Nonlinear temperature control of a batch suspension polymerization reactor

This paper concerns nonlinear temperature control of a batch polymerization reactor where suspension polymerization of methyl methacrylate (MMA) takes place. For this purpose, four control algorithms, namely, a fix proportional‐integral (PI) controller, an adaptive proportional‐integral‐derivative (PID) controller and two globally linearizing control (GLC) schemes, one for known kinetic model (GLC‐I) and the other for unknown kinetic model (GLC‐II), are selected. The performances of these controllers are compared through simulation and real‐time studies in the presence of different levels of parameter uncertainty. The results indicate that GLCI and GLC‐II have better performances than fix PI and adaptive PID, especially in case of strong gel effect. The worst performance belongs to adaptive PID because of rapid model changes in gel effect region. GLC‐II has a simpler structure than GLC‐I and can be used without requiring the kinetic model. In implementation of GLC‐I the closed loop observer should be used because of model uncertainties.     

A tuning of the nonlinear PI controller and its experimental application

Many industrial chemical process control systems consist of conventional PID and nonlinear controllers, even though many advanced control strategies have been proposed. In addition, nonlinear control methods are widely used even for linear processes to achieve better control performance compared with linear PID controllers. However, there are few tuning methods for these nonlinear controllers. In this work, we suggest new controller tuning methods for the error square type of nonlinear PI controller. These control methods can be applied to a large number of linear and nonlinear processes without changing control structures. We also propose new tuning rules for integrating processes. In addition, we suggest application guidelines for performing the proposed tuning rules at the pilot scale multistage level control system. Finally, in this work we confirmed good control performances of the proposed tuning methods through both simulation studies and experimental studies.     

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.     

A method for robustness analysis of controlled nonlinear systems

This paper presents an approach to analyzing robustness properties of nonlinear systems under feedback control. The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters. By analyzing the Hopf bifurcation and saddle-node bifurcation loci with respect to these parameters, bounds on the controller tuning are identified which can serve as a measure for the robustness of the controlled system. These bounds depend upon the type as well as the degree of mismatch that exists between the plant and the model used for controller design.The method is illustrated by analyzing three control systems which are applied to a continuously operated stirred tank reactor: a state feedback linearizing controller and two output feedback linearizing controllers. While model uncertainty has only a minor effect on the tuning of the state feedback linearizing controller, this does not represent a very realistic scenario. However, when an observer is implemented in addition to the controller and an output feedback linearizing scheme is investigated, it is found that the plant-model mismatch has a much more profound impact on the tuning of the observer than it has on the controller tuning. In addition, two observer designs with different level of complexity are investigated and it is found that a scheme which makes use of additional knowledge about the system will not necessarily result in better stability properties as the level of uncertainty in the model increases. These investigations are carried out using the robustness analysis scheme introduced in this paper.     

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.     

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.     

GLOBAL STABILIZATION OF A BIOLOGICAL REACTOR BY LINEAR FEEDBACK CONTROL

A classical substrate inhibition model for biological reactors with PI controllers is subjected to a rigorous nonlinear analysis. The operating conditions and control settings that ensure global stability of the set-point are derived from bifurcation studies of the solution branches with the controller gains as the bifurcation parameters. The global stability of the set-point can be destroyed by co-existing extraneous attracting states, both steady and time-dependent, which may be introduced by the controllers that are designed to stabilize the set-point locally.     

GLOBAL STABILIZATION OF A BIOLOGICAL REACTOR BY LINEAR FEEDBACK CONTROL

A classical substrate inhibition model for biological reactors with PI controllers is subjected to a rigorous nonlinear analysis. The operating conditions and control settings that ensure global stability of the set-point are derived from bifurcation studies of the solution branches with the controller gains as the bifurcation parameters. The global stability of the set-point can be destroyed by co-existing extraneous attracting states, both steady and time-dependent, which may be introduced by the controllers that are designed to stabilize the set-point locally.     

Nonlinear adaptive temperature control of multi-product, semi-batch polymerization reactors

This paper considers the temperature control of semi-batch polymerization reactors in which some of the following issues must be considered: (i) production of multiple products in the same reactor; (ii) changing heat transfer characteristics, during a batch and from batch to batch; (iii) time varying and nonlinear reaction rate due to changing monomer concentration and diffusion controlled termination reactions (gel effect); (iv) the absence of detailed kinetic models for the reactors. The industrial challenge problem published by Chylla and Haase [Chylla, R. W. and Haase, D. R. (1993) Temperature control of semi-batch polymerization reactors (with corrected updates). Comput. Chem. Eng. 17, 257–264) is used as the simulation basis for evaluating these problems.

A nonlinear adaptive controller consisting of a nonlinear controller (based on differential geometric concepts) coupled with an extended Kalman filter (which uses only readily available data and knowledge) is shown to provide excellent control in all the above situations. In particular, the on-line estimation is critical for the strong performance of the nonlinear controller over a broad range of conditions. PID controllers with feedforward terms can perform well at one set of conditions, however, they require retuning as conditions and products change.     

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.     

AN INDIRECT FEEDFORWARD COMPOSITION CONTROLLER FOR DISTILLATION COLUMNS

This paper addresses the problem of designing an indirect feedforward controller, also called cascade control, to regulate the product composition of distillation columns to overcome load disturbances. The overall controller is composed of two cascaded controllers. The primary controller is basically a low-gain controller, which uses slow (delayed) composition measurements to provide servo responses (composition control). The secondary controller has the structure of a high-gain proportional-integral (PI) controller with an antireset windup scheme, which uses fast temperature measurements at a given distillation tray to track the output of the primary controller. In this way, the secondary controller also provides protection against load disturbances. A simulated example is used to illustrate the functioning of the proposed controller.     

An indirect feedforward composition controller for distillation columns

This paper addresses the problem of designing an indirect feedforward controller, also called cascade control, to regulate the product composition of distillation columns to overcome load disturbances. The overall controller is composed of two cascaded controllers. The primary controller is basically a low-gain controller, which uses slow (delayed) composition measurements to provide servo responses (composition control). The secondary controller has the structure of a high-gain proportional-integral (PI) controller with an antireset windup scheme, which uses fast temperature measurements at a given distillation tray to track the output of the primary controller. In this way, the secondary controller also provides protection against load disturbances. A simulated example is used to illustrate the functioning of the proposed controller.     

Control structure comparison for three-product Petlyuk column

The focus of this paper is to investigate different control structures (single-loop PI control) for a dividing wall (Petlyuk) column for separating ethanol, n-propanol and n-butanol. Four control structures are studied. All the results are simulations based on Aspen Plus. Control structure 1 (CS1) is stabilizing control structure with only temperature controllers. CS2, CS3 and CS4, containing also composition controllers, are introduced to reduce the steady state composition deviations. CS2 adds a distillate composition controller (CCDB) on top of CS1. CS3 is much more complicated with three temperature-composition cascade controllers and in addition a selector to the reboiler duty to control the maximum controller output of light impurity composition control in side stream and bottom impurity control in the prefractionator. CS4 adds another high selector to control the light impurity in the sidestream. Surprisingly, when considering the dynamic and even steady state performance of the proposed control structures, CS1 proves to be the best control structure to handle feed disturbances inserted into the three-product Petlyuk column.     

FEEDBACK LINEARIZATION DESIGNS FOR UNCERTAIN NONLINEAR TIME-DELAY PROCESSES: A COMPARATIVE STUDY

This work concerns the phenomena in which the feedback linearization control is applied to uncertain nonlinear time-delay processes. Under the I/O linearization algorithm, both nonlinear controllers are used to stabilize the closed-loop system with transformed delay inputs. When the effect of input perturbations can converge to zero or asymptotically vanish, these nonlinear feedback designs with only an adjustable parameter can directly improve the tracking performance. The simple linearizing controller can directly regulate the system output at unstable operating point. Combined with deadtime compensation the nonlinear predictive controller with the aid of appropriate state prediction is valid for the real process in the presence of large time delay. Finally, via computer simulation and test of control ability of both feedback control designs the useful comparative results are presented.     

NONLINEAR MODEL PREDICTIVE CONTROL

Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers designed using (1) nonlinear variable transformations, (2) a linear controller tuned using the internal model control approach, and (3) open-loop optimal control. NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Unlike the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control. NMPC also demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to its set-point without steady-state offset.     

丙烯精馏塔智能控制系统设计及应用

针对乙烯生产装置丙烯精馏塔的工艺特征和操作特点,利用支持向量机在小样本数据建模中的优势,提出一种基于支持向量机丙烯浓度软测量技术,解决了塔釜建模数据样本少的问题,实现了塔釜丙烯浓度在线测量。在上述软测量系统的基础上,设计了丙烯浓度智能控制系统。该系统采用模糊PID作为丙烯浓度控制器,其输出量作为灵敏板温度控制器的设定值,与灵敏板温度控制构成串级调节系统,同时为了克服进料量对灵敏板温度造成的干扰,设计了进料流量前馈控制器。丙烯浓度智能控制系统对塔釜丙烯指标进行实时控制,提高了塔釜丙烯浓度的控制平稳度,解决了塔釜丙烯浓度超标问题。现场应用效果表明,该丙烯浓度软测量系统测量精度高,控制系统可以有效控制塔釜丙烯浓度,取得了良好的控制效果,满足了工业现场运行的需要。     

FEEDBACK LINEARIZATION DESIGNS FOR UNCERTAIN NONLINEAR TIME-DELAY PROCESSES: A COMPARATIVE STUDY

This work concerns the phenomena in which the feedback linearization control is applied to uncertain nonlinear time-delay processes. Under the I/O linearization algorithm, both nonlinear controllers are used to stabilize the closed-loop system with transformed delay inputs. When the effect of input perturbations can converge to zero or asymptotically vanish, these nonlinear feedback designs with only an adjustable parameter can directly improve the tracking performance. The simple linearizing controller can directly regulate the system output at unstable operating point. Combined with deadtime compensation the nonlinear predictive controller with the aid of appropriate state prediction is valid for the real process in the presence of large time delay. Finally, via computer simulation and test of control ability of both feedback control designs the useful comparative results are presented.     

LINEAR PI TEMPERATURE-CONCENTRATION CASCADE CONTROL FOR TUBULAR REACTORS

In this article we explore the application of linear PI cascade control schemes to improve the performance of industrial PI/PID controllers for controlling outlet reactor concentration. By departing from simple I/O first-order dynamical models obtained from step responses, it is shown that the incorporation of a secondary loop for regulating the reactor temperature at a given interior position significantly improves the control performance in the face of feed composition and temperature disturbances. The effects of the temperature sensor location and the usage of multiple temperature measurements are also evaluated.     

LINEAR PI TEMPERATURE-CONCENTRATION CASCADE CONTROL FOR TUBULAR REACTORS

In this article we explore the application of linear PI cascade control schemes to improve the performance of industrial PI/PID controllers for controlling outlet reactor concentration. By departing from simple I/O first-order dynamical models obtained from step responses, it is shown that the incorporation of a secondary loop for regulating the reactor temperature at a given interior position significantly improves the control performance in the face of feed composition and temperature disturbances. The effects of the temperature sensor location and the usage of multiple temperature measurements are also evaluated.     

An application of a cascaded self tuning regulator to a karr solvent extraction column

An application of a cascaded Clarke-Gawthrop self tuning regulator (STR) to a Karr liquid-liquid solvent extraction column is presented. The Karr column, a reciprocating plate column, exhibits nonlinear asymmetric responses which are complex functions of the operating conditions and requires adaptive control in order to prevent instability. The outer loop of this cascade scheme controls the extract concentration of the continuous phase while the inner loop controls the hydrodynamic holdup in the column and prevents flooding. The manipulated variable was the frequency of reciprocation. The STR-STR cascade arrangement is compared with a fixed parameter Proportional plus Integral (PI) controller in the outer loop and an STR in the inner loop.