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电磁阀和液力偶合器的改善的控制摘要本文针对一个电磁阀连接的液力偶合器的操作法,是一种新、改善的控制方法。通过输送机动力学模拟对该方法进行了验证,在本文将介绍验证结果。1 介绍液力偶合器是自1987 年在南非被用在处理大块固体生产上。但是, 最初的高期望未被履行, 主要由于缺乏对控制系统联结的限制的理解的一些应用。液力偶合器能通过各种各样的方式完成它的性能1,并且对工程师来说是扣人心弦工作,因为唯一的限制也许是某人的假想。扭矩控制最常见的方法依靠电磁阀,电磁阀启动并在被预先确定的极限内由PLC系统监督整体性能。扭矩特征曲线呈锯牙样式。上部和下部的扭矩极限依照具体要求确定。在多数场合这个技术是满足的, 然而, 有不希望的副作用的源头譬如那些与所谓的“抨击”控制技术相关的。尽管这些困难, 但电磁阀是一种有效耐用的设备, 也适合原材料处理产业的环境。随后人们企图运用这个具体设备挖掘它的全部潜能,并在期间用一台输送机的改善的控制技术研制一个适当的控制系统。2 背景知识经过一段时间研究,我们采用控制参量调整分离开关实现连续控制,在电子学和农业领域执行试验并且在区域内通过递象开关方式实施系统。PUTTER 和Gouws2方法,保持相互依赖的参量是可能的,譬如在温室里使用通过风扇、加热器和喷水隆头的分离行动使温度和湿气保持平衡。当接受温室里高变化动力学差异时, 对电磁阀和液力偶合器的应用开发和研究一个相似的概念是有意思的。2.1 控制系统算法近年来,控制系统在现代控制技术上应用有许多种, 譬如模糊逻辑控制4 、神经网络5,它是作为对非线性和多变量控制问题的解决办法。尽管所有成功例子, 许多典型的技术, 譬如比例-积分-导数(PID)控制。PID控制比智能控制技术的优势是少处理器容量和所需时间。但是, 虽然已解决一些问题6, 但PID 控制器仍然保留一个难题, 尤其是在系统中有不可接受的实验错误方法。PID控制的缺点是调节系统非线形性能力受限制。电磁阀和液力偶合器组合应用PID控制技术。通过控制阀门的开关, 电动机/连轴器扭矩能保持不变。系统失效时间是足够短的,但对系统非线形性调节不明显, 在这些情况下,可应用PID控制技术,描述控制等式得如下7: (1-1)E 误差,区别在凝固点和被观察的价值之间;T 所需扭矩变动量Nm;Kc 比例增量;Td 派生导数时间常数s;Tj 累积时间常数s;Ts 样品时间常数s;n 样品数字;公式1-1与常规PID方法相反,它相对于当前的扭矩(T)确定所需变化量。这是一种快而方便的确定输出量的方式, 因为没有数字微分或积分。数字n是当前的测量误差, n-1是早先测量,n-2是n-1的前一个。测量间的时间是重要的。太短的采样时间能引起设备过分循环, 而太长采样的时间能引起超载和不稳定8。常数Kc、Tj、Td最初根据知名的ZIEGLER-NICHOLS方法在理论上确定6。在控制器的性能上这些常数的每个作用用史密斯描述了3, 被总结如下7:Kc值小产生超载现象但稳定性好, 但当Kc值大时减少超载现象但增加设备循环。Tj值小消除恒定值误差, 但导致控制设备迅速循环。反过来, Tj值大导致产生恒定误差。Td值小导致超载大, 当Td值大提高反应时间时, 导致稳定性提高。虽然阀门只能关起, 但如果通过控制开关开启、停滞时间的线性地变化的阀来控制开关是可能的。公式1-2,T被转换成使用率, 被定义如下:使用率:T = (1-2)交换阀门的时间() s;各样品间在一时间间隔期间阀门交换的最大时间的时间(tmax = )s;实际上,转换能以不同方式完成,涉及T与阀门操作的时间之间从一个简单的比例关系到一相当复杂关系,其中要考虑扭矩/油流量变化率。假想的发展或者选择通过几个因素治理,其中由软件控制和硬件限制的简单化是二个最明显部分的。对于这种具体应用,阀门交换每秒不可以超过5次或5赫兹。最大工作循环(tmax)的最佳值要根据指定的标准或动态模仿实验经反复试验确定。机模拟实验校核改善概念的性能:测试概念并通过输送机模拟校核。第一套由计算机编程建造的输送机模型是以两年之前用这种材料的详细设计而研制的。输送机是通过液力偶合器驱动,它连接着三项换向阀。有关系统和输送机的详细的信息可能都来自9。耦合器的应用指标与在11中描述的差不多,比如在南非很有代表性的那种液力偶合器。在重要的零件图中,需要分析启动阶段的转矩。合格的运行结果是通过调节运行周期和控制设置来实现的。这样可以进一步探索启动阶段速度。为了完成进一步的研究工作,制作的模型将拓展到输送机的高配置的动力装置。在这张图表上涉及到了8.5m长带有顶部和尾部驱动装置的输送机。尽管是带有铲斗的系统操作,但是在这些模拟装置中输送机的模型是与液力偶合器连接在单向阀口处。2.2 输送机动态模型的结果3.3km长钢丝输送机扭矩率116.0Nm/s,在开始阶段描绘的图的坡度大,尤其在泵刚工作的前6秒之间。从而,大约延迟12秒后,控制系统开始启动,存在两个问题:1)最初,低扭矩传输不允许输送机机立即加速度,但通过软件的调整这种情况就可以,正如模拟实验的那样,注意速度变化和控制开始的时间不少于在电机启动后的8秒,双向泵启动后的6秒。2)油从耦合器卸荷的速度是有限的,也许不够抵制输送机机的动态反应,因此,在开始的初始阶段注意某种的程度超速。尽管已提出一些问题,但启动开始速度的变化的情况比希望从控制操作的分散模块上解决问题更有深远意义。进一步测试, 运用不同的速度曲线或者控制常数能得到更好的结果。整体的结果是合理的,但是,值得注意是在某种程度上尾部驱动比头部的性能好。对于每个驱动装置,在开始的12秒到22秒之间提高扭矩或者张力是可行的,再一次调整设备或者工作因数,能改善结果。3 结论基于模拟的结果能得一下结果:1)电磁阀的控制概念在很大程度上已实现,把阀的分散运动变成精确的、连续的输出是可能的。2)新系统允许电磁阀的应用可根据原策略的速度,然而,对于扭矩来说控制可能不精确,尤其在开始启动阶段。3)保证控制参数的优化,模拟实验的结果表示选择不当的控制参数会导致不好的性能结果。4)如所示,这个概念能被应用于中长型输送机中,尾部驱动不易限制,然而,在这种情况上,只有对开始的扭矩进行测试。5)PID控制是传统的控制技术,它广泛应用于加工工业中,并能解决不同的控制问题。附录B 外文文献Feedback control of convey systemsSummaryHigh transient stresses are induced when a conveyor belt changes its current status, especially during starting and stopping. These stresses are harmful to the system, which usually shorten the belt life span. And in some serious cases, they can even result in belt splice, belt and pulley structure damage. Therefore, controlled starting and stopping of the drives to the conveyor belt are always needed.In this paper, a feedback control method is introduced to reduce these transient stresses. A discrete strain-velocity model was developed which allows the analysis of the feedback control system to be performed. Comparisons between the step response of a normal open loop system and closed loop systems were made. One of the issues discussed here is the controllability of the system, which is an important factor when the closed loop system is implemented.1.IntroductionBelt conveyor technology is still the most cost-effective way of transporting bulk solids continuously over a long distance. In the present day, it is widely used in many fields such as mining industries to transport coal, iron ore, limestone ect. Problem with this technology is the development of the standing waves in the belt during operations, especially at starting and stopping. These standing waves induce stresses to the belt life span, by causing belt splice or even belt and pulley structure damage. The cost of maintenance would be increased tremendously.Research is conducted to minimize the transient stresses and to lower the cost of maintenance. An initial method to overcome these stresses is to design the belt with a very high factor of safety (F.O.S), which typically has a value of ten to the desired operating F.O.S. However, this will incur high costs to the system. Nowaday, a widely used method reduces the rate of change of belt acceleration and deceleration (“jerk”or “shock”) by controlled starting and stopping of the drives to the belt.This is also commonly known as soft starting or stopping. A number of approaches have been adopted and studied. These are mainly focused on mechanical and electrical soft starting stopping of the conveyor belts. Currently, the soft starting methods used are all open loop approaches. These approaches normally do not give a good performance on starting and stopping of the system. They are also time consuming to set up properly to achieve a satisfactory performance. Some of these methods might not even consist of drive overload protection, which give rise to significant overload costs.In this paper, a power electronic feedback control on the drive motors, which is a closed loop control method, is introduced. A similar method has been briefly discussed in an early paper by HARRISON1, who uses Thysitor/SCR to control DC motor. However, the implementation approach in this research uses the vector control on AC motors2 DC motors are generally more expensive than AC motors, especially when maintenance costs is taken into account. Therefore, AC motors are more commonly used on the conveyor belts in industry, hence, this research will be more applicable in this context.The feedback control system in this research measures the velocities for each segment of the belt to calculate the output power needed for the motors. The velocities measured are transmitted, via a communication cable, to the master stations. These master stations process the data received together with the controller gains. The processed data are then being used on WF drives (variable voltage variable frequency drives), which adopt the concept of vector space to control the AC motors. The advantages of using a feedback control method are mainly concentrated on achieving a better performance system than the open loop system which is currently in common use. Stresses can be minimized by allowing the load to be shared equally among drives in the feedback control system. This system can also limit the maximum output power to avoid drive overload. Zero steady state error can be reached easily using the feedback control system. The advantages of using power electronics control are low cost of maintenance and the ease with which remote on-line monitoring can be achieved. A drawback of the system is a slight increase in installation costs due to the extra devices needed, such as transducers to measure the belt speed, communication devices to transfer data and microprocessors for data processing. This pays in the long run because of low maintenance costs.The first step towards control is to create a good mathematical model for the plant. A number of approaches have been studied in the past . Most of these approaches use discrete models instead of continuous models due to an important disadvantage of the continuous models. The resultant solution from the continuous model, which is normally expressed in the form of partial differential equations, contains very complex relationships. Also, it is very difficult to express the transient characteristics of the conveyor belt using partial differential equations. Therefore, continuous models have not been popularly used on the conveyor belt analysis.A discrete model divides the continuous belt into a finite number of segments and assumes that the dynamics within the same segment are closely identical, i.e., approximately constant velocity, stretch, stress etc. within a segment of the belt. This assumption induces a quantization error in the discrete model, which depends on the number of belt segments and the model used.With a good mathematical model, a satisfactory control strategy can be applied to give valid simulation results. A large modeling error could always result in wrong simulation outputs and incorrect control parameters used.The rheological models used for describing the longitudinal dynamic properties of the belt have been studied by a number of researchers. The KELVIN solids model, which is a spring in parallel with a viscoelastic element, is most commonly used due to the fact that it is analytically simple and relatively accurate for most of the conveyor belt. Quantization error is induced when representing a continuous belt by a discrete model. For the model used, the relative error of the natural frequency of the belt is inversely proportional to the number of segments into which the belt has been divided, as illustrated by Eq. (1)10 (1)Where is, the natural frequency of continuous belt, is the natural frequency of discrete belt and n is the number of belt segments. Although it is desirable to use a large number of belt segments in order to achieve a small quantization error, the simulation time is a drawback as this increases exponentially as n increases.Position-velocity is the most widely used approach to describe the dynamics of the conveyor belt. However, this approach produces a linear time varying system. Which means the forces that apply to each segment of a moving conveyor belt vary from time to time. For example, a motor force is initially applied to segment i of a moving conveyor belt at time t. However, at time t+1, the motor force would no longer be acting on segment i but on segment i+1. Therefore, the segments position must be monitored with respect to time when the belt moves. The expressions for the position-velocity approach will also have to vary according to time. This approach will obviously result in a more complicated model. The strain-velocity approach is adopted in this research, which develops a linear time invariant system. The strains and velocities for each segment of a moving conveyor belt always remain on the same spot with respect to the ground. Hence, this approach avoids the time varying issue and establishes a much simpler model.A discrete model of the conveyor belt. From the forces which act on the segment n of the belt, an equation for the rate of change of velocity can be described by Eq. (2), in terms of strain and velocity which are commonly denoted asand v respectively. is the motor force applied to the conveyor belt. (2)The rate of change of strain is express in Eq.(3) (3)Unlike the rest of the segments, the gravity take up weight has a different model. Therefore, it has to be treated separately. The derivative of velocity and derivative of strain on the gravity take up weight, say segment k, can be described by Eqs. (4) and (5) respectively; (4) (5)All the equations above can be presented in a form equivalent to a standard statespace representation, as in Eq. (6): W= (6)This expression, Eq. (6), is called the Strain-Velocity model. By solving the Strain-Velocity model using a numerical method a given W and u, the strains and velocities for each segment the belt can be obtained. An example of the numerical methods used would be RUNGE-KUTTA method. The man aim is to find tension or stress for each segment of the belt. The stress, commonly denoted by , for a solid model can be expressed by Eq. (7) 3; (7)where E is YOUNGS modulus and is the viscosity coefficient. Eq. (7) shows that by reducing the maximum strains and velocities, the stresses can be minimized.In this point, a Multiple Input-Multiple Output (MIMO) system has been created. The three methods that are commonly used to control a MIMO system are pole placement, Linear Quadratic Regulator (LQR)11 and H-infinity12. The pole placement method requires an accurate model such that poles can be placed at desired locations according to the model used. Otherwise, incorrect placing of poles would result in a waste of energy and controlling errors. The discrete Strain-Velocity model used is an approximation of the continuous plant, therefore, an amount of uncertainty always exists. The pole placement method would not be a good control approach in this case. TheH-infinity method is a good control approach, but is relatively complicated and results in a very high dynamic order for the controller. The LQR method is chosen due to the robustness capability of handling modeling error and its ease in use. However, choosing appropriate control parameters for LQR is difficult. Since inappropriate parameters would easily result in an oscillatory system, i.e. response with overshoots, the control parameters have to be chosen extremely carefully.Fig.1: Illustrates the block diagram of a feedback control system. W represents the weight of the load on the belt, e represents the velocities errors and u is the motors force. The plant, i.e. the conveyor belt, has its dynamics described by the Strain Velocity model. A P1 (proportional and integral) controller with speed reference, V is used to control the drives. As mentioned previously, the LQR method is applied to calculate the proportional and integral gain. The purpose of H matrix is to reduce the number of feedback states from x to x, where x represents the strains and velocities of each belt segment, and x represents the velocities only. This is called the reduced-state feedback. A full-state feedback system would have all the states in the model being fed back to the controller. Due to the difficulty in measuring strains, only velocities are fed back. Velocities can easily be measured using tachometers. It should be noted that as the velocities are the main concerns of the states in this feedback control system, the system would still give a similar response with the reduced-state feedback.Fig1: Block diagram of feedback control of a conveyor system A number of techniques on setting the controller gains have to be emphasized. The main aim of the controller is to achieve an optimum control on the system, which produces fast response on velocity changes and, low steady state and transient stresses. The use of proportional controller is to speed up the response of the system. However, large control efforts are needed to produce high proportional gains. In addition, due to the control method used, reduced-state feedback would cause the high proportional gains to produce high overshoots response, and results in high transient stresses, The integral controller gives a zero steady state error response to the system. A small integral gain slows down the system response, where it takes a long period of time to reach zero steady state error. However, a huge integral gain could result in an unstable system. Therefore, choosing a set of proper controller gains would always help to produce a system with better performance. A minimum transient stress can be achieved, as the sum of the proportional gains for the drives are equal. By setting the same integral gain for all the drives, a minimum steady state stress can be reached. This is due to the equal sharing of the loads among drives. Also, the controller output power has been limited such that it would not require an unreasonably high power from the drives, and to prevent the drives from overloading in practice.If there is a complete power failure, all the electronic controllers and motors will be shut down and result in an uncontrolled stopping of the conveyor belt. A method to overcome this problem is to have some form of energy storage, such as DC bus rectifier capacitors. To regenerate and supply power for both controllers and motors. This will then achieve a controlled stopping of the belt without using too much energy been shifted directly to the left compared to open loop pole. This implies that closed loop control produces a more stable and better performance system. Energy is needed to shift a pole. The large poles are well-damped and of fast response. i.e. low overshoot and short rise time. Therefore, shifting large poles will only be a waste of energy. Shifting small poles, however, can produce better performance, as the frequency and the damping ratio of the components have increased. The closed loop system produces a smooth velocity response whereas the open loop system oscillates as it approaches the set point. The result also shows that the open loop system has a slightly shorter rise time compared to the low gain closed loop system. A way to shorten the rise time of a closed loop system is to increase the proportional gain. This results in the small poles being shiften further to the left. The high gain system increases the proportional gain by four times, but not the integral gain. Too much integral gain results in a system with high overshoot or can even be unstable. The main aim of having integration in the system is to achieve zero steady state error. Therefore, a good system should not be affected too much by the integration during transient state, but still be able to achieve zero steady state errors. The small complex poles start to dominate, resulting in an oscillatory response. However, fast response would be expected since the system is dominated by the high frequencies components. These are the relationships between poles locations and the response 11. The open loop system produces much higher transient stress compared to the low gain closed loop system. Also, the high gain closed loop system produces the highest transient stress. This is many caused by the high rate of change of velocity. Therefore, this concludes that there is always a trade off between the velocity rise time and the transient stress produced. The open loop system has a higher steady stress compared to both closed loop system. This is the result of having load equally shared between both drives in the closed loop system. It produces a minimum steady state stress difference throughout the whole belt.An important issue in this research is the controllability of the system when feedback control is applied. An uncontrollable system has one or more states that are unaffected by the controller, in other words, the system cannot influence all the poles of the model. This results in the system not being able to fully control the response. Uncontrollable large poles do not seem to have any effect on the system, since they are not being shifted by the controller. However, a requirement for using the LQR method is to have a completely controllable system. The first condition to achieve a completely controllable system is to have at least two drives to control the belt. Secondly, dividing the belt symmetrically into finite segments would always be seen as a good and easy way, but this might result in an uncontrollable system. The controllability is determined by the position of the drives which control the standing waves in the belt. With a take-up weight attached to the belt, the standing waves would have been shifted. This results in what could be an uncontrollable system becoming controllable. However, as the take-up weight is relatively small compared to the belt length, the standing waves would not have shifted much. This leads to a weakly controllable system. Therefore, prime number of belt segments is used to model the belt and avoid the uncontrollable issue, i.e. achieving a completely controllable system. An approach to find the degree of controllability can be observed from the condition number of the controllability matrix 12.In this paper, a feedback control system is introduced minimize the longitudinal waves in a conveyor belt. The feedback control system produces a better performance compared to the commonly used open loop control system. The closed loop system can achieve equal load sharing among motors to minimize the stress, whereas it is difficult to have load equally shared among drives in the open loop system. A slight difference in motors will result in different slip producing different torque to the load. The closed loop system can also limit the output power easily to avoid overloading the drives. A drawback of this feedback control system is the extra cost incurred due to the extra devices needed. However, weighting the cost and the performance, the system is found to be worthwhile implementing. The control strategy is an issue that can always be further researched on in order enhance the performance of the system.References1HARRISON, A.:Oritera form minizing transient stresses in conveyor belts; Int. Conf. on Materials Handling, Beltcon 2, May 1983. Republic of South Africa.2BOSE, BK.: Power Electronics and Variable Frequency Drives Technology and Applications; IEEE Press, US 1997.3NORDELL, L.K. and CIOZDA, Z.P.: Transient belt stress during starting and stopping: elastic response simulated by finite element methods; bulk solids handing Vol. 4 (1984) No. 1, pp. 93-98.4ZUR, T.W.: Viscoelastic properties of conveyor belts; bulk solids handling No. 6 (1986) No. 3, pp. 1163-1168.5SCHULZ, G.: Analysis of the belt dynamics in horizontal curves of the long belt conveyers; bulk solids handling Vol. 15, (1995) No. 1, pp. 25-30.6 HAN, H.S., PARK, T.W. and PARK, T.G.: Analysis of a long belt conveyor system using the multibody dynamics program; bulk solids handling Vol. 16(1996) No. 4, pp. 543-549.7KIM, W.J., PARK, T.G. and LEE, S.S : Transient dynamics analysis of belt conveyor system using the lumped parameter method; bulk solids handling Vol. 15 (1995); No.4, pp. 573-577.8HARRISON, A.: Simulation of conveyor dynamics: in. solids handling Vol. 16 (1996) No. 1, pp. 33-36.9LOOEWLIKS,G .: On the application of beam elements in the finite element models of belt conveyors - part I; bulk solids handling Vol. 14 (1994) No. 4. pp. 729-737.10BISHOP, R.E.D., GLANWELL, G.M.L. and MICHAESON,Sn. The Matrix Analysis of Vibration: Cambridge University Press, U.K., pp, 212-21811FRANKLN, G.F., POWELL, J.D. and EMAM I-NAEINI, A.: Feedback Control of Dynamic Systems; 3rd Edition. Addison Wesley, USA, pp. 118-137, pp. 505-514.12SKOCESTED, S. and POSTLETHWAITE ,I.: Multivariable Feedback Control-Analysis and Design: John Wiley & Sons.U.K., pp. 87, pp.122-127, pp. 366-395.Improved control of a solenoid valve and drain couplingSummaryThe paper looks at a new, improved control concept for a fluid coupling operating in conjunction with a solenoid valve.Verification of the method has been done by means of conveyor dynamic simulations and some of the results are presented in the paper.1.IntroductionDrain fluid couplings have been available in South Africa since 1987 and have found acceptance in the bulk solids handling industry. However, initial high expectations have not always been fulfilled, mainly due to some applications which showed a lack of understanding of the couplings limits of performance and/or deficient control systems. The drain coupling can be assisted in its performance by various means1 and in this respect is exciting to work with for an engineer, as the only limit may be ones imagination and/or finances. The most common method of torque control relies on a solenoid valve which operates in an on/off mode supported by a PLC system which supervises overall performance within pre-determined limits. The resulting torque curve is characterized by a saw tooth pattern as presented. The upper and lower torque limits can be adjusted as determined by specific demands.This technique is sufficient in most instances, but, however, may be the source of undesirable side effects such as those associated with so called “bang-bang” control techniques. Despite these difficulties, the solenoid valve remains a cost effective and robust device, well suited to the environment of materials handling industry.Subsequently an attempt has been made to utilize this specific device to its full potential and to develop a suitable control system which would allow improved control of a conveyor during start up.2. Background InformationFor some time research has been performed into continuous control by means of discrete on/off adjustment of control parameters. Trials were performed and systems implemented in areas as far afield from bulk solid handing as switch mode power electronics and agriculture. As an example of the potential of this approach PUTTER and Gouws2 stated that it was possible to maintain a pre-determined level of interdependent parameters such as temperature and humidity in a greenhouse by means of discrete action of fans. heaters and sprinklers. While accepting definite differences in the dynamics of climactic change in a greenhouse and conveyor start up. It was interesting to develop and test a similar concept for the application of a solenoid valve and a drain fluid coupling.2.1 Control System AlgorithmThe control system arena has, in recent years, been filled with publications on modern control techniques, such as fuzzy logic control4 and neural networks5 as solutions to non-linear and multi-variable control problems. Despite all the success stories, more classical techniques, such as Proportional-Integral-Derivative Control (PID). An advantage of PID control, is that less processor capacity and time is required, than with the intelligent control techniques. However, even though many solutions have been suggested6, tuning a PID controller still remains a difficult task, especially in systems where trail and error methods are not acceptable. A disadvantage of PID control is its restricted ability to accommodate system non-linearities.The solenoid valve and drain coupling combination lends itself to the application of PID control. By controlling the switching of the valve, the motor/coupling torque could maintain a pre-determined pattern. The system dead time is short enough not to contribute significantly to system non-linearity, in which case PID control may be applied. The control equation is described as follows7:1where:Eerror, difference between set point and observed valueT required torque change NmKc proportional gain Tdderivative time constant sTjintegral time constant sTssample time constant snsample number.Contrary to the conventional PID approach Eq. (1) determines the change required relative to the current torque (T) and not the amount of torque required as a function of the error. This is a quicker and more convenient way to determine the output, since no numeric integration or differentiation is required.The number n refers to the current error measurement, n1 to the previous measurement and n-2 to the one before that. The time between measurements is critical. A too short sampling time can result in excessive equipment cycling, while a too long sampling time can result in overshoot and instability8. The constants Kc, Tj, Td are originally determined theoretically according to the well-known ZIEGLER-NICHOLS method6. These values serve as a starting point from where further fine tuning was done experimentally. The effect of each of these constants on the controllers performance has been described by SMITH3 and can be summarised as follows7:A small value of Kc produces large overshoot but gives good stability, while larger values of Kc reduce the overshoot but increase equipment cycling.Small values of Tj eliminate constant errors quickly, but result in rapid cycling of control equipment. In turn, large values of Tj cause constant errors to occur.A small value of Td causes large overshoot, while a large value of Td increases the reaction time, which results in increased stability.Although the valve can only be switched on or off, it is still possible to control the switching as if it were a linearly varying valve by controlling the time for which it is switched on or off. By applying Eq. (2), T is converted to a duty cycle, which is defined as follows:Duty cycle = 2where:time for which the valve is switched on () stime between each sample which also represents maximum time for which the valve can be switched on during one interval (tmax = )s.In fact the conversion may be done in several ways ranging from a simple proportional relationship between T and time of valve operation to a rather complex one where rates of torque/oil flow change are taken into account. Development and/or selection of the concept may be governed by several factors of which simplicity of the control software and limitations of the hardware are the two most obvious ones.For this specific application, the valve may not be switched more than 5 times per second or 5 Hz. The optimum length of the maximum duty cycle (tmax) may be determined by trial and error according to specified criteria or by dynamic simulation.Conveyor Simulations Verifying the Performance of the Developed Concept: The concept has been tested and verified by means of conveyor dynamic simulations. The first set of simulations utilised a computer model of a conveyor which was a subject of a detailed design investigation by Dynamika Materials Handing two years ago. The conveyor was supplied with drain couplings working in conjunction with a three way valve. Detailed information about the system and the conveyor may be found in 9. The coupling characteristics utilised are similar to that presented in 11 as it is a representative of drain fluid couplings used in South Africa.The torque based starting strategy was analysed in significant detail. Acceptable performance results were obtained by adjusting the duty cycles and control settings. This led to further exploration of a velocity based starting strategy.To complete the investigation, the simulations were extended to conveyors of greater length and higher installed power. Some of the graphs presented in this paper refer to an 8.5 km long overland conveyor with head and tail drives10. Although the actual system operates with scoop couplings, in these simulations the conveyor was modeled with drain couplings operating in conjunction with solenoid valves.2.2 Results of the Conveyor Dynamic SimulationsTorque was ramped at a rate of 116.0 Nm/s which is suitable for a 3.3 km long conveyor with steel cord belting (2100 Nm should be reached in 15 sec). The resulting ramp is too steep for the coupling during the initial stages, specifically during the initial 6 seconds of pump operation. Consequently, the control system comes into action with an approximate delay of 12 seconds.Two problems are apparent :Initial low torque delivery does not allow instant acceleration of the conveyor. This is possible to rectify by adjustments in the software as is the case for the simulations, it can be noted that the velocity ramp and controlling action starts some 8 seconds after the motors and 6 seconds after the couplings pumps were energized.The rate at which oil is discharged from the coupling is limited and may be insufficient to counteract the dynamic reaction of the conveyor and as a result, a certain degree of overspeed can
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