Special-shaped active vibration isolation platform adaptive to cabin arc surface and LQR control method thereof

Abstract

The invention discloses a special-shaped active vibration isolation platform adaptive to an arc surface of a cabin and an LQR control method of the special-shaped active vibration isolation platform. The special-shaped active vibration isolation platform suitable for the cabin arc surface comprises a top plate, an upper platform, mounting lugs, a lower platform, a supporting structure, mounting holes, a single-axis acceleration sensor, a voice coil actuator and springs. A lower platform of the special-shaped active vibration isolation platform is designed to be an arc surface in order to adapt to the shape of an aircraft cabin section, an upper platform and the lower platform are connected through a spring, a supporting structure is arranged on the lower platform and used for supporting a voice coil actuator, and a single-axis acceleration sensor is installed in the axial direction of the voice coil actuator and used for measuring the axial acceleration value. The special-shaped active vibration isolation platform carries out active and passive mixed vibration isolation under the control of the LQR algorithm, and high and low frequency vibration can be effectively restrained.

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 the research focus in the equipment field. Aerial ground remote sensing and airborne laser communication link building require high-precision payload platforms with multi-sensor integration. However, due to changes in airflow during flight and vibrations of engines and motors in the aircraft body, the normal operation of airborne optoelectronic equipment will be affected. In addition to high-frequency vibration characteristics, the new generation of aircraft also produces strong vibrations in the low-frequency band of less than 100Hz. Vibrations in the low-frequency band are more destructive to airborne equipment, causing premature failure of equipment or even structural damage.

[0003] Traditional active vibration isolation platforms are based on horizontal mounting surfaces, which have high requirements for the flatness of the mounting position. They cannot be installed on the arc surface of the aircraft cabin alone. The currently developed special-shaped vibration isolators adapted to the arc cabin adopt the principle of passive vibration isolation. By damping and dissipating vibration energy, they can effectively suppress disturbances greater than √2 times the system fundamental frequency. In order to adapt to the arc-shaped mounting surface and suppress micro-vibrations in the low-frequency band, it is necessary to carry out research on active vibration isolation platforms based on special-shaped mounting bases.

[0004] Under the special-shaped mounting surface, the special position distribution of the voice coil actuator and the spring causes coupling in multiple degrees of freedom, which is manifested as multiple resonance peaks in the frequency domain. If the traditional proportional-integral-differential (PID) control algorithm is used, the gain coefficient is adjusted for the acceleration feedback in the axial direction of the actuator, which can only meet the optimal output control of the actuator in the single-axis direction, rather than the optimal control in the three-axis directions of x, y, and z of the entire vibration isolator. Although the PID controller can suppress disturbances within its control bandwidth, the amplitude attenuation in the low-frequency band is small, and the control effect is not good. The linear quadratic regulator (LQR) adjusts the parameters in the three-axis direction through the weight matrix, and the system can approach the optimal state within the entire control bandwidth and effectively suppress vibrations in the low-frequency band. Summary of the invention

[0005] In order to adapt to the arc mounting surface of the aircraft cabin section and achieve effective suppression of low-frequency vibration, the present invention provides a special-shaped active vibration isolation platform that adapts to the arc surface of the cabin and its LQR control method. The base of the vibration isolation platform is specially designed to fit the arc surface of the aircraft cabin section to adapt to the shape of the aircraft cabin section. The four corners of the base are symmetrically provided with mounting screw holes, and the entire vibration isolation platform is installed on the aircraft by screws. The special-shaped active vibration isolation platform is provided with a uniaxial acceleration sensor for real-time measurement of acceleration information, and performs active and passive hybrid vibration isolation under the control of the LQR algorithm 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] On the one hand, the present invention provides a special-shaped active vibration isolation platform adapted to the arc surface of the cabin, comprising a top plate, an upper platform, a mounting lug, a lower platform, a supporting structure, a mounting hole, 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 installed on the upper platform, and the four corners of the top plate are symmetrically provided with mounting holes, and the mounting holes are used to install the precision photoelectric load;

[0009] 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 on 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, which are respectively arranged on the lower platform and are used to provide support for the voice coil actuator to reach the designed height position;

[0012] There are eight voice coil actuators, of which four are arranged on the lower platform, two of which are arranged vertically along the z-axis direction, 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, and one of the support structures provides a horizontal installation position for them; the remaining two voice coil actuators are also perpendicular to each other, symmetrical about the x-axis, and the angle between the plane formed by them and the x-axis is 30°, and the other support structure provides them with an installation position with 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 one uniaxial acceleration sensor is installed along the axial direction of each voice coil actuator 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 supporting structure, which is used to provide power to the special-shaped active vibration isolation platform, transmit 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 adapted 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 , active control force provided to the voice coil actuator;

[0024] q p ,q b denote the generalized coordinates of the upper and lower platforms, respectively, 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 respectively, which is amplified by the sensor signal conditioner, collected and transmitted to the LQR controller, and the system state quantity is obtained through matrix conversion and integration;

[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 the smallest, P is obtained by solving the Riccati equation, as shown in formula (4). 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 drive as the final control signal output;

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

[0037] Step 7: Sending a 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 according to 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, and provide an ultra-quiet mechanical environment for the normal operation of airborne equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of a special-shaped active vibration isolation platform adapted to the arc surface of the cabin of 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 It 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 of the present invention, viewed from above;

[0045] Figure 4 It is a schematic diagram of the three-dimensional spatial distribution of the voice coil actuator of the special-shaped active vibration isolation platform adapted to the arc surface of the cabin of the present invention;

[0046] Figure 5 It is a 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 It 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 frequency domain z direction.

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

[0050] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be described in more detail below in conjunction with the drawings of the specification. It should be noted that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work 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 supporting 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 arranged above the lower platform 5, the top plate 1 is mounted on the upper platform 2, and the four corners of the top plate 1 are symmetrically provided with mounting holes 7, which are used to install precision optoelectronic loads. The lower platform 5 is in an arc shape, and the mounting lugs 3 are symmetrically arranged at the four corners of the lower platform 5, and the lower platform is fixed to the aircraft through the mounting lugs. Preferably, the mounting lugs 3 are provided with mounting screw holes, and the special-shaped active vibration isolation platform is mounted on the aircraft as a whole by screws.

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

[0054] There are two support structures 6, which are respectively arranged on the lower platform 5, for providing support for the voice coil actuator to reach the designed height position. Preferably, 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.

[0055] There are 8 voice coil actuators 9, and their specific installation positions are as follows: Figure 3 , Figure 4 As shown. Among them, 4 voice coil actuators are set on the lower platform, and voice coil actuators No. 9-2 and 9-5 are set vertically along the z-axis direction; voice coil actuators No. 9-1 and 9-6 are set along the radial direction of the arc surface, with an angle of 30° with the positive direction of the z-axis; two of the other 4 voice coil actuators are horizontally distributed, that is, voice coil actuators No. 9-3 and 9-4 are horizontally distributed, perpendicular to each other, symmetrical about the x-axis, and a support structure 6 provides a horizontal installation position for them; the remaining 2 voice coil actuators No. 9-7 and 9-8 are also perpendicular to each other, symmetrical about the x-axis, and the plane formed by them is 30° with the x-axis, and another support structure 6 provides an installation position with an angle of 30° with the x-axis. In order to adapt to the arc-shaped installation surface, the control coupling degree of the 8 actuators is high, and the control difficulty is relatively large.

[0056] The spring 10 is installed in parallel with the voice coil actuator 9, and realizes passive vibration isolation by damping and dissipating the energy of high-frequency vibration. As an auxiliary vibration isolation method of the vibration isolation platform, a spring is arranged corresponding to each voice coil actuator 9. The spring 10 mainly performs passive vibration reduction and limit connection between the upper and lower platforms. The vibration acceleration of the lower platform 5 is mainly transmitted to the upper platform 2 through the spring, and the voice coil actuator 9 is used as an actuator of the control system to perform 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 installed 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 respectively used to measure the acceleration values ​​of the lower platform 5 and the upper platform 2 in real time, and feed 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] The embodiment of the present invention further provides a 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 adapted 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 , active control force provided to the voice coil actuator;

[0065] q p ,q b denote the generalized coordinates of the upper and lower platforms, respectively, 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 the smallest, P is obtained by solving the Riccati equation, as shown in formula (4). 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 drive as the final control signal output;

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

[0078] Step 7: Sending a 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 according to the control current to suppress the vibration of the upper platform.

[0080] This special-shaped active vibration isolation platform mainly controls micro-vibrations in the three directions of x, y, and z. When running on the machine, the disturbance acceleration of the lower platform is measured by the three-axis acceleration sensor, and the disturbance is transmitted to the upper platform through the spring. The upper platform is subjected to the disturbance acceleration, which is measured by the single-axis acceleration sensor, and then the speed and position are obtained through matrix conversion and integration, thereby obtaining the state feedback. The feedback gain is solved by the LQR control algorithm to obtain the control signal. The driver inputs the control signal into the voice coil actuator to generate an axial Ampere force to achieve active suppression of the upper platform. At this time, the three-axis acceleration sensor of the upper platform is measured again, and compared with the acceleration measurement value of the lower platform as an evaluation of the vibration isolation effect.

[0081] In this embodiment, 8 voice coil actuators and springs are used for hybrid vibration isolation, wherein 2 actuators are vertically arranged along the z-axis direction; 2 actuators are radially arranged along the arc surface, with an angle of 30° with the positive direction of the z-axis; 2 actuators are horizontally distributed, perpendicular to each other, and symmetrical about the x-axis; the other 2 actuators are also perpendicular to each other, symmetrical about the x-axis, and the angle between the plane formed by them and the x-axis is 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 the system state quantity is obtained through matrix conversion and integration;

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

[0089] 3. Send the control signal to the linear driver 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 driver needs to convert the control voltage signal into a control current signal according to the proportional relationship between the input voltage and the output current;

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

[0091] Furthermore, the LQR control algorithm was 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 shown in Figure 2. 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 vibration isolation effect in the z direction in the time domain 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, it can be found that in the frequency band below 1 Hz, the PID controller cannot effectively suppress vibration, while the LQR controller has an obvious 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 only preferred embodiments of the present invention. For those skilled in the art, without departing from the principles of the present invention, the present invention may be modified, improved, and replaced with equivalents, which are also 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, a mounting lug, a lower platform, a supporting structure, a mounting hole, 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 installed on the upper platform, and the four corners of the top plate are symmetrically provided with mounting holes, and the mounting holes are used to install 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 on the aircraft through the mounting lugs; The upper platform is connected to the lower platform via a spring; There are two support structures, which are respectively arranged on the lower platform and are used to provide support for the voice coil actuator to reach the designed height position; There are eight voice coil actuators, of which four are arranged on the lower platform, two of which are arranged vertically along the z-axis direction, and two of which are arranged radially along the arc surface of the lower platform, with an angle of 30° with 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, and one of the support structures provides a horizontal installation position for them; the remaining two voice coil actuators are also perpendicular to each other, symmetrical about the x-axis, and the angle between the plane formed by them and the x-axis is 30°, and the other support structure provides them with an installation position with an angle of 30° with 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, and 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 one uniaxial acceleration sensor is installed in the axial direction of each voice coil actuator 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 supporting 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 lug is provided with a mounting screw hole, 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 the arc surface of a cabin 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 adapted 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 , active control force provided to the voice coil actuator; q p ,q b denote the generalized coordinates of the upper and lower platforms, respectively, 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 respectively, which is amplified by the sensor signal conditioner, collected and transmitted to the LQR controller, and the system state quantity is obtained through matrix conversion and integration; 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 the smallest, P is obtained by solving the Riccati equation, as shown in formula (4). 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: Sending a 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 according to the control current to suppress the vibration of the upper platform.

Images