Method for detecting and controlling the output of a micro-opto-electro-mechanical mirror

Abstract

The application relates to an output detection control method of a micro-opto-electro-mechanical micro-mirror, which comprises the following steps: 1. based on a dynamic model of the micro-opto-electro-mechanical micro-mirror, an output adjustment design research framework of an output feedback mechanism is constructed, and a tracking control problem of the micro-mirror with transient performance constraints is formed; 2. based on the output adjustment design framework, an internal model is constructed, a coordinate transformation is introduced, the transient performance constraint tracking problem of the micro-opto-electro-mechanical micro-mirror is converted into a transient performance constraint stability design problem of an augmented system, and a lower triangular form augmented system is obtained; and 3. a detection control law is designed for the lower triangular form augmented system, an adaptive learning mechanism is used to learn the driving coefficient relationship between an electromagnetic torque and a driving current, a barrier Lyapunov function is combined, and the Lyapunov stability theory is used to adjust the parameters of the detection control law, so that the micro-electro-mechanical torsional micro-mirror can effectively and asymptotically track a reference trajectory, and the transient performance of the micro-mirror angle output in the tracking process can be efficiently guaranteed.

Description

Technical Field

[0001] This invention relates to the field of micro-opto-electro-mechanical systems technology, specifically to a method for output detection and control of a micro-opto-electro-mechanical micromirror. Background Technology

[0002] Micromirrors, as core components of micro-opto-electro-mechanical systems (MEMS), are widely used in various optical instrument applications, including digital communication, high-quality imaging, and biomedical displays. MEMS micromirrors require high-precision scanning imaging performance, achieved through precise control of the micromirror's rotation angle by MEMS actuators. Furthermore, the high-speed actuators of MEMS micromirrors enable them to accept high-frequency operation and respond quickly. These characteristics have led to the widespread application of torsional micromirror-based MEMS in optical communication, optical displays, and biomedical imaging, providing strong support for achieving high-precision, high-efficiency optical imaging sensing and detection control.

[0003] Scanning and detection control of microelectromechanical torsional micromirrors with transient performance constraints is crucial and represents a core research problem in the field of high-precision detection and control in the micro- and nano-scale domains. Achieving asymptotic tracking of the reference trajectory while satisfying transient performance constraints under quantifiable model parameter uncertainties can help improve the imaging and scanning quality of encapsulated micromirror systems.

[0004] Current detection and control schemes can be roughly divided into two categories: one is open-loop technology based on input-shaping and flatness-based methods, but this technology is not robust to parameter changes caused during the manufacturing process of MEMS devices and is highly susceptible to noise interference; the other is a closed-loop feedback method based on an inverse tracking framework, which relies on available error output differential information. However, in very fast micro- and nano-dynamic processes, sensor noise is easily amplified by the differential link in the inverse tracking framework, which seriously affects the detection and control performance of micro-opto-electro-mechanical micromirrors and may even ultimately lead to the failure of the sensing system based on micro-opto-electro-mechanical micromirror sensors. Summary of the Invention

[0005] To address the problems existing in the prior art, the purpose of this invention is to provide an output detection and control method for micro-opto-electro-mechanical micromirrors, which can achieve effective asymptotic tracking of a reference trajectory by a micro-opto-electro-mechanical torsional micromirror, and efficiently guarantee the transient performance of the micromirror's angle output during the tracking process.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for output detection and control of a micro-opto-electro-mechanical micromirror, including

[0008] Step 1: Based on the dynamic model of the micro-opto-electro-mechanical micromirror, construct a research framework for the output regulation design of the output feedback mechanism, and form a tracking control problem of the micromirror with transient performance constraints;

[0009] Step 2: Based on the output adjustment design framework, construct the internal model, introduce coordinate transformation, and transform the transient performance constraint tracking problem of the micro-opto-electro-mechanical micromirror into the transient performance constraint stability design problem of the augmented system, and obtain the augmented system in the form of a lower triangular shape;

[0010] Step 3: Design a detection and control law for the lower triangular augmented system. Use an adaptive learning mechanism to learn the relationship between the driving coefficients of electromagnetic torque and driving current. Combine the barrier Lyapunov function and apply Lyapunov stability theory to adjust the parameters of the detection and control law, effectively ensuring system stability and transient performance of the micro-opto-electro-mechanical micromirror output.

[0011] Furthermore, in step 1, the dynamic model of the micromirror is as follows:

[0012]

[0013] Where θ, J m B d ,K s ,T field (θ) represent the rotation angle, angular velocity of deflection, angular acceleration of deflection, moment of inertia, damping coefficient, angular spring constant, and electromagnetic torque, respectively.

[0014] Furthermore, for micro-opto-electro-mechanical-electromagnetic driven micromirrors, T field (θ)=VBHcos(θ), where V represents the volume of the magnetic film, B represents the magnetic flux density, and H is the magnetic field strength. Therefore, the system is obtained as follows:

[0015]

[0016] For hard electromagnetically driven micromirrors, there is T field (θ)=K i ×i, where i is the driving current, K i We can assume that the driving current i is an unknown constant, then we can directly use the driving current i as the control input u of the micromirror model, that is, let u = i, and let y = θ. The system can be further represented as follows:

[0017]

[0018] Let Ω = (B) d ,K s ,K i J m )and Let be the actual and nominal values ​​of the micromirror model parameter vector, respectively. Where: ω represents the parameter variation of the nominal value of the micromirror model.

[0019] Furthermore, in the micro-opto-electro-mechanical micromirror-based imaging and scanning system, within the output adjustment design framework, the following external system is used to define the reference angle trajectory information v1(t) for effective tracking of the micromirror output angle:

[0020]

[0021] in, a and b are constants related to the reference trajectory;

[0022] Define the following system

[0023]

[0024] The output detection and control scheme formed within the framework of output regulation research can be summarized as follows: The controlled deflection output angle y of the micromirror achieves asymptotic tracking of a given reference signal v1 with high transient performance, thus ensuring error accuracy. and Where k b (t) represents the desired constraint range for the transient performance of the tracking error.

[0025] Furthermore, the augmentation system in step 2 is constructed by introducing a dynamic filtering system, which is then extended as follows:

[0026]

[0027] Where: λ can be any positive constant, and ξ represents the filter state;

[0028] Combining the systems of (5) and (6) and employing the following transformation

[0029]

[0030] The system can be obtained as follows:

[0031]

[0032] in:

[0033] According to the output regulation design framework, the zero-error steady-state information represented by (z(v,ω),y(v,ω),Ξ(v,ω),u(v,ω)) satisfies the following regulation equation.

[0034]

[0035] The process of solving for the steady-state values ​​y(v,ω), z(v,ω) and Ξ(v,ω) is as follows:

[0036] Let z(v,ω)=Z(ω)v, Z(ω)=[Z 11 Z 12 If ], then Z(ω)A=-Z(ω)+[G(ω)0], where: By simplifying the operations on both sides of the expression, we can obtain...

[0037]

[0038] Then, use the following formula to solve for Ξ(v,ω) in equation (9).

[0039]

[0040] The result is

[0041] Ξ(v,ω)=d 11 v1+d 12 v2 (31)

[0042] in:

[0043] definition We obtain the following formula:

[0044]

[0045] in: Ψ =

[10] , select a controllable matrix pair (M, N), where: M ∈ R 2×2 ,N∈R 2×1 Substituting this into the Sylvester equation TΦ-MT=NΨ, we can obtain a unique invertible matrix solution T;

[0046] The internal model is established as follows:

[0047]

[0048] Combining (8) and (14) yields the augmented system.

[0049] Furthermore, the following coordinate transformations are performed on the augmented system.

[0050]

[0051] in: The system in the lower triangular form is obtained

[0052]

[0053] in:

[0054] Furthermore, the following detection control law is designed for system (16):

[0055]

[0056] in: and In the controller (17) The introduced adaptive learning parameter is used to learn the relationship between the driving coefficients of electromagnetic torque and driving current, while k is the introduced high-gain dynamic parameter used to handle the uncertainty of the micromirror model parameters. Considering the constant selection property of limiting the range of micromirror output error in practice, k is chosen. b (t) = L, where L is a positive constant. The output detection controller can be simplified to the following form:

[0057]

[0058] in: and

[0059] Furthermore, step 3 includes,

[0060] Introducing the barrier Lyapunov function in It is a normal amount. It is a positive definite matrix P that needs to be specified later, and satisfies the Lyapunov equation PM+M. T P = -I², M is the Herwitz matrix, and I² is a given positive definite symmetric identity matrix. The time derivative of V₁ can be calculated as follows:

[0061]

[0062] remember Then there is

[0063]

[0064] Then the controller (17) Substituting into the above equation, we get:

[0065]

[0066] in

[0067] Since ω lies within a compact set W, i.e., ω∈W, there exists a positive constant. and Satisfying g≥4 and l-3||d(ω)T -1 || 2 ≥1; Definition Then there exists a smooth positive definite function. and satisfy choose achievable thus Therefore, for all t≥0,

[0068]

[0069] Therefore, all states and derivatives of the closed-loop system (6), (14), and (17) are bounded, thus indicating that the system possesses stability; at the same time, and Where k b (t) represents the expected range of transient performance constraints.

[0070] Furthermore, it also includes step 4: verifying the effectiveness of the micro-opto-electromechanical detection and control framework through experiments.

[0071] Further, the verification process is as follows: the laser reflected by the micromirror is split into two parts by a beam splitter. One part is collected by a position sensor; the other part is focused by an objective lens to scan the target object and is simultaneously collected by the position sensor. The position sensor measures the position information of the micromirror, while the photodetector detects the light intensity of the laser beam. A real-time controller is used to generate excitation signals and acquire sensor readings. The readout signals of the position sensor and the photodetector are sent to an FPGA pre-loaded with the development controller. The micromirror is driven so that the laser can scan the target object. Whenever the laser beam scans the target object, the scattered laser is collected by the photodetector. Then, the position information obtained by the position sensor and the light intensity of the laser beam detected by the photodetector are used to reconstruct the scanned target object.

[0072] In summary, the present invention has the following advantages:

[0073] This invention provides an output regulation control method based on a combination of barrier Lyapunov functions and adaptive learning mechanisms, developing a high-performance detection and servo control scheme for the output of micro-opto-electro-mechanical (MEMS) micromirrors with enhanced transient performance. This invention utilizes the internal model principle to handle the parameter uncertainties of the MEMS micromirror model and achieves asymptotic tracking of the micromirror output angle to a general reference trajectory. An adaptive learning mechanism is introduced to learn the coefficient relationship between electromagnetic torque and driving current, and the barrier Lyapunov function method is combined to prevent violations of the tracking constraints of the micromirror angle output. This achieves effective asymptotic tracking of the reference trajectory by the MEMS torsional micromirror and efficiently guarantees the transient performance of the micromirror angle output during tracking, avoiding potential collisions between the micromirror device and the physical structure, and improving the lifespan of the micromirror device. Furthermore, this invention ensures that the servo feedback control scheme of the MEMS torsional micromirror does not depend on the angular velocity information of the micromirror, which is beneficial to improving the immunity of the MEMS sensor system to external noise. Therefore, the detection and servo control strategy proposed in this invention does not require an observer algorithm to obtain the angular velocity information of the micromirror for feedback control channels, nor does it require the addition of an extra velocity sensor, thereby reducing hardware costs and shrinking the device size of the micro-opto-electro-mechanical sensor system, which is conducive to further expanding the application scope of micro-electro-mechanical torsional micromirrors in optical imaging scanning and audiovisual perception systems. Attached Figure Description

[0074] Figure 1 This is a framework diagram for detecting and controlling the output angle of a micro-opto-electro-mechanical micromirror according to an embodiment of the present invention.

[0075] Figure 2 This is a design diagram of the micro-opto-electro-mechanical micromirror experimental platform according to an embodiment of the present invention.

[0076] Figure 3 This is a schematic diagram illustrating the micro-opto-electro-mechanical micromirror scanning application principle of an embodiment of the present invention. Detailed Implementation

[0077] The present invention will now be described in further detail.

[0078] This invention provides an output regulation control method based on a combination of obstacle Lyapunov functions and adaptive learning mechanisms, eliminating the requirement for measurement information of the angular velocity of micro-opto-electro-mechanical micromirrors (MEMS) and effectively improving the high-precision scanning performance of imaging scanning equipment based on MEMS systems. The method includes the following steps:

[0079] Step 1: Based on the dynamic model of the micro-opto-electro-mechanical micromirror, construct the output adjustment design framework of the output feedback mechanism to form the tracking control problem of the micromirror with transient performance constraints;

[0080] Step 2: Based on the output regulation design framework, construct the internal model to transform the transient performance constraint tracking problem of the micro-opto-electro-mechanical micromirror into the transient performance constraint stability design problem of the augmented system. This transformation helps to eliminate the measurement requirements of the micromirror angular velocity of the micromirror detection and control system. At the same time, an adaptive learning mechanism is introduced to learn the coefficient relationship between electromagnetic torque and driving current.

[0081] Step 3: Use Lyapunov stability theory to prove the stability of the augmented system and select control system parameters that can effectively guarantee the transient performance of the micro-opto-electro-mechanical micromirror output;

[0082] Step 4: Build an experimental verification design scheme to verify the effectiveness of the micro-opto-electro-mechanical detection and control framework.

[0083] Specifically, the implementation method for each step is as follows:

[0084] Step 1: The dynamic model of the micromirror is as follows:

[0085]

[0086] Where θ, J,B,K,T field (θ) represent the rotation angle, angular velocity of deflection, angular acceleration of deflection, moment of inertia, damping coefficient, angular spring constant, and electromagnetic torque, respectively.

[0087] For micromirrors driven by opto-electro-mechanical-electro-magnetic fields, it can be known that field (θ) = VBHcos(θ), where V represents the volume of the magnetic film, B represents the magnetic flux density, and H is the magnetic field strength. Therefore, the system is obtained as follows:

[0088]

[0089] Due to electromagnetic torque T field (θ) is generated by driving the micromirror with a driving current i through a planar microcoil, and studies have shown that the driving current i is related to the electromagnetic torque T. field (θ) has an approximately linear relationship, therefore T can be set as follows: field (θ)=K i ×i, where K i We can assume it to be an unknown constant, and then let y = θ. With u = i, the system can be further represented as follows:

[0090]

[0091] In the micro-manufacturing process of micro-opto-electro-mechanical micromirrors, various factors can cause changes in the model parameter values. Therefore, let Ω = (B... d ,K s ,K i Jm )and These are the actual and nominal values ​​of the model parameter vector, respectively. Then, let... Where ω represents the parameter variation of its nominal value.

[0092] Imaging and scanning systems based on micro-opto-electro-mechanical micromirrors require that the output angle of the micromirrors can achieve asymptotic tracking with high transient performance to a given reference trajectory. Under the output adjustment design framework, the following external system can be used to define the reference angle trajectory information v1(t) that the micromirror output angle needs to effectively track:

[0093]

[0094] Where a and b are constants related to the reference trajectory.

[0095] Define the following system

[0096]

[0097] e = y - v1 (43)

[0098] To enable the controlled deflection output angle y of the micromirror to achieve asymptotic tracking of a given reference signal v1 with high transient performance, it is necessary to ensure that... and Where k b (t) represents the expected range of transient performance constraints.

[0099] Step 2: Introduce a filtering system to convert system (5) into a lower triangular form, construct an internal model, and transform the transient performance constraint tracking problem of the micro-opto-electro-mechanical micromirror into the transient performance constraint stability design problem of the augmented system.

[0100] First, the dynamic filtering system is extended as follows:

[0101]

[0102] Where λ can be any positive constant, the present invention chooses λ = 1.

[0103] Combining the systems of (5) and (6) and employing the following transformation

[0104]

[0105] The system can be obtained as follows:

[0106]

[0107] e = y - v1 (46)

[0108] in:

[0109] According to the output regulation design framework, the zero-error steady-state information represented by (z(v,ω),y(v,ω),Ξ(v,ω),u(v,ω)) satisfies the following regulation equation.

[0110]

[0111] 0 = y(v) - v1 (47)

[0112] The process of solving for the steady-state values ​​y(v,ω), z(v,ω) and Ξ(v,ω) is as follows:

[0113] Let z(v,ω)=Z(ω)v, where: Z(ω)=[Z 11 Z 12 If , then Z(ω)A=-Z(ω)+[G(ω) 0], By simplifying the operations on both sides of the expression, we can obtain...

[0114]

[0115] Then, use the following formula to solve for Ξ(v,ω).

[0116]

[0117] The result is

[0118] Ξ(v,ω)=d 11 v1+d 12 v2 (50)

[0119] in:

[0120] definition We obtain the following formula:

[0121]

[0122] Ξ(v,ω)=Ψτ(v,ω) (51)

[0123] and Ψ = [1 0], select controllable pairs M ∈ R 2×2 ,N∈R 2×1 Substituting into the Sylvester equation TΦ-MT=NΨ yields a unique invertible matrix solution T.

[0124] The internal model is established as follows:

[0125]

[0126] Combining (8) and (14), we can obtain the augmented system. The following coordinate transformations are then performed on the augmented system.

[0127]

[0128] in: A system in the lower triangular form can be obtained.

[0129]

[0130] in:

[0131] To ensure the stability of system (16), the following detection and control law is designed for it:

[0132]

[0133] in: and

[0134] In the controller (17) The introduced adaptive learning parameters are used to learn the coefficient relationship between electromagnetic torque and drive current; and It is mainly used to prevent the output angle of the micromirror from exceeding the limit, thus improving its transient performance. However, considering the influence of the constraint boundary k... b If (t) becomes too strict, it may require more control over the input action, leading to input saturation. To address this issue, k can be chosen... b (t) = L, thus simplifying the controller to the following form:

[0135]

[0136] in: and

[0137] Step 3: Stability Analysis

[0138] Introducing the barrier Lyapunov function in It is some normal quantity. Therefore, the time derivative of V1 can be calculated as follows:

[0139] remember Then there is

[0140]

[0141] Then the controller (17) Substituting into the above equation, we get:

[0142]

[0143] in

[0144] Since ω lies within a compact set W, i.e., ω∈W, there exists a positive constant. and Satisfying g≥4 and l-3||d(ω)T -1 || 2 ≥1. Definition Then there exists a positive, smooth function. and satisfy choose And satisfied It can be obtained Therefore, for all t≥0

[0145] All

[0146]

[0147] Therefore, all states and derivatives of the closed-loop system (6), (14), and (17) are bounded, thus indicating that the system possesses stability; at the same time, and Where k b (t) represents the expected range of transient performance constraints. Figure 1 This is a framework diagram of the entire detection and control scheme.

[0148] Step 4: In this step, an experimental platform will be set up to verify the detection and control scheme proposed in this invention.

[0149] The main components of the experimental platform include a helium-neon laser, a position sensor detector (PSD), a NIPXI 7852R real-time controller, a voltage-controlled current amplifier (VCCA) circuit, and a micro-opto-electro-mechanical micromirror, such as... Figure 2 As shown. The control algorithm was programmed using LabVIEW software, and the code was written using Xilinx compiler tools. The VCCA circuit consists of an operational amplifier, N-channel and P-channel MOSFETs, and several resistors. This circuit uses a DC voltage source to drive the N-channel and P-channel MOSFETs to provide current amplification.

[0150] Figure 3This diagram illustrates a scanning system based on a micro-opto-electro-mechanical micromirror. The target being scanned is a metal grid pattern. Laser light reflected from the micromirrors is split into two parts by a beam splitter. One part is collected by a PSD (Power Detector). The other part is focused by an objective lens, scanning the target object, and simultaneously collected by a photodetector (PD). The PSD measures the position information of the micromirrors, while the PD detects the intensity of the laser beam. A PXI 7852R real-time controller is used to generate excitation signals and acquire sensor readings. The readout signals from the PSD and PD are sent to an FPGA pre-loaded with the development controller. The micromirrors are driven, enabling the laser to scan the target object. Whenever the laser beam scans the target object (metal grid pattern), the scattered laser light is collected by the PD. The position information obtained by the PSD and the laser beam intensity detected by the PD are then recorded in real time. In this respect, the position information obtained by the PSD and the intensity signal on the PD are displayed and stored in the main computer for reconstructing the scanned target. Due to the reflection of white and black stripes in the metal grid pattern, it is a series of peaks and valleys. Figure 3 In this process, the position signal measured by the PSD and the light intensity signal of the PD are combined to reconstruct an image of the metal grid pattern.

[0151] Experimental results demonstrate that our designed micro-opto-electro-mechanical micromirror detection and tracking controller with enhanced transient performance can avoid measuring the angular velocity information of the micromirror, improve the reliability and durability of the micromirror, and effectively enhance the scanning performance of micromirror-based optical sensors and imaging devices.

[0152] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for output detection and control of a micro-opto-electro-mechanical micromirror, characterized in that: include Step 1: Based on the dynamic model of the micro-opto-electro-mechanical micromirror, construct a research framework for the output regulation design of the output feedback mechanism, and form a tracking control problem of the micromirror with transient performance constraints; Step 2: Based on the output adjustment design framework, construct the internal model, introduce coordinate transformation, and transform the transient performance constraint tracking problem of the micro-opto-electro-mechanical micromirror into the transient performance constraint stability design problem of the augmented system, and obtain the augmented system in the form of a lower triangular shape; Step 3: Design a detection and control law for the lower triangular augmented system. Use an adaptive learning mechanism to learn the relationship between the driving coefficients of electromagnetic torque and driving current. Combine the barrier Lyapunov function and apply Lyapunov stability theory to adjust the parameters of the detection and control law, effectively ensuring system stability and transient performance of the micro-opto-electro-mechanical micromirror output. Perform the following coordinate transformations on the augmented system. ； in: This yields a system in the lower triangular form. ； in: ; The following detection control law is designed for system (16): ； in: ; In the controller (17) The introduced adaptive learning parameters are used to learn the relationship between the electromagnetic torque and the drive current driving coefficients. To introduce high-gain dynamics, which is used to handle the uncertainty of the micromirror model parameters; considering the constant selection property of the limitation range of micromirror output error in practice, the following is selected: ,in: As a positive constant, the output detection controller can be simplified to the following form: ； in: ; Step 3 includes, Introducing the barrier Lyapunov function ,in It is a normal amount. , It is a positive definite matrix that will be specified later. Satisfying the Lyapunov equations , It is the Herwitz matrix. Given a positive definite symmetric identity matrix, it can be calculated that... The time derivative is ； remember Then there is ； Then the controller (17) Substituting into the above equation, we get: ； in ; because Within a compact set W, i.e. Therefore, positive constants exist. and satisfy and ;definition Then there exists a smooth positive definite function. satisfy ,choose , can be obtained ,thus Therefore, for all , All ； Therefore, all states and derivatives of the closed-loop system (6), (14), and (17) are bounded, thus indicating that the system possesses stability; at the same time, and ,in This represents the expected range of transient performance constraints.

2. The output detection and control method according to claim 1, characterized in that: In step 1, the dynamic model of the micromirror is as follows: ； in These represent the rotation angle, angular velocity of deflection, angular acceleration of deflection, moment of inertia, damping coefficient, angular spring constant, and electromagnetic torque, respectively.

3. The output detection and control method according to claim 2, characterized in that: For micro-opto-electro-mechanical-electro-magnetic driven micromirrors Where V represents the volume of the magnetic film, B represents the magnetic flux density, and H is the magnetic field strength, the system is obtained as follows: ； For hard electromagnetically driven micromirrors, there are ,in For driving current, It can be assumed to be an unknown constant, then the driving current can be... Directly used as control input for the micromirror model , that is to say At the same time, The system can be further represented as follows: ； set up and Let be the actual and nominal values ​​of the micromirror model parameter vector, respectively. ,in: The parameter variation represents the nominal value of the micromirror model.

4. The output detection and control method according to claim 3, characterized in that: In an imaging and scanning system based on micro-opto-electro-mechanical micromirrors, within the framework of output adjustment design, the following external system is used to define the reference angle trajectory information for effective tracking of the micromirror output angle. : ； in, , These are constants related to the reference trajectory; Define the following system ； The output detection and control scheme formed within the framework of output regulation research can be summarized as: controlling the deflection angle of the micromirror at the output angle. Achieve the desired response for a given reference signal High transient performance asymptotic tracking, i.e., guaranteeing error and ,in This is the desired constraint range for tracking error transient performance.

5. The output detection and control method according to claim 4, characterized in that: The augmentation system in step 2 is constructed by introducing a dynamic filtering system, which is then extended as follows: ； in: It can be any positive integer. Indicates the filter state; Combining the systems of (5) and (6) and employing the following transformation ； The system can be obtained as follows: ； in: Based on the output adjustment design framework, use The zero-error steady-state information represents the following regulation equation: ； Solve for steady-state values , and The process is as follows: set up , Then there is ,in: By simplifying the operations on both sides of the equation, we can obtain... ； Then use the following formula to solve for the value in equation (9). ; ； The result is ； in: ; definition This yields the following formula: ； in: Select controllable matrix pair ,in: Substitute into the Sylvester equation A unique invertible matrix solution can be obtained. ; The internal model is established as follows: ； Combining (8) and (14) yields the augmented system.

6. The output detection and control method according to claim 1, characterized in that: It also includes step 4: verifying the effectiveness of the micro-opto-electromechanical detection and control framework through experiments.

7. The output detection and control method according to claim 6, characterized in that: The verification process is as follows: the laser reflected by the micromirror is split into two parts by a beam splitter. One part is collected by the position sensor detector; the other part is focused by the objective lens to scan the target object and is also collected by the position sensor detector. A position sensor measures the position information of the micromirror, while a photodetector detects the intensity of the laser beam. A real-time controller generates excitation signals and acquires sensor readings. The readout signals from the position sensor and photodetector are sent to an FPGA pre-loaded with the development controller. The micromirror is driven so that the laser can scan the target object. Whenever the laser beam scans the target object, the scattered laser light is collected by the photodetector. Then, the position information obtained by the position sensor and the intensity of the laser beam detected by the photodetector are used to reconstruct the scanned target object.

Images