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。     

连续搅拌釜式反应器的鲁棒最优控制

针对一类带不确定性的连续搅拌釜式反应器,提出基于滑模控制理论的鲁棒最优控制算法。输入输出线性化方法用于线性化对象模型,假设系统的不确定因素有界,滑模面采用积分型滑模面以确保系统稳态误差为零,将线性二次型理论用于等效控制律的设计中,保证了系统的性能指标最优,自适应滑模切换控制增益的选取在降低系统抖振的前提下补偿了系统的不确定因素及外部扰动,实现了控制器的鲁棒最优。通过仿真实验表明,提出的控制器对匹配的不确定性因素及外部扰动具有鲁棒性,且闭环系统的性能指标最优。     

APPLICATION OF FUZZY ADAPTIVE CONTROLLER IN NONLINEAR PROCESS CONTROL

In general, physical processes are usually nonlinear and control system design based on the linearization technique cannot control the process well for a wide range of operation. Use of the variable transformation method may not always solve the problem. In this paper, a fuzzy adaptive controller is proposed to control the nonlinear process. The CSTR control problem has also been considered. The results are compared with the method of nonlinear model predictive control (NMPC) with constrained and unconstrained control variables. A fuzzy model-following control system scheme is also proposed. The results show that the proposed controller is a feasible control structure for a nonlinear or parameter-variations process control.     

Adaptive and Predictive Control of Liquid‐Liquid Extractors Using Neural‐Based Instantaneous Linearization Technique

Nonlinearity of the extraction process is addressed via the application of instantaneous linearization to control the extract and raffinate concentrations. Two feed‐forward neural networks with delayed inputs and outputs were trained and validated to capture the dynamics of the extraction process. These nonlinear models were then adopted in an instantaneous linearization algorithm into two control algorithms. The self‐tuning adaptive control strategy was compared to an approximate model predictive control in terms of set point tracking capability, efficiency and stability. For the case of large, abrupt set point changes, the performance of the self‐tuning algorithm was poor, especially for the raffinate control. The approximate model predictive control strategy was superior to the self‐tuning control in terms of its ability to force the output to following the set point trajectory efficiently with smooth controller moves.     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

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 adaptive temperature control of multi-product, semi-batch polymerization reactors

This paper considers the temperature control of semi-batch polymerization reactors in which some of the following issues must be considered: (i) production of multiple products in the same reactor; (ii) changing heat transfer characteristics, during a batch and from batch to batch; (iii) time varying and nonlinear reaction rate due to changing monomer concentration and diffusion controlled termination reactions (gel effect); (iv) the absence of detailed kinetic models for the reactors. The industrial challenge problem published by Chylla and Haase [Chylla, R. W. and Haase, D. R. (1993) Temperature control of semi-batch polymerization reactors (with corrected updates). Comput. Chem. Eng. 17, 257–264) is used as the simulation basis for evaluating these problems.

A nonlinear adaptive controller consisting of a nonlinear controller (based on differential geometric concepts) coupled with an extended Kalman filter (which uses only readily available data and knowledge) is shown to provide excellent control in all the above situations. In particular, the on-line estimation is critical for the strong performance of the nonlinear controller over a broad range of conditions. PID controllers with feedforward terms can perform well at one set of conditions, however, they require retuning as conditions and products change.     

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.     

NONLINEAR HEAT EXCHANGER CONTROL THROUGH THE USE OF PARTIALLY LINEARIZED CONTROL VARIABLES

The use of partial linearization by nonlinear state variable feedback has been proposed as a means of reducing the detrimental effects of system nonlinearities upon the performance of linear control schemes used with nonlinear systems. In this paper a set of generalized transformed variables are derived for a single pass shell and tube heat exchanger using this technique. The implementation of these generalized transformed variables, which reduce the apparent nonlinear behavior of single pass heat exchangers, eliminates the need to rederive a nonlinear transformation for each heat exchanger controller design. As shown by open loop transient behavior of the system, the transformed variables reduce the nonlinear characteristics of the system response. The closed loop performance of the heat exchanger system has been evaluated for both servo and regulator control, and the effect of model error upon the robustness of the closed loop controller performance has been investigated.     

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network (NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.     

A simple adaptive control strategy for temperature trajectory tracking in batch processes

In this paper, a simple adaptive control strategy is suggested for temperature tracking control of batch processes. A nonlinear controller, which is in structure very simple and consists of a single parameter, is proposed. To enable this controller to control a batch process adaptively, a simple parameter tuning algorithm is derived based on the Lyapunov stability theorem. The proposed adaptive control scheme is directly operational, which does not depend on process model and the only a priori process information required is the system response direction. To demonstrate the effectiveness and applicability of the proposed scheme, illustrative examples are provided. Extensive simulation results reveal that the proposed adaptive control strategy appears to be a simple and effective approach to batch process control, which provides robust control despite the wide range of operating conditions and nonlinear dynamics of the system.     

ADAPTIVE INTERNAL MODEL CONTROL OF HAMMERSTEIN-NONLINEAR SYSTEMS

Adaptive internal model control is analyzed for a single-input-single-output nonlinear system represented by the Hammerstein model wherein the nonlinearity is an odd order polynomial. The recursive least-squares method of Chang and Luus (1971) is used for parameter estimation. To obtain a stable approximation to the inverse of the process model for use as the controller, Vogel-Edgar's method (1980) for linear system is employed. Simulation results have shown that the adaptive internal model control (IMC) performs well even with non-minimum phase Hammerstein systems in the presence of unmeasured load changes and dead-time variations. The performance of nonlinear IMC is found to be superior to that of linear IMC.     

基于神经网络和多模型的非线性自适应PID控制及应用

针对一类未知的单输入单输出离散非线性系统,提出了基于神经网络和多模型的非线性自适应PID控制方法。该方法由线性自适应PID控制器、神经网络非线性自适应PID控制器以及切换机构组成。采用线性自适应PID控制器可保证闭环系统所有信号有界;采用神经网络非线性自适应PID控制器可改善系统性能;通过引入合理的切换机制,能够在保证闭环系统稳定的同时,提高系统性能。理论分析表明,该方法能够保证闭环系统所有信号有界,如果适当地选择神经网络的结构和参数,系统的跟踪误差将收敛于任意给定的紧集。将所提出的方法应用于连续搅拌反应釜,仿真结果验证了所提出方法的有效性。由于该方法基于增量式数字PID控制器,在工业过程中有着广阔的应用前景。     

Robust controller synthesis for multivariable nonlinear systems with unmeasured disturbances

This work concerns robust controller synthesis using the differential geometric concepts for minimum phase nonlinear systems with unmeasurable disturbances. A pseudo-linearization of the disturbance model at the input-output linearization stage is applied to yield a linear subsystem for controller design. Based on this linear model, a multi-loop controller framework is implemented, whereby μ-synthesis is used to design off-line robust controller in the outer loop while state feedback is implemented in the inner loop. Through proper selection of weights, the outer robust controller is explicitly designed to address both uncertainty and disturbance rejection whereas the inner controller is used for on-line static state feedback. Numerical simulations are used to illustrate robustness of the controller for multi-input multi-output temperature control in two non-isothermal continuous stirred tank reactors in series.     

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.     

FEEDBACK LINEARIZATION DESIGNS FOR UNCERTAIN NONLINEAR TIME-DELAY PROCESSES: A COMPARATIVE STUDY

This work concerns the phenomena in which the feedback linearization control is applied to uncertain nonlinear time-delay processes. Under the I/O linearization algorithm, both nonlinear controllers are used to stabilize the closed-loop system with transformed delay inputs. When the effect of input perturbations can converge to zero or asymptotically vanish, these nonlinear feedback designs with only an adjustable parameter can directly improve the tracking performance. The simple linearizing controller can directly regulate the system output at unstable operating point. Combined with deadtime compensation the nonlinear predictive controller with the aid of appropriate state prediction is valid for the real process in the presence of large time delay. Finally, via computer simulation and test of control ability of both feedback control designs the useful comparative results are presented.     

Nonlinear adaptive control algorithm for a multicomponent batch distillation column

In this article, a nonlinear adaptive control strategy is proposed for a multicomponent batch distillation column. The hybrid control scheme consists of a generic model controller (GMC) and a nonlinear adaptive state estimator (ASE). In the first part of the study, an adaptive observer is designed aiming to estimate the partially known parameters based on the measured compositions in the presence of process/predictor mismatch. The open-loop dynamic behavior of the developed ASE estimator is investigated under initialization error, disturbance, and uncertain parameters. In the subsequent part, the adaptive GMC-ASE controller (GMC control structure in conjunction with ASE estimator) has been synthesized for the example distillation column. A simulation-based comparative study has been conducted between the derived nonlinear GMC-ASE control algorithm and a gain-scheduled proportional integral (GSPI) law in terms of constant composition control. The proposed adaptive control scheme is shown to be quite promising due to the exponential error convergence capability of the ASE estimator in addition to the high-quality performance of the GMC controller.     

Neural‐Networks‐Based Feedback Linearization versus Model Predictive Control of Continuous Alcoholic Fermentation Process

In this work advanced nonlinear neural networks based control system design algorithms are adopted to control a mechanistic model for an ethanol fermentation process. The process model equations for such systems are highly nonlinear. A neural network strategy has been implemented in this work for capturing the dynamics of the mechanistic model for the fermentation process. The neural network achieved has been validated against the mechanistic model. Two neural network based nonlinear control strategies have also been adopted using the model identified. The performance of the feedback linearization technique was compared to neural network model predictive control in terms of stability and set point tracking capabilities. Under servo conditions, the feedback linearization algorithm gave comparable tracking and stability. The feedback linearization controller achieved the control target faster than the model predictive one but with vigorous and sudden controller moves.     

Nonlinear state estimation and control of a batch reactive distillation

This paper deals with the advanced adaptive control of a batch reactive distillation (RD) column for the production of ethyl acetate. The nonlinear adaptive control law consists of the generic model controller (GMC) and an adaptive state estimator (ASE). In the first part of the present work, the design approach of the ASE scheme in two different forms, namely ASE1 and ASE2, has been addressed for a batch reactive rectifier. The predictor model of both the ASE estimators includes only a component mole balance equation around the condenser-reflux drum system and an extra state equation having no dynamics, and therefore, there is a large process/predictor mismatch. In presence of this structural discrepancy, the adaptive estimation schemes compute the imprecisely known parameters quite accurately based on the measured distillate composition under initialization error, disturbance and uncertainty. In the subsequent part, the adaptive GMC–ASE1 control structure has been formulated for the sample reactive column. This nonlinear control strategy shows comparatively better closed-loop performance than the gain-scheduled proportional integral (GSPI) controller due to the exponential error convergence capability of the estimation scheme and the high-quality control of the GMC law.     

Nonlinear model-based dissolved oxygen control in a biological wastewater treatment process

The dissolved oxygen (DO) concentration has been an important process parameter in the biological wastewater treatment process (WWTP). In this paper, we propose a nonlinear control scheme to maintain the dissolved oxygen level of an activated sludge system. Without any linearization or model reduction, it can directly incorporate the nonlinear DO process model with on-line estimation of the respiration rate (R) and the oxygen transfer rate (K_La). Simulation results show that it outperforms a control performance of the PID controller. Since it incorporates the process disturbance and nonlinearity in the controller design, the suggested method can efficiently deal with the operating condition changes that occur frequently in the wastewater treatment process.