Double-command feedforward-feedback control of a nonlinear plant

A design approach is proposed for feedforward-feedback control systems. The basis of the proposed approach is a steady state control law which maintains the desired control output of the system and is employed as the feedforward controller. With this feedforward controller, for a wide class of systems, the stability of the control system is proved if the feedback controller is a gain with an arbitrarily high value; that is, the only limit for the feedback (transient) control command is the actuator’s practical limit. Moreover, in continuous domain, there will be no overshoot. In this article, the proposed method has been applied to a catalytic stirred tank reactor (CSTR) to control the output concentration through adjusting the flow of two valves simultaneously and resulted in an excellent control response.     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

Fuzzy-based nonlinear PID controller and its application to CSTR

This study presents a new design method for a nonlinear variable-gain PID controller, the gains of which are described by a set of fuzzy rules. User-defined parameters are tuned using a genetic algorithm by minimizing the integral of absolute error and the weighted control input deviation index. It was observed in the experimental results on a continuous stirred tank reactor (CSTR) that the proposed controller provided performances: overshoot M _p ≤1.25%, 2% settling time t _s ≤1.71 s and IAE≤1.26 for set-point tracking, perturbance peak M _peak ≤0.05%, 2% recovery time t _rcy ≤3.97 s and IAE≤0.10 for disturbance rejection, and M _peak ≤0.04%, t _rcy ≤2.74 s and IAE≤0.04 for parameter changes. Comparison with those of two other methods revealed that the proposed controller not only led to less overshoot and shorter settling time for set-point tracking and less perturbance peak and shorter recovery time for disturbance rejection, but also showed less sensitivity to parameter changes.     

CSTR工艺与控制系统的集成优化设计方法

与传统的序贯设计方法相比,过程工艺与控制系统的集成优化设计可较大地提高过程的可操作性和经济性能,但基于常规动态优化的集成设计问题求解困难。采用最优控制和分层优化策略的思想,将线性二次调节器(LQR)嵌入到过程工艺与控制系统集成设计框架中,以降低集成优化设计问题的求解难度。将该方法应用于连续搅拌釜式反应器(CSTR)的设计中,通过与传统的序贯设计方法相比较,表明了该方法的有效性。     

Time-optimal control of mmama copolymerization in a CSTR for grade change

The time-optimal control of MMA-MA copolymerization in a CSTR is treated for a grade-change operation. The control objective is to bring system specifications, such as polymer production rate and polymer composition, to desired values in minimum time. The initiator concentration is chosen as a manipulated variable. Two cases are considered: One is to get the time optimal control for both a desired polymer production rate and a desired weight composition of MA in dead copolymer; the other is only for a desired polymer production rate. In numerical calculation, the final t(ⁱ)_f is chosen at each iteration as the time at which the system reached steady-state. This allows us to use a more easily manipulatable form of the performance index and at the same time not directly use the free final time boundary condition.     

连续搅拌釜的非线性模型稳定性判据及算法

针对具有强非线性、时变、有纯滞后等复杂特性的连续搅拌釜(CSTR)反应过程,提出了一种非线性鲁棒模型预测控制方法。先根据搅拌釜中物料反应和温度波动机理,强鲁棒性的系统参数假设在凸多面体中,然后,在温度工作稳定平衡点离散线性化具有高度非线性特点的系统方程。合理建立系统预报方程,提出可保成本性能指标函数并计算李雅普诺夫函数的差分。采用双线性和线性矩阵不等式(BMI和LMI)技术处理鲁棒模型预测控制系统,给出了保持较优性能条件下的闭环系统稳定性判定标准。其次,考虑稳定标准的条件中存在双线性矩阵不等式,设计相应的凸优化算法,便于利用matlab中LMI TOOLBOX求解。最后,通过系统仿真实验,与已有数值结果对比,说明了所提理论的正确性和算法的有效性、优越性。     

Periodic operation of CSTR - II practical control

The periodic operation of CSTR with a coil or a jacket for controlling the temperature is investigated with aid of the necessary conditions for the optimality of the totally singular control. Three reaction systems are examined, the parallel reaction, the consecutive reaction and the reversible reactionA sufficient condition for the superiority of the periodic control to the steady control is obtained. It is also observed by numerical calculations for a set of parameter values that the periodic control is superior to the steady control only when this sufficient condition is satisfied.     

一种基于PWA模型的控制策略在连续搅拌反应釜中的应用

在化工系统实际运行过程中,常常会出现一些不正常的工作状态,为了使系统运行状态能够避开这些不正常的工作状态,往往需要对控制器进行重构。针对这种情况,本文阐述了一种基于分段仿射模型的控制策略,该控制策略采用显式模型预测控制算法对系统进行控制,当检测到系统出现异常工作点时,先对系统进行形式验证,根据验证结果,再决定是否进行控制器重构,这样,既大大节约了生产时间和成本,也提高了控制效率。将该控制策略应用到连续搅拌反应釜系统中,取得了显著的应用成效。     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network,AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

Parametric sensitivity of a CSTR

It is shown that the generalized sensitivity criterion recently developed in the context of thermal explosions and tubular reactors can be easily applied in the case of a CSTR as well. An illustrative example concerning sensitivity analysis of a single nth order irreversible exothermic reaction in a nonadiabatic CSTR is presented. A generalized region of parametric sensitivity is identified where the reactor temperature is parametrically sensitive simultaneously to all the input parameters. Asymptotic analysis for large heats of reaction is performed to investigate limiting behaviour, which leads to the classical Semenov limit in the case of large activation energies. It is shown that parametric sensitivity can occur even when unique steady states exist for all Damköhler number (Da) values. Furthermore, if operating conditions are chosen so as to avoid completely the possibility of parametric sensitivity for all Da, then the possibility of steady-state multiplicity is automatically avoided.     

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013     

Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state

Application of relay feedback controllers to maintain process states near unstable steady states is extended to a second order system, the CSTR with an irreversible, exothermic reaction. The control scheme is successful provided the bandwith (the reactor temperature deviation which causes relay switching) is not chosen too large relative to the drive levels (the deviation in coolant temperature caused by relay switching). In this context Tsypkin's analytical methods for approximate solution of this and higher order problems are elaborated and tested. Tsypkin's technique proves superior to Describing Function analysis in accuracy and in bounds on the maximum permissible bandwidth.     

Refolding of proteins in a CSTR

A model to predict refolding of proteins in a continuous stirred tank reactor (CSTR) was developed and compared to a batch refolding process with simple dilution of the protein in a stirred tank reactor. For experimental verification of the model a continuous refolding of a model protein (α-lactalbumin) was performed in a CSTR. The refolding process of denatured and fully reduced α-lactalbumin could be accurately predicted by a set of differential equations assuming a first order reaction rate for folding and a second order reaction rate for aggregation. The system composed of a CSTR with an additional diafiltration circuit for removal of denaturing agents from the feed solution and to maintain constant refolding conditions. Based on the folding kinetic the dynamic behavior of such a continuous refolding reactor was simulated under different operating conditions. It was shown that the refolding efficiency was higher compared to batch dilution under certain conditions, namely high residence times. The yield of refolded protein could further increased by recycling the outlet stream containing unfolded protein to the reactor entrance.     

Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR

We show how the availability function as defined from the entropy function concavity can be used for the stability analysis and derivation of control strategies for non-isothermal Continuous Stirred Tank Reactors (CSTRs). We first propose an overview of the required thermodynamic concepts. Then, we show how the availability function restricted to the thermal domain can be used as a Lyapunov function. The derivation of the control law and the way the strict entropy concavity is insured are discussed. Numerical simulations illustrate the application of the theory to the open loop stability analysis and the closed loop control of liquid-phase non-isothermal CSTRs. The proposed approach is compared with the classical proportional control strategy. Two chemical reactions are studied: the acid-catalyzed hydration of 2-3-epoxy-1-propanol to glycerol subject to steady state multiplicity and the production of cyclopentenol from cyclopentadiene by acid-catalyzed electrophilic addition of water in dilute solution exhibiting a non-minimum phase behavior.     

Sampled-data control of a nonlinear system

Sampled-data proportional control of an exothermic CSTR has been studied using the classical linear analysis and by the application of the averaging te     

A study of gain scheduling control applied to an exothermic CSTR

This paper describes how gain scheduling control is applied to a continuous stirred tank reactor model. The CSTR process, equipped with a cooling system, is modelled. Based on the resulting nonlinear model, a gain scheduling controller is designed. The gain scheduling follows a scheme denoted bias compensation. Compared to earlier reported gain scheduling schemes, the proposed scheme results in a controller that is less complex, which is advantageous in the controller implementation stage. Numerous simulations are performed, using the gain scheduling controller and two choices of control input to the reactor model. The simulation results indicate that a gain scheduling controller performs better than a linear controller. Simulations using different choices of control input to the reactor model indicate that proper process design is crucial for the controlled process performance.     

Regeneration of polymeric adsorbents in a CSTR

The regeneration step is crucial in the design of cyclic fixed bed adsorbers. In order to understand the regeneration process of a polymeric adsorbent (Duolite ES861) saturated with phenol by using sodium hydroxide simple dynamic experiments in a CSTR were done. Results were explained roughly by a simple equilibrium model and more accurately by a reaction front model which will be later used in a package for the design of cyclic fixed bed adsorption processes.     

Robust nonlinear control of a continuous crystallizer

This paper proposes a nonlinear multivariable robust output feedback controller for a continuous crystallizer with fines trap which is modeled by a highly uncertain population balance model. Initially, the method of moments is applied to the population balance model to reduce it to a small set of differential equations, which is subsequently employed for controller synthesis by using a combination of geometric control methods with Lyapunov techniques. The performance and robustness of the proposed controller are successfully tested through simulations and are shown to be superior to the ones of a nonlinear controller which does not account for uncertainty.     

Computing fuzzy trajectories for nonlinear dynamic systems

One approach for representing uncertainty is the use of fuzzy sets or fuzzy numbers. A new approach is described for the solution of nonlinear dynamic systems with parameters and/or initial states that are uncertain and represented by fuzzy sets or fuzzy numbers. Unlike current methods, which address this problem through the use of sampling techniques and do not account rigorously for the effect of the uncertain quantities, the new approach is not based on sampling and provides mathematically and computationally rigorous results. This is achieved through the use of explicit analytic representations (Taylor models) of state variable bounds in terms of the uncertain quantities. Examples are given that demonstrate the use of this new approach and its computational performance.     

Adaptive type-2 fuzzy logic control of a bioreactor

Two adaptive type-2 fuzzy logic controllers with minimum number of rules are developed and compared by simulation for control of a bioreactor in which aerobic alcoholic fermentation for the growth of Saccharomyces cerevisiae takes place. The bioreactor model is characterized by nonlinearity and parameter uncertainty. The first adaptive fuzzy controller is a type-2 fuzzy-neuro-predictive controller (T2FNPC) that combines the capability of type-2 fuzzy logic to handle uncertainties, with the ability of predictive control to predict future plant performance making use of a neural network model of the nonlinear system. The second adaptive fuzzy controller is instead a self-tuning type-2 PI controller, where the output scaling factor is adjusted online by fuzzy rules according to the current trend of the controlled process. The performance of a type-2 fuzzy logic controller with 49 rules is used as reference.