Systematic controllability analysis for chemical processes

Modern chemical industrial processes are becoming more and more integrated and consist of multiple interconnected nonlinear process units. These strong interactions profoundly complicate a system's inherent properties and further alter the plant‐wide process dynamics. This may lead to a poor control performance and cause plant‐wide operability problems. To ensure entire processes run robustly and safely, with considerable profitability, it is crucial to recognize the inherent characteristics that can jeopardize controllability and process behavior at the early design stage. With a focus on inherently safer designs, from a plant‐wide perspective, a systematic method for chemical processes controllability analysis is addressed in this study. In the proposed framework, based on open‐loop stability/instability and minimum/nonminimum‐phase behavior, the entire operating zone of the process can be categorized into distinct subregions with different inherent properties. Variations in the inherent characteristics of a plant‐wide process with the operation and design conditions, over the feasible operation region, can be probed and analyzed. An attempt of this framework is made to illustrate how to clarify the roots of the poor controllability that arise in the design and operation of a large scale chemical process, and the results can provide guidance for both deciding the optimal operation conditions and selecting the most suitable control structure. Singularity theory is also applied in the framework to improve the computational efficiency. The framework is illustrated with two case studies. One involves a reactor‐external heat exchanger network and the other a more complex plant‐wide process, comprising a reactor, an extractor, and a distillation column. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3096–3109, 2012     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Controllability analysis for the liquid-phase catalytic oxidation of toluene to benzoic acid

The liquid-phase catalytic oxidation of toluene is the main industrial commercial process for producing benzoic acid. It is a strongly exothermic and highly nonlinear process that exhibits poor controllability characteristics with input/output multiplicity and non-minimum phase behavior. Focusing on inherent safety, this study explores the open and closed-loop controllability of this process. The framework contains two parts. First, an approach for analyzing the stability of zero dynamics of the system is used to investigate the phase behavior of the process and is selected as an open-loop indicator for controllability. Second, based on the model predictive controller, closed-loop dynamic simulation, including set-point tracking and disturbances rejection, is performed to illustrate the dynamic performance in various sub-regions with different controllability characteristics. The results of the dynamic simulation confirm everything predicted by the open-loop controllability analysis. The outcomes are expected to guide realistic industrial operation and process control system design. An attempt is made with the help of this liquid-phase oxidation process to show how to clarify and deal with the causes of the complex phenomena that arise in the operation and control of the chemical processes.     

The bifurcation behavior of continuous free-radical solution loop polymerization reactors

The bifurcation behavior of continuous free-radical solution loop polymerization reactors is analyzed in this work. A mathematical model is developed in order to describe the impact of the recycling pump and other external reactor parts upon the process dynamics and stability. Stability analysis is performed using bifurcation theory and continuation methods. It is shown that under certain operational conditions as many as seven steady states are predicted for the loop polymerization reactor. Oscillatory behavior is observed for a wide range of process parameters and onset of oscillations is observed during the transition from operation without material recycling to operation with partial recirculation of the polymer solution. Besides, at certain constrained range of operation conditions, complex dynamics can be observed, including the onset of chaotic behavior. It is also shown that the thermal parameters of the reactor and recycling pump exert a profound effect upon the process stability. For this reason it is shown that oscillatory behavior is very unlikely to occur in actual industrial reactors.     

Dynamic Behavior of Industrial Gas Phase Fluidized Bed Polyethylene Reactors under PI Control

A mathematical model describing the UNIPOL process for the production of polyethylene in the gas phase using a Ziegler‐Natta catalyst in a bubbling fluidized bed is used to analyze the major processes determining the behavior and performance of these industrially important units. The investigation shows that both static bifurcation (multiplicity of the steady states) as well as dynamic bifurcation (stable/unstable periodic attractors) behavior cover wide regions of the design and operating parameter domain. A conventional proportional‐integral (PI) control policy is suggested to stabilize the behavior of the system. The control philosophy covers both aspects of stabilizing unstable steady states as well as compensating for external disturbances. It is shown that for some controller configurations and set points the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The industrial implications of the phenomena discovered for both the open loop (uncontrolled) as well the closed‐loop (controlled) systems are analyzed.     

基于高斯模型的聚乙烯过程设计与控制集成优化

聚乙烯反应过程中物流-能流剧烈交叠、反应-传递相互耦合,使得过程具有强非线性以及多重稳态。传统的顺序设计方法不能保证系统有足够的控制自由度,当存在扰动和过程参数不确定性时,仅依靠设计控制器很难提高产品质量。提出一种聚乙烯工艺稳态设计与运行控制的集成优化方案,创造性地引入Kriging高斯模型同时预测模型动态和模型不确定性。另一个重要的贡献是在聚乙烯工艺设计阶段,设计性能指标,定量描述过程稳态设计对闭环动态的影响。所提出的方法已经通过对气相聚乙烯工艺设计和运行控制的集成优化进行了验证,并在参数不确定性和扰动存在情况下仿真证实了集成优化设计方案的高效性。     

Energy‐efficient complex distillation sequences: Control properties

Four thermally coupled distillation systems were designed for the separation of five‐component mixtures (the light‐ends separation section of a crude distillation plant); their steady‐state design was obtained by starting from a conventional distillation sequence and then optimizing for minimum energy consumption. The thermally coupled distillation systems were compared to sequence based on conventional columns design. Comparison was based on controllability properties under open and closed loop operation, following the dynamic behaviour after common industrial operating disturbances. Simulation results were analyzed by the singular value decomposition technique and with the performance examination of elimination of feed disturbances using PI controllers. It was found that thermally coupled distillation systems are controllable and, sometimes, they exhibit dynamic responses that are easier to manage than in the case of conventional distillation sequences; this result is innovative in the study of this kind of systems.     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

The focus of this work is on economic model predictive control (EMPC) that utilizes well‐conditioned polynomial nonlinear state‐space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well‐conditioned over a broad region of process operation in the sense that they can be correctly integrated in real‐time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state‐space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well‐conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov‐based EMPC (LEMPC) systems for nonlinear processes using the well‐conditioned nonlinear models that can be readily implemented in real‐time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed‐loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3353–3373, 2015     

Optimal start‐up control of injection molding barrel temperature

It is desirable to control injection molding barrel temperatures to set‐point with a minimal start‐up time and near‐zero overshoot for productivity and product quality. This paper, based on time optimal control, developed a start‐up procedure leading to the optimal heating up profile with the shortest rising time with small overshoot. The design parameters are obtained automatically through one simple open‐loop test. Experiments show that the proposed control achieves the design purpose under different conditions. POLYM. ENG. SCI., 47:254–261, 2007. © 2007 Society of Plastics Engineers.     

A temperature‐dependent adaptive controller. Part I: Controller methodology and open‐loop testing

Currently, the controllers for achieving a desired injection velocity setpoint profile are independent of processing conditions in plastic injection molding. The dynamics of the reciprocating screw during injection mold filling is complex and temperature‐dependent. This complexity is based on process parameters that are nonlinear, which can vary spatially in time. Open‐loop tests were performed on two polymers at three melt temperatures and three mold‐fill velocity regimes: low, medium, and high. These tests were based on close‐loop injection mold‐fill setpoints and a derived voltage velocity relationship for the injection velocity hydraulic valve. The results of the open‐loop tests show that mold‐filling injection velocity is polymer‐ and melt temperature‐dependent. Polym. Eng. Sci. 44:1925–1933, 2004. © 2004 Society of Plastics Engineers.     

Chaotic Behavior of Industrial Fluidized‐Bed Reactors for Polyethylene Production

Recent theories of bifurcation and chaos are used to analyze the dynamic behavior of the UNIPOL process for the production of polyethylene in the gas phase using the Ziegler‐Natta catalyst. Dynamic behavior covers wide regions of the design and operating parameters domain of this industrially important unit. A conventional proportional‐integral (PI) controller was implemented to stabilize the desired operating point on the unstable steady‐state branch. The presence of the PI controller stabilized the desired unstable steady‐state regions to a certain range of catalyst injection rate, by contrast, it is found out that the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The practical implications of this analysis can be very serious, since chaos is shown to exist right near the desired operating point where high polyethylene production rates can be achieved     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Controllable optimized designs of an ideal reactive distillation system using genetic algorithm

The steady state economic optimization to obtain the most economical controllable design of a double feed ideal reactive distillation (RD) column is demonstrated using real coded genetic algorithm. The novelty of the work is in the development of a simple procedure based on steady state criteria for controllability. The optimization is performed for four scenarios corresponding to a sequential increase in the number of design variables. Results show that limiting the optimization search space to only those designs that satisfy the controllability criteria leads to optimized designs that are only slightly (<2%) more expensive than the most economical design without controllability considerations. The former designs however exhibit much better controllability in terms of effectively handling a large through-put change using two-point temperature inferential control and avoiding a steady state transition under open loop operation. Results also show that the location of the fresh feeds is a dominant design variable with designs that do not constrain the feed tray location to be immediately above and below the reactive zone being substantially more economical.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Preliminary Design of a Loop Reactor for Bulk Propylene Polymerization

Some typical problems in the early design stages of a tubular loop reactor for bulk propylene polymerization are analyzed. Characteristic variables are identified, and a shortcut method for the preliminary estimation of the reactor dimensions is developed. the influences of process variables such as catalytic activity, suspended solid fraction, and average particle size are studied. In particular, a relationship between the average particle size in the reactor and the particle size at both the inlet and the outlet is obtained. the behavior of the reactor under different operating conditions is studied, and critical parameters are identified. Most relevant results are related to the importance of the particle size inside the reactor. the two goals of maximum yield and maximum productivity for a given loop reactor configuration cannot be achieved simultaneously: While catalyst yield increases with the third power of the average particle size in the reactor, the smaller the average particle size in the reactor, the greater the productivity. the steps to be followed for a preliminary design of a propylene polymerization, loop reactor are discussed. A priority list for the sequence of parameters to be adopted is proposed, according to the relative importance of the variables involved.     

Time Series Modeling of Two‐ and Three‐Phase Flow Boiling Systems with Genetic Programming

The time series of the physical parameters in boiling evaporators with vapor‐liquid (V‐L) two‐phase and vapor‐liquid‐solid (V‐L‐S) three‐phase external natural circulating flows exhibit nonlinear features. Hence, proper system evolution models may be built from the point of view of nonlinear dynamics. In this work, genetic programming (GP) was utilized to find the nonlinear modeling functions necessary to develop global explicit two‐variable iteration models, using wall temperature signals measured from the heated tube in ordinary two‐phase and three‐phase fluidized bed evaporators. The model predictions agree well with the experimental data of the time series, which means that the models established with GP can adequately describe the dynamic evolution behavior of multi‐phase flow boiling systems.     

Composite fast‐slow MPC design for nonlinear singularly perturbed systems

The design of a composite control system for nonlinear singularly perturbed systems using model predictive control (MPC) is described. Specifically, a composite control system comprised of a “fast” MPC acting to regulate the fast dynamics and a “slow” MPC acting to regulate the slow dynamics is designed. The composite MPC system uses multirate sampling of the plant state measurements, i.e., fast sampling of the fast state variables is used in the fast MPC and slow‐sampling of the slow state variables is used in the slow MPC. Using singular perturbation theory, the stability and optimality of the closed‐loop nonlinear singularly perturbed system are analyzed. A chemical process example which exhibits two‐time‐scale behavior is used to demonstrate the structure and implementation of the proposed fast–slow MPC architecture in a practical setting. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1802–1811, 2012     

CONTROL OF MOLECULAR WEIGHT IN A BATCH POLYMERIZATION REACTOR USING LONG-RANGE PREDICTIVE CONTROL METHODS

Recently two powerful control algorithms, namely, dynamic matrix control (DMC) and extended self-tuning regulator (ESTR), have been advocated for the design of robust industrial controllers. The present paper demonstrates the application of DMC and ESTR algorithms to a bulk methyl methacrylate batch polymerization reactor operating under strong diffusional limitations of termination and propagation reactions. A realistic mathematical model is employed to simulate the strong nonlinear, time-varying dynamics of the polymerization process. The general control objective is to maintain the monomer conversion and number-average molecular weight along some desired state trajectories despite the presence of process disturbances in the total initiator concentration. It is shown that both controllers can satisfactorily control the monomer conversion and number-average molecular weight by manipulating the polymerization temperature. The similarities and the main operating features of the two controllers are examined and their closed-loop performance is directly compared to the performance of a conventional linear quadratic controller (LQC). Finally the effects of DMC and ESTR tuning parameters on the calculated control action are investigated.     

Study on dynamic behavior adjustment of nonlinear chemical processes

In nonlinear chemical processes, many economically desirable operating conditions are located in unstable regions, leading to product quality degradation and safety problems. Therefore, determining how to adjust the dynamic behavior to make the process stable within its desired operational range is a topic of common interest within industrial and academic communities. This article presents a dynamic behavior adjustment method based on a washout filter‐aided controller with an improved parameter‐tuning algorithm to stabilize parts of the equilibrium manifold of chemical processes. In addition, applying this method to industrial toluene liquid‐phase catalytic oxidation shows that, by combining a conventional proportional‐integral (PI) controller with the proposed improved washout filter‐aided controller, the performance of set‐point tracking is improved for cases with parameter uncertainty. In general, the proposed dynamic behavior adjustment method will be effective for most chemical processes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3189–3198, 2016