WO2020252875A1 - Simple pendulum apparatus and rapid oscillation control method thereof - Google Patents
Simple pendulum apparatus and rapid oscillation control method thereof Download PDFInfo
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- WO2020252875A1 WO2020252875A1 PCT/CN2019/100800 CN2019100800W WO2020252875A1 WO 2020252875 A1 WO2020252875 A1 WO 2020252875A1 CN 2019100800 W CN2019100800 W CN 2019100800W WO 2020252875 A1 WO2020252875 A1 WO 2020252875A1
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- pendulum
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B15/00—Systems controlled by a computer
- G05B15/02—Systems controlled by a computer electric
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D3/00—Control of position or direction
- G05D3/12—Control of position or direction using feedback
Definitions
- the invention belongs to the field of mechanical structure swing control, in particular to a single pendulum device and a rapid swing control method thereof.
- pendulum structures are widely used in construction, agriculture, aerospace and other fields, such as cranes, tethered drones, and tethered satellites.
- the swing of these structures has a great adverse effect on the equipment.
- Existing swing control methods for simple pendulum structures often take up a lot of space and have low swing suppression efficiency.
- the present invention provides a swing control device and a control method thereof with high versatility and high swing control efficiency.
- the main technical solutions adopted by the present invention include:
- a single pendulum device which includes a supporting system, a bearing with a seat, a photoelectric encoder, a rotating shaft, a connecting device, a stepping motor, a single pendulum structure, a moving slider, and a control and acquisition system;
- the seated bearing is arranged on the supporting system through the bearing seat, and the rotating shaft is fixedly connected with the bearing inner ring of the seated bearing;
- the pendulum structure is fixedly connected with the rotating shaft through the connecting device;
- the moving slider is slidably connected with the pendulum structure and slides under the drive of a stepper motor.
- the swing of the pendulum can be quickly suppressed by the movement of the moving slider on the pendulum structure;
- the rotating shaft of the photoelectric encoder is connected with the rotating shaft
- the photoelectric encoder and stepper motor are connected to the control and acquisition system for communication.
- the pendulum device includes an upper bracket and a lower bracket that are arranged oppositely;
- An optical axis is fixedly arranged between the upper bracket and the lower bracket, and the movable slider is slidably connected with the optical axis.
- the upper bracket is provided with a first timing belt wheel
- the lower bracket is provided with a second timing belt wheel
- the first timing belt wheel and the second timing belt wheel are wound with timing belts
- the moving slider is fixedly connected to the timing belt.
- the first synchronous belt wheel is fixedly connected with the output shaft of the stepping motor, the stepping motor drives the synchronous belt to move through the first synchronous belt wheel, and the synchronous belt drives the slider to move on the single pendulum.
- the photoelectric encoder is connected to the control and acquisition system through a data acquisition card;
- the swing angle of the pendulum structure measured by the photoelectric encoder is input to the control and acquisition system through the data acquisition card.
- control and acquisition system will control the rotation of the stepping motor according to the swing control method.
- a method for quickly controlling the swing of a single pendulum which is used for controlling the operation of the above-mentioned single pendulum device. It is an intermittent motion control method that moves the slider.
- the control method can not only use the swing suppression effect generated by the sliding of the moving slider on the pendulum structure to perform rapid control of the pendulum swing, but also reduce the disturbance of the pendulum device near the stable position during actual swing.
- the algorithm can be implemented without establishing a specific mathematical model of the structure, and specifically includes the following steps:
- Step 1 Collect the swing angle of the pendulum in real time and determine the time when it swings to the maximum angle and the minimum angle (the pendulum vertical position);
- Step 2 When the pendulum swings to the maximum angle, control the moving slider to move upward; when the pendulum swings to the minimum angle, control the moving slider to move downward;
- Step 3 Determine the movement distance of each movement of the moving slider according to the automatic control method.
- the simple pendulum device is allowed to swing freely from a certain initial angle ⁇ 0 , and the photoelectric encoder is used to collect the angle ⁇ of the simple pendulum in real time, and determine the maximum angle and the minimum angle to trigger the rotation of the stepping motor Thereby driving the moving slider to move.
- step 2 when the computer recognizes that the single pendulum reaches the maximum angle, the stepping motor control card will control the stepping motor to make the moving slider move upwards, wherein the upward movement track of the slider is:
- the stepper motor control card will control the stepper motor to move the moving slider downwards, where the downward movement track of the slider is:
- the cosine trajectory is adopted as the moving trajectory of the moving slider.
- step 2 it should be noted that only the form of the movement track of the moving slider is given, and the specific movement position needs to be determined according to the set initial position of the slider and the position after each movement.
- the position after each movement is the starting position of the next movement.
- step 3 the movement distance ⁇ L for each upward and downward movement of the design moving slider is calculated according to the control method, and the expression is
- ⁇ L max is the maximum range of the movable slider; e is the natural base; Is the maximum swing that a single pendulum can reach per cycle; in order to measure the speed of the swing suppression of the single pendulum, set ⁇ sta as the attenuation standard of the single pendulum swing, that is, the time when the single pendulum swings to ⁇ sta is used as a comparison of the influence of different parameters Standard; ⁇ and ⁇ are control parameters to adjust the change of motion range.
- control parameter Its function is to maximize the movement distance at the initial swing angle no matter how much ⁇ is taken, thereby producing a better swing suppression effect.
- step 3 after setting the parameters, it can be predicted in advance that the moving distance of the moving slider is decreasing until ⁇ L is 0 when the pendulum does not move, so as to ensure the stability of the pendulum device movement.
- the present invention provides a single pendulum device and a control method for rapid control of the swing of the single pendulum.
- the computer collects the angle signal of the simple pendulum to trigger the rotation of the stepper motor to drive the movement of the moving slider.
- the proposed simple pendulum structure with a moving slider has a certain general applicability; the proposed control method does not require an accurate mathematical model of the device, and can be used only by judging the maximum and minimum of the angle of the simple pendulum. Applicability and higher swing control efficiency.
- Figure 1 is a schematic diagram of a simple pendulum device
- Figure 2 is a schematic diagram of the upper bracket of the single pendulum structure
- Figure 3 is a schematic diagram of the lower bracket of the single pendulum structure
- Figure 4 is a schematic diagram of a quick control method for the swing of a simple pendulum
- Figure 5 is a schematic diagram of the angular response of the swing of a simple pendulum structure.
- this implementation provides a single pendulum device, which includes: a control and acquisition system, a support system, a bearing 1, a photoelectric encoder 13, a rotating shaft 2, a connecting device 3, a stepping motor 4, a single Pendulum structure and moving slider 9.
- the control and acquisition system includes a data acquisition card 15, a stepping motor control card 16, and a processor 17, where the processor is a computer.
- the supporting system includes a supporting structure and a table 8.
- the supporting structure includes two vertical supporting plates and a horizontal supporting plate 11.
- the two vertical supporting plates are a first vertical supporting plate 12 and a second vertical supporting plate 14 respectively.
- the two vertical support plates are arranged symmetrically.
- the horizontal support plate 11 is arranged at the upper end of the vertical support plate.
- the lower ends of the two vertical support plates are fixed in the T-shaped groove on the table 8 by T-bolts.
- the support plate is fixed by bolts.
- the bearing seat of the seated bearing 1 and the horizontal support plate 11 are connected and fixed by bolts, and the bearing inner ring of the seated bearing 1 and the rotating shaft 2 are fixed by an expansion sleeve.
- the connecting device 3 includes front and rear connecting plates. One end of the connecting plate is fixedly connected to the rotating shaft through an expansion sleeve, and the other end is fixedly connected to the pendulum structure.
- the rotating shaft 2, the connecting device 3 and the bearing inner ring of the seated bearing 1 The single pendulum structure swings together.
- the photoelectric encoder 13 adopts the OMRON 3600P/R photoelectric encoder, which is fixed on the supporting system and connected to the shaft 2.
- the photoelectric encoder 13 is connected to the computer 17 through the data acquisition card 15, and the photoelectric encoder 13 is used for real-time measurement of pendulums.
- the angle of the structure swing, and the collected angle information is transmitted to the computer 17 through the data acquisition card 15.
- the single pendulum structure includes two optical shafts 7, an upper bracket 5 and a lower bracket 10.
- FIG. 2 is a schematic diagram of the structure of the upper bracket.
- the upper bracket 5 also serves as the bracket of the stepping motor 4, and the stepping motor 4 is fixed on the upper bracket 5.
- the upper bracket 5 is connected and fixed to the connecting device 3 by two bolts, and the upper bracket 5 and the connecting device 3 can swing together.
- the upper bracket 5 is provided with a first timing belt wheel 18, and the upper bracket 5 and the two optical shafts 7 are fixedly connected by an expansion sleeve.
- Fig. 3 is a schematic diagram of the structure of the lower bracket.
- the lower bracket 10 is provided with a second timing pulley 19, and the other ends of the lower bracket 10 and the two optical shafts 7 are also fixedly connected by an expansion sleeve.
- the moving slider 9 is sleeved on the optical axis 7 and can slide relative to the optical axis 7.
- the moving slider 9 is fixedly connected with the timing belt 6, and the two ends of the timing belt 6 respectively bypass the first timing pulley 18 and the second timing pulley 19, that is, the timing belt 6 is sleeved on the first timing pulley 18 and the second timing pulley. Synchronous pulley 19 on.
- the output shaft of the stepping motor 4 is connected to the first timing belt wheel 18.
- the stepping motor 4 drives the rotation of the first timing belt wheel 18, the first timing belt wheel 18 drives the timing belt 6 to move, and the moving sliding block 9 follows the timing belt. 6 mobile.
- the movable sliding block 9 includes two linear bearings, and the movable sliding 9 is sleeved on the optical axis 7 through the linear bearings. Therefore, the movable sliding block 9 can move smoothly and quickly on the two optical axes 7.
- the specific motion form of the moving slider 9 is determined by the control method proposed by the present invention.
- a rapid control method for the swing of a single pendulum is provided, which is an intermittent control method for moving a slider.
- the method proposed by the present invention combines active control with automatic control, actively controls the overall movement process of the moving slider, and automatically controls the movement distance of the moving slider.
- the advantage of this method is that the active control method proposed by the present invention can utilize the intermittent movement of the moving slider to achieve rapid suppression of the pendulum swing, and the automatic control method can reduce the disturbance of the pendulum device near the stable position during actual swing. Moreover, the algorithm proposed by the present invention can realize rapid control of swing without establishing a mathematical model with precise structure.
- a rapid control method for swinging of a single pendulum includes the following steps:
- Step 1 Collect the swing angle of the pendulum in real time and determine the time when the pendulum swings to the maximum angle and the minimum angle (the minimum angle refers to when the pendulum is in the vertical position).
- Step 2 When the pendulum swings to the maximum angle, control the moving slider to move upward; when the pendulum swings to the minimum angle, control the moving slider to move downward;
- the computer When the computer recognizes that the single pendulum reaches the maximum angle, it will send a control instruction to the stepper motor control card to control the stepper motor to move the moving slider upward, and the trajectory of the upward movement Determined by the control method shown in formula (1).
- the stepper motor control card When the computer recognizes that the single pendulum reaches the minimum angle, the stepper motor control card will control the stepper motor to make the moving slider move downward, and the trajectory of the downward movement of the slider Determined by the control method shown in formula (2).
- the present invention takes into account that the actual movement of the moving slider needs to have acceleration and deceleration processes, so the cosine trajectory is used as the moving trajectory of the moving slider, and the movement speed is to start from 0 to accelerate the movement to a certain speed and then decelerate to 0.
- it is also necessary to determine l 0 according to the set initial position of the slider and the position after each movement to determine the specific movement position of the moving slider.
- the position after each movement is the starting position of the next movement and does not need to be specified in advance.
- Step 3 Determine the movement distance ⁇ L of each movement of the moving slider according to the automatic control method.
- the moving distance ⁇ L of each upward and downward movement of the moving slider designed by the present invention will be calculated according to the control method, and its expression is
- ⁇ L max is the maximum range of movement available for the movable slider; e is the natural base; It is the maximum swing that a single pendulum can reach per cycle; in order to measure the attenuation speed of the single pendulum, set ⁇ sta as the attenuation standard of the single pendulum swing, that is, the time when the single pendulum swings to ⁇ sta is used as a comparison of the influence of different parameters Standard; ⁇ and ⁇ are both control parameters to adjust the change of motion range.
- the function of the control parameter ⁇ is to control the speed at which the movement range of the moving slider decreases.
- control parameter Its function is to maximize the movement distance at the initial swing angle no matter how much ⁇ is taken, thereby producing a better swing suppression effect.
- step 3 after the parameters are given, it can be predicted in advance that the moving distance of the moving slider will decrease until ⁇ L is 0 when the pendulum does not move, so as to ensure the stable movement of the pendulum device. Sex.
- Figure 4 shows the intermittent movement of the moving slider during the first two cycles of the pendulum swing, where the first cycle of the pendulum swing includes two There are two downward movements of the slider and one upward movement of the slider. The second cycle and each subsequent cycle include two upward and downward movements of the mass.
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Abstract
A simple pendulum apparatus and a rapid oscillation control method thereof. A simple pendulum structure of the simple pendulum apparatus is connected to a mounted bearing (1) by means of a connection apparatus (3). A rotation angle of the simple pendulum structure is converted into an analog signal by means of a photoelectric encoder (13), and a computer (17) acquires and stores the analog signal. A moving slider (9) is connected to a stepping motor (4) by means of a synchronous belt (6) and a synchronous pulley (18), and the stepping motor (4) controls movement of the moving slider on the simple pendulum structure. The rapid oscillation control method comprises the following steps: acquiring and determining an oscillation angle of the simple pendulum in real time; and when the simple pendulum reaches a maximum angle, controlling the moving slider (9) to move upwards, and when the simple pendulum reaches a vertical position, controlling the moving slider (9) to move downwards. A method for controlling movement of the moving slider (9) is designed, and a movement distance ΔL for each movement of the moving slider (9) is designed. The simple pendulum apparatus and the control method efficiently and stably control oscillation, and are applicable to the field of rapid suppression of oscillation of a simple pendulum structure.
Description
本发明属于机械结构摆动控制领域,具体是一种单摆装置及其摆动快速控制方法。The invention belongs to the field of mechanical structure swing control, in particular to a single pendulum device and a rapid swing control method thereof.
目前,单摆类结构广泛应用于建筑、农业及航空航天等领域,例如起重机的吊重、系留无人机以及绳系卫星等结构。然而这些结构的摆动对设备有着很大的不利影响。现有的单摆类结构摆动控制方法往往需要占用很大空间并且摆动抑制效率较低。At present, pendulum structures are widely used in construction, agriculture, aerospace and other fields, such as cranes, tethered drones, and tethered satellites. However, the swing of these structures has a great adverse effect on the equipment. Existing swing control methods for simple pendulum structures often take up a lot of space and have low swing suppression efficiency.
发明内容Summary of the invention
(一)要解决的技术问题(1) Technical problems to be solved
针对现有技术中存在的单摆类结构的摆动控制问题,本发明提供一种通用性和摆动控制效率较高的摆动控制装置及其控制方法。Aiming at the swing control problem of a simple pendulum structure in the prior art, the present invention provides a swing control device and a control method thereof with high versatility and high swing control efficiency.
(二)技术方案(2) Technical solution
为了达到上述目的,本发明采用的主要技术方案包括:In order to achieve the above objectives, the main technical solutions adopted by the present invention include:
一种单摆装置,其包括支撑系统、带座轴承、光电编码器、转轴、连接装置、步进电机、单摆结构,移动滑块,控制与采集系统;A single pendulum device, which includes a supporting system, a bearing with a seat, a photoelectric encoder, a rotating shaft, a connecting device, a stepping motor, a single pendulum structure, a moving slider, and a control and acquisition system;
带座轴承通过轴承座设置在支撑系统上,转轴与带座轴承的轴承内圈固定连接;The seated bearing is arranged on the supporting system through the bearing seat, and the rotating shaft is fixedly connected with the bearing inner ring of the seated bearing;
单摆结构通过连接装置与转轴固定连接;The pendulum structure is fixedly connected with the rotating shaft through the connecting device;
移动滑块与单摆结构滑动连接,并在步进电机的驱动下滑动,通过移动滑块在单摆结构上的移动来快速抑制单摆的摆动;The moving slider is slidably connected with the pendulum structure and slides under the drive of a stepper motor. The swing of the pendulum can be quickly suppressed by the movement of the moving slider on the pendulum structure;
光电编码器的旋转轴与转轴相连;The rotating shaft of the photoelectric encoder is connected with the rotating shaft;
光电编码器和步进电机与控制与采集系统通讯连接。The photoelectric encoder and stepper motor are connected to the control and acquisition system for communication.
优选的,单摆装置包括相对设置的上部支架和下部支架;Preferably, the pendulum device includes an upper bracket and a lower bracket that are arranged oppositely;
上部支架和下部支架之间固定设置有光轴,移动滑块与光轴滑动连接。An optical axis is fixedly arranged between the upper bracket and the lower bracket, and the movable slider is slidably connected with the optical axis.
优选的,上部支架上设置有第一同步带轮、下部支架上设置有第二同步带轮,第一同步带轮和第二同步带轮上缠绕有同步带,移动滑块与同步带固定连接;Preferably, the upper bracket is provided with a first timing belt wheel, the lower bracket is provided with a second timing belt wheel, the first timing belt wheel and the second timing belt wheel are wound with timing belts, and the moving slider is fixedly connected to the timing belt. ;
第一同步带轮与步进电机的输出轴固定连接,步进电机通过第一同步带轮带动同步带移动,同步带带动滑块在单摆上移动。The first synchronous belt wheel is fixedly connected with the output shaft of the stepping motor, the stepping motor drives the synchronous belt to move through the first synchronous belt wheel, and the synchronous belt drives the slider to move on the single pendulum.
优选的,光电编码器通过数据采集卡与控制与采集系统连接;Preferably, the photoelectric encoder is connected to the control and acquisition system through a data acquisition card;
光电编码器测得的单摆结构摆动的角度,通过数据采集卡将角度信号输入到控制与采集系统。The swing angle of the pendulum structure measured by the photoelectric encoder is input to the control and acquisition system through the data acquisition card.
优选的,控制与采集系统将根据摆动控制方法对步进电机的转动进行控制。Preferably, the control and acquisition system will control the rotation of the stepping motor according to the swing control method.
一种单摆摆动快速控制方法,该方法用于控制上述单摆装置的运行。为一种移动滑块的间歇性运动控制方法。控制方法既能利用移动滑块在单摆结构上滑动所产生的摆动抑制效应来进行单摆摆动的快速控制,又能减少实际摆动时单摆装置在稳定位置附近的扰动。该算法无需建立结构的具体数学模型便可实现,具体包括以下步骤:A method for quickly controlling the swing of a single pendulum, which is used for controlling the operation of the above-mentioned single pendulum device. It is an intermittent motion control method that moves the slider. The control method can not only use the swing suppression effect generated by the sliding of the moving slider on the pendulum structure to perform rapid control of the pendulum swing, but also reduce the disturbance of the pendulum device near the stable position during actual swing. The algorithm can be implemented without establishing a specific mathematical model of the structure, and specifically includes the following steps:
步骤一:实时采集单摆摆动的角度并判断摆动到最大角度与最小角度(单摆垂直位置)的时刻;Step 1: Collect the swing angle of the pendulum in real time and determine the time when it swings to the maximum angle and the minimum angle (the pendulum vertical position);
步骤二:在单摆摆动到最大角度时,控制移动滑块向上运动;在单摆摆动到最小角度时,控制移动滑块向下运动;Step 2: When the pendulum swings to the maximum angle, control the moving slider to move upward; when the pendulum swings to the minimum angle, control the moving slider to move downward;
步骤三:根据自动控制方法确定移动滑块每次运动的运动距离。Step 3: Determine the movement distance of each movement of the moving slider according to the automatic control method.
优选的,在步骤一中,令单摆装置从某一初始角度θ
0开始自由摆动,利用光电编码器实时采集单摆的角度θ,并判断出最大角度和最小角度来触发步进电机的转动从而驱动移动滑块运动。
Preferably, in step 1, the simple pendulum device is allowed to swing freely from a certain initial angle θ 0 , and the photoelectric encoder is used to collect the angle θ of the simple pendulum in real time, and determine the maximum angle and the minimum angle to trigger the rotation of the stepping motor Thereby driving the moving slider to move.
优选的,在步骤二中,当计算机识别到单摆达到最大角度时,步进电机控制卡将控制步进电机使移动滑块向上运动,其中滑块向上运动的 轨迹为:Preferably, in step 2, when the computer recognizes that the single pendulum reaches the maximum angle, the stepping motor control card will control the stepping motor to make the moving slider move upwards, wherein the upward movement track of the slider is:
当计算机识别到单摆达到最小角度时,步进电机控制卡将控制步进电机使移动滑块向下运动,其中滑块向下运动的轨迹为:When the computer recognizes that the single pendulum reaches the minimum angle, the stepper motor control card will control the stepper motor to move the moving slider downwards, where the downward movement track of the slider is:
其中,i=1,2,3…代表向上和向下运动的次序。Among them, i=1, 2, 3... represents the sequence of upward and downward movement.
优选的,在步骤二中,ΔT为移动滑块每次运动的运动时间,并要求其小于单摆摆动周期的四分之一来保证单摆摆动的快速抑制;ΔL为移动滑块每次的运动距离。Preferably, in step 2, ΔT is the movement time of each movement of the moving slider, and it is required to be less than a quarter of the swing period of the single pendulum to ensure rapid suppression of the swing of the single pendulum; ΔL is the time required for each movement of the moving slider. Movement distance.
优选的,在步骤二中,考虑到移动滑块实际运动需要存在加、减速过程,因此采用余弦轨迹作为移动滑块的运动轨迹。Preferably, in step 2, considering that the actual movement of the moving slider requires an acceleration and deceleration process, the cosine trajectory is adopted as the moving trajectory of the moving slider.
优选的,在步骤二中,需要注意的是,仅仅给定了移动滑块的运动轨迹的形式,具体的运动位置还需根据所设定的滑块初始位置以及每次运动后的位置来确定式中的l
0,每次运动后的位置便为下一次运动的起始位置。
Preferably, in step 2, it should be noted that only the form of the movement track of the moving slider is given, and the specific movement position needs to be determined according to the set initial position of the slider and the position after each movement. In the formula l 0 , the position after each movement is the starting position of the next movement.
优选的,在步骤三中,设计移动滑块每次向上和向下运动的运动距离ΔL会根据控制方法来计算,其表达式为Preferably, in step 3, the movement distance ΔL for each upward and downward movement of the design moving slider is calculated according to the control method, and the expression is
其中,ΔL
max为可供移动滑块运动的最大范围;e为自然底数;
为单摆每周期所能达到的最大摆幅;为了衡量单摆摆动抑制的速度,设定θ
sta为单摆摆动的衰减标准,即以单摆摆动到θ
sta的时刻作为对比不同参数影响的标准;λ与ε为控制参数来调整运动范围的变化。
Among them, ΔL max is the maximum range of the movable slider; e is the natural base; Is the maximum swing that a single pendulum can reach per cycle; in order to measure the speed of the swing suppression of the single pendulum, set θ sta as the attenuation standard of the single pendulum swing, that is, the time when the single pendulum swings to θ sta is used as a comparison of the influence of different parameters Standard; λ and ε are control parameters to adjust the change of motion range.
优选的,在步骤三中,控制参数
其作用为无论λ取多少都能使运动距离在初始摆角处为最大,从而产生更好的摆动抑制效果。
Preferably, in step three, the control parameter Its function is to maximize the movement distance at the initial swing angle no matter how much λ is taken, thereby producing a better swing suppression effect.
优选的,在步骤三中,给定参数后便可提前预见移动滑块的运动距 离是递减的,直到单摆不动时ΔL即为0,以此来确保单摆装置运动的稳定性。Preferably, in step 3, after setting the parameters, it can be predicted in advance that the moving distance of the moving slider is decreasing until ΔL is 0 when the pendulum does not move, so as to ensure the stability of the pendulum device movement.
(三)有益效果(3) Beneficial effects
本发明的有益效果是:本发明提供了一种单摆装置和一种用于单摆摆动快速控制的控制方法。通过计算机采集单摆的角度信号来触发步进电机的转动从而来驱动移动滑块的运动。所提出的带有移动滑块的单摆结构具有一定的普遍适用性;所提出的控制方法无需装置准确的数学模型,只需判断单摆角度的最大值和最小值便可使用,具有广泛的应用性,同时摆动控制效率更高。The beneficial effects of the present invention are: the present invention provides a single pendulum device and a control method for rapid control of the swing of the single pendulum. The computer collects the angle signal of the simple pendulum to trigger the rotation of the stepper motor to drive the movement of the moving slider. The proposed simple pendulum structure with a moving slider has a certain general applicability; the proposed control method does not require an accurate mathematical model of the device, and can be used only by judging the maximum and minimum of the angle of the simple pendulum. Applicability and higher swing control efficiency.
图1为单摆装置的示意图;Figure 1 is a schematic diagram of a simple pendulum device;
图2为单摆结构的上部支架的示意图;Figure 2 is a schematic diagram of the upper bracket of the single pendulum structure;
图3为单摆结构的下部支架的示意图;Figure 3 is a schematic diagram of the lower bracket of the single pendulum structure;
图4为单摆摆动快速控制方法的示意图;Figure 4 is a schematic diagram of a quick control method for the swing of a simple pendulum;
图5为单摆结构摆动的角度响应示意图。Figure 5 is a schematic diagram of the angular response of the swing of a simple pendulum structure.
其中:among them:
1:带座轴承;2:转轴;3:连接装置;4:步进电机;5:上部支架;6:同步带;7:光轴;8:台面;9:移动滑块;10:下部支架;11:水平支撑板;12:第一竖直支撑板;13:光电编码器;14:第二竖直支撑板;15:数据采集卡;16:步进电机控制卡;17:处理器。1: Bearing with seat; 2: Rotating shaft; 3: Connecting device; 4: Stepping motor; 5: Upper bracket; 6: Timing belt; 7: Optical axis; 8: Table; 9: Moving slide; 10: Lower bracket 11: horizontal support board; 12: first vertical support board; 13: photoelectric encoder; 14: second vertical support board; 15: data acquisition card; 16: stepper motor control card; 17: processor.
为了更好的解释本发明,以便于理解,下面结合附图,通过具体实施方式,对本发明作详细描述。In order to better explain the present invention and facilitate understanding, the present invention will be described in detail below with reference to the accompanying drawings and through specific embodiments.
如图1所示,本实施提供了一种单摆装置,其包括:控制与采集系统、支撑系统、带座轴承1、光电编码器13、转轴2、连接装置3、步进电机4、单摆结构和移动滑块9。As shown in Figure 1, this implementation provides a single pendulum device, which includes: a control and acquisition system, a support system, a bearing 1, a photoelectric encoder 13, a rotating shaft 2, a connecting device 3, a stepping motor 4, a single Pendulum structure and moving slider 9.
控制与采集系统包括数据采集卡15、步进电机控制卡16和处理器17,其中,处理器为计算机。The control and acquisition system includes a data acquisition card 15, a stepping motor control card 16, and a processor 17, where the processor is a computer.
支撑系统包括支撑结构和台面8,支撑结构包括两个竖直支撑板和一个水平支撑板11,两个竖直支撑板分别为第一竖直支撑板12和第二竖直支撑板14。两竖直支撑板对称设置,水平支撑板11设置在竖直支撑板的上端,两个竖直支撑板的下端由T型螺栓固定在台面8上的T型槽内,竖直支撑板与水平支撑板由螺栓固定。The supporting system includes a supporting structure and a table 8. The supporting structure includes two vertical supporting plates and a horizontal supporting plate 11. The two vertical supporting plates are a first vertical supporting plate 12 and a second vertical supporting plate 14 respectively. The two vertical support plates are arranged symmetrically. The horizontal support plate 11 is arranged at the upper end of the vertical support plate. The lower ends of the two vertical support plates are fixed in the T-shaped groove on the table 8 by T-bolts. The support plate is fixed by bolts.
带座轴承1的轴承座与水平支撑板11由螺栓相连并固定,带座轴承1的轴承内圈与转轴2由胀紧套所固定。The bearing seat of the seated bearing 1 and the horizontal support plate 11 are connected and fixed by bolts, and the bearing inner ring of the seated bearing 1 and the rotating shaft 2 are fixed by an expansion sleeve.
连接装置3包括前、后两个连接板,连接板的一端与转轴通过胀紧套固定连接,另一端与单摆结构固定连接,转轴2、连接装置3和带座轴承1的轴承内圈与单摆结构共同摆动。The connecting device 3 includes front and rear connecting plates. One end of the connecting plate is fixedly connected to the rotating shaft through an expansion sleeve, and the other end is fixedly connected to the pendulum structure. The rotating shaft 2, the connecting device 3 and the bearing inner ring of the seated bearing 1 The single pendulum structure swings together.
光电编码器13采用OMRON 3600P/R光电编码器,其被固定于支撑系统上并与转轴2相连,光电编码器13通过数据采集卡15与计算机17连接,光电编码器13用于实时测量单摆结构摆动的角度,并通过数据采集卡15将采集到的角度信息传递给计算机17。The photoelectric encoder 13 adopts the OMRON 3600P/R photoelectric encoder, which is fixed on the supporting system and connected to the shaft 2. The photoelectric encoder 13 is connected to the computer 17 through the data acquisition card 15, and the photoelectric encoder 13 is used for real-time measurement of pendulums. The angle of the structure swing, and the collected angle information is transmitted to the computer 17 through the data acquisition card 15.
单摆结构包括两根光轴7、上部支架5和下部支架10。The single pendulum structure includes two optical shafts 7, an upper bracket 5 and a lower bracket 10.
图2为上部支架的结构示意图,上部支架5同时也作为步进电机4的支架,步进电机4固定在上部支架5上。上部支架5通过两根螺栓与连接装置3相连并固定,上部支架5与连接装置3能够共同摆动。上部支架5上设置有第一同步带轮18,上部支架5与两根光轴7通过胀紧套固定连接。FIG. 2 is a schematic diagram of the structure of the upper bracket. The upper bracket 5 also serves as the bracket of the stepping motor 4, and the stepping motor 4 is fixed on the upper bracket 5. The upper bracket 5 is connected and fixed to the connecting device 3 by two bolts, and the upper bracket 5 and the connecting device 3 can swing together. The upper bracket 5 is provided with a first timing belt wheel 18, and the upper bracket 5 and the two optical shafts 7 are fixedly connected by an expansion sleeve.
图3为下部支架的结构示意图,下部支架10带有第二同步带轮19,下部支架10与两根光轴7的另一端同样由胀紧套固定连接。Fig. 3 is a schematic diagram of the structure of the lower bracket. The lower bracket 10 is provided with a second timing pulley 19, and the other ends of the lower bracket 10 and the two optical shafts 7 are also fixedly connected by an expansion sleeve.
移动滑块9套设在光轴7上,并能够相对于光轴7滑动。移动滑块9与同步带6固定相连,同步带6的两端分别绕过第一同步带轮18和第二同步带轮19,即同步带6套设在第一同步带轮18和第二同步带轮19上。The moving slider 9 is sleeved on the optical axis 7 and can slide relative to the optical axis 7. The moving slider 9 is fixedly connected with the timing belt 6, and the two ends of the timing belt 6 respectively bypass the first timing pulley 18 and the second timing pulley 19, that is, the timing belt 6 is sleeved on the first timing pulley 18 and the second timing pulley. Synchronous pulley 19 on.
步进电机4的输出轴与第一同步带轮18相连,步进电机4通过带动第一同步带轮18的转动,第一同步带轮18带动同步带6移动,移动滑动块9随同步带6移动。The output shaft of the stepping motor 4 is connected to the first timing belt wheel 18. The stepping motor 4 drives the rotation of the first timing belt wheel 18, the first timing belt wheel 18 drives the timing belt 6 to move, and the moving sliding block 9 follows the timing belt. 6 mobile.
移动滑块9包含两个直线轴承,移动滑动9通过直线轴承套设在光轴7上,故此,移动滑块9能够在两根光轴7上平滑而快速的移动。The movable sliding block 9 includes two linear bearings, and the movable sliding 9 is sleeved on the optical axis 7 through the linear bearings. Therefore, the movable sliding block 9 can move smoothly and quickly on the two optical axes 7.
移动滑块9的具体运动形式由本发明提出的控制方法来决定。The specific motion form of the moving slider 9 is determined by the control method proposed by the present invention.
具体的,本实施方式中,提供了一种单摆摆动快速控制方法,其为一种移动滑块的间歇性控制方法。本发明所提出的方法将主动控制与自动控制相结合,对移动滑块的总体运动过程进行主动控制,对其中的移动滑块运动距离进行自动控制。Specifically, in this embodiment, a rapid control method for the swing of a single pendulum is provided, which is an intermittent control method for moving a slider. The method proposed by the present invention combines active control with automatic control, actively controls the overall movement process of the moving slider, and automatically controls the movement distance of the moving slider.
该方法优点在于本发明所提出的主动控制方法能利用移动滑块的间歇运动实现单摆摆动的快速抑制,自动控制方法能减少实际摆动时单摆装置在稳定位置附近的扰动。并且本发明所提出的算法无需建立结构精准的数学模型便可实现摆动的快速控制。The advantage of this method is that the active control method proposed by the present invention can utilize the intermittent movement of the moving slider to achieve rapid suppression of the pendulum swing, and the automatic control method can reduce the disturbance of the pendulum device near the stable position during actual swing. Moreover, the algorithm proposed by the present invention can realize rapid control of swing without establishing a mathematical model with precise structure.
一种单摆摆动快速控制方法,该方法包括以下步骤:A rapid control method for swinging of a single pendulum, the method includes the following steps:
步骤一:实时采集单摆摆动的角度并判断摆动到最大角度与最小角度(最小角度指的是单摆位于垂直位置时)的时刻。Step 1: Collect the swing angle of the pendulum in real time and determine the time when the pendulum swings to the maximum angle and the minimum angle (the minimum angle refers to when the pendulum is in the vertical position).
令单摆装置从某一初始角度θ
0开始自由摆动,利用光电编码器实时采集单摆的角度θ,通过计算机对比每个采样点所采集到的角度来判断出单摆摆动每周期最大角度和最小角度。当单摆达到最大和最小角度时,计算机便会发出指令来控制步进电机的转动从而驱动移动滑块运动。
Make the pendulum device swing freely from a certain initial angle θ 0 , use the photoelectric encoder to collect the angle θ of the pendulum in real time, and compare the angles collected at each sampling point by the computer to determine the maximum angle and Minimum angle. When the simple pendulum reaches the maximum and minimum angles, the computer will issue instructions to control the rotation of the stepper motor to drive the moving slider.
步骤二:在单摆摆动到最大角度时,控制移动滑块向上运动;在单摆摆动到最小角度时,控制移动滑块向下运动;Step 2: When the pendulum swings to the maximum angle, control the moving slider to move upward; when the pendulum swings to the minimum angle, control the moving slider to move downward;
当计算机识别到单摆达到最大角度时,会发出控制指令给步进电机控制卡来控制步进电机使移动滑块向上运动,其中滑块向上运动的轨迹
由式(1)所示的控制方法决定。
When the computer recognizes that the single pendulum reaches the maximum angle, it will send a control instruction to the stepper motor control card to control the stepper motor to move the moving slider upward, and the trajectory of the upward movement Determined by the control method shown in formula (1).
当计算机识别到单摆达到最小角度时,步进电机控制卡将控制步进电机使移动滑块向下运动,其中滑块向下运动的轨迹
由式(2)所示的控制方法决定。
When the computer recognizes that the single pendulum reaches the minimum angle, the stepper motor control card will control the stepper motor to make the moving slider move downward, and the trajectory of the downward movement of the slider Determined by the control method shown in formula (2).
在式(1)和式(2)中,i=1,2,3…代表向上和向下运动的次序;
和
分别为计算机所识别到的单摆角度最大和最小的时刻,即为移动滑块向上和向下运动的起始时刻;ΔT为移动滑块每次运动的运动时间,并要求其小于单摆摆动周期的四分之一来保证单摆摆动的快速控制;ΔL为移动滑块的运动距离,需要由控制方法进一步计算出。
In equations (1) and (2), i=1, 2, 3... represents the order of upward and downward movement; with They are the maximum and minimum moments of the pendulum angle recognized by the computer, which are the starting moments of the upward and downward movement of the moving slider; ΔT is the movement time of each movement of the moving slider, and it is required to be less than the swing of the pendulum A quarter of the period is used to ensure the rapid control of the pendulum swing; ΔL is the movement distance of the moving slider, which needs to be further calculated by the control method.
本发明考虑到了移动滑块实际运动需要存在加、减速过程,因此采用余弦轨迹作为移动滑块的运动轨迹,其运动速度便为从0开始加速运动到某一速度后再减速到0。同时需要注意的是,还需根据所设定的滑块初始位置以及每次运动后的位置来确定l
0从而确定移动滑块具体的运动位置。每次运动后的位置便为下一次运动的起始位置,并不需要提前规定。
The present invention takes into account that the actual movement of the moving slider needs to have acceleration and deceleration processes, so the cosine trajectory is used as the moving trajectory of the moving slider, and the movement speed is to start from 0 to accelerate the movement to a certain speed and then decelerate to 0. At the same time, it should be noted that it is also necessary to determine l 0 according to the set initial position of the slider and the position after each movement to determine the specific movement position of the moving slider. The position after each movement is the starting position of the next movement and does not need to be specified in advance.
步骤三:根据自动控制方法确定移动滑块每次运动的运动距离ΔL。Step 3: Determine the movement distance ΔL of each movement of the moving slider according to the automatic control method.
考虑到单摆在接近稳定位置时整体装置摆动的平稳性,本发明设计移动滑块每次向上和向下运动的运动距离ΔL会根据控制方法来计算,其表达式为Taking into account the stability of the swing of the whole device when the pendulum is close to the stable position, the moving distance ΔL of each upward and downward movement of the moving slider designed by the present invention will be calculated according to the control method, and its expression is
其中,ΔL
max为可供移动滑块的运动最大范围;e为自然底数;
为单摆每周期所能达到的最大摆幅;为了衡量单摆摆动衰减的速度,设定θ
sta为单摆摆动的衰减标准,即以单摆摆动到θ
sta的时刻作为对比不同参数影响的标准;λ与ε都为控制参数来调整运动范围的变化。
Among them, ΔL max is the maximum range of movement available for the movable slider; e is the natural base; It is the maximum swing that a single pendulum can reach per cycle; in order to measure the attenuation speed of the single pendulum, set θ sta as the attenuation standard of the single pendulum swing, that is, the time when the single pendulum swings to θ sta is used as a comparison of the influence of different parameters Standard; λ and ε are both control parameters to adjust the change of motion range.
优选的,在步骤三中,控制参数λ的作用为控制移动滑块运动范围减小的速度。Preferably, in step 3, the function of the control parameter λ is to control the speed at which the movement range of the moving slider decreases.
优选的,在步骤三中,控制参数
其作用为无论λ取多少都能使运动距离在初始摆角处为最大,从而产生更好的摆动抑制效果。
Preferably, in step three, the control parameter Its function is to maximize the movement distance at the initial swing angle no matter how much λ is taken, thereby producing a better swing suppression effect.
优选的,在步骤三中,在给定参数后便可提前预见移动滑块每次的运动距离是递减的,直到单摆不动时ΔL即为0,以此来确保单摆装置运动的稳定性。Preferably, in step 3, after the parameters are given, it can be predicted in advance that the moving distance of the moving slider will decrease until ΔL is 0 when the pendulum does not move, so as to ensure the stable movement of the pendulum device. Sex.
优选的,在步骤三中,为了更好的理解移动滑块的运动距离ΔL,图4展示了单摆摆动前两个周期的移动滑块的间歇运动,其中单摆摆动第一个周期包括两次的滑块向下运动与一次滑块向上运动,第二个周期以及之后的每个周期均包括质量块两次的向上与向下运动。Preferably, in step 3, in order to better understand the movement distance ΔL of the moving slider, Figure 4 shows the intermittent movement of the moving slider during the first two cycles of the pendulum swing, where the first cycle of the pendulum swing includes two There are two downward movements of the slider and one upward movement of the slider. The second cycle and each subsequent cycle include two upward and downward movements of the mass.
下面结合一个具体实验的实例来进一步说明本发明对单摆摆动快速控制的有效性及高效性。In the following, a specific experimental example is combined to further illustrate the effectiveness and efficiency of the present invention on the rapid control of the pendulum swing.
实际测得单摆结构的各参数如下:The actual measured parameters of the pendulum structure are as follows:
M=1.151kg,m=0.156kg,L=1.059m,L
c=0.3726m,I
0=0.326kg·m
2
M = 1.151 kg, m = 0.156 kg, L = 1.059 m, L c = 0.3726 m, I 0 = 0.326 kg·m 2
设定单摆摆动的初始条件:θ
0=0.5rad,θ
sta=0.05rad,规定单摆摆动快速控制方法及移动滑块运动轨迹中的各参数如下:
Set the initial conditions of the pendulum swing: θ 0 =0.5rad, θ sta =0.05rad, specify the rapid control method of the pendulum swing and the parameters in the motion track of the moving slider as follows:
ΔT=0.28s,ΔL
max=0.06m,λ=2,l
0=0.8m。
ΔT=0.28s, ΔL max =0.06m, λ=2, l 0 =0.8m.
控制方法和控制过程下单摆结构的角度响应与移动滑块不动(单摆自由摆动)时的角度响应的对比如图5所示。由图5可看出本发明所提出的带有移动滑块的单摆结构及其摆动控制快速控制方法在所选择的参数下提前70.86s达到θ
sta,可以达到较高的摆动控制效率。本发明提出的摆动快速控制方法所产生的摆动抑制效率会随着移动滑块运动时间ΔT的减小和运动距离ΔL的增大而提高。因此在实际应用中,需要根据装置所能达到的参数来合理地设定运动时间和运动距离来实现更高效的摆动抑制。
The comparison between the angular response of the pendulum structure under the control method and control process and the angular response when the moving slider does not move (the pendulum swings freely) is shown in Figure 5. It can be seen from FIG. 5 that the simple pendulum structure with a moving slider and its rapid control method for swing control proposed by the present invention reach θ sta 70.86s earlier under the selected parameters, which can achieve higher swing control efficiency. The swing suppression efficiency produced by the rapid swing control method proposed by the present invention will increase as the movement time ΔT of the moving slider decreases and the movement distance ΔL increases. Therefore, in practical applications, it is necessary to reasonably set the movement time and movement distance according to the parameters that the device can achieve to achieve more efficient swing suppression.
以上结合具体实施例描述了本发明的技术原理,这些描述只是为了解释本发明的原理,不能以任何方式解释为对本发明保护范围的限制。基于此处解释,本领域的技术人员不需要付出创造性的劳动即可联想到本发明的其它具体实施方式,这些方式都将落入本发明的保护范围之内。The technical principles of the present invention are described above in conjunction with specific embodiments. These descriptions are only for explaining the principles of the present invention and cannot be construed as limiting the protection scope of the present invention in any way. Based on the explanation here, those skilled in the art can think of other specific implementation manners of the present invention without creative work, and these manners will fall within the protection scope of the present invention.
Claims (10)
- 一种单摆装置,其特征在于,包括支撑系统、带座轴承、光电编码器、转轴、连接装置、步进电机、单摆结构,移动滑块,控制与采集系统;A single pendulum device, which is characterized in that it comprises a support system, a bearing with a seat, a photoelectric encoder, a rotating shaft, a connecting device, a stepping motor, a single pendulum structure, a moving slider, and a control and acquisition system;带座轴承通过轴承座设置在支撑系统上,转轴与带座轴承的轴承内圈固定连接;The seated bearing is arranged on the supporting system through the bearing seat, and the rotating shaft is fixedly connected with the bearing inner ring of the seated bearing;单摆结构通过连接装置与转轴固定连接;The pendulum structure is fixedly connected with the rotating shaft through the connecting device;移动滑块与单摆结构滑动连接,并在步进电机的驱动下滑动,通过移动滑块在单摆结构上的移动来快速抑制单摆的摆动;The moving slider is slidably connected with the pendulum structure and slides under the drive of a stepper motor. The swing of the pendulum can be quickly suppressed by the movement of the moving slider on the pendulum structure;光电编码器的旋转轴与转轴相连;The rotating shaft of the photoelectric encoder is connected with the rotating shaft;光电编码器和步进电机与控制与采集系统通讯连接。The photoelectric encoder and stepper motor are connected to the control and acquisition system for communication.
- 根据权利要求1所述的单摆装置,其特征在于,单摆装置包括相对设置的上部支架和下部支架;The single pendulum device according to claim 1, wherein the single pendulum device comprises an upper bracket and a lower bracket which are arranged oppositely;上部支架和下部支架之间固定设置有光轴,移动滑块与光轴滑动连接。An optical axis is fixedly arranged between the upper bracket and the lower bracket, and the movable slider is slidably connected with the optical axis.
- 根据权利要求2所述的单摆装置,其特征在于,上部支架上设置有第一同步带轮、下部支架上设置有第二同步带轮,第一同步带轮和第二同步带轮上缠绕有同步带,移动滑块与同步带固定连接;The single pendulum device according to claim 2, wherein the upper bracket is provided with a first timing belt wheel, the lower bracket is provided with a second timing belt wheel, and the first timing belt wheel and the second timing belt wheel are wound on There is a timing belt, the moving slider is fixedly connected with the timing belt;第一同步带轮与步进电机的输出轴固定连接,步进电机通过第一同步带轮带动同步带移动,同步带带动滑块在单摆上移动。The first synchronous belt wheel is fixedly connected with the output shaft of the stepping motor, the stepping motor drives the synchronous belt to move through the first synchronous belt wheel, and the synchronous belt drives the slider to move on the single pendulum.
- 根据权利要求3所述的单摆装置,其特征在于,光电编码器通过数据采集卡与控制与采集系统连接;The simple pendulum device according to claim 3, wherein the photoelectric encoder is connected to the control and acquisition system through a data acquisition card;光电编码器测得的单摆结构摆动的角度,通过数据采集卡将角度信号输入到控制与采集系统。The swing angle of the pendulum structure measured by the photoelectric encoder is input to the control and acquisition system through the data acquisition card.
- 根据权利要求4所述的单摆装置,其特征在于,控制与采集系统将根据摆动控制方法对步进电机的转动进行控制。The single pendulum device of claim 4, wherein the control and acquisition system will control the rotation of the stepping motor according to the swing control method.
- 一种单摆摆动快速控制方法,其特征在于,该方法用于控制如权利要求1-5任意一项所述的单摆装置的运行,该算法包括以下步骤:A rapid control method for the swing of a single pendulum, characterized in that the method is used to control the operation of the single pendulum device according to any one of claims 1-5, and the algorithm includes the following steps:步骤一:实时采集单摆摆动的角度并判断摆动到达最大角度与最小角度的时刻;Step 1: Collect the swing angle of the pendulum in real time and determine the moment when the swing reaches the maximum angle and the minimum angle;步骤二:在单摆摆动到最大角度时,控制移动滑块向上运动;在单摆摆动到最小角度时,控制移动滑块向下运动;Step 2: When the pendulum swings to the maximum angle, control the moving slider to move upward; when the pendulum swings to the minimum angle, control the moving slider to move downward;步骤三:根据控制方法确定移动滑块每次运动的运动距离。Step 3: Determine the movement distance of each movement of the moving slider according to the control method.
- 根据权利要求6所述的摆动快速控制方法,其特征在于,在步骤一中,令单摆从某一初始角度开始自由摆动并实时采集单摆摆动的角度。The rapid swing control method according to claim 6, wherein in step one, the pendulum is allowed to swing freely from a certain initial angle and the swing angle of the pendulum is collected in real time.
- 根据权利要求6所述的摆动快速控制方法,其特征在于,在步骤二中,当单摆达到最大角度时,滑块向上运动的轨迹为:The rapid swing control method according to claim 6, wherein in step 2, when the single pendulum reaches the maximum angle, the upward movement trajectory of the slider is:当单摆达到最小角度时,滑块向下运动的轨迹为:When the simple pendulum reaches the minimum angle, the downward movement track of the slider is:其中,i=1,2,3…代表向上和向下运动的次序,ΔT为移动滑块每次运动的运动时间;ΔL为移动滑块每次的运动距离。Among them, i=1, 2, 3... represents the sequence of upward and downward movement, ΔT is the movement time of each movement of the moving slider; ΔL is the movement distance of each movement of the moving slider.
- 根据权利要求8所述的摆动快速控制方法,其特征在于,移动滑块每次运动的运动时间小于单摆摆动周期的四分之一。The method for rapid swing control according to claim 8, wherein the movement time of each movement of the moving slider is less than a quarter of the swing period of the simple pendulum.
- 根据权利要求6所述的摆动快速控制方法,其特征在于,在步骤三中,滑块每次向上和向下运动的运动距离将根据如下表达式获得:The method for rapid swing control according to claim 6, characterized in that, in step 3, the moving distance of each upward and downward movement of the slider is obtained according to the following expression:其中,ΔL max为可供移动滑块运动的最大范围;e为自然底数; 为单摆每周期所能达到的最大摆幅;为了衡量单摆摆动抑制的速度,设定θ sta为单摆摆动的衰减标准,即以单摆摆动到θ sta的时刻作为对比不同参数影响的标准;λ与ε为控制参数来调整运动范围的变化。 Among them, ΔL max is the maximum range of the movable slider; e is the natural base; Is the maximum swing that a single pendulum can reach per cycle; in order to measure the speed of the swing suppression of the single pendulum, set θ sta as the attenuation standard of the single pendulum swing, that is, the time when the single pendulum swings to θ sta is used as a comparison of the influence of different parameters Standard; λ and ε are control parameters to adjust the change of motion range.
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