CN107045576A - A kind of comprehensive analysis and its verification method for judging the buffeting of wire feed blower fan - Google Patents
A kind of comprehensive analysis and its verification method for judging the buffeting of wire feed blower fan Download PDFInfo
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Abstract
本发明涉及一种卷烟风力送丝领域，尤其涉及送丝风机抖振判断的综合分析及其验证方法。该方法将约束式预期控制引入到对判断送丝风机抖振的综合分析及其验证方法中，通过对预期控制系数σ和模态量化系数c推演出引起风机抖振的发生过程，较好的解决了短时间、偶发性和高频次等因素影响下的风机抖振原因不确定、分析不准确及验证难以实现的问题。
The invention relates to the field of wind power wire feeding of cigarettes, in particular to a comprehensive analysis and verification method for judging buffeting of a wire feeding fan. This method introduces the constrained anticipatory control into the comprehensive analysis and verification method for judging the chattering of the wire feeding fan, and deduces the occurrence process of the fan chattering through the expected control coefficient σ and the modal quantization coefficient c, which is better It solves the problems of uncertain cause, inaccurate analysis and difficult verification of fan buffeting under the influence of short-term, sporadic and high-frequency factors.
Description
技术领域technical field
本发明涉及一种卷烟风力送丝领域，尤其涉及送丝风机抖振判断的综合分析及其验证方法。The invention relates to the field of wind power wire feeding of cigarettes, in particular to a comprehensive analysis and verification method for judging buffeting of a wire feeding fan.
背景技术Background technique
烟丝是制造卷烟的重要原料之一。在卷烟生产过程中，首先烟丝经过切割、发酵、加湿、添加成分、烘干等工艺流程，通过输送环节到达卷烟机集丝箱；然后卷烟机通过烟丝成型后形成烟条，再由重量控制系统将烟条切割成重量均等的卷烟，最后卷烟通过包装机形成小包和大条。这个过程中，烟丝作为重要的和唯一的流通介质，所以在输送环节中烟丝是否能够保质保量是决定卷烟产品质量高低的重要因素之一。Shredded tobacco is one of the important raw materials for making cigarettes. In the process of cigarette production, firstly, the shredded tobacco is cut, fermented, humidified, added ingredients, dried and other technological processes, and then reaches the wire collecting box of the cigarette machine through the conveying link; then the shredded tobacco is formed by the cigarette making machine to form tobacco rods, and then the weight control system The rods are cut into cigarettes of equal weight, and finally the cigarettes pass through packing machines to form packets and rods. In this process, shredded tobacco is an important and only circulation medium, so whether the shredded tobacco can maintain the quality and quantity in the transportation link is one of the important factors that determine the quality of cigarette products.
风力送丝由于其具有响应速度快、配置灵活、可靠性高等特点被大多数烟草企业所采用，风力送丝依靠送丝风机提供负压吸风，将集丝箱内的烟丝通过送丝管道送往卷烟机生产卷烟，在此过程中，送丝风机受电流波动和风管内风阻影响，送丝风机会产生抖振，当风机产生抖振时，原本匀速规则的空气流会变得不稳定，产生很多不规则的乱流，称作“紊流”。虽然紊流的产生时间相对整个吸丝过程时间微不足道，但仍然会造成烟丝输送的异常，异常现象表现在：当吸丝风速偏低时，就容易产生烟丝偏少或烟丝堵塞的现象，最终导致卷烟机停机；当吸丝风速偏高时，就会增加烟丝与管壁的碰撞与摩擦，增加烟丝的造碎，直接影响烟丝的长丝率等工艺质量指标。另外，频繁的抖振会损坏风机风叶，加速风机内运动部件磨损。一般风机的抖振频率都是由低到高，不间断发生，为此，如何结合风机动力学特性，避免风机抖振，是研究送丝过程稳定性的难题，参考其它设备减小抖振的方法，对此提出的方法有很多。例如安徽科技学院(乔印虎,易克传,等.智能材料的风机叶片振动主动控制分析[J].检测与控制,2009,(9):118-120)提出两种减小设备抖振的控制策略，即主动阻尼策略和变频控制策略，主动阻尼策略通过调整阻尼比使抖振得到有效衰减或抑制，变频控制策略通过保证系统的主要振动模态不被激发或强迫振动能量向着易于耗散的模态传递，从而达到控制抖振的目的。广东工业大学(李忠娟,张新政.变结构控制理论中抖振问题的研究[J].五邑大学学报,2003,17(3):66-69)在分析了常见的四种用于削弱抖振的方法后，提出了基于模糊神经的抖振方法并利用仿真结果以证明。北京理工大学(于亚男,孙博,等.基于新型趋近律的挠性航天器滑模变结构控制[J].航天控制,2013,31(5):62-68)针对应用切换函数带来的挠性航天器滑模变结构控制力矩的高频抖振问题，提出了应用模糊逻辑对改进后的指数趋近率进行自适应智能处理，从而抑制控制力矩的高频抖振。哈尔滨工程大学(金鸿章,罗延明,等.抑制滑模抖振的新型饱和函数法研究[J].哈尔滨工程大学学报,2007,28(3):288-291)提出了一种具有动态边界层的饱和函数控制方法，该方法可使边界层随状态轨迹的收敛而逐渐收缩，从而降低状态轨迹中的抖振频率。中国矿业大学(郑车晓,孙伟,等.变结构控制一种抑制抖振的方法设计[J].中国科技论文在线,2011)设计了一种将趋近律与传统PID控制方法及采用饱和函数为切换函数的传统变结构控制进行比较，从而得到一种新的具有良好控制效果的削弱抖振的方法。西安电子科技大学(申宇.滑模变结构控制中抖振的特性研究与抑制[D].西安电子科技大学学士学位论文,2012)提出了一种采用广义描述函数法稳定判据和变结构切换增益自适应调节方法，用来设计具有较小抖振特性的齿隙补偿控制器和两类二阶采样变结构控制器。军械工程学院(席雷平,陈自力,等.具有抖振抑制特性机械臂快速滑模变结构控制[J].电机与控制学报,2012,16(7):97-102)提出了一种基于新型滑模面和模糊幂次趋近律的滑模变结构控制策略，提高了滑模变结构控制滑动运动阶段的收敛速度，能够在保证抖振抑制效果的前提下,提高系统的趋近运动速度。福州大学机械工程及自动化学院(童超,陈力.基于模糊幂次趋近律的漂浮基空间机器人快速滑模变结构控制[J],2015,10(3):45-51)讨论了一种基于模糊幂次趋近律的快速滑模变结构控制方法，该方法能够使机械臂抖振抑制的效果明显,同时也保证了系统的轨迹跟踪控制效果。清华大学(杨普,张曾科.一类滑模变结构控制系统的抖振控制[J],2005,45(1):34-42)通过分析指数趋近率下滑模变结构控制的抖振过程，给出了抖振幅度、周期和趋近率参数、控制量的变化率之间的定量关系，以减弱塞棒以一定幅度和频率的抖振。湖南工业大学(黄华,李光,等.基于趋近律的机械臂滑模控制方法研究[J],2013,27(1):62-66)分析和设计了指数趋近律，以此为基础，研究和优化了机械臂的运动学特性，减小机械臂在运动过程中的抖振。Wind wire feeding is adopted by most tobacco companies due to its fast response, flexible configuration, and high reliability. Wind wire feeding relies on the wire feeding fan to provide negative pressure suction, and the tobacco in the wire collecting box is sent through the wire feeding pipe. During the production of cigarettes to the cigarette machine, the wire feeding fan is affected by current fluctuations and wind resistance in the air duct, and the wire feeding fan will generate chattering. When the fan generates chattering, the originally uniform and regular air flow will become unstable, resulting in A lot of irregular turbulent flow is called "turbulent flow". Although the generation time of turbulent flow is insignificant compared with the time of the whole suction process, it still causes abnormality in the delivery of shredded tobacco. The cigarette machine is shut down; when the suction wind speed is high, it will increase the collision and friction between the shredded tobacco and the pipe wall, increase the shredding of the shredded tobacco, and directly affect the process quality indicators such as the filament rate of the shredded tobacco. In addition, frequent buffeting will damage the blades of the fan and accelerate the wear of the moving parts in the fan. Generally, the chattering frequency of the fan is from low to high and occurs continuously. Therefore, how to combine the dynamic characteristics of the fan to avoid the chattering of the fan is a difficult problem in the study of the stability of the wire feeding process. Refer to other equipment to reduce chattering method, there are many methods proposed for this. For example, Anhui Institute of Science and Technology (Qiao Yinhu, Yi Kechuan, etc. Analysis of active control of fan blade vibration with smart materials [J]. Detection and Control, 2009, (9): 118-120) proposed two methods to reduce equipment chattering The control strategy is active damping strategy and frequency conversion control strategy. The active damping strategy can effectively attenuate or suppress chattering by adjusting the damping ratio. Dispersed mode transmission, so as to achieve the purpose of controlling chattering. Guangdong University of Technology (Li Zhongjuan, Zhang Xinzheng. Research on Chattering Problems in Variable Structure Control Theory[J]. Journal of Wuyi University, 2003,17(3):66-69) analyzed four common methods for weakening chattering After the chattering method, a chattering method based on fuzzy neurons is proposed and the simulation results are used to prove it. Beijing Institute of Technology (Yu Yanan, Sun Bo, et al. Sliding mode variable structure control of flexible spacecraft based on new reaching law[J]. Aerospace Control, 2013,31(5):62-68) for the application of switching functions The problem of high-frequency chattering of the sliding mode variable structure control torque brought by the flexible spacecraft is proposed, and the application of fuzzy logic is proposed to perform adaptive intelligent processing on the improved exponential approach rate, so as to suppress the high-frequency chattering of the control torque. Harbin Engineering University (Jin Hongzhang, Luo Yanming, et. The saturation function control method, which can make the boundary layer shrink gradually with the convergence of the state trajectory, thereby reducing the chattering frequency in the state trajectory. China University of Mining and Technology (Zheng Chexiao, Sun Wei, et al. Design of a method to suppress chattering by variable structure control [J]. China Science and Technology Papers Online, 2011) designed a method that combines reaching law with traditional PID control and adopts The saturation function is compared with the traditional variable structure control with switching function, and thus a new chattering weakening method with good control effect is obtained. Xidian University (Shen Yu. Research and suppression of chattering characteristics in sliding mode variable structure control [D]. Bachelor's degree thesis of Xidian University, 2012) proposed a stability criterion and variable structure using generalized description function method The switching gain adaptive adjustment method is used to design backlash compensation controllers with small chattering characteristics and two types of second-order sampling variable structure controllers. School of Ordnance Engineering (Xi Leiping, Chen Zili, et al. Fast sliding mode variable structure control of manipulator with chattering suppression characteristics[J]. Journal of Electrical Machinery and Control, 2012,16(7):97-102) proposed a new type based on The sliding mode variable structure control strategy of the sliding mode surface and the fuzzy power reaching law improves the convergence speed of the sliding motion stage of the sliding mode variable structure control, and can improve the approaching motion speed of the system under the premise of ensuring the chattering suppression effect . School of Mechanical Engineering and Automation, Fuzhou University (Tong Chao, Chen Li. Fast sliding mode variable structure control of floating space robot based on fuzzy power reaching law[J], 2015,10(3):45-51) discussed a A fast sliding mode variable structure control method based on fuzzy power reaching law, this method can make the chattering suppression effect of the manipulator obvious, and also ensure the trajectory tracking control effect of the system. Tsinghua University (Yang Pu, Zhang Zengke. Chattering control of a class of sliding mode variable structure control systems[J], 2005,45(1):34-42) by analyzing the chattering of sliding mode variable structure control with exponential approach rate In the process, the quantitative relationship among chattering amplitude, cycle and approach rate parameters, and the rate of change of the control variable is given, so as to weaken the chattering of the stopper rod at a certain amplitude and frequency. Hunan University of Technology (Huang Hua, Li Guang, et al. Research on sliding mode control method of manipulator based on reaching law [J], 2013, 27(1):62-66) analyzed and designed the exponential reaching law. Based on this, the kinematics characteristics of the manipulator are studied and optimized to reduce chattering during the movement of the manipulator.
抖振是风机设备在运行过程中常见的现象，轻微的抖振是正常现象，但如果频繁的或是有严重异响的抖振是会影响风叶内部零部件的使用寿命，造成不可逆转的损伤。由于风机是一个封闭的运行环境，风机抖振都是由轻微逐渐发展为严重的过程，当产生严重抖振时就必须停机维修，更换部件，这会造成生产影响和经济损失，所以如何预先判断风机抖振状况，以抑制或消除抖振趋势，是降低风机系统故障影响风险的措施之一。上述文献更多的是采用调整趋近律的方法，来判断是否减小抖振的幅度、周期和变化率，这适用于具有相对强抗干扰性、间断扰动的物体，但由于风机受本身系统参数和外部环境(电流，强磁场)的影响较大，抗干扰特性相对较弱，容易产生无法测知的持续扰动，所以严格意义上来说，采用调整趋近律的方法判断对于具有不可测知且持续扰动的风机系统是没有意义的。Chattering is a common phenomenon in the operation of fan equipment. Slight chattering is a normal phenomenon, but frequent chattering or severe abnormal noise will affect the service life of the internal parts of the fan blades and cause irreversible damage. damage. Since the fan is a closed operating environment, the buffeting of the fan is a process that gradually develops from slight to serious. When severe buffeting occurs, it must be shut down for maintenance and replacement of parts, which will cause production impact and economic loss, so how to judge in advance The buffeting condition of wind turbines, to suppress or eliminate the buffeting tendency, is one of the measures to reduce the risk of wind turbine system failure impact. The above literatures mostly use the method of adjusting the reaching law to judge whether to reduce the amplitude, period and rate of change of chattering, which is suitable for objects with relatively strong anti-interference and intermittent disturbances, but due to the wind turbine being affected by its own system Parameters and the external environment (current, strong magnetic field) are greatly affected, and the anti-interference characteristics are relatively weak, and it is easy to produce unmeasurable continuous disturbances. And a continuously disturbed fan system is meaningless.
发明内容Contents of the invention
本发明要解决的技术问题是提供一种判断送丝风机抖振的综合分析及其验证方法，将约束式预期控制引入到对判断送丝风机抖振的综合分析及其验证方法中，通过对预期控制系数σ和模态量化系数c推演出引起风机抖振的发生过程，较好的解决了短时间、偶发性和高频次等因素影响下的风机抖振原因不确定、分析不准确及验证难以实现的问题。The technical problem to be solved by the present invention is to provide a comprehensive analysis and verification method for judging the chattering of the wire feeding fan. The expected control coefficient σ and the modal quantization coefficient c deduce the occurrence process of fan buffeting, which better solves the uncertain causes, inaccurate analysis and Verify difficult-to-achieve problems.
本发明为解决上述技术问题所采用的技术方法是：The technical method that the present invention adopts for solving the problems of the technologies described above is:
一种判断送丝风机抖振的综合分析及其验证方法，该方法包括综合分析和验证方法，所述的综合分析包括以下的步骤：A comprehensive analysis and verification method for judging the buffeting of a wire feeding fan, the method includes a comprehensive analysis and a verification method, and the comprehensive analysis includes the following steps:
1)在一个设备送线时段内随机对送丝风机负压吸风的瞬时风压和风量的过程变量进行采样，获得采样矩阵W＝(N*S)，其中N为采样点个数，S为监测变量个数；重复T个生产时段，获得相应的数据矩阵W'＝(T*N*Si)，其中Si为第i个除尘时段内的采样点个数；1) Randomly sample the process variables of the instantaneous wind pressure and air volume of the negative pressure suction of the wire feeding fan within a wire feeding period of the equipment, and obtain the sampling matrix W=(N*S), where N is the number of sampling points, S is the number of variables to be monitored; repeat T production periods to obtain the corresponding data matrix W'=(T*N*S i ), where S i is the number of sampling points in the i-th dust removal period;
2)所述的数据矩阵按照约束变分原理进行测算，获得针对送丝风机抖振的约束控制系数σ，即将送丝风机的送风系统看作为约束式预期控制，对送风过程的综合分析采用有界、增益无穷大的调控控制方法；2) The data matrix is measured and calculated according to the constraint variation principle, and the constraint control coefficient σ for the chattering of the wire feeding fan is obtained, namely The air supply system of the wire feeding fan is regarded as a constrained anticipatory control, and the comprehensive analysis of the air supply process adopts a bounded and infinite gain regulation and control method;
3)所述的送风过程设定为两阶函数，对其送风系统进行调控：当风机工作处于稳定时，则有y＝x,其中y0＝y,x0＝x，其中y为振幅，x为振动频率，其启停切换条件为其中σ为约束控制系数，c为模态量化系数；若当风机发生抖振时，y0与x0的变化就会偏离送风系统预期，其对应关系与约束式预期控制的偏离误差对应，即其中Vxσ为送风系统控制系数变化值，xc为送风系统模态量化后的预估值，xu为送风系统偏离误差值；并且指定送风系统初始状态为xo＜0且σ＞0的条件下，其中xo为送风系统初始状态值；3) The air supply process is set as a two-order function, and the air supply system is regulated: when the blower fan is in a stable operation, then there is y=x, where y 0 =y, x 0 =x, where y is Amplitude, x is the vibration frequency, and its start-stop switching condition is Among them, σ is the constraint control coefficient, and c is the modal quantization coefficient; if the fan chatters, the changes of y0 and x0 will deviate from the expected air supply system, and the corresponding relationship corresponds to the deviation error of the constrained expected control, that is Among them, Vx σ is the change value of the control coefficient of the air supply system, x c is the predicted value after the modal quantization of the air supply system, and x u is the deviation error value of the air supply system; and the initial state of the air supply system is specified as x o <0 and Under the condition of σ>0, where x o is the initial state value of the air supply system;
3)所述的送风系统若是可以调控的，那么按照此前调控方法设计出来的系数σ能够保证送风系统符合(x0',xσ')的初始值，即在tRC＝tσ-t0期间，tσ为送风系统约束控制过程时间，t0为送风系统初始状态时间，tRC为送风系统约束预期控制时间；使送风系统从(x0',xσ')的初始状态到达c模态量化状态，这个过程是便于风机能够符合约束式预期控制的量化状态，过程如图1所示；3) If the air supply system can be adjusted, then the coefficient σ designed according to the previous control method can ensure that the air supply system meets the initial value of (x 0 ', x σ '), that is, at t RC =t σ - During t 0 , t σ is the process time of the air supply system restriction control process, t 0 is the initial state time of the air supply system, t RC is the expected control time of the air supply system restriction; make the air supply system from (x 0 ', x σ ') The initial state reaches the c-mode quantization state. This process is to facilitate the fan to conform to the quantization state of the constrained expected control. The process is shown in Figure 1;
4)所述的图1，图中(x0',xσ')与原点O(0,0)之间连线的斜率表示为d＝-xσ/x0；σ＞0相当于Δd＝xσ-x0＞0，在风机送风系统状态趋近量化状态c期间，必有d＜0，故x+dx＝0所代表的风机送风系统工况模态收敛速度不同于c所代表的工况模态收敛速度，也就是说风机送风系统在还未完全量化状态下的工况模态收敛速度大于约束式预期控制状态下所代表的工况模态收敛速度，风机的抖振还比较明显；在送风系统从(x0',xσ')向c的趋近过程中，其收敛速度逐渐减小到与c的收敛速度一致，即d→c，该趋近过程称为平衡，反之，则为抖振；4) As mentioned in Figure 1, the slope of the line between (x 0 ', x σ ') and the origin O(0,0) in the figure is expressed as d=-x σ /x 0 ; σ>0 is equivalent to Δd ＝x σ -x 0 >0, during the period when the state of the fan air supply system approaches the quantized state c, there must be d<0, so the modal convergence speed of the fan air supply system represented by x+dx=0 is different from c The modal convergence speed of the working condition represented by , that is to say, the modal convergence speed of the fan air supply system in the state of incomplete quantification is greater than the modal convergence speed of the working condition represented by the constrained expected control state. Chattering is still relatively obvious; during the approach of the air supply system from (x 0 ', x σ ') to c, its convergence speed gradually decreases to be consistent with the convergence speed of c, that is, d→c, the approach The process is called balance, otherwise, it is chattering;
5)所述的系数σ在风机启停切换条件(σ'＜0,σ＞0)下求解出来的c存在有可能不同于在送风系统工况模态收敛状态下设计出来的c等价的现象，因为风机产生抖振时的σ有超过极限值的可能，所以不能保证风机一直处于稳定状态，若在送风系统工况模态收敛后仍然发生风机抖振，则必出现预期控制不可实现的现象；5) The coefficient σ obtained under the fan start-stop switching condition (σ'<0, σ>0) may be different from the c equivalent designed under the modal convergence state of the air supply system. Because the σ of the blowing fan may exceed the limit value, it cannot be guaranteed that the fan is always in a stable state. If the blowing vibration of the fan still occurs after the modal convergence of the air supply system, the expected control failure must occur. the realized phenomenon;
6)所述的当出现预期调控不可实现的现象时，此时的斜率d不等于c，与x+cx＝0平行的直线x'+cx≠0，即风机送风系统模态量化的状态无法满足约束式条件，所以送风系统无法起到预期调控的意义；虽然它的斜率不等于量化系数c，但可以将x+cx≠0上下平移；所以可采用平移的办法将斜率等于c，结果是收敛的变化过程(即(x(t),x'(t)))有两种可能，如图2所示，其中第1种可能说明风机抖振可调控，第2种可能说明风机抖振不可调控；6) When the phenomenon that the expected control cannot be realized occurs, the slope d at this time is not equal to c, and the straight line x'+cx≠0 parallel to x+cx=0 is the state of the modal quantization of the fan air supply system The constraint condition cannot be satisfied, so the air supply system cannot play the role of expected regulation; although its slope is not equal to the quantization coefficient c, it can be translated up and down by x+cx≠0; so the slope can be equal to c by means of translation, The result is that there are two possibilities for the change process of convergence (that is, (x(t), x'(t))), as shown in Figure 2, where the first possibility indicates that the buffeting of the fan can be adjusted, and the second possibility indicates that the fan chattering can be adjusted. Chattering cannot be adjusted;
7)所述的图2中，曲线1表明风机发生抖振时可调控，曲线2表明不可调控，在风机送风系统趋近量化c期间，因d＞0送风系统收敛过程必先发散，而后演化为量化c的另一分支，则风机抖振趋向稳定的过程是非单向收敛过程；7) In the above-mentioned Figure 2, curve 1 indicates that the buffeting of the fan can be adjusted, and curve 2 indicates that it cannot be adjusted. During the period when the air supply system of the fan is approaching quantization c, because d>0, the convergence process of the air supply system must diverge first. Then it evolves into another branch of quantization c, the process of fan buffeting tending to be stable is a non-unidirectional convergence process;
8)所述的验证上述分析正确与否的方法包括两个步骤，第一个步骤是确定风机送风系统的启停切换函数σ(x)；第二个步骤是通过满足模态量化状态系数c来达到预期控制的目的；8) The method for verifying that the above-mentioned analysis is correct or not includes two steps, the first step is to determine the start-stop switching function σ(x) of the fan air supply system; the second step is to quantify the state coefficient by satisfying the modal c to achieve the purpose of expected control;
第一个步骤包括以下的步骤：The first step consists of the following steps:
1)所述的第一个步骤中，假定将风机抖振控制问题的对象，即风机工况状态表示为： s＝A(x)+B(y)*0.5，其中A(x)表示振动频繁变化矩阵，B(y)表示振幅变化矩阵，c表示模态量化系数；由于A(x)是n×n维矩阵，B(y)是n×m维矩阵，所以s是n维向量，c∈Rm×n，则风机送风系统的启停切换函数σ(x)指定为状态变量线性组合而成的函数等价为：σ(x)＝s＝A(x)+B(y)*c；1) In the first step, it is assumed that the object of the fan chattering control problem, that is, the working condition of the fan is expressed as: s=A(x)+B(y)*0.5, where A(x) represents the vibration Frequent change matrix, B(y) represents the amplitude change matrix, c represents the modal quantization coefficient; since A(x) is an n×n dimensional matrix, B(y) is an n×m dimensional matrix, so s is an n dimensional vector, c∈R m×n , then the start-stop switching function σ(x) of the fan air supply system is specified as a function formed by a linear combination of state variables, which is equivalent to: σ(x)=s=A(x)+B(y )*c;
2)所述的函数等式中，模态量化系数c∈Rm×n，它是切换函数的线性组合系数，其被控对象可表示为矩阵：其中x1、x2分别为风机发生抖振时采集的负压吸风的瞬时风压和风量的过程变量，若此时在采集过程中，假定期望的风机工况动态过程是渐近稳定的，则对应的σ(x)为：σ(x)＝[c,1][x1,x2]T＝0，其中x1和x2的取值范围称为风机送风系统启停切换函数σ(x)的存在区域，记为θ，另外风机模态量化系数c的取值范围涉及多方面，例如对风机抖振预期调控方法的稳定性，预期调控方法动态过程的快速性等；2) In the function equation described above, the modal quantization coefficient c∈R m×n is the linear combination coefficient of the switching function, and its controlled object can be expressed as a matrix: Among them, x1 and x2 are the process variables of the instantaneous wind pressure and air volume of the negative pressure suction collected when the fan chattering occurs, if at this time in the collection process, it is assumed that the dynamic process of the expected fan working condition is asymptotically stable, then The corresponding σ(x) is: σ(x)=[c,1][x 1 ,x 2 ] T ＝0, where the value range of x1 and x2 is called the switch function σ(x ) is denoted as θ, and the value range of fan modal quantization coefficient c involves many aspects, such as the stability of the expected control method for fan buffeting, the rapidity of the dynamic process of the expected control method, etc.;
3)所述的风机模态量化系数c的取值范围，若想减小风机抖振，满足方法渐近稳定性的要求，仅需c＞0，根据x1可能变化的范围以及对预期调控方法动态过程快速性要求来减小抖振，例如指定c＝0.5，则风机工况状态S定义为：x2＝-0.5x1,-2＜x1＜2，它是S的存在区域θσ中，斜对称于零点的两条线段S1和S2，如图3所示，图中θσ为S的领域；如果希望持续减弱抖振，而且对方法快速性没有特定要求，则仅需减小c且c>0，使方法快速性远低于送风系统快速性即可；3) The value range of the fan modal quantization coefficient c mentioned above, if you want to reduce fan buffeting and meet the requirements of the asymptotic stability of the method, only c > 0, according to the range of possible changes in x1 and the expected control method The rapidity of the dynamic process is required to reduce chattering. For example, if c=0.5 is specified, the working condition S of the fan is defined as: x 2 =-0.5x 1 , -2<x 1 <2, which is the existence area of S θ σ , the two line segments S1 and S2 that are obliquely symmetrical to the zero point, as shown in Figure 3, θ σ in the figure is the field of S; if you want to continuously reduce chattering, and there is no specific requirement for the rapidity of the method, you only need to reduce c and c>0, so that the rapidity of the method is much lower than the rapidity of the air supply system;
第二个步骤包括以下的步骤：The second step consists of the following steps:
1)所述的第二个步骤中，c将送风系统从x0拉到S上的途径有两条：σ(x)＞0将x拉到Sp 上，或σ(x)＜0将x拉到SN上为稳定，其中Sp为预估状态，SN为调控状态；σ(x)＞0将x拉到SN 上，或σ(x)＜0将x拉到Sp上为抖振；虽然它们都到达了S，但动态过程x0(t)不同；若稳定，x0(t) 单向收敛无超调；若抖振，x0(t)则超调；稳定还是抖振，取决于c的确定方法；1) In the second step, there are two ways for c to pull the air supply system from x0 to S: σ(x)>0 to pull x to Sp, or σ(x)<0 to pull x Pulling it to SN is stable, where Sp is the estimated state and SN is the control state; σ(x)>0 pulls x to SN, or σ(x)<0 pulls x to Sp to chatter; although They all reach S, but the dynamic process x 0 (t) is different; if it is stable, x 0 (t) will converge in one direction without overshoot; if it chatters, x 0 (t) will overshoot; whether to stabilize or chatter depends The determination method of c;
2)所述的途径，利用此条件，获取控制的不等式为称为第二个步骤的附加条件，依据附加条件可求解c，在认定c为常数的前提下，有σ(x)＝cx，将此式代入表达式x＝A(x)+B(x)*C,其中x(t0)＝x0，同时代入误差系数u，可得表达式：σ(x)＝cA(x)+cB(x)u，假定(cB(x))-1存在，可求得约束式预期控制的误差系数u’为：u'＝-csgn(σ(x))，式中u’满足的要求；2) said way, utilize this condition, the inequality of obtaining control is It is called the additional condition of the second step. According to the additional condition, c can be solved. On the premise that c is determined to be a constant, there is σ(x)=c x , and this formula is substituted into the expression x=A(x)+B( x)*C, where x(t 0 )=x 0 , while substituting the error coefficient u, the expression can be obtained: σ(x)=cA(x)+cB(x)u, assuming (cB(x)) - 1 exists, the error coefficient u' of constrained predictive control can be obtained as: u'=-csgn(σ(x)), where u' satisfies requirements;
3)所述的约束式预期控制的误差系数u’的表达式，即u'＝-csgn(σ(x))与被控对象表达式两者形成了闭环控制；3) the expression of the error coefficient u' of the described constrained type anticipatory control, i.e. u'=-csgn (σ (x)) and the controlled object expression both form a closed-loop control;
4)所述的误差系数u的表达式进行举例，例如将u'＝[0.51]放入误差系数u’的表达式，可得举例启停式风机控制表达式为：u'＝-0.5sgn(σ(x))；此时u’与被控对象表达式(即x＝A(x)+B(x)*C,其中x(t0)＝x0)形成闭环控制。4) The expression of the error coefficient u is given as an example, for example with Put u'=[0.51] into the expression of error coefficient u', for example, the expression of start-stop fan control can be obtained: u'=-0.5sgn(σ(x)); at this time, u' and the controlled object express The formula (ie x=A(x)+B(x)*C, where x(t 0 )=x 0 ) forms a closed-loop control.
本发明将约束式预期控制引入到对判断送丝风机抖振的综合分析及其验证方法中，通过对预期控制系数σ和模态量化系数c推演出引起风机抖振的发生过程，较好的解决了短时间、偶发性和高频次等因素影响下的风机抖振原因不确定、分析不准确及验证难以实现的问题。The present invention introduces the constrained anticipatory control into the comprehensive analysis and verification method for judging the chattering of the wire feeding fan, and deduces the occurrence process of the chattering of the fan by deducing the expected control coefficient σ and the modal quantization coefficient c, which is better It solves the problems of uncertain cause, inaccurate analysis and difficult verification of fan buffeting under the influence of short-term, sporadic and high-frequency factors.
附图说明Description of drawings
图1为系统趋近可调控状态过程图。Figure 1 is a diagram of the process of the system approaching the controllable state.
图2为(x(t),x'(t))变化过程的两种可能图。Figure 2 shows two possible graphs of the change process of (x(t), x'(t)).
图3为系统渐近稳定性过程图。Figure 3 is the process diagram of the asymptotic stability of the system.
图4为本发明和系统框图。Fig. 4 is a block diagram of the present invention and system.
具体实施方式detailed description
如图4所示的一种判断送丝风机抖振的综合分析及其验证方法，该方法包括综合分析和验证方法，所述的综合分析包括以下的步骤：As shown in Figure 4, a comprehensive analysis and verification method for judging the buffeting of a wire feeding fan, the method includes a comprehensive analysis and a verification method, and the comprehensive analysis includes the following steps:
1)在一个设备送线时段内随机对送丝风机负压吸风的瞬时风压和风量的过程变量进行采样，获得采样矩阵W＝(N*S)，其中N为采样点个数，S为监测变量个数；重复T个生产时段，获得相应的数据矩阵W'＝(T*N*Si)，其中Si为第i个除尘时段内的采样点个数；1) Randomly sample the process variables of the instantaneous wind pressure and air volume of the negative pressure suction of the wire feeding fan within a wire feeding period of the equipment, and obtain the sampling matrix W=(N*S), where N is the number of sampling points, S is the number of variables to be monitored; repeat T production periods to obtain the corresponding data matrix W'=(T*N*S i ), where S i is the number of sampling points in the i-th dust removal period;
2)所述的数据矩阵按照约束变分原理进行测算，获得针对送丝风机抖振的约束控制系数σ，即将送丝风机的送风系统看作为约束式预期控制，对送风过程的综合分析采用有界、增益无穷大的调控控制方法；2) The data matrix is measured and calculated according to the constraint variation principle, and the constraint control coefficient σ for the chattering of the wire feeding fan is obtained, namely The air supply system of the wire feeding fan is regarded as a constrained anticipatory control, and the comprehensive analysis of the air supply process adopts a bounded and infinite gain regulation and control method;
3)所述的送风过程设定为两阶函数，对其送风系统进行调控：当风机工作处于稳定时，则有y＝x,其中y0＝y,x0＝x，其中y为振幅，x为振动频率，其启停切换条件为其中σ为约束控制系数，c为模态量化系数；若当风机发生抖振时，y0与x0的变化就会偏离送风系统预期，其对应关系与约束式预期控制的偏离误差对应，即其中Vxσ为送风系统控制系数变化值，xc为送风系统模态量化后的预估值，xu为送风系统偏离误差值；并且指定送风系统初始状态为xo＜0且σ＞0的条件下，其中xo为送风系统初始状态值；3) The air supply process is set as a two-order function, and the air supply system is regulated: when the blower fan is in a stable operation, then there is y=x, where y 0 =y, x 0 =x, where y is Amplitude, x is the vibration frequency, and its start-stop switching condition is Among them, σ is the constraint control coefficient, and c is the modal quantization coefficient; if the fan chatters, the changes of y0 and x0 will deviate from the expected air supply system, and the corresponding relationship corresponds to the deviation error of the constrained expected control, that is Among them, Vx σ is the change value of the control coefficient of the air supply system, x c is the predicted value after the modal quantization of the air supply system, and x u is the deviation error value of the air supply system; and the initial state of the air supply system is specified as x o <0 and Under the condition of σ>0, where x o is the initial state value of the air supply system;
3)所述的送风系统若是可以调控的，那么按照此前调控方法设计出来的系数σ能够保证送风系统符合(x0',xσ')的初始值，即在tRC＝tσ-t0期间，tσ为送风系统约束控制过程时间，t0为送风系统初始状态时间，tRC为送风系统约束预期控制时间；使送风系统从(x0',xσ')的初始状态到达c模态量化状态，这个过程是便于风机能够符合约束式预期控制的量化状态，过程如图1所示；3) If the air supply system can be adjusted, then the coefficient σ designed according to the previous control method can ensure that the air supply system meets the initial value of (x 0 ', x σ '), that is, at t RC =t σ - During t 0 , t σ is the process time of the air supply system restriction control process, t 0 is the initial state time of the air supply system, t RC is the expected control time of the air supply system restriction; make the air supply system from (x 0 ', x σ ') The initial state reaches the c-mode quantization state. This process is to facilitate the fan to conform to the quantization state of the constrained expected control. The process is shown in Figure 1;
4)所述的图1，图中(x0',xσ')与原点O(0,0)之间连线的斜率表示为d＝-xσ/x0；σ＞0相当于Δd＝xσ-x0＞0，在风机送风系统状态趋近量化状态c期间，必有d＜0，故x+dx＝0所代表的风机送风系统工况模态收敛速度不同于c所代表的工况模态收敛速度，也就是说风机送风系统在还未完全量化状态下的工况模态收敛速度大于约束式预期控制状态下所代表的工况模态收敛速度，风机的抖振还比较明显；在送风系统从(x0',xσ')向c的趋近过程中，其收敛速度逐渐减小到与c的收敛速度一致，即d→c，该趋近过程称为平衡，反之，则为抖振；4) As mentioned in Figure 1, the slope of the line between (x 0 ', x σ ') and the origin O(0,0) in the figure is expressed as d=-x σ /x 0 ; σ>0 is equivalent to Δd ＝x σ -x 0 >0, during the period when the state of the fan air supply system approaches the quantized state c, there must be d<0, so the modal convergence speed of the fan air supply system represented by x+dx=0 is different from c The modal convergence speed of the working condition represented by , that is to say, the modal convergence speed of the fan air supply system in the state of incomplete quantification is greater than the modal convergence speed of the working condition represented by the constrained expected control state. Chattering is still relatively obvious; during the approach of the air supply system from (x 0 ', x σ ') to c, its convergence speed gradually decreases to be consistent with the convergence speed of c, that is, d→c, the approach The process is called balance, otherwise, it is chattering;
5)所述的系数σ在风机启停切换条件(σ'＜0,σ＞0)下求解出来的c存在有可能不同于在送风系统工况模态收敛状态下设计出来的c等价的现象，因为风机产生抖振时的σ有超过极限值的可能，所以不能保证风机一直处于稳定状态，若在送风系统工况模态收敛后仍然发生风机抖振，则必出现预期控制不可实现的现象；5) The coefficient σ obtained under the fan start-stop switching condition (σ'<0, σ>0) may be different from the c equivalent designed under the modal convergence state of the air supply system. Because the σ of the blowing fan may exceed the limit value, it cannot be guaranteed that the fan is always in a stable state. If the blowing vibration of the fan still occurs after the modal convergence of the air supply system, the expected control failure must occur. the realized phenomenon;
6)所述的当出现预期调控不可实现的现象时，此时的斜率d不等于c，与x+cx＝0平行的直线x'+cx≠0，即风机送风系统模态量化的状态无法满足约束式条件，所以送风系统无法起到预期调控的意义；虽然它的斜率不等于量化系数c，但可以将x+cx≠0上下平移；所以可采用平移的办法将斜率等于c，结果是收敛的变化过程(即(x(t),x'(t)))有两种可能，如图2所示，其中第1种可能说明风机抖振可调控，第2种可能说明风机抖振不可调控；6) When the phenomenon that the expected control cannot be realized occurs, the slope d at this time is not equal to c, and the straight line x'+cx≠0 parallel to x+cx=0 is the state of the modal quantization of the fan air supply system The constraint condition cannot be satisfied, so the air supply system cannot play the role of expected regulation; although its slope is not equal to the quantization coefficient c, it can be translated up and down by x+cx≠0; so the slope can be equal to c by means of translation, The result is that there are two possibilities for the change process of convergence (that is, (x(t), x'(t))), as shown in Figure 2, where the first possibility indicates that the buffeting of the fan can be adjusted, and the second possibility indicates that the fan chattering can be adjusted. Chattering cannot be adjusted;
7)所述的图2中，曲线1表明风机发生抖振时可调控，曲线2表明不可调控，在风机送风系统趋近量化c期间，因d＞0送风系统收敛过程必先发散，而后演化为量化c的另一分支，则风机抖振趋向稳定的过程是非单向收敛过程；7) In the above-mentioned Figure 2, curve 1 indicates that the buffeting of the fan can be adjusted, and curve 2 indicates that it cannot be adjusted. During the period when the air supply system of the fan is approaching quantization c, because d>0, the convergence process of the air supply system must diverge first. Then it evolves into another branch of quantization c, the process of fan buffeting tending to be stable is a non-unidirectional convergence process;
8)所述的验证上述分析正确与否的方法包括两个步骤，第一个步骤是确定风机送风系统的启停切换函数σ(x)；第二个步骤是通过满足模态量化状态系数c来达到预期控制的目的；8) The method for verifying that the above-mentioned analysis is correct or not includes two steps, the first step is to determine the start-stop switching function σ(x) of the fan air supply system; the second step is to quantify the state coefficient by satisfying the modal c to achieve the purpose of expected control;
第一个步骤包括以下的步骤：The first step consists of the following steps:
1)所述的第一个步骤中，假定将风机抖振控制问题的对象，即风机工况状态表示为： s＝A(x)+B(y)*0.5，其中A(x)表示振动频繁变化矩阵，B(y)表示振幅变化矩阵，c表示模态量化系数；由于A(x)是n×n维矩阵，B(y)是n×m维矩阵，所以s是n维向量，c∈Rm×n，则风机送风系统的启停切换函数σ(x)指定为状态变量线性组合而成的函数等价为：σ(x)＝s＝A(x)+B(y)*c；1) In the first step, it is assumed that the object of the fan chattering control problem, that is, the working condition of the fan is expressed as: s=A(x)+B(y)*0.5, where A(x) represents the vibration Frequent change matrix, B(y) represents the amplitude change matrix, c represents the modal quantization coefficient; since A(x) is an n×n dimensional matrix, B(y) is an n×m dimensional matrix, so s is an n dimensional vector, c∈R m×n , then the start-stop switching function σ(x) of the fan air supply system is specified as a function formed by a linear combination of state variables, which is equivalent to: σ(x)=s=A(x)+B(y )*c;
2)所述的函数等式中，模态量化系数c∈Rm×n，它是切换函数的线性组合系数，其被控对象可表示为矩阵：其中x1、x2分别为风机发生抖振时采集的负压吸风的瞬时风压和风量的过程变量，若此时在采集过程中，假定期望的风机工况动态过程是渐近稳定的，则对应的σ(x)为：σ(x)＝[c,1][x1,x2]T＝0，其中x1和x2的取值范围称为风机送风系统启停切换函数σ(x)的存在区域，记为θ，另外风机模态量化系数c的取值范围涉及多方面，例如对风机抖振预期调控方法的稳定性，预期调控方法动态过程的快速性等；2) In the function equation described above, the modal quantization coefficient c∈R m×n is the linear combination coefficient of the switching function, and its controlled object can be expressed as a matrix: Among them, x1 and x2 are the process variables of the instantaneous wind pressure and air volume of the negative pressure suction collected when the fan chattering occurs, if at this time in the collection process, it is assumed that the dynamic process of the expected fan working condition is asymptotically stable, then The corresponding σ(x) is: σ(x)=[c,1][x 1 ,x 2 ] T ＝0, where the value range of x1 and x2 is called the switch function σ(x ) is denoted as θ, and the value range of fan modal quantization coefficient c involves many aspects, such as the stability of the expected control method for fan buffeting, the rapidity of the dynamic process of the expected control method, etc.;
3)所述的风机模态量化系数c的取值范围，若想减小风机抖振，满足方法渐近稳定性的要求，仅需c＞0，根据x1可能变化的范围以及对预期调控方法动态过程快速性要求来减小抖振，例如指定c＝0.5，则风机工况状态S定义为：x2＝-0.5x1,-2＜x1＜2，它是S的存在区域θσ中，斜对称于零点的两条线段S1和S2，如图3所示，图中θσ为S的领域；如果希望持续减弱抖振，而且对方法快速性没有特定要求，则仅需减小c且c>0，使方法快速性远低于送风系统快速性即可；3) The value range of the fan modal quantization coefficient c mentioned above, if you want to reduce fan buffeting and meet the requirements of the asymptotic stability of the method, only c > 0, according to the range of possible changes in x1 and the expected control method The rapidity of the dynamic process is required to reduce chattering. For example, if c=0.5 is specified, the working condition S of the fan is defined as: x 2 =-0.5x 1 , -2<x 1 <2, which is the existence area of S θ σ , the two line segments S1 and S2 that are obliquely symmetrical to the zero point, as shown in Figure 3, θ σ in the figure is the field of S; if you want to continuously reduce chattering, and there is no specific requirement for the rapidity of the method, you only need to reduce c and c>0, so that the rapidity of the method is much lower than the rapidity of the air supply system;
第二个步骤包括以下的步骤：The second step consists of the following steps:
1)所述的第二个步骤中，c将送风系统从x0拉到S上的途径有两条：σ(x)＞0将x拉到Sp 上，或σ(x)＜0将x拉到SN上为稳定，其中Sp为预估状态，SN为调控状态；σ(x)＞0将x拉到SN 上，或σ(x)＜0将x拉到Sp上为抖振；虽然它们都到达了S，但动态过程x0(t)不同；若稳定，x0(t) 单向收敛无超调；若抖振，x0(t)则超调；稳定还是抖振，取决于c的确定方法；1) In the second step, there are two ways for c to pull the air supply system from x0 to S: σ(x)>0 to pull x to Sp, or σ(x)<0 to pull x Pulling it to SN is stable, where Sp is the estimated state and SN is the control state; σ(x)>0 pulls x to SN, or σ(x)<0 pulls x to Sp to chatter; although They all reach S, but the dynamic process x 0 (t) is different; if it is stable, x 0 (t) will converge in one direction without overshoot; if it chatters, x 0 (t) will overshoot; whether to stabilize or chatter depends The determination method of c;
2)所述的途径，利用此条件，获取控制的不等式为称为第二个步骤的附加条件，依据附加条件可求解c，在认定c为常数的前提下，有σ(x)＝cx，将此式代入表达式x＝A(x)+B(x)*C,其中x(t0)＝x0，同时代入误差系数u，可得表达式：σ(x)＝cA(x)+cB(x)u，假定(cB(x))-1存在，可求得约束式预期控制的误差系数u’为：u'＝-csgn(σ(x))，式中u’满足的要求；2) said way, utilize this condition, the inequality of obtaining control is It is called the additional condition of the second step. According to the additional condition, c can be solved. On the premise that c is determined to be a constant, there is σ(x)=c x , and this formula is substituted into the expression x=A(x)+B( x)*C, where x(t 0 )=x 0 , while substituting the error coefficient u, the expression can be obtained: σ(x)=cA(x)+cB(x)u, assuming (cB(x)) - 1 exists, the error coefficient u' of constrained predictive control can be obtained as: u'=-csgn(σ(x)), where u' satisfies requirements;
3)所述的约束式预期控制的误差系数u’的表达式，即u'＝-csgn(σ(x))与被控对象表达式两者形成了闭环控制；3) the expression of the error coefficient u' of the described constrained type anticipatory control, i.e. u'=-csgn (σ (x)) and the controlled object expression both form a closed-loop control;
4)所述的误差系数u的表达式进行举例，例如将u'＝[0.51]放入误差系数u’的表达式，可得举例启停式风机控制表达式为：u'＝-0.5sgn(σ(x))；此时u’与被控对象表达式(即x＝A(x)+B(x)*C,其中x(t0)＝x0)形成闭环控制。4) The expression of the error coefficient u is given as an example, for example with Put u'=[0.51] into the expression of error coefficient u', for example, the expression of start-stop fan control can be obtained: u'=-0.5sgn(σ(x)); at this time, u' and the controlled object express The formula (ie x=A(x)+B(x)*C, where x(t 0 )=x 0 ) forms a closed-loop control.
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