Non‐Linear Predictive Control of a Three‐Phase Catalytic Reactor

In this work, the predictive control of a three‐phase catalytic reactor is considered. A predictive control algorithm, which has a non‐linear internal model represented by functional link networks, is proposed. This network structure has been shown to have a good non‐linear approximation capability, with the advantage that the estimation of its weight is a linear optimization problem. The results show the potential of the proposed procedure when it is applied to the 2‐methyl‐cyclohexanol production process, which is a non‐linear, distributed parameter and time‐varying process, typical of many important industrial systems.     

Inferential Control of Reactive Destillation Columns – An Algorithmic Approach

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed‐integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed‐integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.     

Three mode control as an optimal control

Three mode control with Ziegler-Nichols or Cohen-Coon controller settings is shown to be the solution to an optimal control problem for a linear first order system with dead time and a quadratic cost functional. The implication of this result is that in the absence of an economically meaningful cost criterion there is no reason to prefer the results of optimal control theory to traditional design procedures for feedback control systems. The multivariable generalization of the optimal control problem solved here provides the means for extending classical control experience in design of single loop processes to multivariable control systems     

Identifiability of Non‐Linear Differential Algebraic Systems via a Linearization Approach

A system is identifiable if there exists a unique relationship between its input‐output behaviour and the parameter values. Differential‐Algebraic Equation (DAE) systems have an input‐output behaviour that is described by a parameterized set of ordinary differential and algebraic equations. Methods proposed in the literature to test the identifiability of DAE systems are based on the tools of differential algebra and rely on time‐differentiation of model equations. As a result, even when dealing with a few states and parameters, the calculations required for these methods may become intractable. An alternative, which we propose, is to linearize the non‐linear DAE system about some rest point and then test the identifiability properties of the linearized system. In this work, we show that strong local identifiability of the linearized DAE system provides a sufficient condition for the strong local identifiability of the original non‐linear DAE system.     

Dynamic Behavior of Industrial Gas Phase Fluidized Bed Polyethylene Reactors under PI Control

A mathematical model describing the UNIPOL process for the production of polyethylene in the gas phase using a Ziegler‐Natta catalyst in a bubbling fluidized bed is used to analyze the major processes determining the behavior and performance of these industrially important units. The investigation shows that both static bifurcation (multiplicity of the steady states) as well as dynamic bifurcation (stable/unstable periodic attractors) behavior cover wide regions of the design and operating parameter domain. A conventional proportional‐integral (PI) control policy is suggested to stabilize the behavior of the system. The control philosophy covers both aspects of stabilizing unstable steady states as well as compensating for external disturbances. It is shown that for some controller configurations and set points the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The industrial implications of the phenomena discovered for both the open loop (uncontrolled) as well the closed‐loop (controlled) systems are analyzed.     

一类不确定多时滞系统的鲁棒容错控制研究

讨论一类线性不确定多时滞系统的鲁棒容错控制问题.基于Lyapunov稳定性理论和线性矩阵不等式方法（LMI）,针对一类参数有界不确定多时滞系统,给出了状态反馈鲁棒容错控制器设计方法,并且利用该方法得到的闭环控制系统,不仅在执行器失效情况下具有渐进稳定性,对参数不确定也具有良好的鲁棒性.最后,应用设计实例及仿真结果验证该设计方法的可靠性和有效性.     

Integration of Design and Control: A Robust Control Approach Using MPC

This paper presents a new method to integrate process control with process design. The process design is based on steady‐state costs, .i.e., capital and operating costs. Control is incorporated into the design in terms of a variability cost. This term is calculated based on the non‐linear process model, represented here as a nominal linear model supplemented with model parameter uncertainty. Robust control tools are then used within the approach to assess closed‐loop robust stability and to calculate closed‐loop variability. The integrated method results in a non‐linear constrained optimization problem with an objective function that consists of the sum of the steady costs and the variability cost. Optimization using the traditional sequential approach and the new integrated method was applied to design a multi‐component distillation column using a Model Predictive Control (MPC) algorithm. The optimization results show that the integrated method can lead to significant cost savings when compared to the traditional sequential approach. In addition, an RGA analysis was performed to study the effects of process interactions on the optimization results.     

Generalized Common Model Control

Applying the Lie derivative concept, we propose a new control method of generalized common model control (GCMC) by generalizing the CMC algorithm to complex processes with the relative order larger than 1 to overcome the disadvantage of common model control (CMC), i.e., it can only apply to the processes with relative order of 1. The model of the non‐linear controlled plant is directly embedded in the controller, so that the controlled non‐linear system is a linear high order system in the no constrained control input, it is very easy to tune for the controller by applying the method of dominant poles. The simulation results show that the general common model controller is very effective for the non‐linear system.     

A Simplified Numerical Approach to Feedback Controller Design

A generalized parameter optimization method for computing feedback controller parameters is proposed. The method utilizes the downhill simplex method (DSM), a pattern search algorithm, to determine the optimal parameters that minimize an objective function or performance index. The system model, expressed in terms of state‐space equations is integrated with respect to time at each DSM iteration in order to determine the states. A fourth‐order Runge‐Kutta scheme is used for integrating the state equations. A penalty function approach is used for problems with inequality constraints on the state variables or controls. Though relatively inefficient in terms of the number of function evaluations, DSM requires only that the user provide the model equations, and not their derivatives. Additionally, the DSM code is very compact. Thus, a small and straightforward program allows for controller parameter determination for a variety of state‐space and classical PID feedback control design problems.     

On Measuring Closed‐Loop Non‐Linearity: A Topological Approach

The focal point of this paper is to develop a measure of closed‐loop non‐linearity. In this work, the Vinnicombe metric and the Quasi‐Linear Parameter Varying representation of a non‐linear system are exploited for this purpose. It is expected that the proposed measure can serve as a decision making tool for control engineers when considering whether a linear or a non‐linear control strategy should be employed to close the loop for a non‐linear system operating in a prescribed range.     

Dividing Wall Distillation Columns: Optimization and Control Properties

The optimal design of dividing wall columns is a non‐linear and multivariable problem, and the objective function used as optimization criterion is generally non‐convex with several local optimums. Considering this fact, in this paper, we studied the design of dividing wall columns using as a design tool, a multi‐objective genetic algorithm with restrictions, written in Matlab^TM and using the process simulator Aspen Plus^TM for the evaluation of the objective function. Numerical performance of this method has been tested in the design of columns with one or two dividing walls and with several mixtures to test the effect of the relative volatilities of the feed mixtures on energy consumption, second law efficiency, total annual cost, and theoretical control properties. In general, the numerical performance shows that this method appears to be robust and suitable for the design of sequences with dividing walls.     

Low‐order optimal regulation of parabolic PDEs with time‐dependent domain

Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two‐dimensional (2‐D) parabolic partial differential equation with time‐varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time‐varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite‐dimensional plant in terms of a linear time‐varying system. This reduced‐order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2‐D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494–502, 2015     

An Approach to Simple Reaction Control for Auto‐thermal Fuel‐reforming Systems

A simple approach to reaction control for auto‐thermal fuel‐reforming systems was proposed and examined. The amount of air supplied to the fuel‐reforming system was chosen as the variable in the feedback (closed‐loop) control operation, and simply by varying the amount of air supplied, it was attempted to control and stabilize the temperature of the auto‐thermal reforming reaction. The amounts of other fuels and water were chosen from pre‐determined values by open‐loop operation. Since the feedback operation was limited to the air‐supply mechanism, it was expected that both the hardware structure of the system and its software configurations could be significantly simplified. The applicability of this simple feedback control operation was confirmed experimentally by using a methanol reformer of the direct‐injection type.     

Design of multi-parametric NCO tracking controllers for linear dynamic systems

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach.     

Control of a nonadiabatic packed bed reactor under periodic flow reversal

A full parametric study of the open-loop behavior of a packed bed reactor-recuperator system operating under periodic flow reversal produced a series of parametric maps which slow regions of operating conditions for which the system exhibits runaway, stable operation or extinction of the reaction. The reaction is CO oxidation over a Pt/alumina catalyst. A set of optimal operating conditions in terms of cycle time and heat transfer coefficient can be directly extracted from the parametric maps. A preliminary study on the control of periodic flow reversal tested and compared two strategies. 1) feedback PID control of the exit CO concentration and 2) model based feedforward control.     

受扰动非线性系统的反馈线性化最优控制

研究具有外界扰动作用下的非线性系统基于状态反馈精确线性化的最优控制器设计问题。首先基于微分同胚将受扰动非线性系统模型转变为无扰动的伪线性系统模型,然后给出了在关系度等于系统阶数情况下基于二次型性能指标的最优控制器设计方法,通过求解Riccati方程得到系统最优扰动抑制控制律。最后通过仿真实例表明了该方法的有效性。     

燃料电池基于改进遗传算法的多层前向神经网络控制

通过对熔碳酸盐燃料电池（MCFC）温度动态模型的分析,根据控制对象的非线性和参分布的特点,提出了基于遗传算法的反馈型多层向神经网络对顺流型MCFC温度进行控制的方案,通过对传统遗传算法的分析,提出了改进的遗传算法,用该算法对神经网络的权值进行优化,并给出了具体的学习算法,最后结合前人的MCFC模型动特性分析方面的工作和实验数据进行了仿真,结果表明这种控制方法是合理和用效的。     

Real‐time Dynamic Optimization of Non‐linear Batch Systems

In this paper, a methodology for designing and implementing a real time optimizing controller for non‐linear batch processes is discussed. The controller is used to optimize the system input and state trajectories according to a cost function. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov‐based extremum seeking approach is used to compute the trajectory parameters. Smooth trajectories were generated with reduced computing time compared to many optimizations in literature. In this paper, the theory is applied to general non‐flat non‐linear systems in a true on‐line optimization.     

聚合物配置浓度控制中的灰色预测控制

以灰色预测控制理论为基础,首次将非线性GM(1,1)模型引入油田聚合物配置站的聚合物浓度配置控制系统中,将一种新的自调节灰色预测控制器与原有的PID控制器结合,应用到聚合物浓度配置控制中,该控制器可根据系统现有数据预测未来聚合物浓度来自动调整控制器参数,经过生产实践验证了此控制器的有效性.     

基于改进DOB的矿物研磨过程最优运行先进反馈控制(英文)

Advanced feedback control for optimal operation of mineral grinding process is usually based on the model predictive control (MPC) dynamic optimization. Since the MPC does not handle disturbances directly by controller design, it cannot achieve satisfactory effects in controlling complex grinding processes in the presence of strong disturbances and large uncertainties. In this paper, an improved disturbance observer (DOB) based MPC advanced feedback control is proposed to control the multivariable grinding operation. The improved DOB is based on the optimal achievable H 2 performance and can deal with disturbance observation for the nonminimum-phase delay systems. In this DOB-MPC advanced feedback control, the higher-level optimizer computes the optimal operation points by maximize the profit function and passes them to the MPC level. The MPC acts as a presetting controller and is employed to generate proper pre-setpoint for the lower-level basic feedback control system. The DOB acts as a compensator and improves the operation performance by dynamically compensating the setpoints for the basic control system according to the observed various disturbances and plant uncertainties. Several simulations are performed to demonstrate the proposed control method for grinding process operation.