On-line optimization of the Tennessee Eastman challenge problem

On-line, optimal steady state operating conditions were determined for the six modes of operation (with and without disturbances) for the industrial recycle reactor problem proposed by Downs and Vogel (J.J. Downs, E.F. Vogel, A plant-wide industrial process control problem, Computers and Chemical Engineering 17 (1993) 245–255.). The optimization and modeling problem was formulated as a sequential solution of steady state material balances through the process. Optimal operating setpoints were obtained using NPSOL (P.E. Gill et al., User's Guide for NPSOL: A FORTRAN Package for Nonlinear Programming, Technical Report SOL86-2, Stanford University, CA, 1986.) and reactor feed material balances as equality, non-linear constraints. On-line optimization results, without disturbances, compared favorably with the results obtained by Ricker (N.L. Ricker, Optimal steady-state operation of the Tennessee Eastman challenge process, Computers and Chemical Engineering 19 (1995) 949–959.). The optimization objective function tended to be broad and flat around the optimal operating conditions for all six modes of operation. The on-line, steady state, optimization algorithm compared favorably with the more complicated optimization structure designed by Yan (M. Yan, N. L. Ricker, On-line optimization of the Tennessee Eastman challenge process, in: Proceedings of the 1997 American Control Conference.). However, the algorithm presented here required less computational effort and exhibited greater convergence reliability than the work of Yan. On-line optimization was performed every 8 h and required less than 5 min calculation time. Updated model parameters were calculated every minute and filtered using a first order filter with 15 min time constant. Net profit was introduced as a tool to compare economic performance of the plant operating under a knowledgeable operator and operating under an off-line/on-line optimization algorithm for all six modes of operation. For modes 1–3, operating at the setpoints generated by the optimization algorithm provided significant increases in production rate and net profit that amounted to a 16–45% decrease in product operating costs when compared to operation of the plant at the setpoints specified by an operator. By decreasing operating costs and increasing production rate while maintaining a specified G/H ratio, the optimization algorithm increased net profit by 9.3–0.5% for modes 4–6, respectively, when compared to knowledgeable operator optimization of the plant. Also for sustained disturbances, the optimization algorithm decreased the error in the desired G/H ratio and increased process stability when compared to knowledgeable operator optimization of the plant. On-line optimization provided a maximum 1% relative increase in production rate and 1.5% relative increase in net profit compared to off-line optimization for modes 4–6 only when certain sustained, disturbances occurred. The economic justification of on-line optimization over off-line optimization depends upon the type, magnitude, and frequency of the disturbances.     

Double closed-loop optimal control of greenhouse cultivation

Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is investigated. Recent developments enable closure of the outer-loop of this control system because they facilitate on-line recomputation of the optimal control of the slow dynamics on a daily basis. This paper quantifies the benefits obtained from having an outer closed-loop that counteracts errors and changes concerning predictions of crop growth, long-term weather, revenues obtained from selling crops and costs to control greenhouse climate. As a special, important case LED lighting is considered which increases both crop growth and profit. Having an outer closed-loop is especially beneficial in this case.     

工业过程多速率分层运行优化控制

工业过程运行优化控制通常采用基础回路层和运行层两层结构,涉及不同时间尺度特性的被控对象,且由于检测装置采样周期不同难以统一控制与采样周期;此外,运行层动态往往机理复杂难以建模.因此针对这一多层次、多时间尺度且部分模型未知的复杂多速率控制问题,本文提出一种工业过程多速率分层运行优化控制方法.该方法在使用提升技术解决分层多速率问题的基础上,采用一种基于Q-!学习的数据驱动运行层设定值优化方法,更新基础回路层的设定值;并针对提升后的系统采用模型预测控制（Model predictive control,MPC）方法设计基础回路层控制器以跟踪设定值,从而实现运行指标的优化控制.对典型工业闭路磨矿过程进行了仿真实验,验证了本文所提方法的有效性.     

A new approach to inversion-based feedforward control design for nonlinear systems

The finite-time transition between stationary setpoints of nonlinear SISO systems is considered as a scenario for the presentation of a new design approach for inversion-based feedforward control. Design techniques which are based on a stable system inversion result in input trajectories with pre- and/or post-actuation intervals. The presented approach treats the considered transition task as a two-point boundary value problem (BVP) and yields causal feedforward trajectories, which are constant outside the transition interval. The main idea of this approach is to provide free parameters in the desired output trajectory to solve the BVP of the internal dynamics. Thereby, a standard MATLAB function can be used for the numerical solution of the BVP. Feedforward control design techniques are illustrated by simulation results for a simple example.     

Greenhouse climate fuzzy adaptive control considering energy saving

This paper proposes a fuzzy adaptive control approach to solve greenhouse climate control problem. The aim is to ensure the controlled environmental variables to track their desired trajectories so as to create a favorable environment for crop growth. In this method, a feedback linearization technique is first introduced to derive the control laws of heating, fogging and CO2 injection, then to compensate for the saturation of the actuators, a fuzzy logic system (FLS) is used to approximate the differences between controller outputs and actuator outputs due to actuator constraints. A robust control term is introduced to eliminate the impact of external disturbances and model uncertainty, and finally, Lyapunov stability analysis is performed to guarantee the convergence of the closed-loop system. Taking into account the fact that the crop is usually insensitive to the change of the environment inside the greenhouse during a short time interval, a certain amount of tracking error of the environmental variables is usually acceptable, which means that the environmental variables need only be driven into the corresponding target intervals. In this case, an energy-saving management mechanism is designed to reduce the energy consumption as much as possible. The simulation results illustrate the effectiveness of the proposed control scheme.

     

AI approaches to identification and control of total plant production systems

Recent progress in intelligent control techniques has enabled complex systems such as cultivation and fruit-storage processes to be dealt with. This paper presents the application of a hierarchical intelligent control system, which consists of an expert system and an optimizer based on neural networks and genetic algorithms, for optimizing a total plant production process. Environmental factors in the cultivation and storage processes are optimally controlled, based on the physiological status of the plant (or fruit). The expert system determines suitable environmental setpoints throughout growth, and the optimizer determines optimal environmental setpoints during important growth stages and during storage, based on plant responses. In the optimizer, neural networks were used for the identification of plant responses to environmental factors, and genetic algorithms were used to search for the optimal environmental setpoints through the simulation of the identified models. Optimal setpoints of the nutrient concentration in hydroponic tomato cultivation and optimal setpoints of the temperature during tomato storage were determined using this control technique.     

Nonlinear MPC based on a Volterra series model for greenhouse temperature control using natural ventilation

Suitable environmental conditions are a fundamental issue in greenhouse crop growth and can be achieved by advanced climate control strategies. In different climatic zones, natural ventilation is used to regulate both the greenhouse temperature and humidity. In mild climates, the greatest problem faced by far in greenhouse climate control is cooling, which, for dynamical reasons, leads to natural ventilation as a standard tool. This work addresses the design of a nonlinear model predictive control (NMPC) strategy for greenhouse temperature control using natural ventilation. The NMPC strategy is based on a second-order Volterra series model identified from experimental input/output data of a greenhouse. These models, representing the simple and logical extension of convolution models, can be used to approximate the nonlinear dynamic effect of the ventilation and other environmental conditions on the greenhouse temperature. The developed NMPC is applied to a greenhouse and the control performance of the proposed strategy will be illustrated by means of experimental results.     

端边云协同的复杂工业过程运行控制智能系统

针对难以建立数学模型的复杂工业运行控制过程,利用可获得的过程控制系统设定值和运行指标以及相关变量的工业大数据和运行控制过程特性,将系统辨识与深度学习相结合,建立以实际运行指标以及相关变量为输入,以实际过程控制系统设定值为输出的运行控制过程数字孪生模型,提出云-边协同的过程控制系统设定值智能控制方法.所提出方法由云-运行控制过程数字孪生模型、边-过程控制系统设定值智能控制模型和自校正机制组成.将工业互联网与工业过程控制系统相结合,提出端边云协同的工业运行控制智能系统的架构和功能,采用所提出控制系统设定值智能控制方法,研制工业过程运行控制智能系统,并在选矿关键设备—–高压辊磨成功应用.所提出系统安全、可靠和优化运行,取得了显著的节能减排效果.     

小型农作物温室大棚二氧化碳浓度监测系统

针对小型农作物温室环境指标监测的需要,设计实现了农作物温室大棚二氧化碳浓度监测系统。采用STC系列单片机控制,对农作物大棚内二氧化碳浓度进行近距离实时监测,采用TFT彩屏显示实时值和动态曲线,具有阀值调节,超过阀值报警,可实现小型温室农作物的生长环境二氧化碳浓度的实时监控。     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.     

Hamilton-Jacobi-Bellman formalism for optimal climate control of greenhouse crop

The paper describes a simplified dynamic model of a greenhouse tomato crop, and the optimal control problem related to the seasonal benefit of the grower. A HJB formalism is used and the explicit form of the Krotov-Bellman function is obtained for different growth stages. Simulation results are shown.     

Reducing energy consumption through trajectory optimization for a metro network

The techniques of optimal control and optimization are applied to a practical problem of reducing energy consumed by the Montreal Metro (subway) system. The problem considered is the determination of tunnel trajectories in the "equivalent" vertical plane when trains traveling in both directions must follow the same trajectory. The problem is first formulated as a control problem with control and state constraints. Then, under certain simplifying assumptions, an heuristic method employing a direct search algorithm is presented and used in the trajectory optimization. The trajectories are optimized to reduce the sum of the energy consumed by the trains traveling in both directions on the trajectory. The results show an average reduction of 7.73 percent in energy consumption as compared with existing trajectories. The trajectories found using the method presented here will be followed in future tunnel construction.     

Nested partitions for global optimization in nonlinear model predictive control

In Nonlinear Model Predictive Control (NMPC), the optimization problem may be nonconvex. It is important to find a global solution since a local solution may not be able to operate the process at desired setpoints. Also the solution must be available before the control input has to be applied to the process. In this paper, a stochastic algorithm called the Nested Partitions Algorithm (NPA) is used for global optimization. The NPA divides the search space into smaller regions and either concentrates search in one of these regions called the most promising region or backtracks to a larger region in the search space based on a performance index. To adapt the NPA to solve dynamic NMPC with continuous variables, a new partitioning scheme is developed that focuses on the first few control moves in the control horizon. The expected number of iterations taken by the NPA is presented. Convergence speed is improved by reducing the size of the starting most promising region based on a good starting point. The discrete sampling nature of the NPA may cause difficulty in finding the global solution in a continuous space. A gradient-based search is used with the NPA to overcome this difficulty. The solution quality is assessed in terms of the error from the actual global minimum. The algorithm is shown to give a feasible solution that provides asymptotic stability. Case studies are used to show the algorithm performance in terms of tracking setpoints, cost, solution quality and convergence time.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.     

双层预测控制中保证动态控制可行的稳态目标计算策略

在双层结构模型预测控制(Model predictive control, MPC)中, 稳态目标计算(Steady-state targets calculation, SSTC)层(上层)为动态控制(Dynamic control, DC)层(下层)提供操作变量、被控变量设定值和变量约束. 但是,上层可行域和下层吸引域间存在的不一致性可能使得上层给出的设定值无法实现. 本文为下层事先选取若干组放松的软约束, 并对每一组软约束都离线计算出相应的吸引域, 其中最大的一个吸引域包含稳态目标计算的可行域. 在控制过程中, 根据当前状态所属吸引域在线地决定在DC层采用的软约束组. 采用上述方法后, 对所有处于最大吸引域的初始状态, 在跟踪稳态目标的过程中, 下层优化问题都是可行的. 仿真算例证明了该方法的有效性.     

Design of noise and period-time robust high-order repetitive control, with application to optical storage

Repetitive control is useful if periodic disturbances or setpoints act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period time and for reduction of the error spectrum in-between the harmonic frequencies. The high-order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.     

Dynamic start-up optimization of a plate reactor with uncertainties

In this paper, start-up of a plate reactor with an exothermic reaction is considered. Dynamic optimization is used to obtain start-up trajectories, while a feedback control system is designed for on-line control. The problem is challenging, since the process model is highly nonlinear, and subject to uncertainty. Limited bandwidth of the feedback control system requires that the optimization gives optimal solutions with low sensitivity to uncertainty. Special attention is given to the problem of formulating an optimal control problem based on physical insight to reduce the sensitivity of the solution, thus increasing the overall robustness of the closed loop system. The resulting solutions are evaluated in Monte Carlo simulations. The study shows that introducing concentration constraints on the injected chemical in combination with high frequency penalties on the control signals lead to less sensitive optimal solutions, thus yielding a more robust start-up. Automatic computer tools that greatly simplifies the task of formulating complex dynamic optimization problems have been used to obtain the start-up trajectories and are briefly presented.     

基于物联网技术的设施农业在线监控系统

运用物联网技术、嵌入式技术和云服务器技术设计一套基于物联网技术的设施农业在线监控系统,该系统能实时监测农业环境参数信息和作物生长状况,实现对分散在各地的温室环境进行状态监测、设备远程智能控制及实时的在线数据、图像视频查询与信息服务。从而使温室的环境适宜作物生长,提高资源利用率。