NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.     

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。     

Nonlinear Model Algorithmic Control of a pH Neutralization Process

Control of pH neutralization processes is challenging in the chemical process industry because of their inherent strong nonlinearity. In this paper, the model algorithmic control （MAC） strategy is extended to nonlinear processes using Hammerstein model that consists of a static nonlinear polynomial function followed in series by a linear impulse response dynamic element. A new nonlinear Hammerstein MAC algorithm （named NLH-MAC） is presented in detail. The simulation control results of a pH neutralization process show that NLH-MAC gives better control performance than linear MAC and the commonly used industrial nonlinear propotional plus integral plus derivative （PID） controller. Further simulation experiment demonstrates that NLH-MAC not only gives good control response, but also possesses good stability and robustness even with large modeling errors.     

Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.     

反应器-换热器网络的PI-多模型动态矩阵控制

针对反应器-换热器网络动态特性在时间上的多尺度特性,应用奇异摄动法得到它在两个不同时间尺度上的子模型：快时间尺度上的能量平衡模型、慢时间尺度上的物料平衡模型。同时,考虑到反应器-换热器网络非线性特性、存在噪声干扰、参数扰动等模型不确定性,快、慢时间尺度子模型分别采用PI控制、多模型动态矩阵控制。最后,通过与快、慢时间尺度子模型分别采用PI控制、动态输出反馈控制的控制策略的仿真效果比较,表明本文中的控制策略在克服噪声、参数扰动方面具有一定优势。     

Nonlinear model-based feedforward control of distillation columns

An approach to feedforward distillation control based on inverse computation of nonlinear stage models is presented. The feedforward model calculates dynamic trajectories of manipulated variables from measured disturbances and product purity set points independently of the control configuration. Because the model includes the dominant dynamics and nonlinearities of the column, dynamic decoupling of the control loops is achieved. A superimposed linear controller only has to compensate model uncertainties and disturbances that cannot be measured. The proposed approach improves the control performance. Simulation studies show the applicability of the method to multicomponent distillation as well as to distillation trains. Experiments on a pilot plant scale binary distillation column verify the simulation results.     

Model based control of a high purity distillation column

In this paper, the problem of dual product composition control of an industrial high purity distillation column, a deisohexanizer (DIH), is addressed using a Generic Model Control framework. A dynamic simulation of the DIH was performed for preliminary studies of the performance of different controller strategies/algorithms. The performance of Generic Model Control incorporating different process models was studied. Process models are presented ranging from simple first order approximations to mechanistic short cut distillation models where a tradeoff between model complexity and model adaptivity is investigated. The different controllers were implemented and compared using a dynamic simulation of an industrial deisohexanizer (DIH) to select the best condidate controller. A controller using a nonlinear process model emerged as the best controller and was implemented on the actual process, resulting in improved performance over the original controller. Simulation results and industrial plant data are presented.     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

Application of gain scheduling for modeling the nonlinear dynamic characteristics of NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> emissions from utility boilers

A hierarchical gain scheduling (HGS) approach is proposed to model the nonlinear dynamics of NO _x emissions of a utility boiler. At the lower level of HGS, a nonlinear static model is used to schedule the static parameters of local linear dynamic models (LDMs), such as static gains and static operating conditions. According to upper level scheduling variables, a multi-model method is used to calculate the predictive output based on lower-level LDMs. Both static and dynamic experiments are carried out at a 360 MW pulverized coal-fired boiler. Based on these data, a nonlinear static model using artificial neural network (ANN) and a series of linear dynamic models are obtained. Then, the performance of the HGS model is compared to the common multi-model in predicting NO _x emissions, and experimental results indicate that the proposed HGS model is much better than the multi-model in predicting NO _x emissions in the dynamic process. This paper was presented at the 7 ^th China-Korea Workshop on Clean Energy Technology held at Taiyuan, Shanxi, China, June 25–28, 2008.     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

Extended kalman filter based nonlinear geometric control of a seeded batch cooling crystallizer

A nonlinear dynamic model of a seeded potash alum batch cooling crystallizer is presented. The model of the batch crystallizer is based on the conservation principles of mass, energy and population. In order to maintain constant supersaturation, a nonlinear geometric feedback controller is implemented. It is shown that compared to a natural and a simplified optimal cooling policies, the nonlinear geometric control (NCC) leads to a substantial improvement of the final crystal quality. An extended Kalman filter (EKF) is used as a closed loop observer for this nonlinear system to predict the non‐measurable state variables. It is found that the EKF is capable of effectively predicting the first four leading moments of the population density function. The effectiveness of the EKF based nonlinear geometric controller in the presence of plant/model mismatch is also studied. Simulation results show that the EKF based nonlinear geometric controller is reasonably robust in the presence of modeling error.     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A scheduled controller for a nonlinear process of Wiener type based on IMC framework and local models

In this paper, we present an efficient, practical gain scheduled controller for a nonlinear process of Wiener type, pH problem. The main idea is to use locally linearized first-order models to approximate the real process in the neighborhood of steady points, thus resulting in a conventional PI controller within IMC framework. The scheduling variable is chosen to be the measured pH value which is supposed to be at steady state. Once locally linearized first-order models at several steady points are obtained, a simple linear interpolation is carried out for those points in between them. The results show that the practical scheme used can perform satisfactorily.     

基于控制性能比较的非线性不对称系统预测控制

生产过程某些非线性系统常常表现出不对称动态特性,相对于其在工业工程中经常出现的理论研究特别是控制方法研究则十分有限。本文针对基于正反方向上的两个线性模型分别设计PID控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器。在每一步的控制率计算中,正反方向的控制器分别计算控制作用,并通过比较正反控制器的控制性能指标来确定最终采用的控制作用。通过pH值控制的仿真实验证明其对非线性不对称系统的控制效果明显优于传统的在正反方向分别采用PID控制的控制效果。     

pH Process Control with Fictitious Smoothing Tanks

This paper is concerned with pH process control based on sensitivity analysis, applied to a strong acid‐strong base system. The models were developed, using the concept of chemical reaction invariants. Derived from GMC synthesis, a non‐linear PI control law was presented and the results compared to the classical PI controller. The presence of uncertainties or a shift in the system's behavior has been considered, either on steady state or from the dynamic point of view. The analysis showed that sensitivity presents the same behavior in both cases, thus demonstrating the feasibility of the application with the non‐linear PI controller. The results of sensitivity analysis indicate a strategy for improving control structure performance, using the concept of fictitious smoothing tanks, inserted into computer codes for process control, yet without incurring appreciable computational load or additional costs.     

Soft sensor model derived from Wiener model structure: modeling and identification

The processes of building dynamic and static relationships between secondary and primary variables are usually integrated in most of nonlinear dynamic soft sensor models. However, such integration limits the estimation accuracy of soft sensor models. Wiener model effectively describes dynamic and static characteristics of a system with the structure of dynamic and static submodels in cascade. We propose a soft sensor model derived from Wiener model structure, which is an extension of Wiener model. Dynamic and static relationships between secondary and primary variables are built respectively to describe the dynamic and static characteristics of system. The feasibility of this model is verified. Then the expression of discrete model is derived for soft sensor system. Conjugate gradi-ent algorithm is applied to identify the dynamic and static model parameters alternately. Corresponding update method for soft sensor system is also given. Case studies confirm the effectiveness of the proposed model, alternate identification algorithm, and update method.     

基于Min-Max的预测控制鲁棒参数设计

工业控制中模型的不确定性是不可避免的.提出基于Min-Max的预测控制器鲁棒参数设计方法,充分考虑到模型的不确定性.仿真结果表明,控制器在对象模型一定范围内变化时仍具有较好的控制品质,不需要重新整定控制器参数,提高了系统的鲁棒性能.     

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.     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

PROCESS/MODEL MISMATCH COMPENSATION FOR MODEL-BASED CONTROLLERS

Process model-based control algorithms that employ a process model directly in the controller, have been shown to produce good control performance and robust behaviour, despite process modelling errors. However, when the process/model mismatch is large, the closed-loop response, while still being better than responses obtained by conventional controllers, will be degraded. This paper presents a new approach to compensate for process/model mismatch errors, and is based upon the Generic Model Control (GMC) algorithm. This approach is applicable to both linear and nonlinear model-based algorithms. Simulation results are presented to illustrate the efficiency of the approach