ADAPTIVE FUZZY MODEL BASED PREDICTIVE CONTROL OF AN EXOTHERMIC BATCH CHEMICAL REACTOR*

An adaptive fuzzy model based predictive control (AFMBPC) approach is presented to track the desired temperature trajectories in an exothermic batch chemical reactor. The AFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. This approach has the flexibility to cope with different fuzzy model structures whose choice also lead to improve the controller performance. In this approach, adaptation of fuzzy models using dynamic process information is carried out to build a predictive controller, thus eliminating the determination of a predefined fixed fuzzy model based on various sets of known input-output relations. The performance of the AFMBPC is evaluated by comparing to a fixed fuzzy model based predictive controller (FFMBPC) and a conventional PID controller. The results show the better suitability of AFMBPC for the control of highly nonlinear and time varying batch chemical reactors.     

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.     

ROBUST CONTROL OF BATCH REACTORS

The design of robust nonlinear feedback controller is analysed for a trajectory tracking in a single-input single-output nonlinear state variable system x = f(x) + g(x)u, y=cx which arises in nonlinear chemical processes particularly in batch reactor control problems. Simulation results for the batch reactor temperature tracking problem show the effectiveness of the control scheme and its robustness to modelling errors. The method is also applicable to multi-input multi-output system where the number of inputs is equal to that of outputs. The controller design is also analyzed for situations wrier: the kinetics, the activation energy and Ihe heat of reaction are unknown and also only limited measurement of state-variables are available. The method of Youcef-Toumi and Ito (1987) is applied to such problems and the effectiveness of control system is shown by simulation.     

ADAPTIVE POLE-PLACEMENT CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR

A simulation of the polymerization of methylmethacrylate in a CSTR is adaptively controlled by two types of pole-placement algorithms. The strongly nonlinear polymerization process, exhibiting multiple steady states, presents difficult control problems for conventional feedback controllers. The performance of an adaptive explicit SISO controller and that of an adaptive implicit multivariable controller are compared and evaluated as applied to this process. The plant is identified by a recursive least squares estimator. Modifications made to the estimation algorithm help to maintain adequate closed-loop results. A simple warm-up procedure is introduced that successfully initializes the controller and estimator during plant start-up. Good servo and regulatory control are achieved by both pole-placement schemes.     

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.     

MODELING OF THE TRANSIENT AND STEADY STATE OPERATION OF A FLUIDIZED BED REACTOR WITH ADAPTIVE CONTROL OF TEMPERATURE

This paper concerns modeling of the transient and the steady state operation of a fluidized bed reactor for the catalytic ammoxidation of propylene to acrylonitrile. To maintain constant the temperature of the reaction in order to facilitate the phenomenological study as well as to avoid risks of destruction of the catalyst, a self tuning P.I.D. controller has been used. The controller derived from a discrete P.I.D. regulator is based on pole assignment. It uses a recursive parameter estimator based on the least square method. The reactor has been interfaced with an Apple II micro-computer. The results obtained illustrates the inherent capability of self adaptive control to adapt the change of the environment where conventional control fails

Modeling of the reactor is based on the Kato and Wen bubble assemblage model corrected by including the wake of the bubbles with their clouds, as proposed hy Stergiou. This modified model gives good predictions of the operation of the reactor for steady as well as transient operation.     

ADAPTIVE LINEAR QUADRATIC CONTROL OF BATCH AND SEMI-BATCH CEHMICAL REACTORS WITHIN THE DELTA OPERATOR FORMULATION

Batch and semi-batch chemical reactors are extensively used in polymer, fine chemical and pharmaceutical industries. The temperature control is of fundamental importance from product quality and reproductibility points of view. It is then necessary to improve the automation of these plants which are typically controlled using standard PID controllers. An autotuning PID controller is proposed and evaluated by application to a batch and semi-batch pilot plant reactor to investigate advanced control techniques. The involved control design is derived in the spirit of the partial state reference model adaptive control (PSRMAC) approach within the delta operator formulation. PSRMAC is mainly motivated by its suitable tracking capability when only a crude knowledge about the plant to be controlled is available. The delta operator formualtion is particularly motivated by the convergence of the performances to their continuous time counterpart as well as its numerical robustness when the sampling is required to be fast.     

MODELING AND OPTIMIZATION OF LACTIC ACID SYNTHESIS BY THE ALKALINE DEGRADATION OF FRUCTOSE IN A BATCH REACTOR

The present work deals with the determination of the optimal operating conditions of lactic acid synthesis by the alkaline degradation of fructose. It is a complex transformation for which detailed knowledge is not available. It is carried out in a batch or semi-batch reactor. The “Tendency Modeling” approach, which consists of the development of an approximate stoichiometric and kinetic model, has been used. An experimental planning method has been utilized as the database for model development. The application of the experimental planning methodology allows comparison between the experimental and model response. The model is then used in an optimization procedure to compute the optimal process. The optimal control problem is converted into a nonlinear programming problem solved using the sequencial quadratic programming procedure coupled with the golden search method. The strategy developed allows simultaneously optimizing the different variables, which may be constrained. The validity of the methodology is illustrated by the determination of the optimal operating conditions of lactic acid production.     

MODELING AND OPTIMIZATION OF LACTIC ACID SYNTHESIS BY THE ALKALINE DEGRADATION OF FRUCTOSE IN A BATCH REACTOR

The present work deals with the determination of the optimal operating conditions of lactic acid synthesis by the alkaline degradation of fructose. It is a complex transformation for which detailed knowledge is not available. It is carried out in a batch or semi-batch reactor. The “Tendency Modeling” approach, which consists of the development of an approximate stoichiometric and kinetic model, has been used. An experimental planning method has been utilized as the database for model development. The application of the experimental planning methodology allows comparison between the experimental and model response. The model is then used in an optimization procedure to compute the optimal process. The optimal control problem is converted into a nonlinear programming problem solved using the sequencial quadratic programming procedure coupled with the golden search method. The strategy developed allows simultaneously optimizing the different variables, which may be constrained. The validity of the methodology is illustrated by the determination of the optimal operating conditions of lactic acid production.     

ADAPTIVE CONTROL OF A CSTR WITH INPUT CONSTRAINTS

Control of a nonisothermal CSTR with input constraints has been developed. The control system is a multivariable nonlinear one. Indirect adaptive control is applied. An algorithm based on an output direction vector is proposed for determining the constrained input vector. By using the proposed method, it is possible to operate the reactor at an unstable steady state within a stable limit cycle.     

SENSITIVITY ANALYSIS OF OPTIMAL CONTROL POLICIES FOR BATCH PROCESSES

The computation of optimal control policies for batch processes, critically depends on the process model employed. The real process may deviate from the assumed model due to external signal or model parameter variations. In this paper we examine the effects of these variations on

(a) the value of the objective function, when the nominal optimal policy is applied

(b) the optimum value of the objective function.

We present quantitative relations between the perturbed and the nominal problems and demonstrate their use through a number of examples.     

INDIRECT ADAPTIVE CONTROL OF A CHAOTIC SYSTEM

The adaptive control of a simple chaotic system to a steady reference is investigated. An indirect adaptive control scheme with least-mean-squares (LMS) parameter estimation yields a fractal basin boundary between stable and unstable control. This boundary appears self-similar, indicative of a fractal structure, and has a fractal dimension of 2.61. Adaptive control using a least-squares (LS) estimator appears globally stable with the rate of adaptation a complex function of the distance from the desired set point. The effect of control parameters, noise and a step-change perturbation of the system are also reported.     

BOUNDED DISTURBANCES ADAPTIVE CONTROL OF A HEAT EXCHANGER

Adaptive control for systems with bounded disturbances is investigated. The control algorithm is based on the concepts of variable forgetting and dead zones. Two weighting factors are used for old data and new data respectively. The condition of persistent excitation is not required when the prediction error is within a given value. The proposed method for on-line control of a heat exchanger with steam as the control variable demonstrates satisfactory results.     

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.     

ADAPTIVE CONTROL OF A NONISOTHERMAL CSTR WITH OUTPUT CONSTRAINT

A method for adaptive control of a nonisothermal continuous stirred tank reactor with output temperature constraint is developed. The control system is a multivariate nonlinear one. Indirect adaptive control is applied. Based on an allowable temperature rise, the control variables are determined. The reactor temperature is under a constraint to prevent the temperature from overshooting. Simulation studies give satisfactory results.     

论序列活性污泥法技术

阐述了新兴技术序列活性污泥法的原理、特点以及近年来该技术的研究开发。与普通活性污泥法相比,防止污泥膨胀、运行稳定、工程投资少是该技术的最大特点     

FUZZY MODELING AND CONTROL OF BATCH BEER FERMENTATION+

Fuzzy reasoning based modeling of heuristic control rules are employed for control of batch beer fermentation. The effect of different types of membership functions, viz., line, triangular and phi membership functions is evaluated for the fuzzy subset. Various fuzzy model based controllers are presented using two approaches, namely simple fuzzy controller of few rules (FCFR) and rigorous fuzzy controller of many rules (FCM R), and also applied for the temperature control of fermenter. Zadeh's logic and Lukasiewicz's logic are adopted for computing the compositional rule of fuzzy logic inference. The results demonstrate that the proposed fuzzy controllers show better performance than the conventional controllers. FCFR approach provides better control performance, but needs optimum tuning or selection of gains for the fuzzy input and output variables, whereas FCMR approach is preferred due to flexibility in the operation of many control rules. Further, FCMR approach is free from optimum tuning or selection of gains for the fuzzy input and output variables.     

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.     

加压管式反应器的模糊控制

原硝酸铵生产装置中,加压管式反应器的控制方式不能完全满足生产要求。对其进行了分析研究,论述了模糊控制技术在加压管式反应器上的应用方案,成功地用于生产,取得了良好效果。