimator is supported by a simplified dynamic model of reactive batch distillation that includes component balance equations together with thermodynamic relations and reaction kinetics. The performance of the proposed scheme is evaluated by applying it for composition estimation on all trays, reboiler, reflux drum and products of a reactive batch distillation column, in which ethyl acetate is produced through an esterification reaction between acetic acid and ethanol. This quaternary system with azeotropism is highly nonlinear and typically suited for implementation of the proposed scheme. The results demonstrate that the proposed EKF estimation scheme with optimal temperature sensor configuration is effective for inferential estimation of compositions in multicomponent reactive batch distillation.     

Nonlinear static composition estimator for distillation columns using open equation-based nonlinear programming

In distillation column control, secondary measurements such as temperatures and flows are widely used to infer product composition. This paper addresses the development of nonlinear static estimators using secondary measurements for estimating product compositions of distillation columns. An open equationbased optimization problem, which minimizes the differences between the measured outputs and the estimated outputs, has been formulated and solved by using the nonlinear program (NLP) solver, MINOS5. It is shown that the proposed nonlinear estimator is robust and more powerful than the conventional PLS (Partial-Least-Squares) estimator.     

Decentralized Control System Design under Uncertainty Using Mixed‐Integer Optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In this contribution, the optimal control structure and the optimal controller parameters are determined simultaneously using mixed‐integer dynamic optimization (MIDO) under uncertainty, to account for nonlinear process dynamics and various disturbance scenarios. Application of the sigma point method is proposed in order to approximate the expectation and the variance of a chosen performance index with a minimum number of points to solve the MIDO problem under uncertainty. The proposed methodology is demonstrated with a benchmark problem of an inferential control for a reactive distillation column. The results are compared with established heuristic design methods and with previous deterministic approaches.     

Temperature Inferential Control of Heat‐Integrated Distillation Column Based on Variable Sensitive Stage Temperature Set‐point

Heat‐integrated distillation is an improved distillation technique with remarkable energy‐saving potential. A control scheme with a variable sensitive stage temperature set‐point is proposed to solve the control problem of a heat‐integrated distillation column (HIDiC). An online estimator is designed to support the variation of the set‐point. The locations of the stage temperature measurements are carefully selected based on a combination strategy with three steps. First, the sensitive stages are selected. Then, the following stages are determined by a PCA‐based method. Finally, a maximum differentiation method provides the remaining measurement selections. According to the profile parameters estimated by the proposed estimator, the set‐point of the sensitive stage temperature is adjusted adaptively to reduce the influence of the disturbances. Two commonly‐used PID controllers, the sensitive temperature control and the temperature differential control, are developed as the comparative study. The simulation results show that the proposed control scheme has a distinct advantage in restraining different disturbances.     

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.     

Proportion integral-type active disturbance rejection generalized predictive control for distillation process based on grey wolf optimization parameter tuning

The high-purity distillation column system is strongly nonlinear and coupled, which makes it difficult to control. Active disturbance rejection control (ADRC) has been widely used in distillation systems, but it has limitations in controlling distillation systems with large time delays since ADRC employs ESO and feedback control law to estimate the total disturbance of the system without considering the large time delays. This paper designs a proportion integral-type active disturbance rejection generalized predictive control (PI-ADRGPC) algorithm to control the distillation column system with large time delay. It replaces the PD controller in ADRC with a proportion integral-type generalized predictive control (PI-GPC), thereby improving the performance of control systems with large time delays. Since the proposed controller has many parameters and is difficult to tune, this paper proposes to use the grey wolf optimization (GWO) to tune these parameters, whose structure can also be used by other intelligent optimization algorithms. The performance of GWO tuned PI-ADRGPC is compared with the control performance of GWO tuned ADRC method, multi-verse optimizer (MVO) tuned PI-ADRGPC and MVO tuned ADRC. The simulation results show that the proposed strategy can track reference well and has a good disturbance rejection performance.     

ROBUST NONLINEAR PREDICTIVE CONTROL USING A DISTURBANCE ESTIMATOR

A robust nonlinear predictive control strategy using a disturbance estimator is presented. The disturbance estimator is comprised of two parts: one is the disturbance model parameter adaptation and the other is future disturbance prediction. A linear discrete model is proposed as a disturbance model which is formulated by using process inputs and available process measurements. The recursive least square (RLS) method with exponential forgetting is used to determine the uncertain disturbance model parameters and for the future disturbance prediction, future disturbances projected by the future process inputs are used. Two illustrative examples: a jacketed CSTR as a SISO system: an adiabatic CSTR as a MIMO system, and experimental results of the distillation column control are presented. The results indicate that a substantial improvement in nonlinear predictive control performance is possible using the disturbance estimator.     

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。     

A DIRECT NONLINEAR ADAPTIVE CONTROL OF STATE FEEDBACK LINEARIZABLE SYSTEMS

A direct nonlinear adaptive control of state feedback linearizable single-input single-output systems is proposed in the case when parametric uncertainties are represented linearly in the unknown parameters. The main feature of the proposed nonlinear adaptive control system is that the linearizing coordinate transformation and the state feedback are updated by parametric adaptive law, derived using the second method of Lyapunov. The proposed adaptive control scheme is relatively straightforward and simple in the sense that it does not use the concept of augmented error. This adaptive control scheme is numerically applied to an exothermic chemical reactor system and is compared with the nonadaptive stale feedback linearization which has an integral action. The simulation shows that the proposed adaptive control scheme can be applied effectively to highly nonlinear, uncertain chemical systems.