A special-shaped active vibration isolation platform adapted to the arc surface of the cabin and its LQR control method

Abstract

The present invention discloses a special-shaped active vibration isolation platform adapted to the arc surface of an aircraft cabin and its LQR control method. The special-shaped active vibration isolation platform adapted to the arc surface of an aircraft cabin comprises a top plate, an upper platform, mounting lugs, a lower platform, a support structure, mounting holes, a uniaxial acceleration sensor, a voice coil actuator, and a spring. The lower platform of the special-shaped active vibration isolation platform is designed as an arc surface to adapt to the shape of the aircraft cabin section. The upper and lower platforms are connected by a spring. The lower platform is provided with a support structure for providing support for the voice coil actuator. The uniaxial acceleration sensor is installed along the axial direction of the voice coil actuator to measure the axial acceleration value. The special-shaped active vibration isolation platform performs active and passive hybrid vibration isolation under the control of the LQR algorithm, which can effectively suppress high and low frequency vibrations.

Description

Technical Field

[0001] The present invention belongs to the field of active vibration isolation control, and in particular relates to a special-shaped active vibration isolation platform adapted to the arc surface of a cabin and an LQR control method. Background Art

[0002] High-precision aircraft are a research priority in the equipment field. Airborne ground remote sensing and airborne laser communication link establishment require high-precision payload platforms with integrated multi-sensor systems. However, due to airflow fluctuations and vibrations from the aircraft's engines and motors during flight, the proper functioning of onboard optoelectronic equipment can be affected. In addition to high-frequency vibration characteristics, new-generation aircraft also generate strong vibrations in the low-frequency band, below 100 Hz. Low-frequency vibrations are more destructive to onboard equipment, leading to premature failure or even structural damage.

[0003] Traditional active vibration isolation platforms are based on horizontal mounting surfaces, requiring high flatness at the mounting location. They cannot be installed independently on the curved surfaces of aircraft cabin sections. Currently developed special-shaped vibration isolators adapted for curved sections utilize the principle of passive vibration isolation, effectively suppressing disturbances greater than √2 times the system's fundamental frequency by dissipating vibration energy through damping. To adapt to curved mounting surfaces and suppress low-frequency microvibrations, research is needed on active vibration isolation platforms based on special-shaped mounting bases.

[0004] On irregular mounting surfaces, the unique positional distribution of the voice coil actuator and spring creates coupling in multiple degrees of freedom, manifesting as multiple resonance peaks in the frequency domain. Using the traditional proportional-integral-derivative (PID) control algorithm, which adjusts the gain coefficient based on the actuator's axial acceleration feedback, only achieves optimal output control for the actuator in a single axis, rather than for the entire isolator in the x, y, and z axes. While the PID controller can suppress disturbances within its control bandwidth, the amplitude attenuation in the low-frequency range is small, resulting in poor control effectiveness. However, the linear quadratic regulator (LQR) adjusts the parameters in the three axes through a weight matrix, allowing the system to approach the optimal state within the entire control bandwidth, effectively suppressing low-frequency vibrations. Summary of the Invention

[0005] To adapt to the arc-shaped mounting surface of an aircraft cabin and effectively suppress low-frequency vibrations, the present invention provides a specially shaped active vibration isolation platform and its LQR control method. The base of this vibration isolation platform is specifically designed to fit the aircraft cabin's arc-shaped surface. Mounting screw holes are symmetrically arranged at the four corners of the base, and the entire vibration isolation platform is mounted to the aircraft using screws. This shaped active vibration isolation platform is equipped with a uniaxial acceleration sensor for real-time acceleration measurement. Under the control of the LQR algorithm, a hybrid active and passive vibration isolation system is implemented to effectively suppress high- and low-frequency vibrations.

[0006] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is as follows.

[0007] In one aspect, the present invention provides a special-shaped active vibration isolation platform adapted to the arc surface of a cabin, comprising a top plate, an upper platform, mounting lugs, a lower platform, a support structure, mounting holes, a uniaxial acceleration sensor, a voice coil actuator, and a spring, wherein:

[0008] The upper platform is arranged above the lower platform, the top plate is mounted on the upper platform, and the four corners of the top plate are symmetrically provided with mounting holes for mounting precision photoelectric loads;

[0009] The lower platform is arc-shaped, and mounting lugs are symmetrically arranged at the four corners of the lower platform, and the lower platform is fixed to the aircraft through the mounting lugs;

[0010] The upper platform is connected to the lower platform via a spring;

[0011] There are two support structures, each of which is provided on the lower platform and is used to provide support for the voice coil actuator to reach the designed height position;

[0012] There are eight voice coil actuators, four of which are arranged on the lower platform, two of which are arranged vertically along the z-axis, and two of which are arranged radially along the arc surface of the lower platform, with an angle of 30° to the positive direction of the z-axis. Two of the other four voice coil actuators are horizontally distributed, perpendicular to each other, and symmetrical about the x-axis, with one of the support structures providing a horizontal mounting position for them. The remaining two voice coil actuators are also perpendicular to each other and symmetrical about the x-axis, with the plane formed by them forming an angle of 30° with the x-axis, and another support structure providing a mounting position for them at an angle of 30° to the x-axis.

[0013] The spring is installed in parallel with the voice coil actuator and dissipates the energy of high-frequency vibration by damping to achieve passive vibration isolation. One spring is arranged corresponding to each voice coil actuator.

[0014] The uniaxial acceleration sensor is installed along the axial direction of the voice coil actuator, and each voice coil actuator is equipped with one uniaxial acceleration sensor to measure the axial acceleration value;

[0015] The lower platform and the upper platform are respectively provided with a lower platform triaxial acceleration sensor and an upper platform triaxial acceleration sensor, which respectively measure the acceleration of the lower platform and the upper platform in real time to evaluate the vibration isolation effect.

[0016] Furthermore, a power information interface is provided on the side of the support structure for providing power to the special-shaped active vibration isolation platform, transmitting control signals and sensor measurement information.

[0017] Furthermore, packaging plates are provided on the four sides of the upper platform for enclosing the special-shaped active vibration isolation platform.

[0018] Furthermore, the height position is designed so that the vertical distance between the upper surface of the supporting structure and the lower platform is 1 / 2 of the vertical distance between the upper platform and the lower platform.

[0019] Furthermore, a mounting screw hole is provided in the mounting lug, and the special-shaped active vibration isolation platform is mounted on the aircraft by means of screws.

[0020] On the other hand, the present invention also provides an LQR control method for the special-shaped active vibration isolation platform adapted to the arc surface of the cabin, comprising the following steps:

[0021] Step 1: Establish the dynamic model of the special-shaped active vibration isolation platform that adapts to the arc surface of the cabin, as shown in formula (1):

[0022]

[0023] in, m is the mass of the upper platform, I is the moment of inertia of the upper platform, K is the stiffness matrix, K = k·E 8×8 , k is the stiffness of a single spring, C is the damping matrix, C = c·E 8×8 , c is the damping of a single spring, F a =[F1…F8] T , which provides active control force for the voice coil actuator;

[0024] q p ,q b Represent the generalized coordinates of the upper and lower platforms, J p 、J b are the Jacobian matrices of the upper and lower platforms, respectively;

[0025] Step 2: Express formula (1) as a state space equation, as shown in formula (2):

[0026]

[0027] in, u=F a ,

[0028] Step 3: adopting closed-loop feedback control for the special-shaped active vibration isolation platform adapted to the arc surface of the cabin, the entire control system includes a single-axis acceleration sensor, a driver, a sensor signal conditioner, a voice coil motor, and an LQR controller;

[0029] Step 4: The single-axis acceleration sensor measures the acceleration value, which is amplified by the sensor signal conditioner, collected and transmitted to the LQR controller. After matrix conversion and integration, the system state quantity is obtained;

[0030] Step 5: Based on the feedback of the system state quantity, the LQR controller establishes the optimal performance index function J, as shown in formula (3); adjusts the matrices Q and R according to the control requirements. When J is minimized, the Riccati equation is solved, as shown in formula (4), to obtain P. Then, P is substituted into formula (5) to calculate the optimal controller gain K. p , K p Substitute into (6) to complete the design of the control force u;

[0031]

[0032] A T P+PA-PBR -1 BP+Q=0 (4)

[0033] K p =R -1 B T P (5)

[0034] u=-K p z (6)

[0035] Step 6: According to the Ampere force formula, the magnitude of the control force u is solved as the control current I f , as shown in formula (7), B f Indicates the magnetic induction intensity, L f Indicates the length of the straight wire in the magnetic field; then converted into voltage according to the conversion relationship of the linear driver, as the final control signal output;

[0036] I f =u / (B f L f ) (7)

[0037] Step 7: Send the control signal to the driver. The control input of the voice coil motor is current, and the output of the controller is control voltage. The control voltage signal needs to be converted into a control current signal through a linear driver according to the proportional relationship between the input voltage and the output current.

[0038] Step 8: The voice coil motor outputs a control force based on the control current to suppress the vibration of the upper platform.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] Firstly, the present invention is mainly aimed at the design of the cabin section with arc surface, which improves the space utilization rate of the aircraft cabin section;

[0041] Secondly, the vibration isolator can effectively reduce high and low frequency vibrations in the coupled state, providing an ultra-quiet mechanical environment for the normal operation of airborne equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagram of a special-shaped active vibration isolation platform adapted to the arc surface of a cabin according to the present invention;

[0043] Figure 2 It is a cross-sectional view of the front reference plane of the special-shaped active vibration isolation platform adapted to the arc surface of the cabin of the present invention;

[0044] Figure 3 This is a schematic diagram of the internal structure of the hidden top plate of the special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to the present invention;

[0045] Figure 4 3D spatial distribution diagram of the voice coil actuator of the special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to the present invention;

[0046] Figure 5 This is the LQR control block diagram of the special-shaped active vibration isolation platform adapted to the arc surface of the cabin of the present invention;

[0047] Figure 6 This is the acceleration comparison diagram before and after LQR and PID control in the z direction in the time domain;

[0048] Figure 7 It is a comparison diagram of the power spectrum density of LQR and PID control in the z direction of the frequency domain.

[0049] In the figure: 1-top plate; 2-upper platform; 3-mounting lug; 4-power and information interface; 5-lower platform; 6-support structure; 7-mounting hole; 8-uniaxial accelerometer; 9-voice coil actuator; 10-spring; 11-packaging board; 12-lower platform triaxial accelerometer; 13-upper platform triaxial accelerometer. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the present invention more clear, the present invention will be described in more detail below with reference to the accompanying drawings. It should be noted that the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0051] The special-shaped active vibration isolation platform adapted to the arc surface of the cabin of the present invention is suitable for the arc surface base of the aircraft cabin section. The special-shaped active vibration isolation platform includes: a top plate 1, an upper platform 2, a mounting lug 3, a lower platform 5, a support structure 6, a mounting hole 7, a uniaxial acceleration sensor 8, a voice coil actuator 9, and a spring 10.

[0052] like Figure 1 、 Figure 2 As shown, the upper platform 2 is positioned above the lower platform 5, with the top plate 1 mounted on the upper platform 2. Mounting holes 7 are symmetrically located at the four corners of the top plate 1 for mounting precision optoelectronic payloads. The lower platform 5 is arc-shaped, with mounting lugs 3 symmetrically located at the four corners, securing the lower platform to the aircraft. Preferably, mounting screw holes are provided within the mounting lugs 3, allowing the entire shaped active vibration isolation platform to be mounted to the aircraft using screws.

[0053] The upper platform 2 is connected to the lower platform 5 via a spring 10 .

[0054] Two support structures 6 are provided, one on each lower platform 5, to support the voice coil actuator to a desired height. Preferably, the height is designed so that the vertical distance between the upper surface of the support structure and the lower platform is half the vertical distance between the upper platform and the lower platform.

[0055] There are 8 voice coil actuators 9, and their specific installation locations are as follows: Figure 3 、 Figure 4 As shown in the figure, four voice coil actuators are mounted on the lower platform. Voice coil actuators 9-2 and 9-5 are vertically positioned along the z-axis. Voice coil actuators 9-1 and 9-6 are radially positioned along the arc surface, at a 30° angle to the positive z-axis. Two of the remaining four voice coil actuators, 9-3 and 9-4, are horizontally positioned, perpendicular to each other and symmetrical about the x-axis. A support structure 6 provides a horizontal mounting position for each. The remaining two voice coil actuators, 9-7 and 9-8, are also perpendicular to each other and symmetrical about the x-axis. The plane they form forms an angle of 30° with the x-axis. Another support structure 6 provides a mounting position for each actuator at a 30° angle to the x-axis. To accommodate the arc-shaped mounting surface, the eight actuators are highly coupled, making control more challenging.

[0056] Springs 10 are mounted parallel to the voice coil actuators 9. They dissipate high-frequency vibration energy through damping to achieve passive vibration isolation. They serve as an auxiliary vibration isolation method for the isolation platform. One spring is positioned for each voice coil actuator 9. Springs 10 primarily provide passive vibration reduction and limit the connection between the upper and lower platforms. The vibration acceleration of the lower platform 5 is primarily transmitted to the upper platform 2 via the springs. The voice coil actuators 9, acting as actuators in the control system, provide active vibration isolation.

[0057] The uniaxial acceleration sensor 8 is installed along the axial direction of the voice coil actuator 9. Each voice coil actuator 9 is coaxially mounted with one uniaxial acceleration sensor 8 for measuring the axial acceleration value.

[0058] A triaxial acceleration sensor 12 is provided on the lower platform 5, and a triaxial acceleration sensor 13 is provided on the upper platform, which are used to measure the acceleration values ​​of the lower platform 5 and the upper platform 2 in real time, and feed them back to the control system to evaluate the vibration isolation effect.

[0059] Preferably, a power information interface 4 is provided on the side of the supporting structure for providing power to the special-shaped active vibration isolation platform, transmitting control signals and sensor measurement information.

[0060] Preferably, packaging plates are provided on the four side surfaces of the upper platform 2 for enclosing the special-shaped active vibration isolation platform.

[0061] An embodiment of the present invention further provides an LQR control method for a special-shaped active vibration isolation platform adapted to the arc surface of a cabin, comprising the following steps:

[0062] Step 1: Establish the dynamic model of the special-shaped active vibration isolation platform that adapts to the arc surface of the cabin, as shown in formula (1):

[0063]

[0064] in, m is the mass of the upper platform, I is the moment of inertia of the upper platform, K is the stiffness matrix, K = k·E 8×8 , k is the stiffness of a single spring, C is the damping matrix, C = c·E 8×8 , c is the damping of a single spring, F a =[F1…F8] T , which provides active control force for the voice coil actuator;

[0065] q p ,q b Represent the generalized coordinates of the upper and lower platforms, J p 、J b are the Jacobian matrices of the upper and lower platforms, respectively;

[0066] Step 2: Express formula (1) as a state space equation, as shown in formula (2):

[0067]

[0068] in, u=F a ,

[0069] Step 3: adopting closed-loop feedback control for the special-shaped active vibration isolation platform adapted to the arc surface of the cabin, the entire control system includes a single-axis acceleration sensor, a driver, a sensor signal conditioner, a voice coil motor, and an LQR controller;

[0070] Step 4: The single-axis acceleration sensor measures the acceleration value respectively, which is amplified by the sensor signal conditioner, collected and transmitted to the controller, and the system state quantity is obtained through matrix conversion and integration;

[0071] Step 5: Based on the feedback of the system state quantity, the LQR controller establishes the optimal performance index function J, as shown in formula (3); adjusts the matrices Q and R according to the control requirements. When J is minimized, the Riccati equation is solved, as shown in formula (4), to obtain P. Then, P is substituted into formula (5) to calculate the optimal controller gain K. p , K p Substitute into (6) to complete the design of the control force u;

[0072]

[0073] A T P+PA-PBR -1 BP+Q=0 (4)

[0074] K p =R -1 B T P (5)

[0075] u=-K p z (6)

[0076] Step 6: According to the Ampere force formula, the magnitude of the control force u is solved as the control current I f , as shown in formula (7), B f Indicates the magnetic induction intensity, L f Indicates the length of the straight wire in the magnetic field; then converted into voltage according to the conversion relationship of the linear driver, as the final control signal output;

[0077] I f =u / (B f L f ) (7)

[0078] Step 7: Send the control signal to the driver. The control input of the voice coil motor is current, and the output of the controller is control voltage. The control voltage signal needs to be converted into a control current signal through a linear driver according to the proportional relationship between the input voltage and the output current.

[0079] Step 8: The voice coil motor outputs a control force based on the control current to suppress the vibration of the upper platform.

[0080] This special-shaped active vibration isolation platform primarily controls micro-vibrations in the x, y, and z directions. When operating on a machine, the disturbance acceleration of the lower platform is measured by a triaxial accelerometer, which transmits the disturbance to the upper platform via a spring. The upper platform's disturbance acceleration is measured by a uniaxial accelerometer, and then matrix transformation and integration are used to determine velocity and position, providing state feedback. The LQR control algorithm calculates the feedback gain to generate a control signal. The driver inputs this control signal into the voice coil actuator, generating an axial Ampere force to actively suppress the upper platform. The upper platform's triaxial accelerometer then measures the acceleration, which is compared with the lower platform's acceleration to assess the vibration isolation effectiveness.

[0081] In this embodiment, eight voice coil actuators and springs are used for hybrid vibration isolation, wherein two actuators are arranged vertically along the z-axis; two actuators are arranged radially along the arc surface, with an angle of 30° to the positive direction of the z-axis; two actuators are distributed horizontally, perpendicular to each other, and symmetrical about the x-axis; and another two actuators are also perpendicular to each other and symmetrical about the x-axis, with the angle between the plane formed by them and the x-axis being 30°.

[0082] According to the structural characteristics of the special-shaped active vibration isolation platform, a dynamic model is established as shown in the following formula:

[0083]

[0084] Rewrite it as a state space equation as shown below:

[0085]

[0086] like Figure 5 The LQR control block diagram of the special-shaped active vibration isolation platform is shown, which includes the following steps:

[0087] 1. The current platform vibration acceleration is obtained through the upper platform uniaxial acceleration sensor, amplified by the sensor signal conditioner of the test system, collected and transmitted to the controller, and obtained through matrix conversion and integration;

[0088] 2. The controller solves the gain matrix based on the LQR control law and generates the voltage control command after conversion;

[0089] 3. Send the control signal to the linear actuator of the special-shaped active vibration isolation platform. The control input of the voice coil motor is current, and the output of the controller is control voltage. The linear actuator needs to convert the control voltage signal into a control current signal according to the proportional relationship between input voltage and output current.

[0090] 4. The voice coil motor outputs control force based on the control current to suppress the vibration of the upper platform.

[0091] Furthermore, the LQR control algorithm is used to simulate and verify the special-shaped active vibration isolation platform that adapts to the arc surface of the cabin in SIMULINK. The LQR and PID vibration suppression effects in the z direction of the upper platform in the time domain are as follows: Figure 6 shown.

[0092] The input random disturbance signal has a mean of 0 and a variance of 0.1, and the maximum disturbance acceleration is 0.6920 mg (1 mg = 10 - 3 g, 1g=9.8m / s 2 ), the time domain z-direction vibration isolation effect is shown in Table 1, the suppression ratio in the z direction where z out Indicates the maximum acceleration output value in the z direction after vibration isolation, z in Indicates the maximum disturbance acceleration input value in the z direction.

[0093] Table 1 Vibration isolation effect in z direction in time domain

[0094]

[0095] Although the control effects of PID controller and LQR controller in time domain are similar, they can be analyzed in frequency domain. Figure 7 As shown in the figure, it can be found that in the frequency band below 1 Hz, the PID controller cannot effectively suppress vibration, while the LQR controller has a significant suppression effect. It is suitable for suppressing low-frequency bands under airborne special-shaped mounting bases and meets the vibration isolation requirements of airborne equipment.

[0096] It should be noted that the above-described embodiments are merely preferred embodiments of the present invention. Persons skilled in the art will readily appreciate that various modifications, improvements, and equivalent substitutions may be made to the present invention without departing from the principles of the present invention, and such modifications, improvements, and equivalent substitutions are deemed to fall within the scope of protection of the claims of the present invention.

Claims

1. A special-shaped active vibration isolation platform adapted to the arc surface of the cabin, characterized in that: It includes a top plate, an upper platform, mounting lugs, a lower platform, a supporting structure, mounting holes, a uniaxial acceleration sensor, a voice coil actuator, and a spring, wherein: The upper platform is arranged above the lower platform, the top plate is mounted on the upper platform, and mounting holes are symmetrically arranged at the four corners of the top plate, and the mounting holes are used to mount precision photoelectric loads; The lower platform is in an arc shape, and the mounting lugs are symmetrically arranged at the four corners of the lower platform, and the lower platform is fixed to the aircraft through the mounting lugs; The upper platform is connected to the lower platform via a spring; There are two support structures, each disposed on the lower platform, for providing support for the voice coil actuator to reach a designed height position; There are eight voice coil actuators, four of which are arranged on the lower platform, two of which are arranged vertically along the z-axis, and two of which are arranged radially along the arc surface of the lower platform, with an angle of 30° to the positive direction of the z-axis. Two of the other four voice coil actuators are horizontally distributed, perpendicular to each other, and symmetrical about the x-axis, with one of the support structures providing a horizontal mounting position for them. The remaining two voice coil actuators are also perpendicular to each other and symmetrical about the x-axis, with the plane formed by them forming an angle of 30° with the x-axis, and another support structure providing a mounting position for them at an angle of 30° to the x-axis. The spring is installed in parallel with the voice coil actuator, and dissipates the energy of high-frequency vibration by damping to achieve passive vibration isolation. One spring is arranged corresponding to each voice coil actuator; The uniaxial acceleration sensor is installed along the axial direction of the voice coil actuator, and each voice coil actuator is equipped with one uniaxial acceleration sensor to measure the axial acceleration value; The lower platform and the upper platform are respectively provided with a lower platform triaxial acceleration sensor and an upper platform triaxial acceleration sensor, which respectively measure the acceleration of the lower platform and the upper platform in real time to evaluate the vibration isolation effect.

2. The special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to claim 1 is characterized in that: A power information interface is provided on the side of the support structure, which is used to provide power to the special-shaped active vibration isolation platform, transmit control signals and sensor measurement information.

3. The special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to claim 1 is characterized in that: The four sides of the upper platform are all provided with packaging plates for enclosing the special-shaped active vibration isolation platform.

4. The special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to claim 1 is characterized in that: The height position is designed so that the vertical distance between the upper surface of the support structure and the lower platform is 1 / 2 of the vertical distance between the upper platform and the lower platform.

5. The special-shaped active vibration isolation platform adapted to the arc surface of the cabin according to claim 1 is characterized in that: The mounting lugs are provided with mounting screw holes, and the special-shaped active vibration isolation platform is mounted on the aircraft by means of screws.

6. A LQR control method using a special-shaped active vibration isolation platform adapted to a nacelle arc surface according to any one of claims 1 to 5, comprising the following steps: Step 1: Establish the dynamic model of the special-shaped active vibration isolation platform that adapts to the arc surface of the cabin, as shown in formula (1): in, m is the mass of the upper platform, I is the moment of inertia of the upper platform, K is the stiffness matrix, K = k·E 8×8 , k is the stiffness of a single spring, C is the damping matrix, C = c·E 8×8 , c is the damping of a single spring, F a =[F1…F8] T , which provides active control force for the voice coil actuator; q p ,q b Represent the generalized coordinates of the upper and lower platforms, J p 、J b are the Jacobian matrices of the upper and lower platforms, respectively; Step 2: Express formula (1) as a state space equation, as shown in formula (2): in, u=F a , Step 3: adopting closed-loop feedback control for the special-shaped active vibration isolation platform adapted to the arc surface of the cabin, the entire control system includes a single-axis acceleration sensor, a driver, a sensor signal conditioner, a voice coil motor, and an LQR controller; Step 4: The single-axis acceleration sensor measures the acceleration value, which is amplified by the sensor signal conditioner, collected and transmitted to the LQR controller. After matrix conversion and integration, the system state quantity is obtained; Step 5: Based on the feedback of the system state quantity, the LQR controller establishes the optimal performance index function J, as shown in formula (3); adjusts the matrices Q and R according to the control requirements. When J is minimized, the Riccati equation is solved, as shown in formula (4), to obtain P. Then, P is substituted into formula (5) to calculate the optimal controller gain K. p , K p Substitute into (6) to complete the design of the control force u; A T P+PA-PBR -1 BP+Q=0(4) K p =R -1 B T P(5) u=-K p z(6) Step 6: According to the Ampere force formula, the magnitude of the control force u is solved as the control current I f , as shown in formula (7), B f Indicates the magnetic induction intensity, L f represents the length of a straight wire in a magnetic field; Then it is converted into voltage according to the conversion relationship of the linear driver and output as the final control signal; I f =u / (B f L f )(7) Step 7: Send the control signal to the driver. The control input of the voice coil motor is current, and the output of the controller is control voltage. The control voltage signal needs to be converted into a control current signal through a linear driver according to the proportional relationship between the input voltage and the output current. Step 8: The voice coil motor outputs a control force based on the control current to suppress the vibration of the upper platform.

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