Lexicographic optimization based MPC: Simulation and experimental study

Multi-variable prioritized control study is carried out using model predictive control (MPC) algorithms. The conventional MPC algorithm implements multi-variable control through one augmented objective function and requires weights adjustment for required performance. In order to implement explicit prioritization in multiple control objectives, we have used lexicographic MPC. To achieve better tracking performance, we have used a new MPC algorithm, by modifying the lexicographic constraint, referred to as MLMPC, where tuning of weights is not required. The effectiveness of MLMPC algorithm is demonstrated on a PMMA reactor for controlling the number average molecular weight and the reactor temperature. We have also verified the benefits of proposed algorithm on an experimental single board heater system (SBHS) for controlling temperature of a thin metal plate. These simulation and experimental studies demonstrate the superiority of the proposed method over conventional MPC and lexicographic MPC. Finally, we have presented generalized mathematical solutions to the optimization problem in MLMPC.     

Optimization of a batch reactor to produce the elastomeric copolyester prepolymer copoly(ethylene‐polyoxyethylene terephthalate)(CEPT)

A mathematical algorithm that optimizes the reactor to produce the elastomeric copolyester copoly(ethylene‐polyoxyethylene terephthalate), CEPT, is shown in this work. The optimization was carried out this way: First, an initial isothermal guess of temperature profile is made and the differential equtions system, which describes the CEPT production process, is solved, Second, the reaction time is fixed and the objective function is calculated. Third, the adjoint variable equations system is solved and the Hamiltonian's function is calculated. Fourth, a new temperature profile is found by using the control vector iteraction procedure. Finally, steps one to three are repeated until the objective function reaches a minimum value. The results of the optimization establish that the copolytransesterification reactor should be operated initially to high temperature (about 285°C), which should be reduced quickly to near 250°C to purposely diminish the production of by‐products.     

Self-adaptive predictive functional control of the temperature in an exothermic batch reactor

In this paper we study a self-adaptive predictive functional control algorithm as an approach to the control of the temperature in an exothermic batch reactor. The batch reactor is located in a pharmaceutical company in Slovenia and is used in the production of medicines. Due to mixed discrete and continuous inputs the reactor is considered as a hybrid system. The model of the reactor used for the simulation experiment is explained in the paper. Next, we assumed an exothermic chemical reaction that is carried out in the reactor core. The dynamics of the chemical reaction that comply with the Arrhenius relation have been well documented in the literature and are also summarized in the paper. In addition, the online recursive least-squares identification of the process parameters and the self-adaptive predictive functional control algorithm are thoroughly explained. We tested the proposed approach on the batch-reactor simulation example that included the exothermic chemical reaction kinetic model. The results suggest that such an implementation meets the control demands, despite the strongly exothermic nature of the chemical reaction. The reference is suitably tracked, which results in a shorter overall batch-time. In addition, there is no overshoot of the controlled variable T, which yields a higher-quality production. Finally, by introducing a suitable discrete switching logic in order to deal with the hybrid nature of the batch reactor, we were able to reduce the switching of the on/off valves to a minimum and therefore relieve the wear-out of the actuators as well as reduce the energy consumption needed for control.     

OPTIMAL TEMPERATURE CONTROL IN A BATCH POLYMERIZATION REACTOR USING NONLINEAR GENERALIZED PREDICTIVE CONTROL

The application of Non-Linear Generalized Predictive Control (NLGPC) to the free radical solution polymerization of styrene in a jacketed batch reactor has been realized. The dynamic behavior of polymerization reactor is modelled and simulated for control purposes. The optimal temperature policies for minimum time, desired conversion and molecular chain length were obtained at different initiator concentrations by applying the optimal control theory which is based on the Hamiltonian principle. The polynomial Nonlinear auto Regressive Integrated Moving Average with external input (NARIMAX) model is used to relate the reactor temperature with heat input for nonlinear control algorithm. The linear (ARIMAX) and nonlinear (NARIMAX) models are utilized in the GPC algorithm for comparison. A Pseudo Random Binary Sequence (PRBS) signal was employed to operate the system. The model parameters are evaluated by using Levenberg Marquart Method. The NLGPC, Linear Generalized Predictive Control (LGPC) and standard PID controllers are applied experimentally to the polymerization reactor by using on-line computer control system. The performance of NLGPC control system was compared with LGPC and standard PID controller. It is concluded that the NLGPC control gives much better performance than the other.     

A thermal‐flywheel approach to distributed temperature control in microchannel reactors

Microchannel reactors are a promising route for monetizing distributed natural gas resources. However, intensification and miniaturization represent a significant challenge for reactor control. Focusing on autothermal methane‐steam reforming reactors, a novel microchannel reactor temperature control strategy based on confining a layer of phase‐change material (PCM) between the reactor plates is introduced. Melting‐solidification cycles, which occur with latent heat exchange at constant temperature, allow the PCM layer to act as an energy storage buffer—a “thermal flywheel”—constituting a distributed controller that mitigates temperature excursions caused by fluctuations in feedstock quality. A novel stochastic optimization algorithm for selecting the PCM layer thickness (i.e., distributed controller “tuning”) is introduced. Furthermore, a hierarchical control structure, whereby the PCM layer is complemented by a supervisory controller that addresses persistent disturbances, is proposed. The proposed concepts are illustrated in a comprehensive case study using a detailed two‐dimensional reactor model. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2051–2061, 2013     

Set-point optimization of an adiabatic trickle-bed reactor system

A combined system parameter estimation and deactivation model identification procedure is proposed to create a grey model of an adiabatic residue hydrodesulfurization (RDS) trickle-bed reactor. Using the resulting grey model, a precomputed set-point table is used to optimize the set-point of the RDS reactor unit. The objective function chosen is the predetermined reactor outlet sulfur content and the optimal set-point is the reactor inlet temperature. Five crucial case studies using a dynamic simulator of an adiabatic RDS trickle-bed reactor demonstrate the applicability of the proposed algorithm in developing optimal set-points for a commercial process.     

Control of a solution copolymerization reactor using multi-model predictive control

We study the control of a solution copolymerization reactor using a model predictive control algorithm based on multiple piecewise linear models. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function which has finite and infinite horizon cost components and uses multiple linear models in its predictions. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and takes the system to the final operating point. Simulation results on an industrial scale methyl methacrylate vinyl acetate solution copolymerization reactor model demonstrate the ability of the algorithm to rapidly transition the process between different operating points.     

Modelling and simulation of polymerisation processes

In order to model the effects of uneven spatial distribution of components and temperature a computational fluid dynamics (CFD) model has been developed for a living polymerisation reaction in a tubular reactor. The low moments of the molecular weight distribution (MWD) and the dispersiry index of the product as well as the more usual spatial concentration of species and temperature have been calculated. The modelling and simulation work was carried out using the CFD code PHOENICS version 2.1 on Pentium PCs. Additionally, a novel algorithm is described which makes the design of reactor control strategies more tractable by providing a very rapid route to a qualitative approximation of the MWD of products from living polymerisation processes. Numerically simulated data generated using this new procedure are compared with slower but more rigorous approaches to the same problem. The examples cover living polymerisations in an isothermal batch reactor, a steady-state continuous stirred tank reactor (CSTR) and feed-perturbed CSTR. It is demonstrated that, although the novel algorithm comprises only four differential equations, it provides the essential information concerning the position and relative intensity of the peak(s) in a MWD plot needed for the design of reactor control strategies for the production of tailored MWDs.     

An energy effective PID tuning method for the control of polybutadiene latex reactor based on closed-loop identification

The PBL (Polybutadiene Latex) production process is a typical batch process. Changes of the reactor characteristics due to the accumulated scaling with the increase of batch cycles require adaptive tuning of the PID controller being used. In this work we propose a tuning method for PID controllers based on the closed-loop identification and the genetic algorithm (GA) and apply it to control the PBL process. An approximated process transfer function for the PBL reactor is obtained from the closed-loop data by using a suitable closed-loop identification method. Tuning is performed by GA optimization in which the objective function is given by ITAE for the setpoint change. The proposed tuning method showed good control performance in actual operations.     

Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene-toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model.The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.     

Dynamic simulation and control of auto-refrigerated CSTR and tubular reactor for bulk styrene polymerization

Dynamic simulation and control of a two-stage continuous bulk styrene polymerization process is developed to predict the performance of auto-refrigerated CSTR and tubular reactors. The tubular reactor is subdivided into three temperature-control jacket zones. In this paper temperature control of auto-refrigerated continuous stirred tank reactor and tubular reactor are carried out, simultaneously. Two strategies are proposed for the control of tubular reactor. At the first strategy the controlled variable is jacket temperature and in the second strategy the controlled variable is the reactor temperature at the exit of each section. The set points for polymer grade transition are obtained using optimization of reactors temperatures via genetic algorithm (GA). Simulation results show that both of the control strategies are successful but second strategy has better performance in the control of polymer properties in the presence of disturbance and model mismatch.     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor

In this paper we describe the design of hybrid fuzzy predictive control based on a genetic algorithm (GA). We also present a simulation test of the proposed algorithm and a comparison with two hybrid predictive control methods: Explicit Enumeration and Branch and Bound (BB). The experiments involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve. The GA-hybrid predictive control strategy proved to be a suitable method for the control of hybrid systems, giving similar performance to that of typical hybrid predictive control strategies and a significant saving with respect to the computation time.     

A general simulation model of batch chemical reactors for thermal control investigations

This paper describes the development of a dynamic simulation model for stirred tank batch or semi-batch chemical reactors fitted with an alternative heating-cooling system. Heat and mass balances are established for the reactor and its jacket. Since the general purpose of our research is the thermal control of these reactors, special attention is devoted to the behaviour of the heating-cooling system. In this article, we are particularly concerned with an alternative system, i.e. different fluids at a constant temperature can be alternatively delivered to the jacket. The computer simulation programme is flexible, enabling simulation of a batch or semi-batch reaction vessel, ranging from a laboratory pilot plant to a full-scale production plant. A control algorithm is included which allows reactor operation with open or closed-loop temperature control. To demonstrate the good performance of the simulation model, experimental results are presented for both a pilot plant and an industrial reactor.     

APPLICATION OF ADAPTIVE PID CONTROL WITH GENETIC ALGORITHM TO A POLYMERIZATION REACTOR

This article describes the application of adaptive PID control with genetic algorithm (GA) to a jacketed batch polymerization reactor. This method was used to keep the polymerization reactor temperature at the desired optimal path, which was determined by the Hamiltonian maximum principle method. The reactor was simulated and the model equations of this jacketed polymerization reactor were solved by means of Runge-Kutta-Felthberg methods. A genetic algorithm can be a good solution for finding the optimum PID parameters because unlike other techniques it does not impose many limitations and it is simple. In this research, suitability of these parameters was checked by the integral absolute error (IAE) criterion. The control parameters in the PID algorithm were changed with time during the control of a polymerization reactor. It was seen that the genetic algorithm was able to tune the PID controller used in this system in terms of higher robustness and reliability by changing the parameters continuously.     

Use of nonlinear transformations and a self-tuning regulator to develop an algorithm for catalytic reactor temperature control

Prior to developing a multivariable control scheme for conversion and production rates in a packed bed tubular reactor carrying out highly exothermic reactions, it was important to stabilize the reactor temperature. In this paper we illustrate the use of a self-tuning regulator to develop an inner loop controller that satisfies some necessary conditions on temperature response, and that is capable of controlling the reactor over a wide range of operating conditions. The importance of using a nonlinear transformation of the reactor hot-spot temperature is demonstrated. Varying the input constraining parameter in the “one-step optimal” self-tuning controller is shown to be a very effective way of achieving a controller with the desired properties for response smoothness.     

EXPERIMENTAL APPLICATION OF GENERALIZED PREDICTIVE CONTROL OF THE TEMPERATURE IN A POLYSTRENE POLYMERIZATION REACTOR

The performance of generalized predictive control (GPC) was examined and compared with conventional control applied to the temperature of as free radical solution polymerization of styrene in a jacketed batch reactor. Optimal conditions were obtained at different initiator concentrations by applying Lagrange's multiplier to the relevant polymerization reactor. The use of the polynomial ARIMAX model related with reactor temperature and heat input was emphasized. Model parameters were determined using the Kalman algorithm. A pseudo random binary sequence (PRBS) signal was employed in order to operate the system. The GPC control method was based on the ARIMAX model. The performance criteria of GPC in evaluating the temperature control results were the required monomer conversion and molecular weight.     

流化床反应器中气相丙烯聚合反应的动力学和预测控制(英文)

A two-phase dynamic model, describing gas phase propylene polymerization in a fluidized bed reactor, was used to explore the dynamic behavior and process control of the polypropylene production rate and reactor temperature. The open loop analysis revealed the nonlinear behavior of the polypropylene fluidized bed reactor, jus- tifying the use of an advanced control algorithm for efficient control of the process variables. In this case, a central- ized model predictive control （MPC） technique was implemented to control the polypropylene production rate and reactor temperature by manipulating the catalyst feed rate and cooling water flow rate respectively. The corre- sponding MPC controller was able to track changes in the setpoint smoothly for the reactor temperature and pro- duction rate while the setpoint tracking of the conventional proportional-integral （PI） controller was oscillatory with overshoots and obvious interaction between the reactor temperature and production rate loops. The MPC was able to produce controller moves which not only were well within the specified input constraints for both control vari- ables, but also non-aggressive and sufficiently smooth for practical implementations. Furthermore, the closed loop dynamic simulations indicated that the speed of rejecting the process disturbances for the MPC controller were also acceotable for both controlled variables.     

An Approach for Achieving Unstable Convergence for Non‐Isothermal CSTRs

The nonlinearity introduced by the temperature variation in the non‐isothermal continuous stirred tank reactor (CSTR) exhibits concentration multiplicity for certain parameter ranges. The dynamics of reactor temperature under these conditions would be very difficult to observe and maintain. In this work, a novel algorithm is proposed to stabilize the system by designing a cascade of CSTRs that are capable of achieving this inaccessible steady state. Optimization of reactors parameters is performed in an iterative manner to achieve this solution. For a first‐order reaction rate, this method was successful in achieving the inaccessible steady state temperature of 312.5 K using three CSTRs cascades. The suggested algorithm is presented both graphically as well as using computational optimization techniques. The transient simulation studies using the above three CSTRs showed that the unstable steady state is achieved. The newly designed cascade meets the design criteria and achieves the locally unstable steady state temperature to a high degree of accuracy.     

Nonlinear control of polymerization reactor

In this work, nonlinear model based control was applied to the free radical solution polymerization of styrene in a jacketted batch reactor and its performance was examined to reach the required monomer conversion and molecular weight. Optimal temperature profiles for the properties of polymer quality were evaluated using the Hamiltonian optimization method. Total simulation program having mass and energy balances of the jacketed polymerization reactor was used to calculate the optimal trajectories. For control purposes, several experimental and theoretical dynamic studies have been made to observe the validity of simulation program. Experimental and theoretical nonlinear model based control have been investigated to track the temperature at the optimal trajectory Two types of parametric and nonparametric models were evaluated to achieve the temperature control. For this purpose, reaction curve was obtained to calculate the system dynamic matrix as a nonparametric model. In all control work, heat input to the reactor was chosen as a manipulated variable. Nonlinear auto regressive moving average exogenous (NARMAX) giving a relation between heat input and reactor temperature was chosen to represent the system dynamic and this model was used to describe the related control system as a parametric model. NARMAX model parameters were determined by using Levenberg Marquard algorithm. A pseudo random binary sequence (P.R.B.S.) signal was employed to disturb the system. Total simulation program was used to calculate the system and control parameters. Several types and orders were used to construct the NARMAX models. The efficiency and the performance of the nonlinear model based control with the NARMAX model and dynamic matrix were tested to calculate the best model. Nonlinear model based control system was used to control the reactor temperature at desired temperature trajectory experimentally and theoretically. Theoretical simulation results were compared with experimental control data. It was concluded that the control simulation program represents the behavior of the controlled reactor temperature well. In addition, nonlinear model based control keeps the reactor temperature of optimal trajectory satisfactorily.