A precise air-floating active vibration isolation method and system based on LSTM position prediction and state constraint dynamic surface control

Abstract

The application relates to a precision air floating active vibration isolation method and system based on LSTM position prediction and state constraint dynamic surface control, and belongs to the cross field of high-end equipment manufacturing and artificial intelligence technology, and aims to solve the problems that the existing method cannot compensate for system lag, is difficult to cope with strong nonlinearity and coupling interference. The method comprises the following steps: constructing an air floating vibration isolation system high-order nonlinear MIMO model through a throttle valve operation model and an air chamber pressure dynamic model; converting the constrained state into an unconstrained state by using a symmetric barrier function, and building a dynamic surface filter and a controller; constructing an LSTM position prediction module, outputting a future load position prediction value and generating a prediction signal; and combining the prediction signal and a virtual controller in the dynamic surface control to generate a composite control signal. The application solves the lag problem of the air floating vibration isolation system, effectively copes with the strong nonlinearity and coupling interference of the system, and the LSTM module can be integrated in a light weight mode, which is convenient for engineering deployment.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of high-end equipment manufacturing and artificial intelligence technology, specifically involving a precision air-bearing active vibration isolation method and system based on LSTM position prediction and state-constrained dynamic surface control. Background Technology

[0002] In the fields of ultra-precision manufacturing, nanometer measurement, biomedical imaging, ground testing of space optical payloads, and integrated circuits, environmental micro-vibrations at the submicron to nanometer scale can directly cause processing errors, image blurring, or measurement inaccuracies, severely restricting breakthroughs in the performance limits of high-end equipment. Air-bearing vibration isolation systems, with their unique advantages of being contactless, low-friction, highly smooth, and capable of multi-degree-of-freedom load bearing, have become the mainstream passive and active vibration isolation platform supporting such equipment.

[0003] A typical active air-float vibration isolation system uses multiple independent controllable air chambers to regulate gas pressure, thereby offsetting the vibration interference from the ground and the load itself in real time. However, typical active air-float vibration isolation systems face the following problems: First, strong nonlinearity and high-order characteristics. Typical active air-float vibration isolation systems involve proportional valve electromechanical dynamics and nonlinear compressible gas flow, exhibiting high-order nonlinear characteristics, making accurate modeling extremely difficult. Second, strong coupling of multiple variables. In a multi-input multi-output system composed of multiple isolation units, the forces and torques interfere significantly with each other during multi-degree-of-freedom motion. Third, hard constraints across all states. The critical states of load displacement, air chamber pressure, and valve core displacement must be strictly limited within safety boundaries; exceeding these boundaries can easily lead to equipment damage. Traditional control methods cannot simultaneously meet the requirements of full-state constraints, strong robustness, and low-delay response.

[0004] The CNKI (China National Knowledge Infrastructure) published a paper titled "Adaptive Control and Stability Analysis of MIMO Nonlinear Systems," published in 2022, which discloses adaptive tracking control of MIMO nonlinear systems with full-state constraints based on generalized obstacle functions. This existing technology has the following shortcomings: it does not address the sensor detection and actuator response lag issues inherent in air-bearing vibration isolation systems, and cannot compensate for the phase deviation and control accuracy degradation caused by lag; it does not consider the unique dynamic characteristics of air-bearing vibration isolation systems, and cannot effectively cope with the strong nonlinearity intertwined by multiple components and the significant coupling interference from multi-unit collaborative operation. These are the deficiencies of the existing technology.

[0005] In view of this, it is very necessary to provide a precision air-float active vibration isolation method and system based on LSTM position prediction and state-constrained dynamic surface control to solve the above-mentioned defects in the prior art. Summary of the Invention

[0006] To address the unresolved issues of sensor detection and actuator response lag in existing air-bearing vibration isolation systems, which fail to compensate for phase deviation and reduced control accuracy caused by lag, and the inability to effectively handle the strong nonlinearity of multiple interconnected components and significant coupling interference from multi-unit collaborative operation by not incorporating the unique dynamic characteristics of air-bearing vibration isolation systems, this invention provides a precision air-bearing active vibration isolation method and system based on LSTM position prediction and state-constrained dynamic surface control to solve the aforementioned technical problems.

[0007] In a first aspect, the present invention provides a precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control, comprising:

[0008] Step S1: The dynamic modeling step involves constructing a load multi-degree-of-freedom vibration model using the throttle valve operation model and the air chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system.

[0009] The mathematical expression for the throttle valve operation model is:

[0010]

[0011] Where q is the displacement of the throttle valve core. For the quality of the throttle valve core, The damping coefficient is... Where u is the spring stiffness and u is the input voltage. This is the proportionality coefficient. The force is electromagnetic, assumed to be proportional to the input voltage u; AP is the air reaction force; A is the effective cross-sectional area of ​​the airbag; and P is the air chamber pressure. For the first derivative of q, It is the second derivative of q;

[0012] The mathematical expression for the dynamic model of air chamber pressure is:

[0013]

[0014] Where P is the air chamber pressure. For the first derivative of P, Air mass flow rate, For specific heat ratio, Let V be the gas constant and V be the volume of the gas chamber. Assuming linearity, The first derivative of the load displacement w Leakage coefficient;

[0015] The mathematical expression for air mass flow rate is:

[0016]

[0017] in, For flow coefficient, Let the effective area of ​​the valve orifice be assuming , For gas source temperature, It is a nonlinear flow function. Due to upstream pressure, This is due to downstream pressure;

[0018] A multi-degree-of-freedom vibration model of the load is constructed based on the throttle valve operation model and the gas chamber pressure dynamic model. The mathematical expression is:

[0019]

[0020] in, For load quality, For the damping of the air-bearing vibration isolation system, For the stiffness of the air-bearing vibration isolation system, For load displacement, External disturbance;

[0021] The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with side length L.

[0022] The integrated state variable vector of the air-bearing vibration isolation system includes , , , The valve core speed of the throttle valve;

[0023] The mathematical expression for the position and attitude of the platform's center of mass is:

[0024]

[0025] The mathematical expression for the platform's center-of-gravity velocity is:

[0026]

[0027] The mathematical expression for the gas pressure in the gas chamber is:

[0028]

[0029] The mathematical expression for the valve core displacement of a throttle valve is:

[0030]

[0031] The mathematical expression for the spool velocity of a throttle valve is:

[0032]

[0033] The mathematical expression for modeling the air-bearing vibration isolation system as a high-order nonlinear MIMO system is:

[0034]

[0035]

[0036] in, For state variables, , and These are intermediate variables of the state variables. and They are and The first-order differential, For the control gain matrix, It is a composite function vector.

[0037] Step S2: The step of constructing the symmetric barrier function. Based on the symmetric barrier function, the constrained state of the high-order nonlinear MIMO system of the air-bearing vibration isolation system is transformed into an unconstrained state, and a dynamic surface filter is constructed for the transformed air-bearing vibration isolation system.

[0038] State variables Set time-varying boundary constraints to ensure state variables It always operates within its preset safe zone, which can be expressed mathematically as follows:

[0039]

[0040] in, To constrain the lower boundary, For state variables, To constrain the upper boundary;

[0041] Construct a symmetric barrier function to constrain the physical state. Transformation into an unconstrained transformation state Transformation The mathematical expression for the symmetric barrier function is:

[0042]

[0043] in, ;

[0044] The boundary penalty property of the symmetric barrier function indicates that if the transformed state of the air-bearing vibration isolation system... If the entire time domain is bounded, then the original physical state It will inevitably and strictly be confined to the pre-defined constraint area.

[0045] The mathematical expression for an unconstrained high-order nonlinear MIMO system in an air-bearing vibration isolation system is as follows:

[0046]

[0047] in, , , , , , , , These are intermediate variables.

[0048] The mathematical expression for a dynamic surface filter is:

[0049]

[0050] in, As an intermediate variable, For virtual controllers, This is the state of the dynamic surface filter. For the first-order differential of the state of the dynamic surface filter, The time constant matrix;

[0051] Among them, dynamic surface filters Filtering was performed to compensate for the nonlinear terms introduced by the state constraint transformation. and .

[0052] Virtual Controller The mathematical expression is:

[0053]

[0054] in, As an intermediate variable, For the error surface, the mathematical expression is:

[0055]

[0056]

[0057] in, For the desired trajectory Transformed values ​​through the barrier function;

[0058] The actual controller u, used to output voltage signal vectors to the three proportional valves, is mathematically expressed as:

[0059]

[0060] in, As an intermediate variable, Given a nonlinear vector, It is the smoothing constant. This is the dot product between vectors.

[0061] Step S3: The step of constructing the LSTM location prediction module is to use an LSTM network to output the predicted value of the future sequence, and based on the predicted value of the future sequence, construct a location predictor and output the future prediction signal.

[0062] The load position information measured by sensors at three vibration isolation units over a longer period of time is obtained, and the mathematical expression for this position information is as follows: ;

[0063] The location information is standardized and preprocessed; the mathematical expression is as follows:

[0064]

[0065] in, The data is standardized based on location information. The mean of the location information. The standard deviation of the location information;

[0066] The Huber loss function and iterative reweighted least squares method are used to smooth the standardized preprocessed data to obtain a noise-resistant trend signal. ;

[0067] The historical sequence input data is constructed using the following mathematical expression:

[0068]

[0069] Output the predicted value of the future sequence, expressed mathematically as follows:

[0070]

[0071]

[0072] in, For future sequence predictions, For Gaussian window weights, Let h be the center of the Gaussian window, h be the prediction step size, and k be the future step number. This is the width parameter of the Gaussian window;

[0073] A multi-layer LSTM network is used to output predicted values ​​for future sequences. , , ;

[0074] Predicted values ​​for future sequences , , Obtained by destandardization ;

[0075] The mathematical expression for constructing the location predictor is:

[0076]

[0077] in, For adjustable control parameters, This represents the desired trajectory.

[0078] Step S4: The step of generating composite control signals, based on the future prediction signal and the first virtual controller of the dynamic surface filter, generates composite control signals;

[0079] The mathematical expression for the composite control signal generated by the first virtual controller based on the future prediction signal and the dynamic surface filter is:

[0080]

[0081] in, For composite control signals, As the first virtual controller, For location predictors.

[0082] Secondly, the technical solution of the present invention also provides a precision air-bearing active vibration isolation system based on LSTM position prediction and state-constrained dynamic surface control, including a dynamic modeling module, a symmetric barrier function construction module, an LSTM position prediction construction module, and a composite control signal generation module;

[0083] The dynamic modeling module constructs a load multi-degree-of-freedom vibration model through a throttle valve operation model and a gas chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system.

[0084] The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with a side length of L.

[0085] A symmetric barrier function module is constructed. Based on the symmetric barrier function, the constrained state in the high-order nonlinear MIMO system of the air-bearing vibration isolation system is transformed into an unconstrained state. A dynamic surface filter is then constructed for the transformed air-bearing vibration isolation system.

[0086] An LSTM location prediction module is constructed, which uses an LSTM network to output predicted values ​​for future sequences. Based on these predicted values, a location predictor is constructed to output the predicted future signal.

[0087] A composite control signal generation module generates composite control signals based on a first virtual controller that uses a future prediction signal and a dynamic surface filter.

[0088] The beneficial effects of this invention are as follows: This invention provides a precision air-bearing active vibration isolation method and system based on LSTM position prediction and state-constrained dynamic surface control. By introducing an LSTM position prediction module, the future load position is predicted based on the historical state data of the air-bearing vibration isolation system, and a composite control signal is generated. This solves the inherent sensor detection and valve response lag problems of the air-bearing vibration isolation system. Combined with a dynamic surface filter, it achieves the unity of phase lead and closed-loop stability, reducing control error. A high-order nonlinear MIMO integrated model adapted to the characteristics of the air-bearing vibration isolation system is constructed through the throttle valve operation model and the air chamber pressure dynamic model. Then, the transition from constrained state to unconstrained state is completed by relying on the symmetric barrier function. This specifically solves the strong nonlinearity of the multi-link intertwined air-bearing vibration isolation system and the coupling interference of multi-unit collaboration. Moreover, the LSTM module can be lightweight and integrated after offline training, making it easier to achieve real-time deployment in engineering.

[0089] Furthermore, the design principle of this invention is reliable, the structure is simple, and it has a very wide range of application prospects. Attached Figure Description

[0090] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0091] Figure 1 This is a flowchart of a precision air-float active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control provided by the present invention.

[0092] Figure 2 This is a schematic diagram of a precision air-float active vibration isolation system based on LSTM position prediction and state-constrained dynamic surface control, provided by the present invention. Detailed Implementation

[0093] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0094] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0095] Example 1:

[0096] like Figure 1 As shown, this embodiment of the invention provides a precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control, including the following steps:

[0097] Step S1: The dynamic modeling step involves constructing a load multi-degree-of-freedom vibration model using the throttle valve operation model and the air chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system.

[0098] The mathematical expression for the throttle valve operation model is:

[0099]

[0100] Where q is the displacement of the throttle valve core. For the quality of the throttle valve core, The damping coefficient is... Where u is the spring stiffness and u is the input voltage. This is the proportionality coefficient. The force is electromagnetic, assumed to be proportional to the input voltage u; AP is the air reaction force; A is the effective cross-sectional area of ​​the airbag; and P is the air chamber pressure. For the first derivative of q, It is the second derivative of q;

[0101] The mathematical expression for the dynamic model of air chamber pressure is:

[0102]

[0103] Where P is the air chamber pressure. For the first derivative of P, Air mass flow rate, For specific heat ratio, Let V be the gas constant and V be the volume of the gas chamber. Assuming linearity, The first derivative of the load displacement w Leakage coefficient;

[0104] The mathematical expression for air mass flow rate is:

[0105]

[0106] in, For flow coefficient, Let the effective area of ​​the valve orifice be assuming , For gas source temperature, It is a nonlinear flow function. Due to upstream pressure, This is due to downstream pressure;

[0107] A multi-degree-of-freedom vibration model of the load is constructed based on the throttle valve operation model and the gas chamber pressure dynamic model. The mathematical expression is:

[0108]

[0109] in, For load quality, For the damping of the air-bearing vibration isolation system, For the stiffness of the air-bearing vibration isolation system, For load displacement, External disturbance;

[0110] The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with side length L.

[0111] The integrated state variable vector of the air-bearing vibration isolation system includes , , , The valve core speed of the throttle valve;

[0112] The mathematical expression for the position and attitude of the platform's center of mass is:

[0113]

[0114] The mathematical expression for the platform's center-of-gravity velocity is:

[0115]

[0116] The mathematical expression for the gas pressure in the gas chamber is:

[0117]

[0118] The mathematical expression for the spool displacement of a throttle valve is:

[0119]

[0120] The mathematical expression for the spool velocity of a throttle valve is:

[0121]

[0122] The mathematical expression for modeling the air-bearing vibration isolation system as a high-order nonlinear MIMO system is:

[0123]

[0124]

[0125] in, For state variables, , and These are intermediate variables of the state variables. and They are and The first-order differential, For the control gain matrix, It is a composite function vector.

[0126] In this embodiment, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system, and its mathematical expression is as follows:

[0127]

[0128]

[0129] Step S2: The step of constructing the symmetric barrier function. Based on the symmetric barrier function, the constrained state of the high-order nonlinear MIMO system of the air-bearing vibration isolation system is transformed into an unconstrained state, and a dynamic surface filter is constructed for the transformed air-bearing vibration isolation system.

[0130] State variables Set time-varying boundary constraints to ensure state variables It always operates within its preset safe zone, which can be expressed mathematically as follows:

[0131]

[0132] in, To constrain the lower boundary, For state variables, To constrain the upper boundary;

[0133] Construct a symmetric barrier function to constrain the physical state. Transformation into an unconstrained transformation state Transformation The mathematical expression for the symmetric barrier function is:

[0134]

[0135] in, ;

[0136] The boundary penalty property of the symmetric barrier function indicates that if the transformed state of the air-bearing vibration isolation system... If the entire time domain is bounded, then the original physical state It will inevitably and strictly be confined to the pre-defined constraint area.

[0137] The mathematical expression for an unconstrained high-order nonlinear MIMO system in an air-bearing vibration isolation system is as follows:

[0138]

[0139] in, , , , , , , , These are intermediate variables.

[0140] In this embodiment, the mathematical expression for the unconstrained high-order nonlinear MIMO system of the air-bearing vibration isolation system is as follows: .

[0141] The mathematical expression for a dynamic surface filter is:

[0142]

[0143] in, As an intermediate variable, For virtual controllers, This is the state of the dynamic surface filter. For the first-order differential of the state of the dynamic surface filter, The time constant matrix;

[0144] Among them, dynamic surface filters Filtering was performed to compensate for the nonlinear terms introduced by the state constraint transformation. .

[0145] Virtual Controller The mathematical expression is:

[0146]

[0147] in, As an intermediate variable, For the error surface, the mathematical expression is:

[0148]

[0149]

[0150] in, For the desired trajectory Transformed values ​​through the barrier function;

[0151] The actual controller u, used to output voltage signal vectors to the three proportional valves, is mathematically expressed as:

[0152]

[0153] in, As an intermediate variable, Given a nonlinear vector, It is the smoothing constant. This is the dot product between vectors.

[0154] Step S3: The step of constructing the LSTM location prediction module is to use an LSTM network to output the predicted value of the future sequence, and based on the predicted value of the future sequence, construct a location predictor and output the future prediction signal.

[0155] The load position information measured by sensors at three vibration isolation units over a longer period of time is obtained, and the mathematical expression for this position information is as follows: ;

[0156] The location information is standardized and preprocessed; the mathematical expression is as follows:

[0157]

[0158] in, The data is standardized based on location information. The mean of the location information. The standard deviation of the location information;

[0159] The Huber loss function and iterative reweighted least squares method are used to smooth the standardized preprocessed data to obtain a noise-resistant trend signal. ;

[0160] The historical sequence input data is constructed using the following mathematical expression:

[0161]

[0162] Output the predicted value of the future sequence, expressed mathematically as follows:

[0163]

[0164]

[0165] in, For future sequence predictions, For Gaussian window weights, Let h be the center of the Gaussian window, h be the prediction step size, and k be the future step number. This is the width parameter of the Gaussian window;

[0166] A multi-layer LSTM network is used to output predicted values ​​for future sequences. , , ;

[0167] Predicted values ​​for future sequences , , Obtained by destandardization ;

[0168] The mathematical expression for constructing the location predictor is:

[0169]

[0170] in, For adjustable control parameters, This represents the desired trajectory.

[0171] Step S4: The step of generating composite control signals, based on the future prediction signal and the first virtual controller of the dynamic surface filter, generates composite control signals;

[0172] The mathematical expression for the composite control signal generated by the first virtual controller based on the future prediction signal and the dynamic surface filter is:

[0173]

[0174] in, For composite control signals, As the first virtual controller, For location predictors.

[0175] Other virtual controllers and actual controller It remains unchanged.

[0176] Example 2:

[0177] like Figure 2 As shown, this embodiment also provides a precision air-floating active vibration isolation system based on LSTM position prediction and state-constrained dynamic surface control, including a dynamic modeling module 1, a symmetric barrier function construction module 2, an LSTM position prediction construction module 3, and a composite control signal generation module 4.

[0178] Dynamics modeling module 1 constructs a load multi-degree-of-freedom vibration model through the throttle valve operation model and the air chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system.

[0179] The mathematical expression for the throttle valve operation model is:

[0180]

[0181] Where q is the displacement of the throttle valve core. For the quality of the throttle valve core, The damping coefficient is... Where u is the spring stiffness and u is the input voltage. This is the proportionality coefficient. The force is electromagnetic, assumed to be proportional to the input voltage u; AP is the air reaction force; A is the effective cross-sectional area of ​​the airbag; and P is the air chamber pressure. For the first derivative of q, It is the second derivative of q;

[0182] The mathematical expression for the dynamic model of air chamber pressure is:

[0183]

[0184] Where P is the air chamber pressure. For the first derivative of P, Air mass flow rate, For specific heat ratio, Let V be the gas constant and V be the volume of the gas chamber. Assuming linearity, The first derivative of the load displacement w Leakage coefficient;

[0185] The mathematical expression for air mass flow rate is:

[0186]

[0187] in, For flow coefficient, Let the effective area of ​​the valve orifice be assuming , For gas source temperature, It is a nonlinear flow function. Due to upstream pressure, This is due to downstream pressure;

[0188] A multi-degree-of-freedom vibration model of the load is constructed based on the throttle valve operation model and the gas chamber pressure dynamic model. The mathematical expression is:

[0189]

[0190] in, For load quality, For the damping of the air-bearing vibration isolation system, For the stiffness of the air-bearing vibration isolation system, For load displacement, External disturbance;

[0191] The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with side length L.

[0192] The integrated state variable vector of the air-bearing vibration isolation system includes , , , The valve core speed of the throttle valve;

[0193] The mathematical expression for the position and attitude of the platform's center of mass is:

[0194]

[0195] The mathematical expression for the platform's center-of-gravity velocity is:

[0196]

[0197] The mathematical expression for the gas pressure in the gas chamber is:

[0198]

[0199] The mathematical expression for the valve core displacement of a throttle valve is:

[0200]

[0201] The mathematical expression for the spool velocity of a throttle valve is:

[0202]

[0203] The mathematical expression for modeling the air-bearing vibration isolation system as a high-order nonlinear MIMO system is:

[0204]

[0205]

[0206] in, For the control gain matrix, It is a composite function vector.

[0207] A symmetric barrier function module 2 is constructed. Based on the symmetric barrier function, the constrained state in the high-order nonlinear MIMO system of the air-bearing vibration isolation system is transformed into an unconstrained state, and a dynamic surface filter is constructed for the transformed air-bearing vibration isolation system.

[0208] State variables Define time-varying constraint boundaries:

[0209]

[0210] in, To constrain the lower boundary, For state variables, To constrain the upper boundary;

[0211] Construct a symmetric barrier function to constrain the physical state. Transformation into an unconstrained transformation state Transformation The mathematical expression for the symmetric barrier function is:

[0212]

[0213] in, ;

[0214] The mathematical expression for an unconstrained high-order nonlinear MIMO system in an air-bearing vibration isolation system is as follows:

[0215]

[0216] in, , , , , , , , These are intermediate variables;

[0217] The mathematical expression for a dynamic surface filter is:

[0218]

[0219] in, As an intermediate variable, For virtual controllers, This is the state of the dynamic surface filter. For the first-order differential of the state of the dynamic surface filter, The time constant matrix;

[0220] Virtual Controller The mathematical expression is:

[0221]

[0222] in, As an intermediate variable, For the error surface, the mathematical expression is:

[0223]

[0224]

[0225] in, For the desired trajectory Transformed values ​​through the barrier function;

[0226] The mathematical expression for the actual controller u is:

[0227]

[0228] in, As an intermediate variable, Given a nonlinear vector, It is the smoothing constant. This is the dot product between vectors.

[0229] LSTM position prediction module 3 is constructed. It adopts an LSTM network to output the predicted value of the future sequence. Based on the predicted value of the future sequence, a position predictor is constructed to output the future prediction signal.

[0230] The load position information measured by sensors at three vibration isolation units over a longer period of time is obtained, and the mathematical expression for this position information is as follows: ;

[0231] The location information is standardized and preprocessed; the mathematical expression is as follows:

[0232]

[0233] in, The data is standardized based on location information. The mean of the location information. The standard deviation of the location information;

[0234] The Huber loss function and iterative reweighted least squares method are used to smooth the standardized preprocessed data to obtain a noise-resistant trend signal. ;

[0235] The historical sequence input data is constructed using the following mathematical expression:

[0236]

[0237] Output the predicted value of the future sequence, expressed mathematically as follows:

[0238]

[0239]

[0240] in, For future sequence predictions, For Gaussian window weights, Let h be the center of the Gaussian window, h be the prediction step size, and k be the future step number. This is the width parameter of the Gaussian window;

[0241] A multi-layer LSTM network is used to output predicted values ​​for future sequences. , , ;

[0242] Predicted values ​​for future sequences , , Obtained by destandardization ;

[0243] The mathematical expression for constructing the location predictor is:

[0244]

[0245] in, For adjustable control parameters, This represents the desired trajectory.

[0246] The composite control signal generation module 4 generates composite control signals based on the future prediction signal and the first virtual controller of the dynamic surface filter.

[0247] The mathematical expression for the composite control signal generated by the first virtual controller based on the future prediction signal and the dynamic surface filter is:

[0248]

[0249] in, For composite control signals, As the first virtual controller, For location predictors.

[0250] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The methods disclosed in the embodiments are described simply because they correspond to the systems disclosed in the embodiments; relevant details can be found in the method section.

[0251] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0252] In the embodiments provided by this invention, it should be understood that the disclosed systems, methods, and approaches can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or units may be electrical, mechanical, or other forms.

[0253] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0254] In addition, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit.

[0255] Similarly, in the various embodiments of the present invention, each processing unit can be integrated into a functional module, or each processing unit can exist physically, or two or more processing units can be integrated into a functional module.

[0256] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0257] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0258] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control, characterized in that, Includes the following steps: Step S1: The dynamic modeling step involves constructing a load multi-degree-of-freedom vibration model using the throttle valve operation model and the air chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system. Step S2: The step of constructing the symmetric barrier function. Based on the symmetric barrier function, the constrained state of the high-order nonlinear MIMO system of the air-bearing vibration isolation system is transformed into an unconstrained state, and a dynamic surface filter is constructed for the transformed air-bearing vibration isolation system. The mathematical expression for the dynamic surface filter is: in, As an intermediate variable, For virtual controllers, This is the state of the dynamic surface filter. For the first-order differential of the state of the dynamic surface filter, The time constant matrix; Virtual Controller The mathematical expression is: in, As an intermediate variable, For the error surface, the mathematical expression is: in, For the desired trajectory Transformed values ​​through the barrier function; The mathematical expression for the actual controller u is: in, As an intermediate variable, Given a nonlinear vector, It is the smoothing constant. This refers to the dot product between vectors. Step S3: The step of constructing the LSTM location prediction module is to use an LSTM network to output the predicted value of the future sequence, and based on the predicted value of the future sequence, construct a location predictor and output the future prediction signal. Step S4: The step of generating composite control signals, based on the future prediction signal and the first virtual controller of the dynamic surface filter, generates composite control signals.

2. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 1, characterized in that, The mathematical expression for the throttle valve operation model is: Where q is the displacement of the throttle valve core. For the quality of the throttle valve core, The damping coefficient is... Where u is the spring stiffness and u is the input voltage. This is the proportionality coefficient. The force is electromagnetic, assumed to be proportional to the input voltage u; AP is the air reaction force; A is the effective cross-sectional area of ​​the airbag; and P is the air chamber pressure. For the first derivative of q, It is the second derivative of q; The mathematical expression for the dynamic model of air chamber pressure is: Where P is the air chamber pressure, For the first derivative of P, Air mass flow rate, For specific heat ratio, Let V be the gas constant and V be the volume of the gas chamber. Assuming linearity, The first derivative of the load displacement w Leakage coefficient; The mathematical expression for air mass flow rate is: in, For flow coefficient, Let the effective area of ​​the valve orifice be assuming , For gas source temperature, It is a nonlinear flow function. Due to upstream pressure, This is due to downstream pressure.

3. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 2, characterized in that, A multi-degree-of-freedom vibration model of the load is constructed based on the throttle valve operation model and the gas chamber pressure dynamic model. The mathematical expression is: in, For load quality, For the damping of the air-bearing vibration isolation system, For the stiffness of the air-bearing vibration isolation system, For load displacement, This is an external disturbance.

4. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 3, characterized in that, The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with side length L. The integrated state variable vector of the air-bearing vibration isolation system includes , , , The valve core speed of the throttle valve; The mathematical expression for the position and attitude of the platform's center of mass is: The mathematical expression for the platform's center-of-gravity velocity is: The mathematical expression for the gas pressure in the gas chamber is: The mathematical expression for the valve core displacement of a throttle valve is: The mathematical expression for the spool velocity of a throttle valve is: The mathematical expression for modeling the air-bearing vibration isolation system as a high-order nonlinear MIMO system is: in, For state variables, , and These are intermediate variables of the state variables. and They are and The first-order differential, For the control gain matrix, It is a composite function vector.

5. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 4, characterized in that, State variables Define time-varying constraint boundaries: in, To constrain the lower boundary, For state variables, To constrain the upper boundary; Construct a symmetric barrier function to constrain the physical state. Transformation into an unconstrained transformation state Transformation The mathematical expression for the symmetric barrier function is: in, ; The mathematical expression for an unconstrained high-order nonlinear MIMO system in an air-bearing vibration isolation system is as follows: in, , , , , , , , These are intermediate variables.

6. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 1, characterized in that, In step S3, the mathematical expression for location information is defined as follows: ; The location information is standardized and preprocessed; the mathematical expression is as follows: in, The data is standardized based on location information. The mean of the location information. The standard deviation of the location information; The Huber loss function and iterative reweighted least squares method are used to smooth the standardized preprocessed data to obtain a noise-resistant trend signal. ; The historical sequence input data is constructed using the following mathematical expression: Output the predicted value of the future sequence, expressed mathematically as follows: in, For future sequence predictions, For Gaussian window weights, Let h be the center of the Gaussian window, h be the prediction step size, and k be the future step number. This is the width parameter of the Gaussian window; A multi-layer LSTM network is used to output predicted values ​​for future sequences. , , ; Predicted values ​​for future sequences , , Destandardization process is performed to obtain ; Build a location predictor The mathematical expression is: in, For adjustable control parameters, This represents the desired trajectory.

7. The precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control according to claim 1, characterized in that, The mathematical expression for the composite control signal generated by the first virtual controller based on the future prediction signal and the dynamic surface filter is: in, It is a composite control signal. As the first virtual controller, For location predictors.

8. A system for the precision air-bearing active vibration isolation method based on LSTM position prediction and state-constrained dynamic surface control as described in claim 1, characterized in that, It includes a dynamic modeling module, a symmetric barrier function construction module, an LSTM position prediction construction module, and a composite control signal generation module; The dynamic modeling module constructs a load multi-degree-of-freedom vibration model through a throttle valve operation model and a gas chamber pressure dynamic model. Based on the load multi-degree-of-freedom vibration model, the air-bearing vibration isolation system is modeled as a high-order nonlinear MIMO system. The symmetric barrier function construction module, based on the symmetric barrier function, transforms the constrained state in the high-order nonlinear MIMO system of the air-bearing vibration isolation system into an unconstrained state, and constructs a dynamic surface filter for the transformed air-bearing vibration isolation system. The LSTM location prediction module is constructed by using an LSTM network to output predicted values ​​for future sequences. Based on these predicted values, a location predictor is constructed and outputs a future prediction signal. The module for generating composite control signals generates composite control signals based on the future prediction signal and the first virtual controller of the dynamic surface filter.

9. The system according to claim 8, characterized in that, The air-bearing vibration isolation system consists of three vibration isolation units, which are installed at the three vertices of an equilateral triangle with a side length of L.

Images