Time optimal control of high dimensional systems by iterative dynamic programming

For time optimal control, the problem is first transformed into a finite dimensional optimization problem by using time stages of varying lengths to enable accurate switching, and then solved by iterative dynamic programming. In high dimensional systems care is necessary to ensure convergence to the global optimum. Incorporating penalty functions into the performance index and using an adequate number of stages can yield the global optimum. The use of a continuation approach, where the number of stages in an intermediate solution is systematically increased, appears to be more effective. Three linear systems are used to develop and to test the approaches.     

On solving optimal control problems with free initial condition using iterative dynamic programming

For solving optimal control problems where the initial conditions of some of the state variables are not specified, a procedure based on iterative dynamic programming (IDP) is presented. In this procedure, the free initial conditions are taken to be additional control variables for the first time stage only; then the search for the optimal initial conditions and also the optimal control policy is carried out simultaneously using IDP. The procedure is straightforward, and as illustrated with two nonlinear optimal control problems, for each case the optimum performance index is readily obtained.     

Evaluation of the parameters used in iterative dynamic programming

To apply iterative dynamic programming (IDP) to optimal control problems having a very large number of control variables the use of randomly chosen values for control at each grid point is required. To gain insight into the effect of the number of allowable values for control, the region contraction factor, and the number of grid points for the state vector to be used, computational results are presented for two nonlinear systems, one of which possesses numerous local optima. The reliability of obtaining the global optimum for the bifunctional catalyst blend optimization problem was found to be somewhat higher by using randomly chosen values for control rather than by choosing the control values over a uniform distribution. The global optimum is obtained even when a small number of allowable values for control at each grid point and a small number of grid points for the states are used. There is a wide range of the region contraction factor for which rapid convergence to the optimum is obtained. Also the number of grid points for the state can be very small without adversely affecting convergence to the optimum.     

分壁精馏塔分离芳烃的稳态及动态研究

采用分壁精馏塔（DWC）严格稳态模型,对比苯、甲苯、二甲苯以及均三甲苯四组分混合物的常规分离和分壁精馏塔分离方法,稳态分析结果表明：直接序列分壁精馏塔流程较常规三塔分离序列可减小再沸器负荷18.9%,年度总成本TAC可降低13.0%,DWC有效避免了常规塔器分离过程中中间组分的返混现象。在Aspen Dynamic环境下对最优序列进行组分控制,结果表明组分控制可很好地应对进料流量和组分组成波动。     

A disjunctive programming approach for the optimal design of reactive distillation columns

A generalized disjunctive programming formulation is presented for the optimal design of reactive distillation columns using tray-by-tray, phase equilibrium and kinetic based models. The proposed formulation uses disjunctions for conditional trays to apply the MESH and reaction kinetics equations for only the selected trays in order to reduce the size of the nonlinear programming subproblems. Solution of the model yields the optimal feed tray locations, number of trays, reaction zones, and operating and design parameters. The disjunctive program is solved using a logic-based outer-approximation algorithm where the MILP master problem is based on the big-M formulation of disjunctions, and where a special initialization scheme is used to reduce the number of initial NLP subproblems that need to be solved. Two examples are presented that include reactive distillation for the metathesis reaction of 2-pentene and for the production of ethylene glycol. The results show that the proposed method can effectively handle these difficult nonlinear optimization problems.     

醋酸甲酯侧反应精馏过程的多变量动态控制

侧反应器与精馏塔的耦合结构与物料交换方式的灵活性,造成系统的自由度高、设计变量多,增加了该过程的稳态优化模拟和动态控制的难度。针对侧反应精馏过程(SRC)的平滑操作和自动控制问题,以醋酸甲酯工业生产过程为例,采用基于独立反应量的稳态设计方法获取最佳的反应精馏集成结构和操作参数,在此基础上设计了以产品成分调节变比值控制为主的多变量控制方案,并通过在Aspen流程模拟软件建立醋酸甲酯侧反应精馏动态流程模拟系统,验证控制方案的有效性。     

Economic optimal control applied to a solar seawater desalination plant

This paper discusses the formulation of an optimal control strategy taking into account economic objectives in the fresh water production process through a solar seawater desalination plant. It contributes both a linearised model of the solar-field dynamics and a simplified model of the produced distillate as a function of the outlet solar field water temperature. Then such linear models are used to design an economic receding horizon optimal controller. In particular, it comprises incomes related to the production of fresh water and the costs dealing with the electricity. Several simulations validate the proposed models and show the performance of the proposed economic optimal control strategy. In both cases, actual disturbances from physical experiments have been included in the simulations. Notice that the AQUASOL facility available at the Plataforma Solar de Almería (Spain) has been considered in this work as testbed.     

邻甲酚塔的参数优化和控制分析

精馏塔是石油化工和医药领域常见的生产过程设备,本文利用Aspen Pus软件分别采用简捷法和严格法对提酚装置中邻甲酚塔进行了设计计算。针对本项目研究的邻甲酚精馏塔,首先通过简捷法估算出精馏塔的回流比、塔板数以及进料位置。然后采用严格法的灵敏度分析得出回流比为6、塔板数为80块、进料位置为30。增加精馏塔回流比5%,分析回流比变化对塔板温度的影响,发现精馏段灵敏板的位置为26块,提馏段灵敏板的位置为43块。分别采用了精馏段温度控制方案和提馏段温度控制方案研究在进料流量、进料组成以及进料温度波动时,精馏塔的动态响应过程。研究表明:提馏段温度控制方案较精馏段温度控制方案具有明显的动态响应快,抗干扰能力强,建立平衡时间短等优点。     

最优控制方法在矿山建设规划中的应用

根据最优控制理论中的最小值原理，建立矿山长远建设规划最优控制离散模型，并以梯度法求解．     

Decentralized temperature control of a pilot dividing wall column

The technology of dividing wall columns offers to save high amounts of operating and investment cost compared to conventional distillation columns and their configurations. The practical application is still limited due to a lack of experience and high interactions among the process variables.The present work deals with the development and test of a control system for a pilot dividing wall column. Within this, decentralized temperature control systems are designed by a systematic approach. Furthermore, these systems are evaluated concerning the process stability, the providing of defined product purities and the respective requirement of energy in case of disturbances. The focus is on simulative and experimental investigations in order to assure the practicability of the developments. The presented results show the effectiveness of the applied methods.     

Effect of the choice of final time in optimal control of nonlinear systems

The choice of the final time, t_j, in the optimal control of nonlinear systems is shown to be very important. By choosing t_f to be small, and repeatedly optimizing the system operation over the short time intervals gives a highly oscillatory type of control for a particular nonlinear chemical reactor. The cumulative profit as compared to that obtained by choosing t_f to be large, is substantially lower. In the operation of a batch reactor it is shown that if t_f is small, bang-bang control with singular sub-arcs results. When t_f is large, the optimal control policy tends to be relatively smooth and the profitability is substantially improved.     

Approximate dynamic programming based approach to process control and scheduling

Multi-stage decision problems under uncertainty are abundant in process industries. Markov decision process (MDP) is a general mathematical formulation of such problems. Whereas stochastic programming and dynamic programming are the standard methods to solve MDPs, their unwieldy computational requirements limit their usefulness in real applications. Approximate dynamic programming (ADP) combines simulation and function approximation to alleviate the ‘curse-of-dimensionality’ associated with the traditional dynamic programming approach. In this paper, we present the ADP as a viable way to solve MDPs for process control and scheduling problems. We bring forth some key issues for its successful application in these types of problems, including the choice of function approximator and the use of a penalty function to guard against over-extending the value function approximation in the value iteration. Application studies involving a number of well-known control and scheduling problems, including dual control, multiple controller scheduling, and resource constrained project scheduling problems, point to the promising potentials of ADP.     

Parametric and nonparametric model based control of a packed distillation column

Parametric and nonparametric model based control systems were applied to control the overhead temperature of a packed distillation column separating methanol–water mixture. Experimental and theoretical studies have been done to observe the efficiency and performance of both control systems. Generalized predictive control (GPC) system based on a parametric model has been tried to keep the overhead temperature at the desired set point. First, a parametric model which is controlled auto regressive integrated moving average (CARIMA) was developed and then the parameters of this model were identified by applying pseudo random binary sequence (PRBS) and using Bierman algorithm. After that this model was used to design the GPC system. Tuning parameters of the GPC system have been calculated using the simulation program of the packed distillation column. Using the predicted parameters, experimental and theoretical GPC systems were found very effective in controlling the overhead temperature. Dynamic matrix control (DMC) system based on a nonparametric model has been used to track the overhead temperature of the packed distillation column. For this purpose, a nonparametric model known as the dynamic matrix was determined using the reaction curve method. A step change in heat input to the reboiler was applied to the manipulated variable and the temperature of the overhead product was observed. After that, the dynamic matrix was used to design the DMC system. Several calculations have been done to define the DMC control parameters. The best values of the tuning parameter were used to realize the DMC system for controlling the overhead temperature experimentally and theoretically. In the presence of some disturbances, the DMC system gives oscillation and offset in experimental studies.     

Kaibel分壁精馏塔分离芳烃的稳态和动态模拟

Kaibel分壁精馏塔(Kaibel divided-wall column,KDWC)可在一个塔内实现四组分混合物的高纯度分离。本文以分离苯、甲苯、二甲苯和均三甲苯为研究对象,建立了KDWC严格稳态模型,获得了优化的塔体结构。通过研究KDWC分离17组进料组成的基础上,获得了KDWC的稳态分离的初步规律:实现KDWC的高纯度分离,既需要通过分液比控制预分馏段顶部馏出气相中的二甲苯含量,又需要通过分气比控制预分馏底部馏出液相中甲苯含量;两个侧线的组成中,重组分杂质的含量要远多于轻组分杂质的含量;中间组分甲苯在预分馏段仍有返混。随后,在Aspen Dynamic环境下建立了KDWC的组分控制模型,控制结果表明该模型可以应对±10%的流量和进料组成波动,但二甲苯产品纯度会出现少量偏差。     

A unified data-driven design framework of optimality-based generalized iterative learning control

This paper proposes a unified design framework for data-driven optimality-based generalized iterative learning control (DDOGILC), including data-driven optimal ILC (DDOILC), data-driven optimal point-to-point ILC (DDOPTPILC), and data-driven optimal terminal ILC (DDTILC). First, a dynamical linearization in the iteration domain is developed. Then three specific DDOGILC approaches are proposed. Both design and analysis of the controller only require the measured I/O data without relying on any explicit model information. The optimal learning gain can be updated iteratively, which makes the proposed DDOGILC more adaptable to the changes in the plant. Furthermore, the proposed DDOPTPILC and DDOTILC only depend on the tracking error at specific points, and thus they can deal with the scenario when the system outputs are measured only at some time instants. Moreover, the proposed DDOPTPILC and DDOTILC approaches do not need to track the unnecessary output reference points so that the convergence performance is improved.     

Active disturbance rejection generalized predictive control for a high purity distillation column process with time delay

High purity distillation processes have been widely used in the chemical industry. These processes have unique characteristics including higher order, nonlinearity, strong coupling, and time delay. In order to overcome these control issues, an active disturbance rejection generalized predictive control strategy is designed for the distillation column with time delay. The strategy combines the structures of both active disturbance rejection control and generalized predictive control. A delayed designed extended state observer can estimate the model uncertainty and external disturbance, and a non‐incremental generalized predictive control is proposed to deal with the integrators with time delay. Therefore, it rejects disturbances well and has the capability of overcoming time delay. The computation load is also less than the generalized predictive control. In the simulation experiments, the proposed strategy is compared with robust control and model predictive control. The results illustrate that the proposed control strategy has improved robustness performance in dealing with model uncertainties, various disturbances, and time delay.     

组合式精馏塔在甲烷氯化物装置精馏系统中的应用

通过对规整填料塔与板式塔的特点进行分析,运用规整填料的低压降、大通量、高效率等特点,以及板式塔的操作稳定性结合在甲烷氯化物精馏塔的改造,通过流程模拟结果及创新性的采用填料与塔板复合的型式,结合填料塔与浮阀塔各自优点形成组合塔,优化了精馏塔运行。     

迭代动态规划在树脂牌号切换最优化模型中的应用

本文运用迭代动态规划求解牌号切换模型的最优化问题,有效地避免了运用一般方法求解系统最优化问题时的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ－Ｂｅｌｌｍａｎ方程以及高维系统可能出现的计算量激增的问题,成功地解得树脂牌号切换过程产生的过渡料数量最少时聚合温度、氯气和共聚单体的浓度、催化剂流率和料位高度等５个操作变量的最优轨迹。     

Energy saving in a crude distillation unit with a divided wall column

An energy-efficient crude distillation unit (CDU) with a divided wall column was introduced to evaluate its performance compared to the conventional CDU. The large energy demand of the CDU in the United States—equivalent to more than a half of biofuel produced—was reduced by applying a divided wall column to the unit also known as the energy-efficient distillation column. The divided wall column lowers mixing at feed tray and raises the thermodynamic efficiency of the CDU. The performance evaluation of the proposed unit indicates that the unit saves 37% of heat supply over the conventional unit and cooling by 17%. The economic analysis shows a 9% of investment saving and a 26% decrease in the utility cost from the proposed unit. The thermodynamic efficiency of the proposed CDU is improved by 8%. The modification of conventional CDU was minimal, suggesting an easy revamping of the current conventional CDUs.