Active quasi-zero stiffness construction method and system based on nonlinear characteristic digital fitting

Abstract

The application discloses an active quasi-zero stiffness construction method based on nonlinear characteristic digital fitting, and steps include: a quasi-zero stiffness system completes automatic zero point calibration, a force actuator unit drives a load platform to make a low-speed quasi-static scanning within a preset stroke, displacement and static force signals are synchronously collected, and a full-stroke force-displacement data set of a support assembly is constructed; then, a numerical approximation algorithm is used for fitting the data set, a digital twin mechanical model containing a high-order nonlinear term is established, and parameters are stored in a control unit. When the system is running, a high-frequency displacement detection unit collects instantaneous displacement of the load platform in real time, the control unit calls the model to calculate a current positive stiffness restoring force, generates a negative stiffness compensation instruction, drives the actuator unit to apply a compensation force to offset the positive stiffness, and makes the system present a quasi-zero stiffness characteristic within a working stroke. The method realizes quasi-zero stiffness, has advantages of no friction, parameter self-adaptation, large dynamic range and the like, and can be widely used in scenes such as spacecraft ground microgravity simulation and high-precision constant force assembly.

Description

Technical Field

[0001] This invention relates to the fields of precision motion control, physical environment simulation and vibration engineering technology, and in particular to a method and system for realizing quasi-zero stiffness characteristics of mechanical structures and constructing a micro-low gravity environment through digital compensation of the master dynamics model. Background Technology

[0002] With the deepening of aerospace, semiconductor manufacturing, and basic scientific research, the demand for "extremely low stiffness" or "constant force support" environments is becoming increasingly urgent. For example, in spacecraft ground deployment tests, it is necessary to use a suspension system to counteract gravity, while requiring the suspension system to have near-zero stiffness in the vertical direction to simulate the unconstrained state in space; in the field of precision vibration isolation, according to vibration theory, the lower the natural frequency of the system (i.e., the lower the stiffness), the better the isolation effect on low-frequency vibrations.

[0003] Traditional implementation methods are mainly divided into passive and semi-active, but both have significant technical limitations.

[0004] Existing passive quasi-zero stiffness systems typically employ a parallel connection of positive stiffness elements (such as helical springs) and negative stiffness mechanisms (such as magnetic springs or buckling beams). While theoretically the positive and negative stiffnesses can cancel each other out, this approach has the following drawbacks in practical engineering:

[0005] - Difficulty in nonlinear matching: The negative stiffness curve of the magnetic force or buckling beam is highly nonlinear, making it difficult to perfectly match the linear stiffness of the helical spring over a large stroke. This results in the system being effective only near a very small equilibrium point, with an extremely narrow dynamic range.

[0006] - Unavoidable hysteresis: Mechanical structures inevitably have friction and material hysteresis, which prevents the system from achieving true "zero stiffness" and seriously affects the accuracy of microgravity simulation and vibration isolation performance.

[0007] - Fixed parameters: Once the mechanical structure is manufactured, its stiffness characteristics are fixed. If the load mass changes (such as replacing a satellite payload with a different model), the springs must be redesigned or replaced, lacking adaptability.

[0008] To address the limitations of passive structures, semi-active control schemes based on voice coil motors or linear motors have been proposed (e.g., some commercially available active vibration isolation tables). Existing semi-active control strategies are typically based on simple linear feedback models (i.e., The proposed linear control method attempts to compensate for spring stiffness using linear gain. However, at the micrometer or even nanometer level of precision control, physical springs are not ideal linear components. They are affected by manufacturing errors, temperature drift, and material properties, exhibiting significant high-order nonlinear stiffness characteristics. The linear control method described above ignores these high-order nonlinear terms, leading to the following problems:

[0009] - Residual stiffness fluctuation: The motor cannot accurately generate a counteracting force that is a perfect mirror image of the nonlinear force of the spring, causing the stiffness of the system to fluctuate during motion, making it impossible to achieve smooth constant force floating.

[0010] - Low-frequency divergence risk: In pursuit of zero stiffness, excessively increasing the linear feedback gain can easily lead to low-frequency oscillations or divergence when the system is disturbed.

[0011] Therefore, the industry currently lacks a method that can accurately digitally characterize the nonlinear characteristics of physical support components and achieve "software-defined stiffness" through algorithms, thereby eliminating residual mechanical positive stiffness throughout the entire stroke and constructing an ideal quasi-zero stiffness physical model. Summary of the Invention

[0012] To address some issues with existing quasi-zero stiffness systems, such as the inability to simultaneously achieve low-frequency vibration isolation and static load-bearing capacity during vibration isolation; the inability to adapt to changes in load mass once the mechanical structure is fixed during microgravity simulations; and the problems of unadjustable parameters and susceptibility to instability in existing quasi-zero stiffness devices, this invention provides a systematic solution combining high-order numerical fitting and active force compensation, offering a method and system for constructing active quasi-zero stiffness based on nonlinear characteristic digital fitting. In this method, a high-precision digital twin model of the physical support components is constructed in the digital domain. Controllable electromagnetic forces, pneumatic pressures, and hydraulic pressures are generated using force-actuated units to form negative stiffness, precisely offsetting the positive mechanical stiffness at the physical level, thereby achieving quasi-zero stiffness characteristics with micron-level precision.

[0013] To address the aforementioned technical problems, this invention proposes an active quasi-zero stiffness construction method based on nonlinear characteristic digital fitting. This method employs a quasi-zero stiffness system comprised of a base, load platform, physical support components, force-actuated unit, high-frequency displacement detection unit, and control unit, and includes the following steps:

[0014] S1. Global characteristic identification: After the quasi-zero stiffness system is automatically calibrated to zero, during the system initialization phase, the force actuation unit is controlled to drive the load platform to perform low-speed quasi-static scanning motion within a preset working stroke; the displacement signal of the load platform and the static force signal required to maintain the displacement are collected simultaneously to construct the original force-displacement dataset of the physical support component within the entire stroke.

[0015] S2. Digital Twin Model Generation: A numerical approximation algorithm is used to fit the original force-displacement dataset to establish a digital twin mechanical model that characterizes the nonlinear elastic features of the physical support components and includes higher-order nonlinear terms. And store the polynomial coefficients or lookup table of the model in the control unit;

[0016] S3. Real-time micro-displacement sensing: During system operation, the high-frequency displacement detection unit collects the instantaneous displacement signal of the load platform relative to the mechanical balance zero point in real time. (Unit: mm);

[0017] S4. Negative stiffness compensation force calculation: The control unit calculates the instantaneous displacement signal. The digital twin mechanical model can be invoked in real time. (Unit: N) Calculate the positive stiffness restoring force generated by the physical support component at the current position, and generate a negative stiffness compensation force of equal magnitude and in the same direction as the displacement. This compensation force is denoted as... (Unit: N);

[0018] S5. Closed-loop force control execution: Drive the force actuation unit to respond to the compensation command of the negative stiffness compensation force issued by the control unit, and apply a continuously changing compensation force to the load platform to actively counteract the mechanical positive stiffness of the physical support component at the physical level, so that the system exhibits quasi-zero stiffness or constant force physical characteristics within the working stroke.

[0019] Furthermore, in the active quasi-zero stiffness construction method of the present invention, wherein:

[0020] In step S1, the automatic zero-point calibration includes: after the system is powered on, the control unit monitors the rate of change of the value of the high-frequency displacement detection unit; when the rate of change of the value is continuously lower than a set threshold within a preset time, it is determined that the load platform is in a state of mechanical static balance; the control unit automatically captures the current displacement reading and marks it as the zero stiffness balance zero point, and subsequent model calculations are all based on this zero point for relative coordinate transformation.

[0021] In step S2, the numerical approximation algorithm employs one of the following: Chebyshev spectral method, cubic spline interpolation algorithm, or least squares polynomial fitting algorithm; the digital twin mechanical model It is configured to include linear stiffness terms and higher-order nonlinear stiffness terms of the physical support component to compensate for manufacturing errors and material nonlinearities of the physical support component.

[0022] In step S2, if a numerical approximation algorithm is used to fit the original force-displacement dataset to a function, the polynomial coefficients of the model are stored in the control unit; if the collected original force-displacement dataset is used directly, the lookup table is stored in the control unit.

[0023] Before the closed-loop force control is executed in step S5, an active damping injection step may also be included: the control unit, based on the displacement signal Real-time motion speed of the differential computation load platform (Velocity: mm / s); Generate a virtual damping force command in the opposite direction to the motion velocity. (Unit: N), where The virtual damping coefficient is adjustable; the virtual damping force command is superimposed on the negative stiffness force compensation command to form the final control command, so that the negative stiffness compensation force generated in step S5 is... This is to suppress the divergence and oscillation of the system in the zero stiffness state.

[0024] Furthermore, this invention also proposes a quasi-zero stiffness system for implementing the aforementioned active quasi-zero stiffness construction method. This quasi-zero stiffness system includes a base, a load platform, a physical support component, a force actuation unit, a high-frequency displacement detection unit, and a control unit. The load platform can move relative to the base along the direction of gravity. The force actuation unit is connected in parallel with the physical support component between the base and the load platform. The physical support component bears the load gravity and provides static bearing capacity, exhibiting positive stiffness characteristics. The high-frequency displacement detection unit is composed of a non-contact displacement sensor and is positioned between the base and the load platform to receive the detected position information of the load platform in real time. The control unit stores a digital twin model of the physical support component generated based on measured data. Both the high-frequency displacement detection unit and the force actuation unit are electrically connected to the control unit. Based on the stored digital twin model, the control unit performs real-time calculations upon receiving the load platform displacement detected by the high-frequency displacement detection unit and sends control commands to the force actuation unit. The force actuation unit outputs a continuously controllable thrust according to the received control commands.

[0025] Furthermore, the quasi-zero stiffness system is characterized in that the physical support component is one or more of the following: a metal helical spring, a magnetic spring, and an air buoyancy support component.

[0026] The force-actuating unit is controlled by an electromagnetic device or is a device with controllable mechanical output performance; the electromagnetic device is one of a voice coil motor, a linear motor, or a moving magnet electromagnetic actuator; the device with controllable mechanical output performance is a pneumatic cylinder or a hydraulic cylinder.

[0027] The high-frequency displacement detection unit is a non-contact displacement sensor, which is one of the following: a grating ruler, a laser displacement sensor, and a capacitive displacement sensor.

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] (1) Extremely high stiffness resolution accuracy: Unlike traditional linear approximation control, the digital model generated by fitting measured data in this invention includes the nonlinearity, high-order error and hysteresis characteristics of the physical spring. Through algorithm compensation, the residual stiffness of the system can be reduced to close to the theoretical zero value, thereby achieving a near-perfect "constant force suspension" or "unrestrained" state on a macroscopic scale.

[0030] (2) Software-defined stiffness and parameter adaptation: This system does not rely on complex mechanical negative stiffness mechanisms (such as complex magnet arrays or buckling beams). When the load mass changes, there is no need to replace the hardware. The control parameters can be updated by simply rerunning the "scan-fit" process (i.e., steps S1 and S2 in feature one), which greatly improves the versatility and adaptability of the system.

[0031] (3) Multifunctional application scenarios: Because a digital twin model can be generated and called upon, the system stiffness can be defined as "quasi-zero" by software. This invention can be used for ultra-low frequency micro-vibration isolation (natural frequency) It can also be used for microgravity simulation on the ground of spacecraft, providing a constant force unloading environment in the vertical direction for precision payloads, thus achieving multiple uses in one machine.

[0032] (4) High stability and frictionless characteristics: The use of force-actuated units (such as voice coil motors) and virtual damping algorithms (i.e. active damping injection steps) avoids the friction and wear problems introduced by traditional mechanical negative stiffness mechanisms, and effectively solves the stability problem of zero stiffness systems that are prone to divergence when disturbed.

[0033] The construction method proposed in this invention can be used for ground testing of spacecraft, providing a gravity unloading and constant force support environment for deployment mechanisms such as solar panels and antennas; for ultra-precision measurement and manufacturing, providing ultra-low frequency micro-vibration isolation for equipment such as interferometers and lithography machines; and for high-sensitivity sensor calibration, constructing an equivalent free-floating test environment. Attached Figure Description

[0034] Figure 1 This is a flowchart of the active quasi-zero stiffness construction method of the present invention;

[0035] Figure 2 A block diagram of a quasi-zero stiffness system for realizing the active quasi-zero stiffness construction method of the present invention;

[0036] Figure 3 This is a two-dimensional schematic diagram of an adjustable zero-stiffness device according to an embodiment of the present invention. Detailed Implementation

[0037] The design concept of this invention, an active quasi-zero stiffness construction method based on nonlinear characteristic digital fitting, addresses the problems of nonlinear matching difficulties, large hysteresis, and unadjustable parameters in traditional mechanical negative stiffness mechanisms by proposing a digital twin model compensation strategy. First, a high-precision stiffness digital model containing high-order nonlinear terms is constructed by performing a full-stroke quasi-static scan and numerical approximation fitting on the physical support components. During system operation, load displacement is acquired in real time, and this model is used to calculate and drive the force actuation unit (such as a voice coil motor) to output a negative stiffness force that mirrors the physical elastic force in real time, thereby actively and accurately offsetting the mechanical positive stiffness at the physical level. This invention effectively solves the problem that linear control cannot eliminate residual stiffness, and achieves the equivalent zero stiffness or constant force characteristics of the system through software definition. It has advantages such as frictionless operation, adaptive parameter adjustment, and a large dynamic range, and is widely applicable to spacecraft ground microgravity simulation, high-precision constant force assembly, and ultra-low frequency micro-vibration isolation.

[0038] To realize the active quasi-zero stiffness construction method based on nonlinear characteristic digital fitting proposed in this invention, a quasi-zero stiffness system is designed in this invention, consisting of a base, load platform, physical support components, force actuation unit, high-frequency displacement detection unit, and control unit. For example... Figure 2 As shown, the load platform can move relative to the base along the direction of gravity; the force actuation unit is connected in parallel with the physical support component between the base and the load platform; the physical support component is used to bear the load gravity and provide static bearing capacity, exhibiting positive stiffness characteristics; the high-frequency displacement detection unit is composed of a non-contact displacement sensor, and is located between the base and the load platform to receive the detected position information of the load platform in real time; the control unit stores a digital twin model of the physical support component generated based on measured data; the high-frequency displacement detection unit and the force actuation unit are both electrically connected to the control unit; the control unit performs real-time calculations based on the stored digital twin model after receiving the load platform displacement detected by the high-frequency displacement detection unit, and sends control commands to the force actuation unit; the force actuation unit outputs a continuous and controllable thrust according to the received control commands.

[0039] In the quasi-zero stiffness system of this invention, the physical support component is one or more combinations of a metal helical spring, a magnetic spring, and an air-bearing support component. The force actuation unit is controlled by an electromagnetic device or a device with controllable mechanical output performance; the electromagnetic device is one of a voice coil motor, a linear motor, or a moving-magnet electromagnetic actuator; the device with controllable mechanical output performance is a pneumatic cylinder or a hydraulic cylinder. The high-frequency displacement detection unit is a non-contact displacement sensor, which is one of a grating ruler, a laser displacement sensor, and a capacitive displacement sensor.

[0040] The above-mentioned quasi-zero stiffness system is used to implement an active quasi-zero stiffness construction method based on nonlinear characteristic digital fitting, such as... Figure 1 As shown, it includes the following steps:

[0041] S0. Automatic zero-point calibration includes the following steps: after the system is powered on, the control unit monitors the rate of change of the value of the high-frequency displacement detection unit; when the rate of change of the value is continuously lower than a set threshold within a preset time, it is determined that the load platform is in a state of mechanical static balance; the control unit automatically captures the current displacement reading and marks it as the zero stiffness balance zero point, and subsequent model calculations are all based on this zero point for relative coordinate transformation.

[0042] S1. Global characteristic identification: After the quasi-zero stiffness system is automatically calibrated to zero, during the system initialization phase, the force actuation unit is controlled to drive the load platform to perform low-speed quasi-static scanning motion within a preset working stroke; the displacement signal of the load platform and the static force signal required to maintain the displacement are collected simultaneously to construct the original force-displacement dataset of the physical support component within the entire stroke.

[0043] S2. Digital Twin Model Generation: A numerical approximation algorithm is used to fit the original force-displacement dataset to establish a digital twin mechanical model that characterizes the nonlinear elastic features of the physical support components and includes higher-order nonlinear terms. (Unit: N), and store the polynomial coefficients or lookup table of the model in the control unit.

[0044] In step S2, the numerical approximation algorithm employs one of the following: the Chebyshev spectral method, the cubic spline interpolation algorithm, or the least squares polynomial fitting algorithm; the digital twin mechanical model It is configured to include linear stiffness terms and higher-order nonlinear stiffness terms of the physical support component to compensate for manufacturing errors and material nonlinearities of the physical support component.

[0045] In step S2, if a numerical approximation algorithm is used to fit the original force-displacement dataset to a function, the polynomial coefficients of the model are stored in the control unit; if the collected original force-displacement dataset is used directly, the lookup table is stored in the control unit.

[0046] S3. Real-time micro-displacement sensing: During system operation, the high-frequency displacement detection unit collects the instantaneous displacement signal of the load platform relative to the mechanical balance zero point in real time. (Unit: mm)

[0047] S4. Negative stiffness compensation force calculation: The control unit calculates the instantaneous displacement signal. The digital twin mechanical model can be invoked in real time. Calculate the positive stiffness restoring force generated by the physical support component at the current position, and generate a negative stiffness compensation force of equal magnitude and in the same direction as the displacement. This compensation force is denoted as... (Unit: N).

[0048] S5. Closed-loop force control execution: The force actuation unit responds to the compensation command of the negative stiffness compensation force issued by the control unit and applies a continuously changing compensation force to the load platform to actively counteract the mechanical positive stiffness of the physical support component at the physical level, so that the system exhibits quasi-zero stiffness or constant force physical characteristics within the working stroke.

[0049] To suppress divergence and oscillation of the system in a zero-stiffness state, an active damping injection step can be added before S5: that is, before step S5, the control unit, based on the displacement signal... Real-time motion speed of the differential computation load platform (Unit: mm / s); Generate a virtual damping force command opposite to the direction of the motion velocity. (Unit: N), where The adjustable virtual damping coefficient (unit: N·s / mm); the virtual damping force command is superimposed on the negative stiffness force compensation command to form the final control command, so that the negative stiffness compensation force generated in the subsequent S5 step is... This is to suppress the divergence and oscillation of the system in the zero stiffness state.

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0051] Example:

[0052] like Figure 3 As shown, this embodiment constructs a high-precision physical experiment platform, which mainly includes a base 1, an air-bearing guide rail assembly 2, a load platform 3, a physical support assembly 6, a force actuation unit 4, a high-frequency displacement detection unit 5, and a control unit.

[0053] The base 1 serves as a fixed reference frame. In this embodiment, the load platform 3, together with the base 1 and the air-bearing guide rail assembly 2, is used to support the object under test. The object under test can be, for example, a spacecraft deployment mechanism or a precision optical instrument. The object under test is restricted to vertical (gravity direction) movement by the air-bearing guide rail assembly 2. The air-bearing design eliminates mechanical friction, providing a foundation for high-precision force control. The physical support assembly 6 uses a high-stiffness metal helical spring. One end of the metal helical spring is fixed to the base 1, and the other end supports the load platform 3. The function of the metal helical spring is to bear the static gravity of the load. (Unit: N). At this point, the system exhibits positive stiffness characteristics, with a stiffness coefficient of... The force-actuating unit 4 is preferably a voice coil motor. The mover of the voice coil motor is connected to the load platform 3, and the stator of the voice coil motor is fixed to the base 1. The voice coil motor has the characteristics of fast response, high thrust linearity, and no hysteresis, and is used as a negative stiffness actuator in the construction method of this invention. The high-frequency displacement detection unit 5 is a non-contact grating ruler with a resolution better than 0.1μm, used to collect micro-displacement signals of the load platform 3 relative to the equilibrium position in real time. The collected signals are then fed back to the control unit.

[0054] The control principle and working process of the construction method of this invention lie in the digital twin stiffness model and compensation algorithm running inside the control unit. This construction method does not rely on a specific hardware structure and can achieve the compensation of the stiffness of the physical support component (spring) through software definition alone.

[0055] The specific control process in this embodiment includes the following steps:

[0056] System initialization and zero-point calibration steps: After the system is powered on, the control unit first monitors the rate of change of the displacement sensor readings. When the rate of change remains below a set threshold, it is determined that the load is in a state of mechanical static balance (i.e., the spring force and gravity are balanced). The control unit automatically captures the current position coordinates and marks them as the zero-stiffness balance zero point. All subsequent control calculations are based on this relative coordinate system.

[0057] Global Characteristic Identification (Scanning Mode) Steps: Before formal operation, the system enters global characteristic identification mode. The control unit sends a command to drive the voice coil motor at an extremely low speed (e.g., 0.5 mm / s) to move the load platform within the allowable stroke (e.g., ...). The device performs a reciprocating motion. During this process, the control unit simultaneously records two sets of data at a high sampling rate (e.g., 5kHz): the real-time position of the displacement sensor. The voice coil motor current required to maintain this position, converted into thrust. (Unit: N). Due to the extremely slow speed of motion, inertial and damping forces are negligible, and the recorded... This accurately reflects the elastic restoring force of the physical support component (spring) at that location.

[0058] Nonlinear model construction (digital twin) steps: Acquire the original force-displacement dataset Subsequently, the control unit uses its internally integrated numerical approximation algorithm to fit the model. Considering that metal coil springs are not ideal linear components and that slight deviations may occur during installation, a simple linear model is used. This approach cannot meet the requirements for micrometer-level control. This embodiment employs Chebyshev polynomial interpolation or cubic spline interpolation to construct a high-precision digital model of elastic force. :

[0059]

[0060] in, is the force-displacement characteristic function of the metal helical spring, in N; x is the displacement of the load platform, in mm; (n is 1, 2, 3, ..., a positive integer) represents the polynomial coefficients in the interpolation function, i.e., the coefficients of the nth-order x multipliers in the above formula, in N / (mm^n). The value of n is flexibly determined as needed: when selecting, the nonlinearity of the force-displacement characteristics of the spring itself, the complexity of characteristic deviations introduced by processing and assembly, and the control accuracy requirements of the actual application scenario should be comprehensively considered. While ensuring that the fitting accuracy meets the requirements, the computational overhead of the control unit should also be taken into account to avoid overfitting. In this embodiment, for the high-precision requirements of micron-level control, the fitting verification was performed on multiple sets of measured original force-displacement datasets: when the value is 4, the fitting error of the elastic force digital model can be controlled within the allowable error range of micron-level control, and it will not increase the unnecessary computational load of the control unit. Therefore, the value is 4 in this embodiment. This digital twin model accurately captures the nonlinear stiffness characteristics, hysteresis, and processing errors of the physical components, and establishes an accurate elastic force digital model of the metal helical spring in the controller.

[0061] Quasi-zero stiffness real-time compensation (working mode) steps: After modeling is completed, the system enters the quasi-zero stiffness working mode and cyclically executes the following process: sensing micro-displacement - solving spring normal stiffness force - generating compensation force command - executing compensation force command - physical effect process:

[0062] 1) Sensing micro-displacement: The sensor reads the micro-displacement of the load in real time. .

[0063] 2) Calculate the normal stiffness force of the spring: The controller will... Substitute into the digital model Calculate the normal stiffness force generated by the current metal helical spring.

[0064] 3) Generate negative stiffness compensation force command: The controller generates a negative stiffness compensation force of equal magnitude but opposite direction (i.e., in the same direction of propulsion). And send the compensation force command to the voice coil motor:

[0065]

[0066] in, The target negative stiffness compensation force is generated, in N; x(t) is the instantaneous displacement of the load platform at time t, in mm.

[0067] 4) Execute compensation force command: After receiving the voice coil motor compensation force command, the negative stiffness compensation force is output.

[0068] 5) Physical effect: the system exhibits quasi-zero stiffness characteristics. At this point, the total resultant force on the load is:

[0069]

[0070] in, (x) represents the actual normal stiffness force of the metal coil spring, in N; This represents the magnitude of the negative stiffness compensation force output by the voice coil motor, measured in N. The stiffness of the metal helical spring is perfectly canceled out by the electromagnetic force, and the total dynamic stiffness of the system approaches zero. At this point, the system exhibits quasi-zero stiffness characteristics.

[0071] Active damping injection (stability enhancement) steps: To prevent the zero-stiffness system from diverging under external transient impacts, the control unit can calculate the differential of displacement (velocity) simultaneously with calculating the spring normal stiffness force in step 2) above. ), and superimpose a virtual damping force:

[0072]

[0073] in, is the virtual damping force, in N; c is the virtual damping coefficient, in N·s / mm; c is a positive real number greater than 0, which can be set to a fixed constant value or dynamically adjusted adaptively according to the real-time operating status of the system; its value can be flexibly determined according to actual application requirements: when selecting, the inherent dynamic characteristics of the zero-stiffness system, the expected magnitude of transient impact to be suppressed, and the upper limit of the system's allowable response speed should be comprehensively considered. Under the premise of ensuring that the system does not oscillate or diverge after being impacted and that the positioning error after the impact disturbance meets the accuracy requirements, excessively large values ​​of c should be avoided to prevent system response lag and decreased dynamic tracking performance. v is the velocity signal obtained by differentiating the displacement signal, in mm / s.

[0074] In this embodiment, for micron-level precision positioning applications, the value of c is determined to be 0.012 N·s / mm through multiple sets of transient impact calibration tests. Under this value, when the system is subjected to a transient impact of the maximum design magnitude, the oscillation can converge within one motion cycle, the maximum positioning deviation caused by the impact does not exceed 2μm, and the system response delay is less than 10ms, which can simultaneously meet the requirements of impact suppression and dynamic accuracy.

[0075] The damping force injection command is generated only during motion, does not affect the static load-bearing capacity of the system, and does not disrupt the quasi-zero stiffness property of the system. After the calculation is completed, it is superimposed on the electromagnetic negative stiffness force command in step 3) above, and executed in step 4).

[0076] The final resultant force on the load is (Unit: N), where This refers to the total resultant force on the load when there is no damping force superposition in step 5 above.

[0077] The implementation effect of this embodiment is as follows: This embodiment eliminates motion friction by utilizing the air-bearing guide rail assembly 2, bears heavy loads by utilizing the elastic support assembly 6, and achieves precise force-adjustable negative stiffness by utilizing the voice coil motor 4. This structure is compact and solves the contradiction between load-bearing capacity and low-frequency vibration isolation performance that traditional passive vibration isolation cannot simultaneously address. At the same time, through the high-precision feedback of the non-contact displacement sensor 5, the calculation of the vibration isolation output function, real-time parameter input, and real-time adjustment are realized.

[0078] Although the present invention has been described above in conjunction with the accompanying drawings, it should be understood that the specific embodiments described above are merely illustrative of the method principles of the present invention and are not restrictive. Those skilled in the art can make many improvements and variations based on the teachings of the present invention without departing from its spirit. For example, although a voice coil motor is used as the force actuation unit in this embodiment, those skilled in the art can replace it with other electromagnetic actuators or precision force output devices. These all fall within the protection scope of the present invention.

Claims

1. A method for constructing active quasi-zero stiffness based on nonlinear characteristic digital fitting, characterized in that, A quasi-zero stiffness system is adopted, consisting of a base, load platform, physical support components, force actuation unit, high-frequency displacement detection unit, and control unit, and includes the following steps: S1. Global characteristic identification: After the quasi-zero stiffness system is automatically calibrated to zero, during the system initialization phase, the force actuation unit is controlled to drive the load platform to perform low-speed quasi-static scanning motion within a preset working stroke; the displacement signal of the load platform and the static force signal required to maintain the displacement are collected simultaneously to construct the original force-displacement dataset of the physical support component within the entire stroke. S2. Digital Twin Model Generation: A numerical approximation algorithm is used to fit the original force-displacement dataset to establish a digital twin mechanical model that characterizes the nonlinear elastic features of the physical support components and includes higher-order nonlinear terms. The unit is N, and the polynomial coefficients or lookup table of the model are stored in the control unit; S3. Real-time micro-displacement sensing: During system operation, the high-frequency displacement detection unit collects the instantaneous displacement signal of the load platform relative to the mechanical balance zero point in real time. The unit is mm; S4. Negative stiffness compensation force calculation: The control unit calculates the instantaneous displacement signal. The digital twin mechanical model can be invoked in real time. Calculate the positive stiffness restoring force generated by the physical support component at the current position, and generate a negative stiffness compensation force of equal magnitude and in the same direction as the displacement. The unit is N; S5. Closed-loop force control execution: The force actuation unit receives the compensation command of the negative stiffness compensation force issued by the control unit and applies a continuously changing negative stiffness compensation force to the load platform to actively counteract the mechanical positive stiffness of the physical support component at the physical level, so that the system exhibits quasi-zero stiffness characteristics within the working stroke.

2. The active quasi-zero stiffness construction method according to claim 1, characterized in that, In step S1, the automatic zero-point calibration includes: after the system is powered on, the control unit monitors the rate of change of the value of the high-frequency displacement detection unit; when the rate of change of the value is continuously lower than a set threshold within a preset time, it is determined that the load platform is in a state of mechanical static balance; the control unit automatically captures the current displacement reading and marks it as the zero stiffness balance zero point, and subsequent model calculations are all based on this zero point for relative coordinate transformation.

3. The active quasi-zero stiffness construction method according to claim 1, characterized in that, In step S2, the numerical approximation algorithm employs one of the following: Chebyshev spectral method, cubic spline interpolation algorithm, or least squares polynomial fitting algorithm; the digital twin mechanical model It is configured to include linear stiffness terms and higher-order nonlinear stiffness terms of the physical support component to compensate for manufacturing errors and material nonlinearities of the physical support component.

4. The active quasi-zero stiffness construction method according to claim 1, characterized in that, In step S2, if a numerical approximation algorithm is used to fit the original force-displacement dataset, the polynomial coefficients of the model are stored in the control unit. If the original force-displacement dataset is used directly, the lookup table is stored in the control unit.

5. The active quasi-zero stiffness construction method according to claim 1, characterized in that, Prior to step S5, an active damping injection step is included: the control unit, based on the displacement signal... Real-time motion speed of the differential computation load platform The unit is mm / s; generate a virtual damping force command opposite to the direction of the motion velocity. The unit is N, where The adjustable virtual damping coefficient; The virtual damping force command is superimposed on the negative stiffness force compensation command to form the final control command, thus the negative stiffness compensation force generated in step S5 is... This is to suppress the divergence and oscillation of the system in the zero stiffness state.

6. A quasi-zero stiffness system for implementing the active quasi-zero stiffness construction method according to any one of claims 1 to 5, characterized in that, The load platform can move relative to the base along the direction of gravity; The force-actuating unit is connected in parallel with the physical support component between the base and the load platform; The physical support components are used to bear the load and provide static bearing capacity, exhibiting positive stiffness characteristics; The high-frequency displacement detection unit is composed of a non-contact displacement sensor. The high-frequency displacement detection unit is disposed between the base and the load platform and is used to receive the detected position information of the load platform in real time. The control unit stores a digital twin model of the physical support component generated based on measured data. The high-frequency displacement detection unit and the force actuation unit are both electrically connected to the control unit. The control unit performs real-time calculations based on the stored digital twin model after receiving the load platform displacement detected by the high-frequency displacement detection unit, and sends control commands to the force actuation unit. The force actuation unit outputs a continuous and controllable thrust according to the received control commands.

7. The quasi-zero stiffness system according to claim 6, characterized in that, The physical support component is one or more of the following: metal helical spring, magnetic spring, and air buoyancy support component.

8. The quasi-zero stiffness system according to claim 6, characterized in that, The force-actuated unit is controlled by an electromagnetic device or is a device with controllable mechanical output performance; The electromagnetic device is one of a voice coil motor, a linear motor, or a moving magnet electromagnetic actuator. The device with controllable mechanical output performance is a pneumatic cylinder or a hydraulic cylinder.

9. The quasi-zero stiffness system according to claim 5, characterized in that, The high-frequency displacement detection unit is a non-contact displacement sensor, which is one of the following: a grating ruler, a laser displacement sensor, and a capacitive displacement sensor.

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