A method, system and storage medium for stable amplitude control of a MEMS resonator

Abstract

The application discloses a kind of stable amplitude control method, system and storage medium of MEMS resonator, method includes the following steps: the equivalent dynamic model of MEMS resonator is converted into state space equation;Change the expression form of input matrix in state space equation, convert non-standard state space equation into standard linear feedback equation;According to the performance index function of LQR minimization of the state weight matrix Q and control weight matrix R set, obtain the input gain matrix under optimal control rule;According to input gain matrix and linear feedback equation, judge whether drive closed loop system is stable, when drive closed loop system is stable, obtain the coefficient matrix N of determination gain matrix;According to the coefficient matrix N of determination gain matrix, construct LQR regulator, and the control signal of drive closed loop system is generated according to the reference signal and the feedback signal of drive closed loop system received by the LQR regulator.The application realizes faster amplitude stability speed and smaller overshoot.

Description

Technical Field

[0001] This application relates to the field of MEMS gyroscope technology, specifically to a stable amplitude control method, system, and storage medium for a MEMS resonator. Background Technology

[0002] MEMS gyroscopes operate based on the Coriolis force principle. According to the Coriolis force formula, the amplitude and frequency of the driving vibration directly affect the scaling factor and zero-bias performance of the MEMS gyroscope. Therefore, ensuring the amplitude stability of the gyroscope driving mode is a key prerequisite for realizing a high-precision gyroscope.

[0003] Currently, the driving circuits of silicon micromachined gyroscopes all adopt a closed-loop driving method. Among them, the scheme based on AGC technology for driving amplitude stabilization and PLL technology for frequency control is relatively mature and widely used. The control system of MEMS gyroscopes typically uses the traditional PI control method. The setting of PI parameters has a significant impact on the system's settling time and overshoot. Since the setting of PI parameters usually requires multiple adjustments based on experience, this method is not only time-consuming but also cannot meet the requirements of linear time-varying systems. Furthermore, in actual operation, the system parameters of the gyroscope will change, making it difficult to achieve good control results using a PI controller. Summary of the Invention

[0004] The purpose of this application is to provide a stable amplitude control method, system and storage medium for MEMS resonators, so as to solve the disadvantage of the contradiction between overshoot and settling time in the prior art using PI controllers.

[0005] To achieve the above objectives, this application employs the following technical solution:

[0006] In a first aspect, this application discloses a method for stable amplitude control of a MEMS resonator, including:

[0007] The equivalent dynamic model of the MEMS resonator is transformed into a state-space equation.

[0008] By changing the expression of the input matrix in the state-space equation, the non-standard state-space equation can be converted into a standard linear feedback equation.

[0009] Based on the set state weight matrix Q and control weight matrix R, minimize the performance index function of LQR to obtain the input gain matrix under the optimal control rule. ];

[0010] Based on the input gain matrix [ The linear feedback equation is used to determine whether the drive closed-loop system is stable. When the drive closed-loop system is stable, a definite input gain matrix is ​​obtained. The coefficient matrix N;

[0011] Based on the determined input gain matrix [ The coefficient matrix N is used to construct the LQR regulator, which generates the control signal for driving the closed-loop system based on the received reference signal and the feedback signal of the driving closed-loop system.

[0012] Furthermore, the expression for the linear feedback equation is:

[0013] = + = ;

[0014] in, This represents the driving resonant frequency of the MEMS resonator. This represents the quality factor of the MEMS resonator drive shaft. Indicates the error of the state variable. Represents a state variable.

[0015] Furthermore, based on the input gain matrix [ Determining the stability of a drive closed-loop system using linear feedback equations includes:

[0016] The coefficient matrix N of LQR is obtained according to the linear feedback equation; where, the coefficient matrix N = ;

[0017] Based on the input gain matrix [ Determine whether the eigenvalues ​​of the coefficient matrix N are less than 0. If they are less than 0, then the closed-loop system is stable.

[0018] Furthermore, the eigenvalue solving equation for the coefficient matrix N is as follows:

[0019] -( ) + =0.

[0020] Furthermore, the expression for the performance index function of LQR is:

[0021] J= ;

[0022] in, Represents the state vector. This represents the target moment when the closed-loop system reaches stability. This represents the weight matrix of the state vector in the performance index. This indicates the transpose operation. This represents the input matrix.

[0023] Furthermore, the expression for the state-space equation is:

[0024] = + ;

[0025] in, , This represents the force acting on the driving shaft of the MEMS resonator. This represents the equivalent mass of the MEMS harmonic oscillator. This represents the driving resonant frequency of the MEMS resonator. This represents the quality factor of the MEMS resonator drive shaft. Represents a state variable.

[0026] Furthermore, it also includes: based on the determined input gain matrix [ The coefficient matrix N is used to obtain the equivalent transfer function X(s) of LQR;

[0027] The equivalent transfer function X(s) is input into the open-loop and closed-loop transfer functions of the drive closed-loop system to obtain the open-loop and closed-loop transfer functions of the drive closed-loop system using LQR control, so as to analyze the stability index of the drive closed-loop system.

[0028] In a second aspect, this application discloses a computer-readable storage medium storing a computer program / instructions thereon, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of any of the stable amplitude control methods described in the first aspect.

[0029] Thirdly, this application discloses a computer system, comprising:

[0030] Memory, used to store computer programs / instructions;

[0031] A processor for executing the computer program / instructions to implement the steps of the stable amplitude control method described in any one of the first aspects.

[0032] Fourthly, this application discloses a computer program product, including a computer program / instructions, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of the stable amplitude control method described in any one of the first aspects.

[0033] The beneficial effects of this application are as follows:

[0034] This application uses the equivalent dynamic model of a MEMS resonator to transform it into a state-space equation. By changing the expression of the input matrix, the system is transformed into a standard linear feedback system. The stability of the system can be determined by the eigenvalues ​​of the coefficient matrix, and the input gain matrix under the optimal control rule can be obtained by function calculation. The linear quadratic regulator of this invention avoids the disadvantage of the contradiction between overshoot and settling time of the PI controller, achieving faster amplitude stabilization speed and smaller overshoot. Furthermore, the smaller feedback input results in a lower noise level in the system, thereby further improving the stability of the amplitude output voltage. Attached Figure Description

[0035] Figure 1 This is a system block diagram of the linear quadratic regulator LQR of the present invention;

[0036] Figure 2 This is the Bode plot of the open-loop system under linear quadratic regulator control according to the present invention;

[0037] Figure 3 This invention presents a Bode plot of a closed-loop system controlled by a linear quadratic regulator.

[0038] Figure 4 The diagram shows the effect of the PI control response curve and the linear quadratic regulator response curve when KP=10 and KI=5 in this invention.

[0039] Figure 5 The diagram shows the effect of the PI control response curve and the linear quadratic regulator response curve when KP=1 and KI=5 in this invention.

[0040] Figure 6 This is a diagram illustrating the effect of the drive excitation signal generated by the PI controller in a noisy environment according to the present invention.

[0041] Figure 7 This is a diagram illustrating the effect of the drive excitation signal generated by the linear quadratic regulator of the present invention in a noisy environment;

[0042] Figure 8 This is a block diagram of the MEMS resonator drive closed-loop system based on LQR control of the present invention. Detailed Implementation

[0043] To make the technical means, creative features, objectives and effects of this application easier to understand, the following describes this application in conjunction with specific implementation methods.

[0044] like Figures 1 to 8 As shown, this application discloses a method for stable amplitude control of a MEMS resonator, including the following steps:

[0045] The equivalent dynamic model of the MEMS resonator is transformed into a state-space equation.

[0046] By changing the expression of the input matrix in the state-space equation, the non-standard state-space equation can be converted into a standard linear feedback equation.

[0047] Based on the set state weight matrix Q and control weight matrix R, minimize the performance index function of LQR to obtain the input gain matrix under the optimal control rule. ].

[0048] Based on the input gain matrix [ The linear feedback equation is used to determine whether the drive closed-loop system is stable. When the drive closed-loop system is stable, a definite input gain matrix is ​​obtained. The coefficient matrix N.

[0049] Based on the determined input gain matrix [ The coefficient matrix N is used to construct the LQR regulator, which generates the control signal for driving the closed-loop system based on the received reference signal and the feedback signal of the driving closed-loop system.

[0050] This application obtains the linear feedback equation and determines the input gain matrix. The LQR regulator can be constructed by using the coefficient matrix N and the LQR performance index function. This application employs the LQR method to provide a precise control strategy, ensuring that the drive amplitude of the MEMS resonator remains stable at the desired level, even under external disturbances or parameter changes.

[0051] Example 1

[0052] The present application will be described below through specific embodiments.

[0053] Figure 1 The diagram shows the system block diagram of the linear quadratic regulator proposed in this invention, including a reference signal input, a coefficient matrix, an input gain coefficient, and an integrator. The reference signal represents the desired stable output amplitude state of the drive closed-loop system. When the drive closed-loop system receives the reference signal, the LQR regulator compares the current feedback output of the drive closed-loop system with the reference signal. If the feedback output deviates from the stable amplitude indicated by the reference signal, the LQR regulator calculates an appropriate control signal based on the deviation between the feedback output and the reference signal to prompt the drive closed-loop system to revert to the target stable amplitude. This process is repeated until the actual amplitude stabilizes near the value set by the reference signal, thereby achieving closed-loop control.

[0054] In a linear quadratic regulator, the performance index can be expressed in general form as:

[0055] J= (1)

[0056] In equation (1), Q represents the state weight matrix and R represents the control weight matrix. Both are positive definite symmetric matrices. Usually, Q and R are chosen as diagonal matrices, and the elements on the diagonal are all greater than 0. Represents the state vector. This represents the target moment when the closed-loop system reaches stability. This represents the weight matrix of the state vector in the performance index. This indicates the transpose operation. This represents the input matrix.

[0057] Based on the dynamic model of the MEMS resonator, its driving mode can be equivalently represented as a second-order spring-damped system. Therefore, the MEMS resonator can be transformed into a state-space equation form, where the state variables are... State variables , , This represents the force acting on the driving shaft of the MEMS resonator. The equivalent mass of the MEMS harmonic oscillator is represented by the state variables, which specifically represent the oscillation amplitude and oscillation velocity.

[0058] The equivalent transfer function of the driving mode can be expressed as:

[0059] (2)

[0060] in, This represents the driving resonant frequency of the MEMS resonator. This represents the quality factor of the MEMS resonator drive shaft.

[0061] The state-space equation corresponding to the equivalent transfer function of the driving mode can be expressed as:

[0062] = + (3)

[0063] Take the state variable error as ,in, For a certain constant value, the control action of the linear quadratic regulator in the MEMS resonator driving mode of the closed-loop system is set so that it always stays near this equilibrium state. Therefore, the state-space equation can be rewritten as:

[0064] = + + (4)

[0065] As can be seen from the above equation, due to the presence of suffix terms, this state-space equation is not a standard linear feedback system. Therefore, the expression for the input matrix u is transformed into:

[0066] (5)

[0067] In the above formula, and These are the state variable error e and the state variable respectively. The gain coefficient can simplify the state-space equation of the driving modal state regulator into a standard linear feedback equation:

[0068] = + = (6)

[0069] An equivalent model of LQR can be established according to formula (6), where and All are definite constants. and The value of can be obtained by solving the Riccati equation to obtain the optimal solution that minimizes J, where the two weight matrices Q and R are set according to the requirements of system performance (fast stability and reduced overshoot).

[0070] When the eigenvalues ​​of the coefficient matrix N are less than 0, the zeros and poles of the driving closed-loop system are all located in the left half of the polar coordinate plane, and the driving closed-loop system is in a stable state. The coefficient matrix N is then:

[0071] N= (7)

[0072] Therefore, when designing a linear quadratic state regulator, the stability of the drive closed-loop system can be determined by solving for the eigenvalues ​​of the coefficient matrix N. The equations for solving the eigenvalues ​​of the coefficient matrix N are as follows:

[0073] -( ) + =0 (8)

[0074] Find the eigenvalues ​​of the coefficient matrix N and They are respectively:

[0075] , (9)

[0076] in, and The resulting matrix is ​​called the input gain matrix, and its size is determined by the state weight matrix Q and the control weight matrix R. The input gain matrix under the optimal control rule can be obtained by calculating the LQR function. Regarding the selection of the state weight matrix Q and the control weight matrix R, in general, a larger value for the Q matrix means that a smaller state vector x(t) is needed to minimize the cost function J. This means the eigenvalues ​​of the driving closed-loop system matrix (A-BK) are located further to the left of the S-plane, causing the driving closed-loop system to decay to 0 more quickly. A larger value for the R matrix indicates greater emphasis on the input gain matrix. The size of the input vector Decreasing means that the state decay will be slower.

[0077] Based on the block diagram of the linear quadratic controller, the equivalent transfer function X(s) of the linear quadratic controller can be derived as follows:

[0078] (10)

[0079] Where s is a Laplace variable.

[0080] Therefore, substituting equation (10) into the open-loop and closed-loop transfer functions of the MEMS resonator drive closed-loop system, we can obtain the open-loop transfer function of the drive closed-loop system controlled by a linear quadratic regulator. and closed-loop transfer function :

[0081] (11)

[0082] (12)

[0083] in, This represents the gain coefficient of the low-pass filter. This represents the gain coefficient of the front-end amplifier circuit. This indicates the cutoff frequency of the low-pass filter. It is the force-to-electricity conversion coefficient, A ref This is the reference signal input for the linear quadratic regulator. Wherein, , It is the capacitance-to-current conversion factor. It is the transimpedance gain of the preamplifier. and This refers to the ADC to DAC conversion gain coefficient, see... Figure 8 .

[0084] According to Equation 11, the amplitude-frequency and phase-frequency characteristic curves of the open-loop system under linear quadratic regulator control can be plotted as follows: Figure 2As shown in the figure, the system's gain margin is 12.7 dB and its phase margin is 54°. The amplitude-frequency response curve of formula (12) was obtained by solving the equation using mathematical calculation software. Figure 3 The Bode plot of the drive closed-loop system shown indicates that the bandwidth of the drive closed-loop system is 59.7 Hz, and all the above indicators meet the requirements for normal system operation.

[0085] To verify the advantages of the linear quadratic regulator of this invention compared to the PI controller, the control effects of a traditional PI controller and the linear quadratic regulator were compared in a drive closed-loop system. Figure 4 and Figure 5 It can be seen that the PI controller has a contradictory relationship between overshoot and settling time. Reducing the settling time will inevitably increase the overshoot, and a longer settling time is needed to avoid excessive overshoot. The advantage of using a linear quadratic regulator is that the system's settling time is only 0.11s, which is less than the 0.32s settling time of the PI controller, and it does not produce overshoot. The input gain matrix obtained through optimal control theory […]. This allows the system to reach a stable state with an optimal control trajectory, which has significant advantages over traditional PI control.

[0086] To further analyze the control effects of the two controllers under disturbance conditions, a white noise module is introduced into the simulation model of the drive closed-loop system to simulate random disturbances in the system. Figure 6 and Figure 7 As shown, the drive mode excitation signal generated by the linear quadratic regulator (representing the output voltage of the drive closed-loop system controlled by the linear quadratic regulator) is more stable, while the excitation signal generated by the PI controller fluctuates more significantly due to noise. From the perspective of the control system, the smoother feedback input generated by the linear quadratic regulator is beneficial to the stable control of the drive closed-loop system. Furthermore, simulation results from the drive mode detection current signal show that, under disturbance input conditions, the control method using the linear quadratic regulator can give the drive closed-loop system higher anti-interference capability.

[0087] Example 2

[0088] The embodiments of this application also provide an electronic device, which may be a tablet computer, a smartphone, a personal digital assistant, etc.

[0089] Electronic devices may include: memory, processor, communication interface and communication bus, the communication bus being used to enable communication between these components.

[0090] The memory is used to store all model data, as well as various data such as the calculation program instructions corresponding to the stable amplitude control method and system provided in the embodiments of this application. The memory can be random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable read-only memory (EPROM), etc.

[0091] When the processor reads and runs the computer program instructions corresponding to the stable amplitude control method stored in the memory, it executes the stable amplitude control method provided in the embodiments of this application.

[0092] A processor may be an integrated circuit chip with signal processing capabilities. The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), discrete gate or transistor logic devices, or discrete hardware components.

[0093] Example 3

[0094] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0095] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0096] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0097] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0098] As is known from common technical knowledge, this application can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative in all respects and are not the only ones. All modifications within the scope of this application or equivalent to this application are included in this application.

Claims

1. A method for stabilizing the amplitude of a MEMS resonator, characterized in that, include: The equivalent dynamic model of the MEMS resonator is transformed into a state-space equation. By changing the expression of the input matrix in the state-space equation, the non-standard state-space equation can be converted into a standard linear feedback equation. Based on the set state weight matrix Q and control weight matrix R, minimize the performance index function of LQR to obtain the input gain matrix under the optimal control rule. ]; Based on the input gain matrix [ The stability of the drive closed-loop system is determined by the linear feedback equation. When the drive closed-loop system is stable, a definite input gain matrix is ​​obtained. The coefficient matrix N; Based on the determined input gain matrix [ The coefficient matrix N is used to construct the LQR regulator, which generates the control signal for driving the closed-loop system based on the received reference signal and the feedback signal of the driving closed-loop system. The expression for the linear feedback equation is: = + = ； in, This represents the driving resonant frequency of the MEMS resonator. This represents the quality factor of the MEMS resonator drive shaft. Indicates the error of the state variable. Represents a state variable.

2. The method for stabilizing the amplitude of a MEMS resonator according to claim 1, characterized in that, Based on the input gain matrix [ Determining the stability of a drive closed-loop system using linear feedback equations includes: The coefficient matrix N of LQR is obtained according to the linear feedback equation; where, the coefficient matrix N = ; Based on the input gain matrix [ Determine whether the eigenvalues ​​of the coefficient matrix N are less than 0. If they are less than 0, then the closed-loop system is stable.

3. The method for stabilizing the amplitude of a MEMS resonator according to claim 2, characterized in that, The equation for solving the eigenvalues ​​of the coefficient matrix N is: -( ) + =0。 4. The method for stabilizing the amplitude of a MEMS resonator according to claim 1, characterized in that, The expression for the performance metric function of LQR is: J= ； in, Represents the state vector. This represents the target moment when the closed-loop system reaches stability. This represents the weight matrix of the state vector in the performance index. This indicates the transpose operation. This represents the input matrix.

5. The method for stabilizing the amplitude of a MEMS resonator according to claim 1, characterized in that, The expression for the state-space equation is: = + ； in, , This represents the force acting on the driving shaft of the MEMS resonator. This represents the equivalent mass of the MEMS harmonic oscillator. This represents the driving resonant frequency of the MEMS resonator. This represents the quality factor of the MEMS resonator drive shaft. Represents a state variable.

6. The method for stabilizing the amplitude of a MEMS resonator according to claim 1, characterized in that, Also includes: Based on the determined input gain matrix [ The coefficient matrix N is used to obtain the equivalent transfer function X(s) of LQR; The equivalent transfer function X(s) is input into the open-loop and closed-loop transfer functions of the drive closed-loop system to obtain the open-loop and closed-loop transfer functions of the drive closed-loop system using LQR control, so as to analyze the stability index of the drive closed-loop system.

7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the stable amplitude control method according to any one of claims 1-6.

8. A computer system, characterized in that, include: Memory, used to store computer programs / instructions; A processor for executing the computer program / instructions to implement the steps of the stable amplitude control method according to any one of claims 1-6.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the stable amplitude control method according to any one of claims 1-6.

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