文献翻译-皮带输送机运行效率的最优控制

英文原文Optimal Control of Operation Efficiency of Belt Conveyor1Shirong Zhang and Yuling TangDepartment of Automation, Wuhan University, Wuhan 430072, ChinaEmails: (S. Zhang); (Y. Tang)AbstractIn literature, variable speed control of belt conveyors is recommended to save energy consumption. However, the current implementations mostly focus on lower level control loops without operational considerations at the system level. This paper intends to take a model based optimization approach to improve the operation efficiency of belt conveyors with consideration of various constraints. Specifically, three optimization problems of a typical belt conveyor system are formulated, respectively, with solutions in simulation for a case study.I. INTRODUCTIONMaterial handling forms an important sector of industry, where a considerable proportion of the total power supply is consumed. For instance, material handling contributes about 10% of the total maximum demand in South Africa 1. Belt conveyors are widely employed to form the key parts of material handling systems because of their high efficiency of transportation. Hence, it is important to improve energy efficiency of belt conveyors. In 2, energy efficiency of an energy system is cast to four levels: performance, operation, equipment and technology. Specifically, the improvement ofenergy efficiency of belt conveyors are generally achieved at operation and equipment levels.In practice, the equipment efficiency of belt conveyors is mainly improved by equipment retrofitting or replacement. The idler 34, belt 5 and drive system 6 are the main targets. The equipment oriented strategy needs extra investment and the improvement opportunities are limited to certain parts. Operation efficiency of an energy system is usually improved through the coordination of two or more internal subsystems,or through the coordination of the system components and time, or through the coordination of the system and human operators 2. Specifically, variable speed drive (VSD) is proposed for operation efficiency of belt conveyors in literature789 and 10. It improves operation efficiency of belt conveyors by the coordination of belt speed and feed rate.However, The current strategies of speed control employ lower control loops to improve the operation efficiency of belt conveyors without consideration of system constraints and external constraints, such as time-of-use (TOU) tariff and production requirement. The main propose of this paper is to use the methodology of optimization to improve the operation efficiency of belt conveyors and satisfy various constraints atthe same time. We begin with an analytical energy model.Supported by the Fundamental Research Funds for the Central Universities Then three optimization problems with regard to a typical belt conveyor will be formulated. The optimization will be done at the operation level with performance indicators, energyconsumption and energy cost, employed as the objectives of the optimization. In addition, the time-of-use (TOU) tariff and the constraints from the production requirement, the feed rate, the belt speed, the unit mass and the ramp rate of the belt speed will be taken into account. The simulation results will be presented.The layout of the paper is as follows: In section 2, an analytical energy model is reviewed. Section 3 proposes three optimization problems with regard to the energy efficiency of belt conveyors. In section 4, the simulation results of the three optimization problems are presented. The last section is conclusion.II. ENERGY MODELA practical energy model is much needed for the optimization of the operation efficiency of belt conveyors. In 11, an analytical energy model of belt conveyors is proposed. This analytical energy model is as follows（1）6.3),(242321 TVVTVfP where f P (V, T) is the power of the belt conveyor (kW), V is the belt speed (m/s), T is the feed rate (t/h) and 14 are the coefficients, which come from the design parametersof belt conveyors or are obtained by parameter identification. Moreover, V and T obey the following relation: T = 3.6QGV , where QG is the unit mass of the material along the belt (kg/m). Incorporated with the efficiency of the drive system, model (1) is rewritten as follows（2）mdPTVVTVf *6.3),( 242321 where m and d are the efficiency of motor and the drive, respectively. The analytical energy model (2) is suitable for the energy optimization of belt conveyors.III. OPERATION EFFICIENCY OPTIMIZATIONThe operation efficiency of a belt conveyor can be improved through the coordination of its belt speed and feed rate or through the coordination of its operation status and time. In fact, the coordination of belt speed and feed rate is reflected as the variable speed drive or speed control in literature. Generally, the operation efficiency of an energy system contributes The operation efficiency of a belt conveyor can be improved through the coordination of its belt speed and feed rate or through the coordination of its operation status and time. In fact, the coordination of belt speed and feed rate is reflected as the variable speed drive or speed control in literature. Generally,the operation efficiency of an energy system contributesFor a belt conveyor, the total energy consumption, JE, is related to the electrical power and the time period for calculation. It can be expressed as an integration of theelectrical power, fP (V, T), between t0 and tf as follows（3）ftPEdtTVJ0)(,where t0 tf is the time period for total energy consumption calculation. Similarly, the total energy cost, JC, can be calculated as follows（4）ftPCtptJ0 )(),(where p(t) is the TOU tariff function. JE and JC are performance indicators, which are to be employed as the objectives of the following optimization problems. A belt conveyor may be operated in different ways. Accordingly, several optimization problems of operation efficiency of belt conveyor will be investigated.A. Optimization problem oneFor a typical belt conveyor, as shown in Fig.1, generally, there is a total production requirement, TSUM, over a certain time period, t0 tf . In this optimization problem, the total energy consumption, JE, is taken as the objective for minimization. Three variables, belt speed, feed rate and working time, denoted by tw, will be optimized to minimize the total energy consumption. The constraints for this optimization problem are listed as follows.1) The belt speed should be within its feasible domain,0 V VMAX.2) The unit mass should be within its feasible domain, 0 QG QGMAX.3) The total production of the belt conveyor is great thanor equal to its requirement, T.tw TSUM.4) The working time is within t0 tf , 0 tw (tf t0).Eventually, optimization problem one is formulated asmin JE(V, T, tw) = fP (V, T)tw,subject to0 V VMAX,0 QG QGMAX,T.tw TSUM0 tw (tf t0). (5)V , T, and tw are the optimization variables of this problem. The solution, denoted by V , T, and tw, is the optimal operational instruction, which schedules the belt speed, feed rate, and working time of the belt conveyor optimally to minimize the energy consumption subject to the above constraints. 图 1 试验皮带机示意图B. Optimization problem twoThis optimization problem considers the energy cost of the belt conveyor subject to TOU tariff. We take JC, a performance indicator, as the objective of this problem. Forease of discrete-time numerical analysis, the cost function (4) are discretized. Let the sampling time t s = tft0 N , we can obtain the discrete form of total energy cost as（6）j sjjpCtTVfJ1)(where V j , T j , and p j are the belt speed, the feed rate, and the electricity price at the jth sample time. In optimization problem two, the optimization variables, V and T, are vectors instead of scalar as in problem one. Optimization problem two shares the first two constraints of problem one. However, the third one, concerning the total production, is lightly different from that of problem two and should be expressed as（7）SUMNjsTt1Hence, this optimization problem is finally formulated as followsThe solution to this problem, , is the operational instructions for 1:,NjTVjthe belt conveyor, where and 221NTC. Optimization problem threeThis optimization problem is similar to problem two. The difference between the two is that optimization problem three takes an extra issue, ramp rate of belt speed, into account during the optimization. In practice, large ramp rate of belt speed does harm to certain equipment or components of the belt conveyor. One way to reduce the ramp rate of belt speed is to integrate it into the objective function for minimization. Thus, an additional part, is added to the objective function (6). The NjjjV12)(modified objective function is expressed as follows（9）121 )(),(NjjjNj sjjpC VtTfJwhere _ is a weight, which is employed to balance the economic performance and the technical specification. Thus, optimization problem three is formulated asIn this section, the three optimization problems are solved through simulation for a typical belt conveyor, as shown in Fig.1. The belt conveyor is supposed to have the sameparameters as that used for case study in 11. Hence, we get the coefficients of energy model as = 2.373104 8.566 103 0.0031 51.680T . The efficiency of the motor and the drive, m and d, are set to 0.941 and 0.945, respectively. The optimization interval and sampling time are set to 24 hours and 10 minutes, hence, the sample number N = 144.The TOU tariff is an important input of problem two and problem three. In this case study, It can be described bywhere t is the time of any day in hours (from 1 to 24); po, ps and pp are the off-peak, standard and peak TOU energy tariff in an anonymous monetary unit, A/kWh. The values of po, ps and pp vary according to the time of day, the day of the week as well as the season. We take the high-demand season June- August for investigation where po=0.6304 A/kWh, ps=0.0906 A/kWh and pp=0.1667 A/kWh.For the sake of reliability and feasibility, most of the belt conveyors are intentionally over designed, consequently, the belt conveyors fulfil the required tasks with reduced working time. Considering this practical condition, we set the totalproduction requirement, TSUM, to 43,200 t, 33,600 t and 24,000 t for investigation, respectively. They equal to 90%, 70%, and 50% of the maximum amount of material that can be transferred by the belt conveyor within 24 hours. Similar results are obtained under the three conditions. Specifically, the simulation results of the three optimization problems with.TSUM=33,600 t are presented.The proposed three optimization problems are real-value optimization problems. All simulations are carried out in the MATLAB environment. Specifically, the fmincon function of MATLAB Optimization Toolbox is used to solve these problems.Firstly, optimization problem one is simulated with TSUM=33,600 t. The simulation result is shown as Fig.2. optimization problem one does not consider the TOU tariff,consequently, its feed rate and belt speed keep constant all through. For a given total production requirement, the belt speed and feed rate of optimization problem one are reduced in tandem to obtain the minimum energy consumption by extending the working time. Secondly, optimization problem two is simulated with TSUM=33,600 t. The simulation result is shown as Fig.3. The TOU tariff is integrated into the objective of problem two. Consequently, the optimal solution to problem two runs the belt conveyor with maximum capacity during off peak time, operates the belt conveyor with reduced feed rate and belt speed during standard time, further, stops the belt conveyorduring peak time as shown in Fig.3. Hence, load shifting of the belt conveyor is also achieved through the operation efficiency optimization. Problem two does not deal with the ramp rate of belt speed, hence, large changes happen to both the belt speed and feed rate. It may harm certain equipment or components of belt conveyors. Thirdly, optimization problem three is simulated with result as shown in Fig.4. Two values, 50 and 500, are selected for to show the influence from the weight. Problem three involves ramp rate of belt speed into objective for minimization, consequently, the belt speed and feed rate in this problem are much smoother than those in problem two. Moreover, the weight affects the ramp rate in such a way that a larger results in smoother belt speed and feed rate, as shown in Fig.4. Further, The corresponding energy consumption and energy cost of the three optimization problems with TSUM=33,600 t are listed in Tab.I. As shown in Tab.I, transferring the same amount of material within one day, optimization problem one consumes the least energy, however, it results in the highest energy cost because the TOU tariff is not considered by this optimization problem. Optimization problem threeconsumes more energy, consequently, results in more cost than problem two. However, this sacrifice is compensated by the improvement of the profiles of the belt speed and feed rate. As can be seen, integrating a technical constraint into the objective function can indeed balance an economic indicator and a technical indicator.V. CONCLUSIONBelt conveyors are consuming a considerable part of the total energy supply. This paper focuses on the energy saving of belt conveyors through the improvement of operation efficiency where optimization is employed. We begin with the energy model of belt conveyors which is the base of optimization. Subsequently, energy optimization is put to belt conveyors at the operation level. Three optimization problems concerning different aspects of the belt conveyors are proposed and formulated. A typical belt conveyor system is used for simulation. It is shown by simulation that the variable speedcontrol of belt conveyors can indeed save energy. A belt conveyor can be driven in its optimal operation efficiency through the optimization of its performance indicators, e.g.,energy consumption or energy cost. With the consideration of TOU tariff, load shifting is achieved by operation efficiency optimization. Further, by integrating a technical issue into the objective function, a balance between the economic indicator and the technical indicator can be obtained.In this paper, the operation efficiency optimization of belt conveyors is formulated as general optimal control problems, hence, various optimization techniques and tools can be used. Further, extra constraints, e.g., the ones from silo capacity or stockpile capacity, can be easily formulated.中文译文皮带输送机运行效率的最优控制张世荣 唐玉玲（武汉大学机械工程学院，武汉，430072）摘要：本文通过对皮带输送机变频调速控制的研究，以节省能源消耗。然而，基于目前的皮带机运行主要集中在较低的水平控制回路，还没有在系统一级业务的考虑。本文拟采取的优化模型与方法，以提高各种限制皮带输送机的工作效率。特别地，通过三个典型输送带系统优化问题，分别制定对模拟解决方案进行了案例研究。1. 引言目前的物料运输已经形成了一个产业，那里消耗相当大的比例总电源，是社会中重要的部门。例如，在南非 1，物料运输贡献了大约 10总最高需求量。皮带输送机广泛采用，形成物料处理系统，因为他们高效率的交通关键部位。因此，重要的是要提高能源效率的皮带输送机。在2，能源效率的能源系统转换为四个层次：性能，操作，设备和技术。特别，能源效率的提高皮带输送机一般都在运作，实现装备水平。在实践中，皮带输送机设备的效率，主要是提高了设备的运行或更换。文献3 、 4、5和驱动系统6的主要目标。该设备需要额外投资导向的战略和改善的机会是有限的某些部分。能源系统的运作效率，通常是通过两个或更多的内部子系统的协调改善，或通过系统组件和时间协调，或通过系统的协调和人类操作2。特别地，变速驱动（VSD）的运作效率提出了带式输送机的文献7 、8、 9和10。它提高了皮带的速度和传送速度的协调运作，进而保证了皮带输送机的效率。然而，目前的速度控制策略，主要采用较低的控制回路来改善那些没有制度约束和外部约束，如审议的皮带输送机运行效率时间的使用问题和生产需要。本文主要是使用最优化方法，以改善皮带输送机的运行效率，满足在同一时间不同的限制。因此，本文中我们首先分析与能量模型。对于一个典型的带式输送机，本文提出了 3 种优化问题，主要以优化操作水平与、绩效指标、低能耗、低能量消耗，受雇为目标的优化。此外，在耗时(TOU)的标准和约束条件下，从生产要求，输送量、皮带速度，单位质量和渐变率的皮带速度会被考虑，相应的仿真结果将得出。论文的布局如下：第二部分的能量模型，分析研究进展进行了评述；第 3 部分，提出三个优化问题方面的带式输送机的能源效率；在第四节的仿真结果，给出了三种优化问题；最后一章是结论。2.能量模型为优化带式输送机的运行效率，一种实用的能量模型是非常必要的。在文献11中，一种分析能量模型提出的带式输送机，这个分析能量模型如下式（1）所示： （1）6.3),( 242321 TVVTVfP 上式中：f P(V,T) 表示带式输送机的功率(kW)；V 表示皮带速度(m/s)；T是输送量(T/h)和 14 是相应系数、带式输送机的设计参数和取得的参数识别。此外,V 和 T 遵守以下关系：T =3.6QGV，Q G表示输送带的单位质量 (公斤/米)。结合效率的驱动系统、模型(1)会被改写如下式（2）：（2）mdPTVf *6.3),( 242321 式（2）中 d、 m表示电机和传送装置的效率。能量分析模型（2）尤其适用于皮带输送机能量优化模型。3. 运行效率优化可以通过提高带式输送机协调速度、进给速率或通过其运行状况的协调和时间来提高其运行效率。事实上，以往的文献研究主要集中于协调速度和进给速率反映的变速驱动或速度控制。然而，一般来说，一个能量的运行效率系统有助于其执行效率，执行效率可以驱动运行使得其达到最优效率。因此，我们本着取节能降耗和能量消耗，通过提高典型的性能指标效率，来达到目标的优化。对于皮带输送机来说，总的能量消耗 JE主要和电动机的功率以及传送时间有关。在时间段 t0 和 t f内，它可以被整合表示为下式中的 fP (V, T)：（3）tPEdtTtVJ0)(,式（3）中t 0 tf 表示皮带机总能量消耗的持续时间段。相应地，总的能量成本 JC可以按照下式进行计算：（4）ftPCtptJ0 )(),(上式中的 p（t）表示持续时间函数。J E 和 JC都是皮带机运行绩效指标，都可以为以下优化问题的目标函数。皮带输送机可能在不同的情形下运行。因此，需要对不同运行情况下运行效率进行研究。3.1 优化问题 1对于一个如图 1 所示的典型带式输送机，一般在一定时期t 0，t f 有总生产计划的需求 TSUM。对于这个优化问题，能够保证找到总能量消耗 JE作为为极小化优化目标的三个变量，即：皮带输送速度、进给速率和工作时间,通过引入变量 tw，将最大限度地减少总能量消耗。这个优化问题的约束如下：1) 皮带的速度应该在可行的运行区间内，即 0 V V MAX；2) 皮带的单位质量应该在可行的区间内，即 0 Q G Q GMAX；3) 皮带输送机输送量应该大于或者等于需要的运输量，即 T*t w T SUM。4) 工作时间范围为t 0 tf , 0 t w (t f t0).因此，优化问题可以表述为下优化问题：Min JE(V, T, tw) = fP (V, T)tw0 V V MAX,0 Q G Q GMAXT.tw T SUM0 t w (t f t0) (5)() s. t.上式中 V，T 和 tw为优化问题的决策变量，其解值分别为 、 和 表示在上VTwt述约束下的皮带机在最小的能量消耗下的电机运行速度、皮带输送量以及工作时间。图 1 试验皮带机示意图3.2 优化问题 2这个优化问题考虑皮带机在时间消耗约束下的能量消耗，用 JC表示能量消耗指标作为问题的解决目标。在不连续时间分析下，对成本函数（4）进行离散化处理。利用标准化时间参数 ，我们可以获得不连续状态下的总能Nttfs0量耗费成本如（6）式所示：（6）Nj sjjpCtTVfJ1),(式中的 和 分别表示在 j 时刻的皮带机电机速度、输送速度和电力价格。jTV,jp在优化问题 2 种，优化变量 V 和 T 按照梯度进行等级排序。问题 2 和问题 1 的前两个约束是一样的。然而，第三个约束考虑到总产量我们表述为（7）：（7）SUMNjst1因此，这一优化问题最终被表述为： Nj sjjPjC tpTVfTVinJ1),():,(s. t. 问题（8）的解值 就是皮带机在 和1:,NjTVj,21NV时的运行参数。,21NT0 V j V MAX,0 Q G-j Q GMAX (8)SUMNjst3.3 优化问题 3这个优化问题和问题 2 相似，不同之处在于优化问题 3 增加了额外的一个参数，即皮带机运行速度等级。实践中，皮带速度过大容易损坏皮带机部件。降低皮带机速度的办法之一就是将之整合考虑进目标函数进行最小化。因此，优化问题就在问题（6