A Vibration Control Method for Axial Eddy Current Damper Considering Time Delay

Abstract

The present invention discloses a vibration control method for an axial eddy current damper considering time delay, which changes the traditional passive energy dissipation and vibration reduction mode of the axial eddy current damper through a wireless remote telescopic adjustment device. The axial eddy current dampers are symmetrically arranged on both sides of the bogie at the bottom of the straddle-type monorail vehicle along the vehicle center line to perform wireless remote active energy dissipation and vibration reduction on the vibration response of the straddle-type monorail during operation. Moreover, aiming at the time delay phenomenon between the control command and the output, a correction method for eliminating the influence of the time delay on the system control effect is designed, and the gain feedback matrix of the optimal lateral control force required by the system obtained by calculating and analyzing the system under the ideal state is instantaneously corrected to obtain the corrected optimal lateral control force. Thus, by remotely controlling the output device in the eddy current damper, the wireless remote vibration control effect of the system in the presence of time delay is improved, and the riding comfort and smoothness are enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic vibration control, and more specifically, relates to a vibration control method for an axial eddy current damper considering time delay. Background Art

[0002] As a type of monorail, straddle-type monorail traffic belongs to an urban rail transit system. A straddle-type monorail is supported, stabilized, and guided by a single track, and the vehicle body runs on the track beam by means of rubber tires. When the near-ground wind with pulsating components bypasses the track beam with a non-streamlined cross-section, vortex shedding and flow separation phenomena are likely to occur, resulting in complex aerodynamic forces acting on the vehicle running on the track beam, generating a large-amplitude lateral vibration response, which will significantly reduce the safety and comfort of vehicle operation. However, due to limited available space, it is not convenient to install generally large-sized vibration damping devices on straddle-type monorails.

[0003] In the prior art, eddy current dampers usually achieve vibration control of structures in a passive form. Through innovative structural design, the magnitude of the damping force can be actively adjusted and controlled according to actual needs. For example, the axial eddy current damper is disclosed in the paper "New Technology of Permanent Magnet Eddy Current Damping and Its Application in Civil Engineering, China Journal of Highway and Transport, Vol. 33, No. 11, November 2020" by Academician Chen Zhengqing. Three different ball screw type eddy current axial dampers can achieve semi-active vibration damping control by adjusting the current intensity and other means. Therefore, eddy current dampers can achieve active energy-dissipating vibration damping of structures through control algorithms and external energy input to cope with extremely variable environmental changes. With the rapid development of current social wireless remote communication technology and the actual demand for structural vibration control intelligence, traditional wired structural vibration control can no longer meet the needs of the rapid development of current society. Wireless remote vibration control has become a current industry hotspot. Although using eddy current dampers for wireless remote vibration control of structures is a brand-new vibration damping method, there are still technical bottlenecks to be broken through in wireless remote structural vibration control. There is a certain time lag between the issuance of the signal command of the front-end controller and the damping force output of the end damper, and the real-time performance cannot be effectively guaranteed, which greatly affects the effect of structural vibration control. In severe cases, it will also cause the system to diverge, making the system lose stability and balance, causing damage to the structure and the damper itself, and increasing the operation and maintenance costs.

[0004] Therefore, for the relatively compact straddle-type monorail, it is urgent to innovate the new technology of vibration damping and energy dissipation for straddle-type monorail traffic and design a vibration control method for an axial eddy current damper considering time delay, so as to improve the wireless remote vibration control effect of the system in the presence of time delay, effectively suppress the vibration response under various operating conditions, and thus improve the riding comfort and safety. Summary of the Invention

[0005] (1) Technical Problem to be Solved

[0006] Based on the defects mentioned in the above background art, the present invention discloses a vibration control method for an axial eddy current damper considering time delay. By means of a wirelessly controlled telescopic adjustment device, the traditional passive energy dissipation and vibration reduction mode of the axial eddy current damper is changed. The axial eddy current dampers are symmetrically arranged along the vehicle center line on the bogies at the bottom of the straddle-type monorail vehicle, and wireless remote active energy dissipation and vibration reduction are carried out on the vibration response of the straddle-type monorail during operation. Moreover, aiming at the time delay phenomenon existing between the control command and the output in the wireless remote vibration control system, that is, a correction method for eliminating the influence of the time delay on the system control effect is designed at the control end. The gain feedback matrix of the optimal lateral control force required by the system obtained by calculating and analyzing the system under the ideal state (without time delay) is instantaneously corrected to obtain the corrected optimal lateral control force. Thus, by remotely controlling the output device in the eddy current damper, the damping force of the eddy current damper is actively changed to adapt to the continuously changing control force requirements of the system, and finally the active energy dissipation and vibration reduction of the axial eddy current damper are realized, the wireless remote vibration control effect of the system in the presence of time delay is improved, and the riding comfort and smoothness are enhanced.

[0007] (2) Technical Solution

[0008] The present invention discloses a vibration control method for an axial eddy current damper considering time delay. The axial eddy current dampers are symmetrically arranged on the left and right sides of the bogie at the bottom of the vehicle along the cross-section center line of the straddle-type monorail vehicle. One end of the axial eddy current damper is fixed to the bogie, and the other end is fixed to the bottom of the straddle-type monorail vehicle. The included angle between the axial eddy current damper and the horizontal plane is θ. A plurality of wireless remote telescopic adjustment devices are arranged along the circumference on the ball screw of the axial eddy current damper. A permanent magnet is fixed on the wireless remote telescopic adjustment device. The wireless remote telescopic adjustment device can wirelessly receive the control command sent by the remote control end to adjust the distance between the permanent magnet and the conductor circular tube in the radial direction; the remote control end can execute the vibration control method for the axial eddy current damper considering time delay:

[0009] Step 1: Real-time collect the lateral speed v(t) and acceleration a(t) during the operation of the straddle-type monorail vehicle.

[0010] Step 2: Judge whether a(t) > a0 holds, where a0 is a preset acceleration threshold. If so, execute the next step; if not, at this time a(t) ≤ a0, no control command will be sent to the wireless remote telescopic adjustment device.

[0011] Step 3: Establish the state equation of the vehicle system where \(S(t)\) is the state vector of the vehicle system, including the lateral velocity \(v(t)\) of the vehicle, is the derivative of the state vector of the vehicle system, including the lateral acceleration \(a(t)\) of the vehicle, \(A\) is the system characteristic matrix, which can be obtained according to the mass, damping, and stiffness of the vehicle, \(U(t)\) is the required lateral control force of the system, \(B\) is the action position matrix of the control force, which can be obtained according to the action position coordinates of the output damping force of the damper, \(F(t)\) is the environmental disturbance, and \(D\) is the position matrix of the environmental disturbance, all of which are measured by sensors;

[0012] Step 4: Considering the existence of system time delay, calculate the optimal lateral control force \(U''(t)\) through the optimal control algorithm;

[0013] Step 4.1: Solve the state equation through the embedded optimal control algorithm to obtain the control force gain matrices \(G_1\) and \(G_2\), and the optimal lateral control force is expressed as where \(G_1\) and \(G_2\) are the gain matrices of velocity and acceleration respectively. Considering the existence of system time delay, in order to correct the influence brought by the time delay, the optimal lateral control force is expressed as where \(\Delta t\) s is the time delay of velocity feedback, is the time delay of acceleration feedback. In order to make up for the influence of time delay on the control system, the controller instantaneously corrects the feedback gains \(G_1\) and \(G_2\), and the optimal lateral control force is expressed as: where \(G_1'\) and \(G_2'\) are the corrected feedback gains respectively;

[0014] Step 4.2: The essence of the existence of system time delay is the lag of the phase of velocity and acceleration gain feedback. In the time-delay system, the phases of velocity and acceleration feedback lag by \(\omega\Delta t\) s and \(\omega\Delta t\) s respectively, where \(\omega\) is the natural frequency of the vehicle system. According to the phase difference, the velocity feedback matrix is decomposed into \(G_1'S(t)\cos(\omega\Delta t\) s ), \(-G_1'S(t)\sin(\omega\Delta t\) s ), and the acceleration feedback matrix is decomposed into To make the actual control system equivalent to the ideal control system, that is, the time-delay system is equivalent to the time-delay-free system, the following formula needs to be satisfied:

[0015]

[0016] Step 4.3: Considering that the stiffness and damping of the two systems must be kept consistent, that is From this, the velocity and acceleration control force matrices \(G_1'\) and \(G_2'\) required for the time-delay system are calculated, and the final actively corrected optimal lateral control force is obtained

[0017] After obtaining the optimal lateral control force U″(t), the axial eddy current damper is actively vibration-damped through a wireless remote telescopic adjustment device.

[0018] Preferably, in step 1, the sensors for collecting the lateral velocity v(t) and acceleration a(t) include an acceleration sensor and a velocity sensor. The sensors wirelessly transmit the collected lateral velocity v(t) and acceleration a(t) data to the remote control terminal, which can save and analyze the data to perform subsequent judgment and calculation analysis steps, and can control the wireless remote telescopic adjustment device to actively adjust the damping force.

[0019] Preferably, the acceleration sensor and the velocity sensor are installed at both ends of the top of the straddle-type monorail vehicle body, and the remote control terminal is installed in the cab of the straddle-type monorail.

[0020] Preferably, it further includes the following step 5:

[0021] Step 5: According to the established line of the straddle-type monorail transit, judge the turning radius situation of the line where the current vehicle is located; when the turning radius R≥1000m, the damping force of the axial eddy current damper provides the optimal lateral control force U″(t) of the vehicle system, and according to the vehicle structure characteristics and the spatial layout of the axial eddy current damper, the relationship between the damping force and the optimal lateral control force U″(t) is as follows:

[0022]

[0023] where f c is the axial damping force of a single axial eddy current damper, r is the inner radius of the conductor circular tube, d is the lead of the rolling resistance screw, ρ is the number of pairs of permanent magnet poles, A m is the projected area of a single permanent magnet on the conductor circular tube, σ is the magnetic permeability of the conductor circular tube, B re is the remanent magnetic flux density, t1 is the thickness of the permanent magnet, t2 is the spacing between the permanent magnet and the conductor, t3 is the thickness of the conductor circular tube, and at this time t2 is the controllable variable to be solved;

[0024] When the turning radius R<1000m, the damping force of the axial eddy current damper provides the lateral control force U(t) and the centrifugal force of the vehicle system, and satisfies:

[0025]

[0026] where M is the vehicle mass of the straddle-type monorail, v 车 is the running speed of the vehicle, and the spacing t2 between the permanent magnet and the conductor circular tube as the controllable variable is solved according to the above formula.

[0027] Preferably, it further includes the following step 6:

[0028] Step 6: According to the newly calculated distance t2 between the permanent magnet and the conductor circular tube in Step 5, control the wireless remote telescopic adjustment device to drive the permanent magnet to approach the conductor circular tube radially, so that the elongation length of the wireless remote telescopic adjustment device is Δ = t2’ - t2, where t2’ is the original distance between the permanent magnet and the conductor circular tube when the wireless remote telescopic adjustment device is in the initial passive state, and provide the optimal lateral control force required by the system in real time for active balance control.

[0029] Preferably, the above Steps 1-6 are executed in a preset cycle.

[0030] (III) Beneficial effects

[0031] 1. The present invention uses an axial eddy current damper instead of a traditional viscous oil damper for active energy dissipation vibration reduction of straddle-type monorail vehicles, completely solving the oil leakage problem, improving the service life of the damper, reducing the operation and maintenance cost. And because the installation space under the straddle-type monorail is narrow, the structural design of the axial eddy current damper is improved, and the permanent magnet is designed to be adjustable in height through a wireless remote telescopic adjustment device, which can actively change the magnitude of the damping force wirelessly and remotely in real time, realizing the output of active control force, improving the scope of the system vibration control ability, and the active adaptation ability to cope with extreme situations.

[0032] 2. In the active control algorithm of the controller of the present invention, considering the influence of time delay on vibration control according to the actual situation, a time delay correction method is proposed, the corrected velocity and acceleration feedback gain matrices are solved, and the magnitude of the effective optimal lateral control force is obtained. Thus, the controller can issue relevant instructions to remotely control the damper to output the corresponding damping force magnitude, realizing the effective control of vibration response, and avoiding poor control effect or even system divergence and instability caused by the existence of system time delay.

[0033] 3. The present invention establishes the functional relationship between the magnitude of the damping force of the axial damper and various core parameters, and realizes the precise adjustment control of the damping force of the damper based on different working conditions on the turning radius, providing accurate and stable control force output for the system, and improving the driving comfort and smoothness. Description of the drawings

[0034] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the embodiments:

[0035] Figure 1 is the flowchart of the vibration control method of the axial eddy current damper considering time delay of the present invention;

[0036] Figure 2Schematic diagram of the overall layout of the axial eddy current damper of the present invention installed on the straddle monorail transit; among them, (a) is the front view and (b) is the side view;

[0037] Figure 3 is Figure 2 Schematic diagram of the structure of the axial eddy current damper in the middle. Specific implementation manner

[0038] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0039] In order not to affect the normal operation of the straddle monorail transit and effectively suppress vibration, as Figure 2 shown, the present invention symmetrically arranges the axial eddy current dampers on the left and right sides of the bogie at the bottom of the vehicle along the center line of the cross-section of the straddle monorail vehicle. One end of the axial eddy current damper is fixed to the bogie, and one end is fixed to the bottom of the straddle monorail vehicle. The included angle between the axial eddy current damper and the horizontal plane is θ.

[0040] As Figure 3 shown, the axial eddy current damper of the present invention is specifically an improvement on the axial eddy current damper of the inner rotating tube type by Academician Chen Zhengqing. Of course, the axial eddy current damper can also be an outer rotating tube type or a disc type axial eddy current damper. Inside the axial eddy current damper, there is mainly an outer layer of back iron cylinder, which is mainly used to ensure the magnetic field strength and magnetic conductivity and prevent magnetic leakage. The conductor circular tube is fixed inside the back iron cylinder, which is mainly the carrier for generating eddy currents and for heat dissipation. The innermost part is a ball screw, which is mainly used to convert the axial linear motion of the damper screw into rotation around the screw and significantly amplify the axial speed, so as to significantly increase the energy dissipation density. A number of wireless remote telescopic adjustment devices are arranged along the circumference of the ball screw. The wireless remote telescopic adjustment device can receive the control instruction for adjusting its axial length sent by the remote control terminal to adjust the distance of t2 along the radial direction and complete the instruction output. A permanent magnet is fixed on each wireless remote telescopic adjustment device to provide the magnetic field required for the operation of the axial eddy current damper. Wireless speed sensors and acceleration sensors are respectively arranged at both ends of the top of the straddle monorail vehicle body, which can collect the lateral speed v(t) and acceleration data a(t) of the vehicle in real time and wirelessly transmit them to the remote control terminal.

[0041] It is worth mentioning that the reason why the present invention uses a wireless remote telescopic adjustment device with wireless communication and telescopic control functions to control the distance t2 between the permanent magnet and the conductor circular tube is mainly to minimize the overall volume of the damper as much as possible while maintaining controllability, so that it can be installed on the underframe of the straddle-type monorail transit, and can actively suppress the vibration of the upper car body under normal vehicle operation.

[0042] The present invention takes the axial eddy current damper of the inner-rotating tube type as an example to illustrate the working principle of the damper: when the distance between the permanent magnet and the conductor circular tube is adjusted, the axial eddy current damper is driven to move axially repeatedly under the action of the vibration of the straddle-type monorail vehicle. Through the action of the ball screw, the axial movement is converted into rotation, driving the permanent magnet on the ball screw to make a rapid circular motion, causing the conductor circular tube to generate a magnetic induction line cutting motion, generating an eddy current effect in the conductor. Due to the resistance of the conductor, the vibration energy is dissipated through the resistance effect, and at the same time, a damping force opposite to the direction of motion is generated to suppress the vibration response and improve the running smoothness and comfort of the vehicle.

[0043] As Figure 1 shown, based on the hardware improvement of adding a wireless remote telescopic adjustment device at the permanent magnet of the above-mentioned axial eddy current damper, the vibration control method of the axial eddy current damper considering time delay of the present invention can be executed by a remote control terminal, including the following steps:

[0044] Step 1: Real-time collect the lateral speed v(t) and acceleration a(t) during the operation of the straddle-type monorail vehicle;

[0045] In another embodiment, the sensors for collecting the lateral speed v(t) and acceleration a(t) include the acceleration sensor and speed sensor shown above Figure 2 The sensors with wireless communication functions wirelessly send the collected lateral speed v(t) and acceleration a(t) data to the remote control terminal. The remote control terminal can save and analyze the data to execute subsequent judgment and calculation analysis steps, and can control the wireless remote telescopic adjustment device to actively adjust the damping force. In addition, the remote control terminal can preferably be set in the cab of the straddle-type monorail.

[0046] Step 2: Judge whether a(t) > a0 holds, where a0 is a preset acceleration threshold. If so, execute the next step. If not, at this time a(t) ≤ a0, indicating that the vibration response of the vehicle system is small, and no control instruction will be sent to the wireless remote telescopic adjustment device.

[0047] In another embodiment, when the acceleration a(t) ≤ a0, the eddy current damper only plays a passive control function, and the controller will not send control instructions to the conductor circular tube height adjustment device, and suppresses the system vibration response by generating a damping effect, improving the running stability and comfort. When the acceleration a(t) > a0, it indicates that the vibration response of the current vehicle system is relatively large, and the damping force required for vibration suppression by the system is relatively large. At this time, the passive effect of the eddy current damper can no longer meet the vibration reduction and energy consumption requirements. At this time, the controller needs to remotely send control instructions to the wireless remote telescopic adjustment device to actively suppress vibration.

[0048] Step 3: Establish the state equation of the vehicle system where S(t) is the state vector of the vehicle system, including the vehicle lateral velocity v(t), is the derivative of the state vector of the vehicle system, including the vehicle lateral acceleration a(t), A is the system characteristic matrix, which can be obtained according to the mass, damping, and stiffness of the vehicle, U(t) is the required lateral control force of the system, B is the action position matrix of the control force, which can be obtained according to the action position coordinates of the output damping force of the damper, F(t) is the environmental disturbance, and D is the position matrix of the environmental disturbance, all of which are measured by sensors.

[0049] Step 4: Considering the existence of system time delay, calculate the optimal lateral control force U″(t) through the optimal control algorithm.

[0050] In another embodiment, in order to obtain the optimal active lateral control force considering the existence of the wireless communication system time delay in the present invention, Step 4 specifically includes:

[0051] Step 4.1: Solve the state equation through the embedded optimal control algorithm to obtain the control force gain matrices G1 and G2, and the optimal lateral control force is expressed as where G1 and G2 are the gain matrices of velocity and acceleration respectively. Considering the existence of system time delay, in order to correct the influence brought by the time delay, the optimal lateral control force is expressed as where Δt s is the time delay of velocity feedback, is the time delay of acceleration feedback. In order to make up for the influence of time delay on the control system, the controller instantaneously corrects the feedback gains G1 and G2, and the optimal lateral control force is expressed as: where G1′ and G2′ are the corrected feedback gains respectively.

[0052] Step 4.2: The essence of the existence of system time delay is the lag of the phase of velocity and acceleration gain feedback. In the time-delay system, the phases of velocity and acceleration feedback lag by ωΔt s 、ωΔt s, where ω is the natural frequency of the vehicle system. According to the phase difference, the speed feedback matrix is decomposed into G1′S(t)cos(ωΔt s ), -G1′S(t)sin(ωΔt s ), and the acceleration feedback matrix is decomposed into To make the actual control system equivalent to the ideal control system, that is, the time-delay system equivalent to the non-time-delay system, the following formula needs to be satisfied:

[0053]

[0054] Step 4.3: Considering that the stiffness and damping of the two systems must be kept consistent, that is From this, the required speed and acceleration control force matrices G1′ and G2′ of the time-delay system are calculated, and the final actively corrected optimal lateral control force

[0055] After obtaining the optimal lateral control force U″(t) based on Step 4, the remote control end can control the damping force of the axial eddy current damper through the wireless remote telescopic adjustment device for active vibration reduction. The specific adjustment method is shown in the subsequent Steps 5-6.

[0056] Step 5: According to the established line of the straddle monorail transit, judge the turning radius of the line where the current vehicle is located. When the turning radius R≥1000m, the damping force of the axial eddy current damper provides the optimal lateral control force U″(t) of the vehicle system, and according to the vehicle structure characteristics and the spatial layout of the axial eddy current damper, the relationship between the damping force and the optimal lateral control force U″(t) is output as follows:

[0057]

[0058] Among them, f c is the axial damping force of a single axial eddy current damper, r is the inner radius of the conductor circular tube, d is the lead of the rolling resistance screw, ρ is the number of pole pairs of the permanent magnet, A m is the projected area of a single permanent magnet on the conductor circular tube, σ is the magnetic permeability of the conductor circular tube, B re is the remanent magnetic flux density, t1 is the thickness of the permanent magnet, t2 is the distance between the permanent magnet and the conductor, t3 is the thickness of the conductor circular tube, v(t) is the lateral speed of the vehicle, θ is the angle between the axial damper and the horizontal plane, and at this time t2 is the controllable variable to be solved;

[0059] When the turning radius R<1000m, the damping force of the axial eddy current damper provides the lateral control force U(t) and the centrifugal force of the vehicle system, and satisfies:

[0060]

[0061] where M is the vehicle mass of the straddle monorail, and v 车 is the running speed of the vehicle. According to the above formula, the distance t2 between the permanent magnet and the conductor tube, which is a controllable variable, is solved.

[0062] In another embodiment, it can be known that the 1-km turning radius threshold in step 5 is a threshold preset according to the track layout of the monorail. When the turning radius R ≥ 1000 m, the system determines that the track passed by the current vehicle is a straight track, and the influence of the vehicle centrifugal force on the riding comfort can be ignored. Considering the spatial layout of the axial eddy current damper, the optimal lateral control force required by the system is provided by the lateral components of the damping forces of the two eddy current dampers. During the process of the eddy current damper providing passive control to provide additional structural damping, the distance t2 between the permanent magnet and the conductor tube is actively adjusted by remotely controlling the wireless remote telescopic adjustment device on one side of the permanent magnet, so as to change the magnitude of the eddy current output damping force to meet the requirements of system vibration control. When the turning radius R < 1000 m, at this time, it is necessary to consider the influence of the track turning radius on the riding comfort. The balance between the optimal lateral control force required by the system and the vehicle centrifugal force is provided by the lateral components of the damping forces of the two eddy current dampers, that is, the magnitude of the damping force is adjusted by remotely controlling the distance t2 between the permanent magnet and the conductor tube to meet the requirements of system vibration control.

[0063] Step 6: According to the newly calculated distance t2 between the permanent magnet and the conductor tube in step 5, control the wireless remote telescopic adjustment device to drive the permanent magnet to approach the conductor tube radially, so that the elongation length of the wireless remote telescopic adjustment device is Δ = t2’ - t2, where t2’ is the original distance between the permanent magnet and the conductor tube when the wireless remote telescopic adjustment device is in the initial passive state, and provide the optimal lateral control force required by the system in real time for active balance control.

[0064] In another embodiment, referring to Figure 1 it can be known that steps 1-6 can be cyclically executed according to a preset period. The remote controller actively adjusts the distance between the permanent magnet and the conductor tube by outputting signals, and specifically adjusts the elongation length of the wireless remote telescopic adjustment device to be Δ = t 2原间距 -t 2新间距 = t2’ - t2, where t2’ is the original distance between the permanent magnet and the conductor tube when the wireless remote telescopic adjustment device is in the initial passive state (at this time, the elongation length Δ is 0), so that the permanent magnet approaches the conductor tube radially to increase and control the damping force, and provide the optimal lateral control force required by the system in real time, suppress the vibration response of the vehicle system in various situations, and improve the riding smoothness and comfort.

[0065] It can be seen from this that the present invention changes the traditional passive energy dissipation and vibration reduction method of the axial eddy current damper through a wirelessly controllable wireless remote telescopic adjustment device. The axial eddy current dampers are symmetrically arranged on the bogies at the bottom of the straddle monorail vehicle along the vehicle center line to perform wireless remote active energy dissipation and vibration reduction on the vibration response of the straddle monorail during operation. Moreover, for the time delay phenomenon existing between the control instruction and the output in the wireless remote vibration control system, that is, the time delay includes the acquisition time Δt1 of sensor data, the calculation and analysis time Δt2 of the controller, the response time Δt3 of the output device, and the remote transmission time Δt4 between wireless, which are all the main reasons for constituting the total system time delay Δt. A correction method for eliminating the influence of the time delay on the system control effect is designed at the control end, and the gain feedback matrix of the optimal lateral control force required by the system calculated and analyzed for the system in the ideal state (without time delay) is instantaneously corrected to obtain the corrected optimal lateral control force, and the damping force magnitude of the eddy current damper is actively changed by remotely controlling the output device in the eddy current damper to adapt to the continuously changing control force requirements of the system, ultimately realizing the active energy dissipation and vibration reduction of the axial eddy current damper, improving the wireless remote vibration control effect of the system in the presence of time delay, and improving the riding comfort and smoothness of the vehicle.

[0066] It is worth mentioning that, compared with the prior art, the present invention has the following innovation points:

[0067] 1. The present invention innovatively installs the axial eddy current dampers symmetrically on the left and right sides of the bogies at the bottom of the straddle monorail vehicle, without occupying extra space of the vehicle body, without the need to modify the prototype vehicle body structure, and is convenient for inspection, maintenance and operation.

[0068] 2. The present invention innovatively designs the internal structure of the axial eddy current damper. A wireless remote telescopic adjustment device is arranged below one side of the permanent magnet, which can freely control the tiny distance between the permanent magnet and the conductor circular tube, change the magnetic field strength, and establish the relationship between the output damping force of the axial eddy current damper and the movement displacement of the permanent magnet, which can provide the magnitude of the output damping force in a timely and accurate manner for the wireless remote control of the vehicle system.

[0069] 3. The present invention innovatively establishes a wireless remote active control method for the state feedback of the straddle monorail vehicle considering time delay. By wirelessly monitoring the lateral speed and acceleration magnitude of the running vehicle, analyzing the motion state of the vehicle system, and correcting and processing the system time delay problem, the influence of the time delay on the system control effect is eliminated, and an effective optimal lateral control force is provided in a timely manner.

[0070] 4. The present invention fully considers the magnitude of the centrifugal force existing during the vehicle running through a small curve radius line. By modeling the axial eddy current damper and outputting the damping force for balance, the riding comfort and smoothness of passengers are further improved.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A vibration control method for an axial eddy current damper considering time delay, characterized in that, The axial eddy current damper is symmetrically arranged on the left and right sides of the bogie at the bottom of the vehicle along the cross-section center line of the straddle-type monorail vehicle. One end of the axial eddy current damper is fixed to the bogie, and the other end is fixed to the bottom of the straddle-type monorail vehicle. The included angle between the axial eddy current damper and the horizontal plane is θ. A number of wireless remote telescopic adjustment devices are arranged along the circumference on the ball screw of the axial eddy current damper. A permanent magnet is fixed on the wireless remote telescopic adjustment device. The wireless remote telescopic adjustment device can wirelessly receive control instructions sent by the remote control terminal to adjust the distance between the permanent magnet and the conductor circular tube radially; The remote control terminal can execute the vibration control method of the axial eddy current damper considering time delay: Step 1: Real-time collect the lateral speed v(t) and acceleration a(t) during the operation of the straddle-type monorail vehicle; Step 2: Judge whether a(t) > a0 holds, where a0 is a preset acceleration threshold. If so, execute the next step. If not, at this time a(t) ≤ a0, no control instruction will be sent to the wireless remote telescopic adjustment device; Step 3: Establish the state equation of the vehicle system where S(t) is the state vector of the vehicle system, including the lateral velocity v(t) of the vehicle, is the derivative of the state vector of the vehicle system, including the lateral acceleration a(t) of the vehicle, A is the system characteristic matrix, which can be obtained according to the mass, damping, and stiffness of the vehicle, U(t) is the required lateral control force of the system, B is the action position matrix of the control force, which can be obtained according to the action position coordinates of the output damping force of the damper, F(t) is the environmental disturbance, and D is the position matrix of the environmental disturbance, all of which are measured by sensors; Step 4: Consider the existence of system time delay and calculate the optimal lateral control force U″(t) through the optimal control algorithm; Step 4.1: Solve the state equation by embedding the optimal control algorithm to obtain the control force gain matrices G1 and G2. The optimal lateral control force is expressed as where G1 and G2 are the gain matrices of velocity and acceleration respectively. Considering the existence of time delay in the system, in order to correct the influence brought by the time delay, the optimal lateral control force is expressed as where Δt s is the time delay of velocity feedback, is the time delay of acceleration feedback. In order to make up for the influence of time delay on the control system, the controller instantaneously corrects the gain matrices G1 and G2 of velocity and acceleration. The optimal lateral control force is expressed as: where G1′ and G2′ are the control force matrices of velocity and acceleration required by the time-delay system respectively; Step 4.2: The essence of the time delay in the system is the lag of the phase of the speed and acceleration gain feedback. In the time-delay system, the phases of the speed and acceleration feedback lag by ωΔt respectively s , where ω is the natural frequency of the vehicle system. According to the phase difference, the gain matrix G1 of the speed is decomposed into G1′S(t)cos(ωΔt s ), -G1′S(t)sin(ωΔt s ) / ω, and the gain matrix G2 of the acceleration is decomposed into To make the actual control system equivalent to the ideal control system, that is, the time-delay system equivalent to the non-time-delay system, the following formula needs to be satisfied: Step 4.3: Considering that the stiffness and damping of the two systems must be consistent, i.e., The velocity and acceleration control force matrices G1′ and G2′ required for the time-delay system are calculated therefrom, and the optimal lateral control force for the final active correction is obtained. After obtaining the optimal lateral control force U″(t), control the axial eddy current damper through the wireless remote telescopic adjustment device for active vibration reduction.

2. The vibration control method of the axial eddy current damper considering time delay according to claim 1, characterized in that, The sensors for collecting the lateral speed v(t) and acceleration a(t) in Step 1 include an acceleration sensor and a speed sensor. The sensors wirelessly send the collected lateral speed v(t) and acceleration a(t) data to the remote control terminal. The remote control terminal can save and analyze the data to execute subsequent judgment and calculation analysis steps, and can control the wireless remote telescopic adjustment device to actively adjust the damping force.

3. The axial eddy current damper vibration control method considering time delay according to claim 2, characterized in that The acceleration sensor and the speed sensor are installed at both ends of the top of the straddle-type monorail vehicle body, and the remote control terminal is installed in the cab of the straddle-type monorail.

4. The axial eddy current damper vibration control method considering time delay according to claim 1, characterized in that It also includes the following Step 5: Step 5: Judge the turning radius situation of the current vehicle's location according to the established line of the straddle-type monorail traffic; when the turning radius R ≥ 1000 m, the damping force of the axial eddy current damper provides the optimal lateral control force U″(t) of the vehicle system, and according to the vehicle structure characteristics and the spatial layout of the axial eddy current damper, the relationship between the damping force and the optimal lateral control force U″(t) is output as follows: Among them, f c is the axial damping force of a single axial eddy current damper, r is the inner radius of the conductor circular tube, d is the lead of the rolling resistance screw, ρ is the number of pole pairs of the permanent magnet, A m is the projected area of a single permanent magnet on the conductor circular tube, σ is the magnetic permeability of the conductor circular tube, B re is the remanent magnetic flux density, t1 is the thickness of the permanent magnet, t2 is the spacing between the permanent magnet and the conductor, t3 is the thickness of the conductor circular tube, and at this time t2 is the controllable variable to be determined; When the turning radius R < 1000 m, the damping force of the axial eddy current damper provides the lateral control force U(t) and the centrifugal force of the vehicle system, and satisfies: Among them, M is the mass of the straddle-type monorail vehicle, and v 车 is the running speed of the vehicle. According to the above formula, the distance t2 between the permanent magnet and the conductor circular tube as a controllable variable is obtained by solving the equation.

5. The axial eddy current damper vibration control method considering time delay according to claim 4, characterized in that, It also includes the following Step 6: Step 6: According to the newly calculated distance t2 between the permanent magnet and the conductor circular tube in Step 5, control the wireless remote telescopic adjustment device to drive the permanent magnet to approach the conductor circular tube radially, so that the elongation length of the wireless remote telescopic adjustment device is Δ = t2' - t2, where t2' is the original distance between the permanent magnet and the conductor circular tube when the wireless remote telescopic adjustment device is in the initial passive state, and provide the optimal lateral control force required by the system in real time for active balance control.

6. The axial eddy current damper vibration control method considering time delay according to claim 5, characterized in that The steps 1-6 are cyclically executed according to a preset period.

Images