An Accelerated Adaptive Control Method for Event-Triggered MEMS Gyroscope Coupled Network Systems

Abstract

This invention discloses an event-triggered accelerated adaptive control method for a MEMS gyroscope coupled network system, comprising the following steps: S1, establishing a MEMS gyroscope coupled network model based on a series-parallel coupling mechanism; S2, performing dynamic analysis of the coupled network using phase diagrams, time history diagrams, and Lyapunov exponents; S3, designing an equivalent analog circuit based on Kirchhoff's laws; S4, building a semi-hardware experimental platform using a double-layer PCB circuit board, and empirically verifying the nonlinear chaotic oscillations in the coupled network system through experimental measurements using an oscilloscope and a power signal generator; S5, designing an accelerated adaptive controller.

Description

Technical Field

[0001] This invention relates to the field of gyroscope control methods, and in particular to an event-triggered adaptive control method for MEMS gyroscope coupled network systems. Background Technology

[0002] Microelectromechanical systems (MEMS) gyroscopes are key components in modern inertial sensing technology, converting rotational motion into electrical signals through the Coriolis effect. Benefiting from their small size, low power consumption, and high integration, MEMS gyroscopes have been widely used in navigation systems, aerospace equipment, industrial automation, and emerging intelligent devices. With the rapid development of these application areas, increasingly stringent requirements are being placed on the accuracy, bandwidth, and robustness of MEMS gyroscopes. Current research mainly focuses on single-mass or dual-mass MEMS gyroscopes. Fei and Zhou established a dynamic model of a single-mass three-axis MEMS gyroscope, which includes spring asymmetry terms caused by manufacturing defects. Deng et al. derived a dynamic model of a fractional-order MEMS three-axis gyroscope based on the Lagrange equation. Gao et al. developed a mathematical model of a dual-mass MEMS gyroscope and improved its sensitivity by eliminating the influence of common-mode error. Wu et al. established a mathematical model of a dual-mass MEMS gyroscope by considering the interaction between the driving mode and the sensing mode. Hu et al. constructed a mathematical model of a Duffing-type MEMS gyroscope with a fully decoupled structure. With the rapid development of inertial navigation, autonomous driving, and industrial control technologies, the performance requirements for MEMS gyroscopes are becoming increasingly stringent. Traditional single-mass and dual-mass structures, due to their limited differential output capabilities or insufficient symmetry, are insufficient to meet the demands of high-performance applications. Therefore, employing multi-mass coupled networks has become a necessary means to improve system performance. However, the elastic and damping interactions between mass blocks can easily induce high-frequency chaotic oscillations, potentially leading to system instability under extreme conditions. As the network scale increases and the number of nodes grows, more control channels are needed, while traditional continuous or periodic updates result in a large amount of redundant communication, posing challenges to the management of communication and computing resources. Furthermore, improving sensitivity and bandwidth through the structural evolution of the MEMS gyroscope system increases the complexity of the coupled network, making dynamic analysis more difficult. To conduct a more comprehensive analysis of the dynamic behavior of MEMS gyroscopes, many researchers have conducted in-depth studies on their dynamic characteristics. Wei et al. proposed a nonparametric method based on Hilbert transform to analyze the nonlinear dynamic characteristics of MEMS gyroscopes. Hou et al. used the complex exponential method to compare the detection characteristics of amplitude ratio and amplitude difference, and analyzed the dynamic behavior of MEMS gyroscopes through numerical simulation. Li et al. used phase and Lyapunov exponent plots to study the inherent nonlinear characteristics of dual-mass MEMS gyroscopes.

[0003] Furthermore, analog integrated circuits are effective tools for dynamic analysis of high-order nonlinear systems. They can transmit, convert, process, and amplify analog signals, and accurately detect parameters related to chaotic characteristics in MEMS accelerometer systems. Therefore, analog integrated circuits have been widely used in chaotic systems. Tchitnga et al. demonstrated the existence of chaos in autonomous implicit Hartley oscillators through simulation experiments using analog circuits and identified the chaotic domain. Luo et al. constructed an analog integrated circuit for a fractional-order weakly coupled MEMS oscillator and revealed its inherent chaotic behavior. Elsonbaty et al. achieved adaptive chaotic synchronization between two systems using analog circuits. Luo et al. constructed an analog integrated circuit for a fractional-order MEMS accelerometer based on an analog experimental platform and revealed its nonlinear dynamic characteristics. Luo et al. established an equivalent analog circuit for a fractional-order dual-mass MEMS gyroscope based on a field-programmable gate array (FPGA) and demonstrated its harmful chaotic oscillation phenomenon. However, current research on the nonlinear dynamic characteristics of chaotic systems mainly focuses on numerical simulations. Although numerical simulations can reproduce the basic dynamic behavior of a system, they face two main challenges when dealing with highly complex nonlinear dynamics: (1) they cannot accurately capture transient responses on the microsecond scale; and (2) discrete calculations cannot fully reflect the continuous evolution of the system state, especially the formation process of chaotic attractors. Therefore, it is necessary to develop a simulation circuit scheme for nonlinear systems in order to verify their dynamic characteristics at the hardware level.

[0004] In recent years, integrating multiple algorithms into the backstepping derivation framework has become an important trend in control scheme design. Chen et al. proposed an accelerated backstepping control scheme for multi-motor drive systems (MMDS), thereby achieving load tracking performance of MMDS. Liu et al. developed a backstepping control method based on a nonlinear disturbance observer. Barrean et al. used backstepping techniques to solve the trajectory tracking problem of a quadrotor system with a suspended load. However, in the classic backstepping derivation control framework, the complex differentiation of the virtual control input inevitably leads to the problem of derivative term expansion, which is particularly prominent in high-order nonlinear systems. This recursive differentiation process leads to the "complexity explosion" effect, which seriously impairs the stability of the system. To solve this problem, researchers have incorporated first-order filters, state observers, and tracking differentiators into the backstepping control scheme. Zhang et al. studied an adaptive fuzzy backstepping control method with command filtering for fractional-order chaotic systems, in which a fractional-order command filter is used to solve the derivative expansion problem inherent in the backstepping propulsion framework. Xia et al. used filtering techniques to alleviate the complexity explosion problem in nonlinear systems. Liu et al. combined backstepping with command filtering to address the "computational explosion" phenomenon and introduced an error compensation mechanism to mitigate the impact of filtering errors. Sun introduced a non-smooth command filter to solve the complex differentiation problem of virtual control inputs in high-order nonlinear systems. Hua et al. designed a backstepping controller by using a state observer to estimate the unmeasured system state and proved that the system achieves asymptotic stability under the proposed control scheme. Cheng et al. reconstructed the system state using state observation techniques, thereby reducing the direct dependence on derivative terms and avoiding complex differentiation of virtual control signals. Wang et al. used the output of a tracking differentiator to approximate the derivative of the virtual control input, thus avoiding subsequent complex calculations. Zhao et al. developed a second-order tracking differentiator, successfully solving the "complexity explosion" problem. Luo et al. designed a finite-time convergent tracking differentiator to eliminate the repetitive iterative process in the backstepping framework.

[0005] To improve the convergence speed and accuracy of the tracking differentiator, Li et al. added a velocity function to the tracking differentiator and proposed a new accelerated differentiator. Hu et al. developed an accelerated second-order tracking differentiator to solve the derivative extension problem, achieving a faster convergence speed while maintaining system performance. However, for high-order MEMS gyroscope systems exhibiting complex nonlinear dynamics, the performance of the aforementioned filters, state observers, and tracking differentiators still needs further improvement to achieve a more accurate approximation of the derivative of the virtual control input. Furthermore, nonlinear oscillations are unavoidable in single / dual-mass MEMS gyroscopes and coupled networks. Such oscillations can severely degrade system stability and even lead to system collapse. Moreover, the coupled networks of MEMS gyroscope systems are highly coupled and multivariable, making them extremely sensitive to external disturbances. Once external disturbances occur, the system's stability is severely threatened, leading to a significant performance degradation or even complete system collapse.

[0006] Given these challenges, there is an urgent need to study the nonlinear dynamic behavior of the coupled network of MEMS gyroscope systems, construct an equivalent analog circuit experimental platform to verify its nonlinear dynamic characteristics, and subsequently develop an adaptive control scheme to address issues including response speed, chaotic oscillations, and communication congestion. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides an event-triggered adaptive control method for MEMS gyroscope coupled network systems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: An event-triggered adaptive control method for MEMS gyroscope coupled network systems includes the following steps: S1. Establish a MEMS gyroscope coupling network model based on the serial-parallel coupling mechanism; S2. Dynamic analysis of coupled networks using phase diagrams, time history diagrams, and Lyapunov exponents; S3. Design an equivalent analog circuit based on Kirchhoff's laws; S4. A semi-hardware experimental platform was built using a double-layer PCB circuit board. The nonlinear chaotic oscillation in the coupled network system was empirically verified through experimental measurements using an oscilloscope and a power signal generator. S5. Design an accelerated adaptive controller.

[0009] In step S1, the MEMS gyroscope coupling network structure consists of four equivalent MEMS gyroscopes, a coupling suspension beam, a coupling crossbeam, and a lever support beam. The MEMS gyroscope coupling network model includes: Based on Newton's laws of motion, the dynamic equation of a MEMS gyroscope is shown in equation (1). , in, These represent the mass matrix, damping matrix, stiffness matrix, asymmetric stiffness matrix, and nonlinear stiffness matrix, respectively. , To facilitate design and analysis, the following dimensionless variables and parameters are introduced to simplify the mathematical model of the MEMS gyroscope coupling network: , Where the reference length and natural frequency Selected respectively and , Then, equation (1) is rewritten as: , in, .

[0010] In step S3, the analog circuit mainly consists of resistors, capacitors, an analog multiplier AD7633JN, and an integrated operational amplifier TL074N, wherein the node voltage signal... The variables in the dimensionless model (2) Furthermore, in order for electronic components to function properly within their operating bandwidth, it is necessary to scale the time, i.e. Then, combining Kirchhoff's voltage law, the dimensionless model of the MEMS gyroscope coupling network is transformed into the following circuit equations: .

[0011] Step S5 includes: S5-1. Design an interval-type II fuzzy neural network, including: Input layer: The initial values ​​of the system are used as the input to the T2FNN, i.e. ; Fuzzification layer: The membership function is defined as the Gaussian function. This network architecture has N inputs, each with M fuzzy sets and M upper / lower membership functions. The upper / lower membership function of the m-th rule in the i-th input is defined as follows: , in, , are defined as the upper bound, lower bound, and center value of the membership function, respectively; Rule layer: There are N IF-THEN fuzzy rules, each defined as follows: if yes , yes , ..., yes ,but ,in, and It is the input of the Gaussian membership function; An opportunistic reasoning mechanism is employed, and the upper and lower triggering degrees of the rules are represented as follows: , Level reduction: A simple level reduction method is used to simplify a type-II fuzzy set into a type-I fuzzy set. , Output layer: The output of T2FNN is: , in, Represents the weight vector, and , According to the general approximation principle of T2FNN, for any continuous and smooth unknown nonlinear function... They all exist. ,in, yes A compact set, Indicates the approximation error. Optimal weight vector Defined as: , in, express The set, This represents the weight parameter, and it has... ; S5-2, Controller Design, specifically: To further improve the system's response speed and accelerate the convergence of the system's tracking error, a velocity function was designed: , in, Indicates time parameter, It is a velocity parameter, and it satisfies the condition. ,at the same time, It has continuous and bounded derivatives and satisfies the initial conditions. , The tracking error of the MEMS gyroscope coupling network is defined as: , in, and These represent the reference trajectory and the actual trajectory of the coupled network, respectively. Indicates virtual control input. Based on the velocity function (17) and the tracking error (18), the acceleration error Defined as: , Within the backstepping control framework, the design of the acceleration adaptive controller is systematically divided into sixteen consecutive stages: Step 1: Define the first Lyapunov function: , The derivative with respect to time is: , in, , Virtual control input Designed as: , Substituting equation (22) into equation (21), we get: , Step 2: The second Lyapunov function is constructed as follows: , The derivative with respect to time is: , in, , Due to the complexity of the operating environment of MEMS gyroscope coupled networks, it is impossible to accurately determine the system parameters, resulting in unknown parameters in the system state equations. To solve this problem, T2FNN is used for approximation. This unknown nonlinear function is expressed in the form of: , In step 2, the traditional backstepping method suffers from a complexity explosion problem, resulting in a very cumbersome calculation process. To solve this problem, a high-precision AEITD method is proposed, the design details of which are as follows: , in, , , and These are design parameters, and they satisfy... Furthermore, the approximation error of AEITD is... , Next, control the input. And adaptive law Designed as: , , Based on equations (28) and (29), equation (25) can be further derived as: , To reduce redundant control signal updates, an event-triggered mechanism is introduced between the controller and the actuator. This framework ensures that control signal transmission and communication are activated only when specified triggering conditions are met, thereby optimizing the utilization of channel resources. An event-triggered strategy based on a relative threshold is adopted, defined as follows: , in, and These represent the current trigger time and the next trigger time, respectively. Indicates the event triggering error, where, It meets the conditions Positive design parameters, Lemma 1: For any The following inequalities hold true. , Next, equation (31) can be derived as follows: , in, It is a real-valued function and satisfies , Based on equation (35), the following derivation can be obtained: , At this stage, the following inequalities can be derived: , Then, equation (25) is updated to: , By combining the control input equation (28), the adaptive law equation (29), the event triggering mechanism equation (31), and equation (36), along with Lemma 1, equation (38) can be further derived as follows: , By combining equations (30) and (39), we can Simplified to: ; Step 3: Construct the third Lyapunov function for: , The derivative is defined as: , Virtual control input It is deduced as: , Equation (42) is further derived as follows: , Step 4: Design the fourth Lyapunov function as follows , The derivative with respect to time is: , in, Using T2FNN to approximate unknown nonlinear functions , , AEITD output value Can be used as Approximate value, control input And adaptive law Designed as follows: , From equation (35), we can derive for: , Step 5: Construct the fifth Lyapunov function for, , Step 6: Design the sixth Lyapunov function for, , in, , AEITD is used for approximate virtual control input. The derivative of , while T2FNN is used to estimate unknown nonlinear functions. Its expression is: , Step 7: The seventh Lyapunov function Defined as , The derivative with respect to time is: , , Step 8: The Eighth Lyapunov Function Selected as: , Inspired by step 6, Estimated by AEITD, and at the same time Approximate calculations are performed using T2FNN, i.e. , Corresponding control input And adaptive law Defined as: , Subsequently, the control input of the event triggering mechanism Designed as: , At the same time, equation (68) is updated to: .

[0012] This also includes steps 9 to 16. By observing the dimensionless model (2) of the MEMS gyroscope coupling network, it can be clearly found that the dimensionless control equations of the sensing axis and the driving axis have highly similar structural features. Therefore, in the design of the backstepping controller of the driving axis, steps 9 to 16 are the same as steps 1 to 8 in the design of the sensing axis controller. To simplify the design process, the control input and adaptive law of the driving axis in the coupling network are given directly as follows: , In the controller design process, all control input parameters All of these are defined positive constants, while all adaptive law parameters... All of these are positive design parameters.

[0013] This also includes: S5-3, Stability Analysis, specifically... Theorem 1: For MEMS gyroscope coupled networks exhibiting nonlinear chaotic oscillations and uncertainties, an event-triggered acceleration adaptive backstepping control strategy is proposed. The control inputs are chosen as equations (28), (48), (59), (70), (74), (76), (78), and (80), while the adaptive laws are chosen as equations (29), (49), (60), (71), (75), (77), (79), and (81). By selecting appropriate controller parameters and T2FNN related parameters, the following conditions can be satisfied: I) All signals in a closed-loop system are uniformly bounded eventually. II) The inherent nonlinear chaotic oscillations within the MEMS gyroscope coupling network are completely eliminated. Ⅲ) There exists a lower limit value for the trigger interval. This value ensures that the update interval of all control inputs meets the requirements. This avoids the Zeno phenomenon. Proof: For the coupled network of a MEMS gyroscope, the global Lyapunov function is defined as follows: , The derivative of equation (82) can be derived as follows: , According to Young's inequality, the following relationship holds: , Substituting equation (84) into equation (83), we get: , in, , Further derivation of the solution to equation (85) yields: , in, It is the initial time.

[0014] In step S5-3, to prove that the Zeno phenomenon does not exist in the control scheme proposed based on the event-triggered mechanism, a positive lower limit value for the trigger interval is defined. This value satisfies Therefore, we can conclude that: , because Since it is continuous and all signals in the closed-loop system are consistent and eventually bounded, there exists a positive constant. , making At the same time, based on the event triggering conditions Furthermore, it can be deduced that... satisfy Therefore, the proposed control scheme successfully avoids the Zeno phenomenon.

[0015] The beneficial effects of this invention are: 1. This invention addresses the dual constraints of high-frequency chaotic oscillations and limited communication and computing resources in practical applications of MEMS gyroscope coupled networks. This paper proposes an accelerated adaptive control scheme incorporating an event-triggered mechanism. First, a MEMS gyroscope coupled network model is established based on a series-parallel coupling mechanism. The dynamic evolution mode of the coupled network is revealed through phase diagrams, time history diagrams, and Lyapunov exponents. To further explore the dynamics of the coupled network at the hardware level and facilitate future chip-level implementation, an equivalent analog circuit is designed based on Kirchhoff's laws. Then, a semi-hardware experimental platform is built using a double-layer PCB circuit board. Experimental measurements using an oscilloscope and a power signal generator are used to empirically verify the nonlinear chaotic oscillations in the coupled network system. The experimental results show good agreement with the theoretical dynamic analysis. This control scheme integrates a velocity function, an event-triggered mechanism, a Type-2 fuzzy neural network (T2FNN), and an accelerated exponential integral tracking differentiator (AEITD) to enhance convergence, compensate for uncertainties, eliminate the "complexity explosion," and reduce communication burden under limited resource conditions, while maintaining control performance.

[0016] 2. This invention establishes a mathematical model for the coupled network of a MEMS gyroscope and reveals its nonlinear dynamic characteristics through phase diagrams, time history diagrams, and Lyapunov exponents. Furthermore, a schematic diagram and a double-layer printed circuit board are designed to construct a hardware equivalent model of the coupled network, enabling experimental verification of the system dynamics. To effectively eliminate the inherent chaotic behavior in the coupled network and address issues such as uncertainty, slow convergence, and communication congestion, an event-triggered accelerated adaptive backstepping control scheme is proposed.

[0017] 3. Regarding structural design, existing research mainly focuses on single-mass and dual-mass MEMS gyroscopes. However, single-mass structures lack differential output, while dual-mass devices lack complete symmetry, which limits high-bandwidth / high-sensitivity applications. To address these limitations, this invention proposes a MEMS gyroscope coupling network model incorporating asymmetric and nonlinear terms. This configuration combines the structural symmetry of single-mass systems with the differential output advantages of dual-mass designs, providing a theoretical basis for improving system sensitivity.

[0018] 4. Regarding experimental verification, unlike previous studies, this invention utilizes a two-layer printed circuit board technology to develop a semi-hardware experimental platform. Experimental measurements using an oscilloscope and a power signal generator confirmed the existence of nonlinear chaotic oscillations in the coupled network. This method more accurately captures the dynamic characteristics of MEMS gyroscopes, providing valuable reference for their design and manufacturing.

[0019] 5. Regarding the control method, compared with existing methods, the proposed AEITD algorithm not only effectively solves the inherent complexity explosion problem in traditional backstepping methods, but also achieves faster convergence speed and higher tracking accuracy. Furthermore, an event-triggered mechanism is incorporated into the control framework to cope with limited communication resources. By updating the control input only when specified conditions are met, this strategy effectively mitigates chaotic oscillations while significantly reducing redundant data transmission, thereby improving communication efficiency. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the coupling network of the present invention; Figure 2 The present invention includes a time history diagram and a phase diagram of the coupled network. Figure 3 Phase diagrams for different initial states of the present invention; Figure 4 Lyapunov exponent for electromechanical gyroscope coupling networks; Figures 5 to 12 This is an analog electronic circuit diagram of the coupling network of the present invention; Figure 13 This is a phase and time history diagram of the present invention on the hardware platform; Figure 14 This is a structural diagram of the T2FNN of the present invention; Figure 15 This is a control flowchart of the coupled network of the present invention; Figure 16 This is a schematic diagram of the hardware platform of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of the invention.

[0022] An event-triggered adaptive control method for MEMS gyroscope coupled network systems includes the following steps: S1. Establish a MEMS gyroscope coupling network model based on the serial-parallel coupling mechanism; S2. Dynamic analysis of coupled networks using phase diagrams, time history diagrams, and Lyapunov exponents; S3. Design an equivalent analog circuit based on Kirchhoff's laws; S4. A semi-hardware experimental platform was built using a double-layer PCB circuit board. The nonlinear chaotic oscillation in the coupled network system was empirically verified through experimental measurements using an oscilloscope and a power signal generator. S5. Design an accelerated adaptive controller.

[0023] In step S1, as follows Figure 1 As shown, the MEMS gyroscope coupling network structure consists of four equivalent MEMS gyroscopes, a coupling suspension beam, a coupling crossbeam, and a lever support beam. To facilitate dynamic modeling of coupled networks, this paper makes the following assumptions: Assumption 1: All four mass blocks move and rotate at a certain linear velocity.

[0024] Assumption 2: The displacement of the mass block is small; the Coriolis force dominates the inertial effect, while the centrifugal force can be ignored.

[0025] The MEMS gyroscope coupling network model includes: Based on Newton's laws of motion, the dynamic equation of the MEMS gyroscope is shown in equation (1), and its specific parameters are shown in Table 1. , in, These represent the mass matrix, damping matrix, stiffness matrix, asymmetric stiffness matrix, and nonlinear stiffness matrix, respectively. , To facilitate design and analysis, the following dimensionless variables and parameters are introduced to simplify the mathematical model of the MEMS gyroscope coupling network: , Where the reference length and natural frequency Selected respectively and , Then, equation (1) is rewritten as: , in, .

[0026] Step S2 is as follows: The dynamic behavior of MEMS gyroscope coupled networks has a significant impact on system performance and device reliability. To gain a deeper understanding of the network's nonlinear characteristics and potential chaotic behavior, a dynamic analysis of the system was conducted based on the established mathematical model. All parameters of equation (2) are selected as follows: , Figure 2 The phase diagram and time history of the MEMS gyroscope coupling network are shown. Due to differences in the spring, damping coefficients, and coupling coefficients, the system exhibits different chaotic characteristics. It can be observed that each gyroscope mass generates chaotic oscillations. The different chaotic characteristics of the system are due to variations in the spring, damping coefficients, and coupling coefficients. Figure 3 This indicates that the system exhibits different nonlinear characteristics when the system parameters and initial conditions change, and is highly sensitive to the parameters.

[0027] Figure 4 The Lyapunov exponent diagram under initial conditions is shown. It can be observed that the Lyapunov exponent has a positive value, therefore, during the operation of the MEMS gyroscope coupled network, it gradually enters a chaotic state.

[0028] In step S3, the analog circuit mainly consists of resistors, capacitors, an analog multiplier AD7633JN, and an integrated operational amplifier TL074N, wherein the node voltage signal... The variables in the dimensionless model (2) Furthermore, in order for electronic components to function properly within their operating bandwidth, it is necessary to scale the time, i.e. Then, combining Kirchhoff's voltage law, the dimensionless model of the MEMS gyroscope coupling network is transformed into the following circuit equations: .

[0029] In step S4, to analyze the dynamic characteristics of the MEMS gyroscope coupling network at the hardware level, a circuit diagram of the coupling network was designed based on the equivalent analog circuit of step S4, as shown below. Figures 5-12 as well as Figure 16As shown, a semi-hardware experimental platform using a double-layer PCB was constructed. This platform, through experimental measurements using an oscilloscope and a power signal generator, empirically verified the nonlinear chaotic oscillations in the coupled network system. The principle is as follows: 1. System power supply and excitation initialization. At the start of the experiment, a stable DC voltage is provided to the entire hardware platform using a DC power supply module. Simultaneously, a preset excitation signal is generated by the signal generator, which serves as the system's input source, driving the MEMS gyroscope coupled network into a dynamic working state.

[0030] 2. Signal Preprocessing and Input Signal. When inputting the signal to the MEMS gyroscope coupling network PCB, it needs to undergo conditioning through three key circuit stages: Signal Filter: This filters out high-frequency noise from the input signal and the circuit, ensuring the purity of the signal entering the MEMS gyroscope coupling array. The MEMS gyroscope coupling array is... Figures 5-12 The analog circuit shown includes: a signal attenuator to adjust the signal amplitude according to experimental requirements and prevent excessive voltage from damaging subsequent sensitive analog components; and a signal amplifier to amplify the conditioned signal to a level sufficient to drive the MEMS gyroscope coupling array, ensuring the full activation of the system's dynamic characteristics.

[0031] 3. Signal Output and Display. The processed signal is fed into the core component—the MEMS gyroscope coupling array. In this stage, complex interactions occur between the nodes, exhibiting rich nonlinear dynamic behavior. The analog signal output from the array is converted into a digital signal by an analog-to-digital converter (ADC) for real-time buffering and recording. Then, a digital-to-analog converter (DAC) is used to restore the processed digital sequence back to an analog signal. A dual-channel oscilloscope outputs the system's phase diagram and time history. By observing the limit cycles or chaotic attractors in the phase diagram and the waveform changes in the time history, the nonlinear dynamic characteristics of the MEMS gyroscope coupling network under specific parameters are verified.

[0032] like Figure 13 As shown, experimental results demonstrate the existence of inherent nonlinear high-frequency chaotic oscillations in the coupled network. Furthermore, the observed waveforms closely match the results obtained from dynamic analysis. These experimental results, obtained from a semi-hardware experimental platform, more accurately capture the actual dynamic behavior of the MEMS gyroscope coupled network, thus providing important guidance for subsequent structural optimization and system-level design. Moreover, this inherent nonlinear chaotic oscillation can severely degrade system stability and may even lead to functional failure. Therefore, it is necessary to develop an effective control strategy to suppress chaotic oscillations and ensure stable system operation.

[0033] Step S5 includes: S5-1, such as Figure 14As shown, the design of an interval type II fuzzy neural network includes: Input layer: The initial values ​​of the system are used as the input to the T2FNN, i.e. ; Fuzzification layer: The membership function is defined as the Gaussian function. This network architecture has N inputs, each with M fuzzy sets and M upper / lower membership functions. The upper / lower membership function of the m-th rule in the i-th input is defined as follows: , in, , are defined as the upper bound, lower bound, and center value of the membership function, respectively; Rule layer: There are N IF-THEN fuzzy rules, each defined as follows: if yes , yes , ..., yes ,but ,in, and It is the input of the Gaussian membership function; An opportunistic reasoning mechanism is employed, and the upper and lower triggering degrees of the rules are represented as follows: , Level reduction: A simple level reduction method is used to simplify a type-II fuzzy set into a type-I fuzzy set. , Output layer: The output of T2FNN is: , in, Represents the weight vector, and , According to the general approximation principle of T2FNN, for any continuous and smooth unknown nonlinear function... They all exist. ,in, yes A compact set, Indicates the approximation error. Optimal weight vector Defined as: , in, express The set, This represents the weight parameter, and it has... ; S5-2, Controller Design, specifically: To further improve the system's response speed and accelerate the convergence of the system's tracking error, a velocity function was designed: , in, Indicates time parameter, It is a velocity parameter, and it satisfies the condition. ,at the same time, It has continuous and bounded derivatives and satisfies the initial conditions. , The tracking error of the MEMS gyroscope coupling network is defined as: , in, and These represent the reference trajectory and the actual trajectory of the coupled network, respectively. Indicates virtual control input. Based on the velocity function (17) and the tracking error (18), the acceleration error Defined as: , like Figure 15 As shown, within the backstepping control framework, the design of the acceleration adaptive controller is systematically divided into sixteen consecutive stages: Step 1: Define the first Lyapunov function: , The derivative with respect to time is: , in, , Virtual control input Designed as: , Substituting equation (22) into equation (21), we get: , Step 2: The second Lyapunov function is constructed as follows: , The derivative with respect to time is: , in, , Due to the complexity of the operating environment of MEMS gyroscope coupled networks, it is impossible to accurately determine the system parameters, resulting in unknown parameters in the system state equations. To solve this problem, T2FNN is used for approximation. This unknown nonlinear function is expressed in the form of: , In step 2, the traditional backstepping method suffers from a complexity explosion problem, resulting in a very cumbersome calculation process. To solve this problem, a high-precision AEITD method is proposed, the design details of which are as follows: , in, , , and These are design parameters, and they satisfy... Furthermore, the approximation error of AEITD is... , Next, control the input. And adaptive law Designed as: , , Based on equations (28) and (29), equation (25) can be further derived as: , To reduce redundant control signal updates, an event-triggered mechanism is introduced between the controller and the actuator. This framework ensures that control signal transmission and communication are activated only when specified triggering conditions are met, thereby optimizing the utilization of channel resources. An event-triggered strategy based on a relative threshold is adopted, defined as follows: , in, and These represent the current trigger time and the next trigger time, respectively. Indicates the event triggering error, where, It meets the conditions Positive design parameters, Lemma 1: For any The following inequalities hold true. , Next, equation (31) can be derived as follows: , in, It is a real-valued function and satisfies , Based on equation (35), the following derivation can be obtained: , At this stage, the following inequalities can be derived: , Then, equation (25) is updated to: , By combining the control input equation (28), the adaptive law equation (29), the event triggering mechanism equation (31), and equation (36), along with Lemma 1, equation (38) can be further derived as follows: , By combining equations (30) and (39), we can Simplified to: ; Step 3: Construct the third Lyapunov function for: , The derivative is defined as: , Virtual control input It is deduced as: , Equation (42) is further derived as follows: , Step 4: Design the fourth Lyapunov function as follows , The derivative with respect to time is: , in, Using T2FNN to approximate unknown nonlinear functions , , AEITD output value Can be used as Approximate value, control input And adaptive law Designed as follows: , From equation (35), we can derive for: , Step 5: Construct the fifth Lyapunov function for, , Step 6: Design the sixth Lyapunov function for, , in, , AEITD is used for approximate virtual control input. The derivative of , while T2FNN is used to estimate unknown nonlinear functions. Its expression is: , Step 7: The seventh Lyapunov function Defined as , The derivative with respect to time is: , , Step 8: The Eighth Lyapunov Function Selected as: , Inspired by step 6, Estimated by AEITD, and at the same time Approximate calculations are performed using T2FNN, i.e. , Corresponding control input And adaptive law Defined as: , Subsequently, the control input of the event triggering mechanism Designed as: , At the same time, equation (68) is updated to: .

[0034] The present invention further includes steps 9 to 16. By observing the dimensionless model (2) of the MEMS gyroscope coupling network, it can be clearly found that the dimensionless control equations of the sensing axis and the driving axis have highly similar structural features. Therefore, in the design of the backstepping controller of the driving axis, steps 9 to 16 are the same as steps 1 to 8 in the design of the sensing axis controller. To simplify the design process, the control input and adaptive law of the driving axis in the coupling network are given directly as follows: , In the controller design process, all control input parameters All of these are defined positive constants, while all adaptive law parameters... All of these are positive design parameters.

[0035] The present invention also includes: S5-3, Stability Analysis, specifically... Theorem 1: For MEMS gyroscope coupled networks exhibiting nonlinear chaotic oscillations and uncertainties, an event-triggered acceleration adaptive backstepping control strategy is proposed. The control inputs are chosen as equations (28), (48), (59), (70), (74), (76), (78), and (80), while the adaptive laws are chosen as equations (29), (49), (60), (71), (75), (77), (79), and (81). By selecting appropriate controller parameters and T2FNN related parameters, the following conditions can be satisfied: I) All signals in a closed-loop system are uniformly bounded eventually. II) The inherent nonlinear chaotic oscillations within the MEMS gyroscope coupling network are completely eliminated. Ⅲ) There exists a lower limit value for the trigger interval. This value ensures that the update interval of all control inputs meets the requirements. This avoids the Zeno phenomenon. Proof: For the coupled network of a MEMS gyroscope, the global Lyapunov function is defined as follows: , The derivative of equation (82) can be derived as follows: , According to Young's inequality, the following relationship holds: , Substituting equation (84) into equation (83), we get: , in, , Further derivation of the solution to equation (85) yields: , in, It is the initial time.

[0036] In step S5-3, to prove that the Zeno phenomenon does not exist in the control scheme proposed based on the event-triggered mechanism, a positive lower limit value for the trigger interval is defined. This value satisfies Therefore, we can conclude that: , because Since it is continuous and all signals in the closed-loop system are consistent and eventually bounded, there exists a positive constant. , making At the same time, based on the event triggering conditions Furthermore, it can be deduced that... satisfy Therefore, the proposed control scheme successfully avoids the Zeno phenomenon.

[0037] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. An event-triggered adaptive control method for MEMS gyroscope coupled network systems, characterized in that, Includes the following steps: S1. Establish a MEMS gyroscope coupling network model based on the serial-parallel coupling mechanism; S2. Dynamic analysis of coupled networks using phase diagrams, time history diagrams, and Lyapunov exponents; S3. Design an equivalent analog circuit based on Kirchhoff's laws; S4. A semi-hardware experimental platform was built using a double-layer PCB circuit board. The nonlinear chaotic oscillation in the coupled network system was empirically verified through experimental measurements using an oscilloscope and a power signal generator. S5. Design an accelerated adaptive controller.

2. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 1, characterized in that, In step S1, the MEMS gyroscope coupling network structure consists of four equivalent MEMS gyroscopes, a coupling suspension beam, a coupling crossbeam, and a lever support beam. The MEMS gyroscope coupling network model includes: Based on Newton's laws of motion, the dynamic equation of a MEMS gyroscope is shown in equation (1). ， in, These represent the mass matrix, damping matrix, stiffness matrix, asymmetric stiffness matrix, and nonlinear stiffness matrix, respectively. ， To facilitate design and analysis, the following dimensionless variables and parameters are introduced to simplify the mathematical model of the MEMS gyroscope coupling network: ， Where the reference length and natural frequency Selected respectively and , Then, equation (1) is rewritten as: ， in, 。 3. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 2, characterized in that, In step S3, the analog circuit mainly consists of resistors, capacitors, an analog multiplier AD7633JN, and an integrated operational amplifier TL074N, wherein the node voltage signal... The variables in the dimensionless model (2) ; Furthermore, in order for electronic components to function properly within their operating bandwidth, it is necessary to scale the time, i.e. ; Then, combining Kirchhoff's voltage law, the dimensionless model of the MEMS gyroscope coupling network is transformed into the following circuit equations: 。 4. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 3, characterized in that, Step S5 includes: S5-1. Design an interval-type II fuzzy neural network, including: Input layer: The initial values ​​of the system are used as the input to the T2FNN, i.e. ; Fuzzy layer: The membership function is defined as the Gaussian function. The network architecture has N inputs, each of which has M fuzzy sets and M upper / lower membership functions; The membership function of the m-th rule for the i-th input is defined as follows: ， in, , are defined as the upper bound, lower bound, and center value of the membership function, respectively; Rule layer: There are N IF-THEN fuzzy rules, each defined as follows: if yes , yes , ..., yes ,but ,in, and It is the input of the Gaussian membership function; An opportunistic reasoning mechanism is employed, and the upper and lower triggering degrees of the rules are represented as follows: ， Level reduction: A simple level reduction method is used to simplify a type-II fuzzy set into a type-I fuzzy set. ， Output layer: The output of T2FNN is: ， in, Represents the weight vector, and , According to the general approximation principle of T2FNN, for any continuous and smooth unknown nonlinear function... They all exist. ,in, yes A compact set, Indicates the approximation error. Optimal weight vector Defined as: ， in, express The set, This represents the weight parameter, and it has... ; S5-2, Controller Design, specifically: To further improve the system's response speed and accelerate the convergence of the system's tracking error, a velocity function was designed: ， in, Indicates time parameter, It is a velocity parameter, and it satisfies the condition. ,at the same time, It has continuous and bounded derivatives and satisfies the initial conditions. , The tracking error of the MEMS gyroscope coupling network is defined as: ， in, and These represent the reference trajectory and the actual trajectory of the coupled network, respectively. Indicates virtual control input. Based on the velocity function (17) and the tracking error (18), the acceleration error Defined as: ， Within the backstepping control framework, the design of the acceleration adaptive controller is systematically divided into sixteen consecutive stages: Step 1: Define the first Lyapunov function: ， The derivative with respect to time is: ， in, , Virtual control input Designed as: ， Substituting equation (22) into equation (21), we get: ， Step 2: The second Lyapunov function is constructed as follows: ， The derivative with respect to time is: ， in, , Due to the complexity of the operating environment of MEMS gyroscope coupled networks, it is impossible to accurately determine the system parameters, resulting in unknown parameters in the system state equations. To solve this problem, T2FNN is used for approximation. This unknown nonlinear function is expressed in the form of: ， In step 2, the traditional backstepping method suffers from a complexity explosion problem, resulting in a very cumbersome calculation process. To solve this problem, a high-precision AEITD method is proposed, the design details of which are as follows: ， in, , , and These are design parameters, and they satisfy... Furthermore, the approximation error of AEITD is... , Next, control the input. And adaptive law Designed as: ， ， Based on equations (28) and (29), equation (25) is further derived as: ， To reduce redundant control signal updates, an event-triggered mechanism is introduced between the controller and the actuator. This framework ensures that control signal transmission and communication are activated only when specified triggering conditions are met, thereby optimizing the utilization of channel resources. An event-triggered strategy based on a relative threshold is adopted, defined as follows: ， in, and These represent the current trigger time and the next trigger time, respectively. Indicates the event triggering error, where, It meets the conditions Positive design parameters, Lemma 1: For any The following inequalities hold true. ， Next, equation (31) is derived as follows: ， in, It is a real-valued function and satisfies , Based on equation (35), the following derivation is obtained: ， At this stage, the following inequalities are derived: ， Then, equation (25) is updated to: ， By combining the control input equation (28), the adaptive law equation (29), the event triggering mechanism equation (31), and equation (36), along with Lemma 1, equation (38) is further derived as follows: ， By combining equations (30) and (39), Simplified to: ； Step 3: Construct the third Lyapunov function for: ， The derivative is defined as: ， Virtual control input It is deduced as: ， Equation (42) is further derived as follows: ， Step 4: Design the fourth Lyapunov function as follows ， The derivative with respect to time is: ， in, Using T2FNN to approximate unknown nonlinear functions , ， AEITD output value As Approximate value, control input And adaptive law Designed as follows: ， From equation (35) we can derive for: ， Step 5: Construct the fifth Lyapunov function for, ， Step 6: Design the sixth Lyapunov function for, ， in, , AEITD is used for approximate virtual control input. The derivative of , while T2FNN is used to estimate unknown nonlinear functions. Its expression is: ， Step 7: The seventh Lyapunov function Defined as ， The derivative with respect to time is: ， ， Step 8: The Eighth Lyapunov Function Selected as: ， Inspired by step 6, Estimated by AEITD, and at the same time Approximate calculations are performed using T2FNN, i.e. ， Corresponding control input And adaptive law Defined as: ， Subsequently, the control input of the event triggering mechanism Designed as: ， At the same time, equation (68) is updated to: 。 5. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 4, characterized in that, It also includes steps 9 to 16, By observing the dimensionless model (2) of the MEMS gyroscope coupling network, it can be clearly found that the dimensionless control equations of the sensing axis and the driving axis have highly similar structural features. Therefore, in the design of the backstepping controller of the driving axis, steps 9 to 16 are the same as steps 1 to 8 in the design of the sensing axis controller. To simplify the design process, the control input and adaptive law of the driving axis in the coupling network are given directly as follows: ， In the controller design process, all control input parameters All of these are defined positive constants, while all adaptive law parameters... All of these are positive design parameters.

6. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 5, characterized in that, Also includes: S5-3, Stability Analysis, specifically... Theorem 1: For MEMS gyroscope coupled networks exhibiting nonlinear chaotic oscillations and uncertainties, an event-triggered acceleration adaptive backstepping control strategy is proposed. The control inputs are chosen as equations (28), (48), (59), (70), (74), (76), (78), and (80), while the adaptive laws are chosen as equations (29), (49), (60), (71), (75), (77), (79), and (81). By selecting appropriate controller parameters and T2FNN related parameters, the following conditions are satisfied: I) All signals in a closed-loop system are uniformly bounded. II) The inherent nonlinear chaotic oscillations within the MEMS gyroscope coupling network are completely eliminated. Ⅲ) There exists a lower limit value for the trigger interval. This value ensures that the update interval of all control inputs meets the requirements. This avoids the Zeno phenomenon. Proof: For the coupled network of a MEMS gyroscope, the global Lyapunov function is defined as follows: ， The derivative of equation (82) can be derived as follows: ， According to Young's inequality, the following relationship holds. ， Substituting equation (84) into equation (83), we get: ， in, , Further derivation of the solution to equation (85) yields: ， in, It is the initial time.

7. The event-triggered adaptive control method for MEMS gyroscope coupled network systems according to claim 6, characterized in that, In step S5-3, to prove that the Zeno phenomenon does not exist in the control scheme proposed based on the event-triggered mechanism, a positive lower limit value for the trigger interval is defined. This value satisfies Therefore, we can conclude that: ， because Since it is continuous and all signals in the closed-loop system are consistent and eventually bounded, there exists a positive constant. , making At the same time, based on the event triggering conditions Further deduction satisfy Therefore, the proposed control scheme successfully avoids the Zeno phenomenon.

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