Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

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.     

Robust model predictive control of nonlinear process systems: Handling rate constraints

This work considers the problem of stabilization of control affine nonlinear process systems subject to constraints on the rate of change and magnitude of control inputs in the presence of uncertainty. We first handle rate constraints within a soft constraints framework. A new robust predictive controller formulation that minimizes rate constraint violation while guaranteeing stabilization and input constraint satisfaction from an explicitly characterized stability region is designed. We then derive conditions that allow for guaranteed satisfaction of hard rate constraints. Subsequently, a predictive controller is designed that ensures rate constraints satisfaction when the required conditions are satisfied, relaxing them otherwise to preserve feasibility and robust stability. The implementation of the proposed predictive controllers is illustrated via a chemical reactor example.     

Nonlinear control of a batch crystallizer

A nonlinear geometric feedback controller with and without state estimation (the extended continuous-discrete Kalman filter) is developed and applied to a 0.027 m 3 potash alum batch crystallizer. The manipulated variable isthetemperature of the inlet cooling water supplied to the jacket of the crystallizer, and the controlled variable is the supersaturation. It is shown that the controller eliminates the large initial peak in the supersaturation (which results in excessive nucleation) and maintains the supersaturation at its set-point, provided that themanipulated variable does not reach its constraints. The controller performs well with only two measured states (the crystallizer temperature and the soluteconcentration) and results in larger terminal crystal mean size in com-parison with natural cooling and linear cooling policies with fines dissolution.     

NONLINEAR CONTROL OF A BATCH CRYSTALLIZER

A nonlinear geometric feedback controller with and without state estimation (the extended continuous-discrete Kalman filter) is developed and applied to a 0.027 m 3 potash alum batch crystallizer. The manipulated variable isthetemperature of the inlet cooling water supplied to the jacket of the crystallizer, and the controlled variable is the supersaturation. It is shown that the controller eliminates the large initial peak in the supersaturation (which results in excessive nucleation) and maintains the supersaturation at its set-point, provided that themanipulated variable does not reach its constraints. The controller performs well with only two measured states (the crystallizer temperature and the soluteconcentration) and results in larger terminal crystal mean size in com-parison with natural cooling and linear cooling policies with fines dissolution.     

Detection and management of actuator faults in controlled particulate processes using population balance models

This paper presents a methodology for the design of an integrated fault detection and fault-tolerant control (FD-FTC) architecture for particulate processes described by population balance models (PBMs) with control constraints, actuator faults and a limited number of process measurements. The architecture integrates model-based fault detection, state estimation, nonlinear feedback and supervisory control on the basis of an appropriate reduced-order model that captures the dominant dynamics of the process and is obtained through application of the method of weighted residuals. The architecture comprises a family of control configurations together with a fault detection filter and a supervisor. For each configuration, a stabilizing output feedback controller with well-characterized stability properties is designed through the combination of a state feedback controller and a state observer that uses the available measurements of principal moments of the particle size distribution (PSD) and the continuous-phase variables to provide appropriate state estimates. A fault detection filter that simulates the behavior of the fault-free, reduced-order model is designed, and its discrepancy from the behavior of the actual process state estimates is used as a residual for fault detection. Finally, a switching law based on the stability regions of the constituent control configurations is derived to reconfigure the control system in a way that preserves closed-loop stability in the event of fault detection. Appropriate fault detection thresholds and control reconfiguration criteria that account for model reduction and state estimation errors are derived for the implementation of the FD-FTC architecture on the particulate process. Finally, the methodology is applied to the problem of constrained, actuator fault-tolerant stabilization of an unstable steady-state of a continuous crystallizer.     

A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes

This paper presents a methodology for the robust detection, isolation and compensation of control actuator faults in particulate processes described by population balance models with control constraints and time-varying uncertain variables. The main idea is to shape the fault-free closed-loop process response via robust feedback control in a way that enables the derivation of performance-based fault detection and isolation (FDI) rules that are less sensitive to the uncertainty. Initially, an approximate finite-dimensional system that captures the dominant process dynamics is derived and decomposed into interconnected subsystems with each subsystem directly influenced by a single manipulated input. The decomposition is facilitated by the specific structure of the process input operator. A robustly stabilizing bounded feedback controller is then designed for each subsystem to enforce an arbitrary degree of asymptotic attenuation of the effect of the uncertainty in the absence of faults. The synthesis leads to (1) an explicit characterization of the fault-free behavior of each subsystem in terms of a time-varying bound on an appropriate Lyapunov function and (2) an explicit characterization of the robust stability region in terms of the control constraints and the size of the uncertainty. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI in each subsystem, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the system within the stability region and declaring a fault if the threshold is breached. The thresholds are linked to the achievable degree of asymptotic uncertainty attenuation and can therefore be properly tuned by proper tuning of the controllers, thus making the FDI criteria less sensitive to the uncertainty. The robust FDI scheme is integrated with a robust stability-based controller reconfiguration strategy that preserves closed-loop stability following FDI. Finally, the implementation of the fault-tolerant control architecture on the particulate process is discussed and the proposed methodology is applied to the problem of robust fault-tolerant control of a continuous crystallizer with a fines trap.     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

改进的模糊预测控制算法及其在CSTR过程中的应用

A finite horizon predictive control algorithm,which applies a saturated feedback control law as its local control law,is presented for nonlinear systems with time-delay subject to input constraints.In the algorithm,N free control moves,a saturated local control law and the terminal weighting matrices are solved by a minimization problem based on linear matrix inequality(LMI) constraints online.Compared with the algorithm with a nonsaturated local law,the presented algorithm improves the performances of the closed-loop systems such as feasibility and optimality.This model predictive control(MPC) algorithm is applied to an industrial continuous stirred tank reactor(CSTR) with explicit input constraint.The simulation results demonstrate that the presented algorithm is effective.     

Safe-parking of nonlinear process systems: Handling uncertainty and unavailability of measurements

This work considers the problem of handling actuator faults in nonlinear process systems subject to input constraints, uncertainty and availability of limited measurements. A framework is developed to handle faults that preclude the possibility of continued operating at the nominal equilibrium point using the existing robust or reconfiguration-based fault-tolerant control approaches. The key consideration is to operate the plant using the depleted control action at an appropriate ‘safe-park’ point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-repair. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller that enhances the set of initial conditions from which closed-loop stability is achieved. The stability region characterization provided by the robust predictive controller is subsequently utilized in a safe-parking algorithm that appropriately selects ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators) to preserve closed-loop stability upon fault-repair. Specifically, a candidate parking point is termed a safe-park point if (1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action and uncertainty) and (2) the safe-park candidate resides within the stability region of the nominal control configuration. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.     

LMI-based robust model predictive control for a continuous MMA polymerization reactor

A linear matrix inequality (LMI)-based robust model predictive control (MPC) is applied to a continuous stirred-tank reactor for the polymerization of methyl methacrylate (MMA). The polytopic model is constructed to predict the responses to various control input sequences by using Jacobians of uncertain nonlinear model at several operating points and the controller design is characterized as the problem of minimizing an upper bound on the ‘worst-case’ infinite horizon objective function subject to constraints on the control input and plant output. Simulation studies under different conditions are conducted to validate the feasibility of the optimization problem and evaluate the applicability of such a control scheme. Simulation results show that, despite the model uncertainty, the LMI-based robust model predictive controller performs quite satisfactorily for the property control of the continuous polymerization reactor and guarantees the robust stability.     

A two-tier architecture for networked process control

Traditionally, process control systems utilize dedicated, point-to-point wired communication links using a small number of sensors and actuators to regulate appropriate process variables at desired values. While this paradigm to process control has been successful, chemical plant operation could substantially benefit from an efficient integration of the existing, point-to-point control networks (wired connections from each actuator/sensor to the control system using dedicated local area networks) with additional networked (wired or wireless) actuator/sensor devices. However, augmenting existing control networks with real-time wired/wireless sensor and actuator networks challenges many of the assumptions made in the development of traditional process control methods dealing with dynamical systems linked through ideal channels with flawless, continuous communication. In the context of control systems which utilize networked sensors and actuators, key issues that need to be carefully handled at the control system design level include data losses due to field interference and time delays due to network traffic. Motivated by the above technological advances and the lack of methods to design control systems that utilize hybrid communication networks, in the present work, we present a novel two-tier control architecture for networked process control problems that involve nonlinear processes and heterogeneous measurements consisting of continuous measurements and asynchronous, delayed measurements. This class of control problems arises naturally when nonlinear processes are controlled via control systems based on hybrid communication networks (i.e., point-to-point wired links integrated with networked wired/wireless communication) or utilizing multiple heterogeneous measurements (e.g., temperature measurements which can be taken to be continuous and species concentration measurements which are fed to the control system at asynchronous time instants and frequently involve delays). While point-to-point wired links are very reliable, the presence of a shared communication network in the closed-loop system introduces additional delays and data losses and these issues should be handled at the controller design level. In the two-tier control architecture presented in this work, a lower-tier control system, which relies on point-to-point communication and continuous measurements, is first designed to stabilize the closed-loop system, and an upper-tier networked control system is subsequently designed, using Lyapunov-based model predictive control theory, to profit from both the continuous and the asynchronous, delayed measurements as well as from additional networked control actuators to improve the closed-loop system performance. The proposed two-tier control architecture preserves the stability properties of the lower-tier controller while improving the closed-loop performance. The applicability and effectiveness of the proposed control method is demonstrated using two chemical process examples.     

Optimization and nonlinear control of a batch crystallization process

Crystallization process has been widely used for separation in many chemical industries due to its capability to provide high purity product. To obtain the desired quality of crystal product, an optimal cooling control strategy is studied in the present work. Within the proposed control strategy, a dynamic optimization is first preformed with the objective to obtain the optimal cooling temperature policy of a batch crystallizer, maximizing the total volume of seeded crystals. Two different optimization problems are formulated and solved by using a sequential optimization approach. Owing to the complex and nonlinear behavior of the batch crystallizer, the nonlinear control strategy which is based on a generic model control (GMC) algorithm is implemented to track the resulting optimal temperature profile. The optimization integrated with nonlinear control strategy is demonstrated on a seeded batch crystallizer for the production of potassium sulfate.     

Predictive control of particlesize distribution of crystallization process using deep learning based image analysis

The challenges to regulate the particle-size distribution (PSD) stem from on-line measurement of the full distribution and the distributed nature of crystallization process. In this article, a novel nonlinear model predictive control method of PSD for crystallization process is proposed. Radial basis function neural network is adopted to approximate the PSD such that the population balance model with distributed nature can be transformed into the ordinary differential equation (ODE) models. Data driven nonlinear prediction model of the crystallization process is then constructed from the input and output data and further be used in the proposed nonlinear model predictive control algorithm. A deep learning based image analysis technology is developed for online measurement of the PSD. The proposed PSD control method is experimentally implemented on a jacketed batch crystallizer. The results of crystallization experiments demonstrate the effectiveness of the proposed control method.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Product quality improvement of batch crystallizers by a batch-to-batch optimization and nonlinear control approach

Batch crystallization is one of the widely used processes for separation and purification in many chemical industries. Dynamic optimization of such a process has recently shown the improvement of final product quality in term of a crystal size distribution (CSD) by determining an optimal operating policy. However, under the presence of unknown or uncertain model parameters, the desired product quality may not be achieved when the calculated optimal control profile is implemented. In this study, a batch-to-batch optimization strategy is proposed for the estimation of uncertain kinetic parameters in the batch crystallization process, choosing the seeded batch crystallizer of potassium sulfate as a case study. The information of the CSD obtained at the end of batch run is employed in such an optimization-based estimation. The updated kinetic parameters are used to modify an optimal operating temperature policy of a crystallizer for a subsequent operation. This optimal temperature policy is then employed as new reference for a temperature controller which is based on a generic model control algorithm to control the crystallizer in a new batch run.