Energy-efficient receding horizon trajectory planning of high-speed trains using real-time traffic information

Optimal trajectory planning of high-speed trains (HSTs) aims to obtain such speed curves that guarantee safety, punctuality, comfort and energy-saving of the train. In this paper, a new shrinking horizon model predictive control (MPC) algorithm is proposed to plan the optimal trajectories of HSTs using real-time traffic information. The nonlinear longitudinal dynamics of HSTs are used to predict the future behaviors of the train and describe variable slopes and variable speed limitations based on real-time traffic information. Then optimal trajectory planning of HSTs is formulated as the shrinking horizon optimal control problem with the consideration of safety, punctuality, comfort and energy consumption. According to the real-time position and running time of the train, the shrinking horizon is updated to ensure the recursive feasibility of the optimization problem. The optimal speed curve of the train is computed by online solving the optimization problem with the Radau Pseudo-spectral method (RPM). Simulation results demonstrate that the proposed method can satisfy the requirements of energy efficiency and punctuality of the train.     

A hybrid method for hydroelectric generation scheduling using an artificial neural network

This paper presents a decomposition method for finding an optimal operating policy of interconnected hydroelectric power plants using an artificial neural network. The coupling constraints on reservoir storage at the end of the planning horizon are relaxed using coordinating multipliers that result in interval wise decomposition of the overall problem. Resulting subproblems are solved sequentially, which reduces the complexity of the problem. Each subproblem is solved using a two-phase neural network approach. An efficient heuristic algorithm is developed to find the feasible solution. A case study considering scheduling of the Bhakra-Beas reservoir system is also presented in this paper. The new method demonstrates the potential of achieving an improved performance.     

Shrinking‐horizon dynamic programming

We describe a heuristic control policy for a general finite‐horizon stochastic control problem, which can be used when the current process disturbance is not conditionally independent of the previous disturbances, given the current state. At each time step, we approximate the distribution of future disturbances (conditioned on what has been observed) by a product distribution with the same marginals. We then carry out dynamic programming (DP), using this modified future disturbance distribution, to find an optimal policy, and in particular, the optimal current action. We then execute only the optimal current action. At the next step, we update the conditional distribution, and repeat the process, this time with a horizon reduced by one step. (This explains the name ‘shrinking‐horizon dynamic programming’). We explain how the method can be thought of as an extension of model predictive control, and illustrate our method on two variations on a revenue management problem. Copyright © 2010 John Wiley & Sons, Ltd.     

Real-time energy management for electric arc furnace operation

Electric arc furnaces are used extensively in the steel industry for steel production. Development of energy savings strategies for the highly energy-intensive batch process is extremely challenging due to the complexity of the process and lack of measurements due to the harsh operating conditions. Here we introduce a new energy management approach that effectively curtails the energy cost in real-time through the implementation of economically optimal operating decisions. An economics- oriented shrinking horizon nonlinear model predictive control (NMPC) algorithm that exploits time-varying electricity prices is coupled with a multi-rate moving horizon estimator (MHE) to form an integrated decision- making framework. With a detailed first-principles dynamic model functioning at the core, the multi-variable interactions and plant variations are successfully incorporated into the control strategy to achieve reliable performance. We also present a novel initialization scheme for obtaining fast on-line solutions of the economic NMPC and multi-rate MHE dynamic optimization problems. Using this initialization algorithm, we show that the optimal input decisions are obtained with sufficient computational speed for real-time implementation. The energy usage optimization results indicate a significant reduction in the operating cost and peak electricity demand compared to the case where the electricity price profile is not updated.     

Consistent hierarchical economic NMPC for a class of hybrid systems using neighboring-extremal updates

A hierarchical two-layer control algorithm is developed for a class of hybrid (discrete-continuous dynamic) systems to support economically optimal operation of batch or continuous processes with a predefined production schedule. For this class of hybrid systems, the optimal control moves as well as the controlled switching times between two adjacent modes are determined online. In contrast to closely related schemes for integrated scheduling and control, the sequence of modes is not optimized. On the upper layer, the economic optimal control problem is solved rigorously by a slow hybrid economic model predictive controller at a low sampling rate. On the lower layer, a fast hybrid neighboring-extremal controller is based on the same economic optimal control problem as the slow controller to ensure consistency between both layers. The fast neighboring-extremal controller updates rather than tracks the optimal trajectories from the upper layer to account for disturbances. Consequently, the fast controller steers the process to its operational bounds under disturbances and the economic potential of the process is exploited anytime. The suggested two-layer control algorithm provides fully consistent control action on the fast and slow time-scale and thus avoids performance degradation and even infeasibilities which are commonly encountered if inconsistent optimal control problems are formulated and solved.     

A sparse and condensed QP formulation for predictive control of LTI systems

The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. We present a formulation where the input is expressed as an affine function of the state such that the closed-loop dynamics matrix becomes nilpotent. Using this approach and removing the equality constraints leads to a compact and sparse optimization problem to be solved at each sampling instant. The problem can be solved with a cost per interior-point iteration that is linear with respect to the horizon length, when this is bigger than the controllability index of the plant. The computational complexity of existing condensed approaches grow cubically with the horizon length, whereas existing non-condensed and sparse approaches also grow linearly, but with a greater proportionality constant than with the method presented here.     

A fuzzy control system with application to production planning problems

A considerable part of the literature on fuzzy sets is devoted to the field of fuzzy control system. In this paper, an alternative control system is introduced to describe a dynamic system with fuzzy white noise. In order to find optimal ways to control such a system, fuzzy optimal control theory is further developed. Specifically, a linear quadratic model is formulated and solved as a fuzzy optimal control problem. The formulation and solution of this model provide an economic interpretation of a production planning model both in the finite horizon and in the infinite horizon.     

聚合物驱最优控制问题求解算法的设计与实现

为了获得聚合物驱油的最大利润,通过最优控制来确定聚合物的最佳注入策略是一种有效的方法。该最优控制问题的数值解涉及到油藏数值模拟、伴随方程和非线性规划问题。给出了基于面向对象的算法设计方案及其实现细节。利用全隐式差分格式离散化聚合物驱模型,并采用Newton-Raphson求解所得到非线性方程组,在求解前向模型的同时构造了伴随方程。对一个三维聚合物驱注入问题进行了实例求解,表明了所实现算法的实用性和有效性。     

On the finite time performance of model predictive control

This paper addresses the finite time performance of model predictive control (MPC) for linear-time-invariant (LTI) systems without constraints. The performance of MPC is compared with that of finite horizon optimal control to find out how well model predictive control can perform relative to the optimal performance with the same or different horizons. By exploring the properties of the Riccati difference equation (RDE), an upper and a lower bound of the ratio between the finite time performance of MPC and finite horizon optimal cost are obtained. It is possible to extend the obtained results to more complicated systems such as nonlinear dynamic systems with constraints with appropriate generalizations. Simulation example supports our results.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.     

Robust model predictive control using tubes

A form of feedback model predictive control (MPC) that overcomes disadvantages of conventional MPC but which has manageable computational complexity is presented. The optimal control problem, solved on-line, yields a ‘tube’ and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty; computational complexity is linear (rather than exponential) in horizon length. Asymptotic stability of the controlled system is established.     

应用离散事件系统控制理论求解生产调度的新方法

众所周知, 生产调度问题属组合优化问题, 一般来说不存在求得精确最优解的多项式算法. 因此, 对于大规 模调度问题, 人们应用启发式算法和元启发式算法以企求得满意解. 在实际的应用中, 许多工业过程需要满足严格 的工艺约束. 对于这类过程的调度问题, 很难应用启发式算法和元启发式算法, 因为这些方法难于保证所求得调度 的可行性. 为了解决这一问题, 本文以半导体芯片制造中组合设备的调度问题作为例子, 介绍了一种基于离散事件 系统控制理论的生产调度新方法. 利用Petri网建模, 任何违反约束的状态均被描述为非法状态, 而使非法状态出现 的调度则是不可行调度. 通过可行调度的存在性分析, 该方法获得可行解空间并将调度问题转化为连续优化问题, 从而可以有效求解. 并且指出, 该方法可以应用于其他应用领域.     

基于遗传算法的滚动调度策略*

本文研究了动态加工环境下的一类Ｊｏｂ－Ｓｈｏｐ调度问题，提出了一种基于遗传算法的滚动调度策略，其要点是：１）借鉴预测控制的思想，采用ｔｉｍｅ－ｂａｓｅｄ和ｊｏｂ－ｂａｓｅｄ的滚动调度策略适应动态环境和要求的多变性。２）以遗传算法和分派规则相结合，处理考虑与操作序列有关的工件安装时间和工件到期时间约束的复杂调度问题。文中给出了在工件到期时间发生改变的动态环境中两种滚动调度算法的调度结果，并与静态调度     

Medium term scheduling of a hydro-thermal system using stochastic model predictive control

A multistage stochastic programming formulation is presented for monthly production planning of a hydro-thermal system. Stochasticity from variations in water reservoir inflows and fluctuations in demand of electric energy are considered explicitly. The problem can be solved efficiently via Nested Benders Decomposition. The solution is implemented in a model predictive control setup and performance of this control technique is demonstrated in simulations. Tuning parameters, such as prediction horizon and shape of the stochastic programming tree are identified and their effects are analyzed.     

Control of the common rail pressure in gasoline engines through an extended state observer based MPC

In this paper, a model predictive control (MPC) solution, assisted by extended state observer (ESO), is proposed for the common rail pressure control in gasoline engines. The rail pressure dynamic, nonlinear with large uncertainty, is modeled as a simple first order system. The discrepancy of the model from the real plant is lumped as ``total disturbance'', to be estimated in real-time by ESO and then mitigated in the nonlinear MPC, assuming the total disturbance does not change in the prediction horizon. The nonlinear MPC problem is solved using the Newton/generalized minimum residual (GMRES) algorithm. The proposed ESO-MPC solution, is compared with the conventional proportional-integral-differential (PID) controller, based on the high-fidelity model provided in the benchmark problem in IFAC-E-CoSM. Results show the following benefits from using ESO-MPC relative to PID (benchmark): 1) the disturbance rejection capability to fuel inject pulse step is improved by 12% in terms of recovery time; 2) the transient response of rail pressure is improved by 5% in terms of the integrated absolute tracking error; and 3) the robustness is improved without need for gain scheduling, which is required in PID. Additionally, increasing the bandwidth of ESO allows reducing the complexity of the model implemented in MPC, while maintaining the disturbance rejection performance at the cost of high noise-sensitivity. Therefore, the ESO-MPC combination offers a simpler and more practical solution for common rail pressure control, relative to the standard MPC, which is consistent with the findings in simulation.     

多速率分段线性系统预测控制的显式设计

针对输出采样周期是输入更新周期N倍的多速率分段线性(Piecewise linear, PWL)系统, 本文提出了保证稳定性的显式预测控制器设计方法. 首先, 基于动态规划原理将预测控制优化问题分解为多个单级优化问题; 然后, 根据分段线性系统各子模型以及目标函数的具体形式, 进一步将各单级优化问题分为若干个子问题, 再利用多参数二次规划(Multiparametric quadratic programming, MP-QP)方法求解;最后,通过比较各子问题的解从而得到系统的最优显式控制律. 在设计过程中, 将系统的最大正不变集作为优化问题的终端约束集, 从而保证了系统的稳定性. 仿真结果表明本文提出的显式预测控制方法能够有效降低多速率分段线性系统的在线计算时间, 在保证系统稳定性的同时, 满足其对输入更新速度的要求.     

An application of model predictive control to the dynamic economic dispatch of power generation

Two formulations exist for the problem of the optimal power dispatch of generators with ramp rate constraints: the optimal control dynamic dispatch (OCDD) formulation based on control system models, and the dynamic economic dispatch (DED) formulation based on optimization. Both are useful for the dispatch problem over a fixed time horizon, and they were treated as equivalent formulations in literature. This paper first shows that the two formulations are in fact different and both formulations suffer from the same technical deficiency of ramp rate violation during the periodic implementation of the optimal solutions. Then a model predictive control (MPC) approach is proposed to overcome such a technical deficiency. Furthermore, it is shown that the MPC solutions, which are based on the OCDD framework, converge to the optimal solution of an extended version of the DED problem and they are robust under certain disturbances and uncertainties. Two standard examples are studied: the first one of a ten-unit system shows the difference between the OCDD and DED, and possible ramp rate violations, and the second one of a six-unit system shows the convergence and robustness of the MPC solutions, and the comparison with OCDD as well.     

MINLP‐based hybrid strategy for operating mode selection of TES‐backed‐up refrigeration systems

This brief deals with the satisfaction of the daily cooling demand by a hybrid system that consists of a vapor‐compression refrigeration cycle and a thermal energy storage (TES) unit, based on phase change materials. The addition of the TES tank to the original refrigeration plant allows to schedule the cooling production regardless of the instantaneous demand, given that the TES tank can store cold energy and release it whenever deemed appropriate. The scheduling problem is posed as an optimization problem based on mixed‐integer nonlinear programming (MINLP) since it includes both discrete and continuous variables. The latter corresponds to the references on the main cooling powers involved in the problem (cooling production at the evaporator and TES charging/discharging), whereas the discrete variables define the operating mode scheduling. Therefore, in addition to the hybrid features of the physical plant, a hybrid optimal control strategy is also proposed. A receding horizon approach is applied, similar to model predictive control (MPC) strategies, while economic criteria are imposed in the objective function, as well as feasibility issues. The TES state estimation is also addressed since its instantaneous charge ratio is not measurable. The proposed strategy is applied in simulation to a challenging cooling demand profile, and the main advantages of the MINLP‐based strategy over a nonlinear MPC‐based scheduling strategy previously developed are highlighted, regarding operating cost, ease of tuning, and ability to adapt to cooling demand variations.