A DIRECT NONLINEAR ADAPTIVE CONTROL OF STATE FEEDBACK LINEARIZABLE SYSTEMS

A direct nonlinear adaptive control of state feedback linearizable single-input single-output systems is proposed in the case when parametric uncertainties are represented linearly in the unknown parameters. The main feature of the proposed nonlinear adaptive control system is that the linearizing coordinate transformation and the state feedback are updated by parametric adaptive law, derived using the second method of Lyapunov. The proposed adaptive control scheme is relatively straightforward and simple in the sense that it does not use the concept of augmented error. This adaptive control scheme is numerically applied to an exothermic chemical reactor system and is compared with the nonadaptive stale feedback linearization which has an integral action. The simulation shows that the proposed adaptive control scheme can be applied effectively to highly nonlinear, uncertain chemical systems.     

NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.     

NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.     

ADAPTIVE NONLINEAR MODEL CONTROL

Significant improvements in control system performance and robustness can be obtained if the major process nonlinearities are included in the control system design. Nonlinear model control achieves this through the use of simple parallel and series compensation. In the paper we demonstrate the use of this method. New theoretical results on controller robustness are presented; it is in particular shown how series nonlinear model compensation using state and disturbance feedback can be used to improve control system performance. The theoretical results are supported by simulation and pilot plant experiments using a modified version of the self-tuning regulator.     

ADAPTIVE CONTROL OF A BATCH REACTOR

A globally stable adaptive predictive control system (APCS) is evaluated by application to a simulated PVC batch reactor. The reactor is run under APCS control with the objective of either temperature setpoint tracking or constant reaction rate. The batch nature of this system makes it possible to learn about the physical problem from successive runs. This knowledge is incorporated into the control strategy to improve the performance of the reactor. The problem of excessive manipulation of the control variable has been recognized and resolved by using control weighting. Performance of the adaptive technique is compared with previous results using self-tuning and PID control of the same reactor. APCS provides good, robust control despite the nonlinear dynamics of the system.     

AUTOMATED GAIN SCHEDULE GENERATION FOR NONLINEAR ADAPTIVE CONTROL

The generalized minimum variance (GMV) control law includes a penalty function that permits control activity to become more or less vigorous as process character changes. This penalty, if cast as a function of steady state process gain, can enable control of nonlinear processes. To make such an approach easy to implement, a method is detailed for automatically generating and updating a gain schedule while the process is in closed loop. The method is demonstrated on a simulated process that possesses a very nonlinear character. The scope of this paper is limited to single-input single-output, open-loop stable processes     

化学反应器的神经元自适应观测和非线性控制

提出了一种基于神经网络的自适应观测和非线性控制策略,证明了自适应观测器的收敛件和非线性控制系统的稳定性,将其用于连续搅拌釜式放热反应器的浓度控制。根据可在线测量的反应温度,在线估计不可在线测量的反应物浓度和辨识Arrhenius指前因子,并利用重构的状态信息设计出带约束的非线性控制策略。仿真结果表明,观测器/控制器的组合提供了满意的闭环特性,证实了本文方法的有效性。     

NONLINEAR FEEDBACK CONTROL OF A CSTR

The design of a robust nonlinear feedback controller is analyzed for temperature control of continuous stirred tank reactors (CSTRs)which have strong nonlinearities and steady-state multiplicities. The present method treats the original nonlinear system as it is without transforming into an equivalent linear system. The controller is robust to modelling errors and random disturbances occurring in the system. The controller design is also analyzed for situation when the kinetics, activation energy and heat of reaction are unknown and also only limited state-variables measurements are available.     

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.     

模糊非线性内模控制算法及其在pH值控制中的应用

pH值控制过程具有较强的非线性,历来是过程控制研究的一大热点,本文针对pH值控制系统提出了一种基于模糊推理网的非线性内模控制算法（FNIMC）。模糊推理网用于辨识对象的模糊模型;FNIMC由一个逆模控制器和具有一个可调参数的鲁棒滤波器组成。仿真结果表明该算法优于非线性PID调节器,且计算效率高。     

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.     

CONTROL AND ESTIMATION FOR PERTURBED NONLINEAR PROCESSES WITH DEADTIME

Feedback linearization techniques are used to deal with the nonlinear controller designs which have attracted many researchers' attention in recent years. The approach has been applied successfully to solve a number of practical nonlinear control problems, but typically requires on-line full state measurement which is usually not the case in real chemical process industries. In this paper, we address the problem of synthesizing nonlinear state feedback controllers for time-delay nonlinear systems which are perturbed by disturbances. On-line estimation of the unmeasurable disturbances and unavailable state variables is introduced to facilitate the implementation of coordinate transformations and state feedback and prediction. Two kinds of dynamic compensators are then proposed to handle the process deadtime. Finally numerical simulations in a CSTR example demonstrate the promising performance of the overall nonlinear control structure in disturbance rejection.     

自适应广义一般模型控制

针对一般模型控制的缺点,提出了两种改进的自适应广义一般模型控制方法.它们把传统的一般模型控制推广到相对阶大于1 同时又具有时变参数的复杂非线性过程.第1种控制策略主要利用强跟踪滤波器直接在线估计时变参数,来修正过程模型;另一种方法是将所有干扰因素归结为输入等价干扰,通过估计它来实现对过程的前馈控制.仿真实验结果验证了所提出方法的有效性.     

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.     

A safe-parking framework for plant-wide fault-tolerant control

This work addresses the problem of handling actuator faults in a chemical plant. We consider a multi-unit nonlinear process system subject to input constraints and actuator faults in one unit that preclude the possibility of operating the unit at its nominal equilibrium point. The interconnected nature of the units in a plant brings forth unique opportunities as well as challenges that simply do not exist when handling faults in isolated units. In particular, the fact that the outlet streams from a faulty unit go through subsequent (well functioning) units raises the possibility of better restricting the effects of the fault to the faulty unit. At the same time, handling a fault in a unit may necessitate appropriate action in the downstream unit, which is not a result of a fault in the downstream unit. To address such issues that arise when handling faults in chemical plants, in this work we present a safe-parking framework (we define, in a previous work on handling faults in isolated units, a safe-park point as an operating point where in the event of a fault, a unit can be operated in a way that prevents onset of hazardous situation and allows smooth resumption of nominal operation) for plant-wide fault-tolerant control. We first consider the case where there exists a safe-park point for the faulty unit such that the effect of safe-parking can be completely rejected (via changing the nominal values of the manipulated variables) in the downstream unit. Steady-state as well as dynamic considerations (including the presence of input constraints) is used in determining the necessary conditions for safe-parking the multi-unit system. We next consider the problem where no viable safe-park point for the faulty unit exists such that its effect can be completely rejected in the subsequent unit. A methodology is presented to simultaneously safe-park the consecutive units. Finally, we incorporate performance considerations in the safe-parking framework and illustrate the implementation of the safe-parking framework using a multi-unit chemical reactor system.     

BATCH-TO-BATCH OPTIMAL CONTROL OF BATCH PROCESSES BASED ON RECURSIVELY UPDATED NONLINEAR PARTIAL LEAST SQUARES MODELS

A batch-to-batch optimal control approach for batch processes based on batch-wise updated nonlinear partial least squares (NLPLS) models is presented in this article. To overcome the difficulty in developing mechanistic models for batch/semi-batch processes, a NLPLS model is developed to predict the final product quality from the batch control profile. Mismatch between the NLPLS model and the actual plant often exists due to low-quality training data or variations in process operating conditions. Thus, the optimal control profile calculated from a fixed NLPLS model may not be optimal when applied to the actual plant. To address this problem, a recursive nonlinear PLS (RNPLS) algorithm is proposed to update the NLPLS model using the information newly obtained after each batch run. The proposed algorithm is computationally efficient in that it updates the model using the current model parameters and data from the current batch. Then the new optimal control profile is recalculated from the updated model and implemented on the next batch. The procedure is repeated from batch to batch and, usually after several batches, the control profile will converge to the optimal one. The effectiveness of this method is demonstrated on a simulated batch polymerization process. Simulation results show that the proposed method achieves good performance, and the optimization with the proposed NLPLS model is more effective and stable than that with a batch-wise updated linear PLS model.     

丙烯腈连续水相聚合的过程分析及控制

简要介绍丙烯腈水相聚合过程的机理及其数学模型，从而导出过程的参变数及对聚合过程目标值的影响。在此基础上，提出丙烯腈水相连续（共）聚合过程的控制方案。     

RELATIVE ORDER REDUCTION OF MULTIVARIABLE NONLINEAR PROCESSES FOR GENERIC MODEL CONTROL (GMC)

To be implemented within Generic Model Control, a process model must have a relative order of one. When systems have relative orders greater than one (“high relative order systems”) techniques are required to enable model based control to take place. In this paper, a relative order model reduction algorithm is presented, which reduces high relative order models to relative order one. The reduction algorithm is based on the singular perturbation model reduction method. The reduction method conserves some of the important linear qualities of the system, making implementation of the model within a nonlinear model based controller such as GMC attractive.     

自适应PID控制的安全保护的几点考虑

本文就自适应ＰＩＤ控制在实际应用中所面临的安全性问题，提出了针对安全保护的几点考虑。