Parallel rotating mirror type interferometer system control method and system

Abstract

The invention provides a parallel rotating mirror interferometer system control method and system, and the method comprises the steps: analyzing the relation between the angular speed of a voice coil motor and the optical path difference speed, and building a mathematical model of a parallel rotating mirror interferometer according to the relation; and a CMAC-PID composite control strategy is adopted to control the parallel rotating mirror interferometer so as to suppress nonlinear factor disturbance of the mathematical model. The technical problems that the spectral signal-to-noise ratio obtained through inversion is influenced by the stability of the OPD speed, and the control precision is low and the control performance is poor due to time-varying interference are solved.

Description

Technical Field

[0001] The present invention relates to the field of gas analysis equipment control, and in particular to a parallel rotating mirror interferometer system control method and system. Background Art

[0002] Fourier transform spectroscopy (FTS) technology is widely used in environmental monitoring, atmospheric monitoring, and the petrochemical industry, enabling high-precision, real-time analysis of gas composition and content. Based on the interferometer implementation method, FTS can be primarily categorized into time-modulated and space-modulated types. In a time-modulated Fourier transform spectrometer, the stability of the optical path difference (OPD) velocity in the interferometer system directly impacts the signal-to-noise ratio (SNR) of the inverted spectrum.

[0003] The motion system of the interferometer is the core of the Fourier transform spectrometer. The interferometer system based on rotation solves the non-collinearity problem in the motion system. For example, the existing invention patent application document "Fourier transform infrared spectrometer and gas concentration detection method" with publication number CN113390812A, wherein the Fourier transform infrared spectrometer includes: a laser source for providing laser; an interference module for causing the laser emitted by the laser source to interfere, wherein the interference module includes: a prism for refracting the laser generated by the laser source; a beam splitter for dividing the laser refracted by the prism into reflected laser light and transmitted laser light; a quarter wave plate for causing the reflected laser reflected by the beam splitter to pass through the quarter wave plate in a direction perpendicular to the quarter wave plate to generate ordinary light and extraordinary light with a phase difference; a fixed mirror for the laser light generated by the quarter wave plate The ordinary light and extraordinary light with phase difference are reflected and returned to the beam splitter along the original path; a compensation plate is used to compensate for the transmitted laser light transmitted by the beam splitter; and a movable mirror is used to reflect the transmitted laser light compensated by the compensation plate and return it to the beam splitter along the original path, and the movable mirror reciprocates along the direction of the transmitted laser light so that the transmitted laser light returned to the beam splitter has an optical path difference with the ordinary light and extraordinary light and interferes with each other, thereby generating a first laser interference signal and a second laser interference signal with a phase difference; and an optoelectronic information conversion module includes: a beam splitter prism for dividing the generated first laser interference signal and second laser interference signal with a phase difference into two paths; and two photoelectric tubes for respectively receiving the first laser interference signal and second laser interference signal with a phase difference and converting the first laser interference signal and the second laser interference signal into electrical signals. According to the specific implementation content of the existing solution, the interference module of the Fourier transform infrared spectrometer also includes: a voice coil motor for driving the movable mirror to move along the direction of the transmitted laser light. However, the presence of a rotating mechanism typically introduces a time-varying relationship between the optical path difference (OPD) velocity of the interferometer system and the angular velocity of the voice coil motor, resulting in time-varying loads on the voice coil motor. Furthermore, nonlinear factors such as friction, platform vibration, and airflow disturbances during transmission can also affect the OPD velocity stability in the interferometer system.To achieve a high-performance interferometer control system, researchers have designed various control algorithms to improve the stability of the OPD scanning speed and overcome the effects of nonlinear disturbances. These algorithms include model-referenced adaptive control, interpolation-based repetitive control, fuzzy PID algorithms, and dual closed-loop control with active disturbance rejection. For example, in the patent application for invention CN115857317A, "Control System of Voice Coil Adaptive Deformable Mirror Based on Look-up Fuzzy PID," the voice coil actuators are controlled in parallel. Each voice coil actuator is controlled using closed-loop negative feedback control based on a position loop, and each voice coil actuator controller uses a look-up fuzzy PID control algorithm. By outputting different displacements from the voice coil actuators, the deformable mirror produces different shapes, thus completing the adaptive optics correction task. A discretization method for the input variables of the look-up fuzzy controller was designed. And the existing invention patent application document with publication number CN115940737A "A dual closed-loop control method for the swing arm motion of a Fourier infrared spectrometer", in which the inner loop is a current loop and the outer loop is a speed loop, comprising the following steps: Step 1, taking a mechanism consisting of a rotary voice coil motor and a spring disturbing shaft as a controlled object, constructing a transfer function model of the controlled object based on the working principle of the rotary voice coil motor, the specific expression of the transfer function model of the controlled object is: where U is the voltage across the motor, R is the resistance of the voice coil motor moving coil, LΣ is the sum of the voice coil motor moving coil inductance and the circuit inductance, JΣ is the total rotational inertia of the motor, k is the spring coefficient of the flexible support, KT=Blr, B is the magnetic density of the cut voice coil motor moving coil conductor, l is the effective length of the voice coil motor moving coil conductor, and r is the distance from the force point of the voice coil motor moving coil to the rotating shaft; Step 2, constructing the current loop as the inner loop, designing a PI controller, simplifying the inherent part of the current loop into two inertia links, in A controller Gc1 is added to the controlled object, and the controller transfer function is: where Kp1 and Ti1 are the proportional coefficient and integral time constant of the PI controller, respectively. The current loop is adjusted to a typical type I system using the PI controller, and the parameter calculation formula for the current loop controller is: Step 3: Construct a velocity loop as the outer loop and design a PID controller. The velocity loop is added to the current loop, making the current loop equivalent to a link in the velocity loop, and design a velocity loop controller. Based on the limitations of the discrete velocity feedback signal, the system is corrected using a digital PID controller using discrete error quantities. The discrete PID control law for the velocity loop is: where e(k) and e(k-1) are the deviation values ​​at the kth and k-1th sampling times, respectively, and m(k) is the output of the PID controller at the kth sampling time. Step 4: Build a dual closed-loop control system and select parameters based on the swing arm performance requirements. Step 5: Control the motion of the moving mirror at the end of the swing arm system of a Fourier transform infrared spectrometer using the dual closed-loop control method. Furthermore, Guo et al. proposed a model reference adaptive control (MRAC) algorithm for a translational interferometer system driven by a permanent magnet linear synchronous motor (PMLSM).However, the performance of this controller depends heavily on the convergence of its parameters. In practical systems, parameter convergence can be affected by noise, measurement errors, and model inaccuracies, resulting in inaccurate or slow parameter convergence. Guo et al. also designed interpolation repetitive control (IRC), but IRC is sensitive to changes in system parameters, can only suppress periodic disturbances, and lacks sufficient robustness. Langraf et al. studied the electric drive control system for the angular reflector of a mid-infrared Fourier transform spectrometer on a meteorological satellite. This system employed a dual closed-loop control scheme based on current and voltage. However, the simulation model did not consider nonlinear factors. Liu et al. proposed fuzzy PID control, but the determination of fuzzy rules in the fuzzy PID controller is complex, and control accuracy is limited due to computer limitations. Liangjie Zhi et al. addressed an interferometer system with a mirror pendulum structure and proposed an improved anti-interference dual-loop controller (IADR-DCLC). However, the parameter adjustment complexity of the IADR-DCLC, as well as its performance, depend heavily on accurately estimating the disturbance. Therefore, this study focuses on finding an effective control strategy to compensate for disturbances and enhance system performance.

[0004] As a rotating interferometer, the parallel mirror interferometer has the advantages of simple structure and easy adjustment, and is widely used in Fourier transform spectrometers. In this study, we focused on a specific type of parallel mirror interferometer system. First, we analyzed the relationship between the optical path difference velocity and the angular position of the voice coil motor and established a mathematical model of the parallel mirror interferometer motion system. Based on this model, we designed a CMAC-PID composite controller and developed a real-time control model for the voice coil motor (RT-VCM) in MATLAB. Finally, simulation analysis verified the CMAC-PID control.

[0005] In summary, the spectral signal-to-noise ratio obtained by inversion in the prior art is affected by the stability of the optical path difference (OPD) speed and the existence of time-varying interference, resulting in low control accuracy and poor control performance. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: how to solve the technical problem in the prior art that the spectral signal-to-noise ratio obtained by inversion is affected by the stability of the optical path difference (OPD) speed, and the existence of time-varying interference leads to low control accuracy and poor control performance.

[0007] The present invention solves the above technical problems by adopting the following technical solutions: A parallel rotating mirror interferometer system control method includes:

[0008] S1. Analyze the relationship between the angular velocity of the voice coil motor and the optical path difference speed, and establish a mathematical model of a parallel rotating mirror interferometer based on this. During the operation of parallel mirror rotation, determine the optical path difference (OPD) between the reflected light beam and the projected light beam on the detector to generate optical interference. Obtain the optical path difference speed (OPDV) function, and use this to determine the relationship between the optical path difference speed and the voice coil motor speed. Obtain the dynamic voltage balance equation, dynamic force balance equation, and torque balance equation of the parallel rotating mirror interferometer, and use this to obtain the open-loop transfer function of the parallel rotating mirror interferometer to establish the mathematical model of the interferometer.

[0009] S2. A CMAC-PID composite control strategy is used to control a parallel mirror interferometer to suppress nonlinear disturbances in the interferometer mathematical model. The cerebellum model neural network controller (CMAC) in the CMAC-PID composite control strategy includes: an input space segmentation component, a nonlinear mapping component from the input layer to the output layer, and a weight learning component in the output layer.

[0010] In the input space segmentation component and the input layer to output layer nonlinear mapping component, nonlinear mapping and linear mapping are used to realize the nonlinear relationship between input and output, and increase the number of network layers and generalization parameters of the cerebellum model neural network controller CMAC:

[0011] The weight learning component in the output layer is used to obtain the corresponding output value y(t) at the end of each control cycle of the parallel rotating mirror interferometer for comparison with the reference signal r(t). The weight value is updated using the supervised δ learning algorithm according to the learning rate η for weight learning. The cerebellar model neural network controller CMAC is used for self-learning, and the PID controller is used to adjust the PID parameters to obtain the overall output control signal to control the parallel rotating mirror interferometer.

[0012] This paper proposes a control strategy for a parallel-mirror interferometer based on CMAC-PID composite control. The effectiveness of this controller is verified through simulation, achieving high-performance control of the parallel-mirror interferometer system. The paper analyzes the relationship between the optical path velocity difference and the angular position of the voice coil motor and establishes a mathematical model of the parallel-mirror interferometer motion system. Based on this model, a CMAC-PID composite controller is designed and a real-time control model for the voice coil motor (RT-VCM) is developed in MATLAB. Finally, simulation analysis verifies the effectiveness of the CMAC-PID control strategy.

[0013] In a more specific technical solution, the parallel mirror interferometer in step S1 includes: a voice coil motor (VCM), a rotating platform with a flexible pivot, an interferometer, a detector, a controller, a power driver, a reference laser, a parallel mirror, and a beam splitter.

[0014] The rotating voice coil motor (VCM) drives the rotating platform to adjust the optical path difference and generate optical interference. The optical path difference speed is controlled by adjusting the rotation speed of the voice coil motor (VCM).

[0015] No less than two parallel mirrors are fixed on the same rotating platform, and the rotating platform drives the parallel mirrors to rotate simultaneously through bearings;

[0016] The beam splitter is installed on a preset fixed platform so that the light incident at a specific angle is split into a reflected light beam and a projected light beam by the beam splitter. The reflected light beam and the transmitted light beam are reflected by the parallel mirror and return to the beam splitter along the original optical path and converge on the detector.

[0017] In a more specific technical solution, during the operation of parallel mirror rotation, the optical path difference OPD between the reflected light beam and the projected light beam on the detector is determined using the following logic to generate optical interference, wherein the optical interference includes: Michelson interference:

[0018]

[0019] Where R is the distance between the parallel mirrors and t is the time within the motion cycle.

[0020] In a more specific technical solution, in step S1, the following logic is used to perform a derivative operation on the time t within the motion cycle of the parallel rotating mirror interferometer to obtain the optical path difference velocity OPDV function:

[0021]

[0022] in,

[0023] α1=sin(π / 4-ωt)

[0024] α2=sin(π / 4+ωt)

[0025] β1=cos(2ωt)

[0026] β2=sin(2ωt)

[0027] ρ1=cos(π / 4+ωt)

[0028] ρ2=cos(π / 4-ωt)

[0029] Simplifying equation (2), we get the simplified optical path difference velocity OPDV function:

[0030] OPDV≈4R*ω / sin(π / 4+ωt) (3)

[0031] According to the simplified optical path difference velocity OPDV function, the relationship between the optical path difference velocity and the speed of the voice coil motor is determined, wherein ω is the rotational angular velocity of the voice coil motor.

[0032] In the parallel mirror interferometer system of the present invention, the optical path difference velocity is controlled by the rotation speed of the VCM. The present invention realizes a stable optical path difference velocity OPDV in the interferometer system and improves the signal-to-noise ratio of the Fourier transform spectroscopy FTS interferometer.

[0033] In a more specific technical solution, the voice coil motor VCM further includes: a driving component RT-VCM; wherein the RT-VCM is a key component of the parallel rotating mirror interferometer system;

[0034] Using the following logic, we analyze the relationship between voltage and back electromotive force and derive the dynamic voltage balance equation:

[0035]

[0036] Where u(t) is the armature voltage, i(t) is the coil current, R is the total resistance of the coil, L is the coil inductance, Ea is the back electromotive force generated by the coil winding under the action of the electromagnetic force, B is the magnetic field strength, l is the effective length of the RT-VCM coil, v is the angular velocity of the motor rotor, and Ke is the motor torque coefficient;

[0037] The dynamic force balance equation of the driving component RT-VCM is expressed using the following logic:

[0038]

[0039] Where N is the number of turns of the coil, and Km=NBl is the electromagnetic force coefficient;

[0040] The voice coil motor is connected to the rotating platform through bearings. The charged coil is placed in a constant magnetic field, and the Ampere force is generated to drive the rotating platform to rotate around the axis.

[0041] The torque balance equation of the drive component RT-VCM is expressed using the following logic:

[0042]

[0043] Where r is the distance between the coil and the center of rotation, m(t) is the bearing friction torque, J is the moment of inertia of the rotating platform, and w(t) is the angular velocity;

[0044] Using the following Laplace transform logic, the time domain expressions of the dynamic voltage balance equation (4), the dynamic force balance equation (5), and the torque balance equation (6) are converted into s-domain expressions:

[0045]

[0046] The open-loop transfer function of the parallel rotating mirror interferometer is expressed using the following logic:

[0047]

[0048] The RT-VCM used in the present invention has the advantages of small size and good control performance. Based on the performance advantages of the RT-VCM, the response speed and steady-state accuracy requirements of the parallel mirror interferometer are met.

[0049] In a more specific technical solution, in step S2, nonlinear mapping and linear mapping are used to realize a nonlinear relationship between input and output, wherein the nonlinear mapping and linear mapping are represented by the following logic:

[0050] U→AC, AC→AP.

[0051] In a more specific technical solution, in step S2, let the input signal be u(t), and use the following logic to perform nonlinear function quantization on the input signal U of the parallel mirror interferometer to obtain a quantization space S:

[0052] Signed power function:

[0053]

[0054] Signed Gaussian function:

[0055]

[0056] The quantization space S is divided into N+2C sub-quantization intervals using the following logic:

[0057]

[0058] In a more specific technical solution, step S2 includes:

[0059] S21. Use the following logic to express the activation status of storage space AC:

[0060]

[0061] S22. When the input signal U is quantized into the quantization space S, the C units in the storage space AC are activated and multiplied by the weights in the storage weight space AP to obtain the CMAC network output:

[0062]

[0063] Where u n (k) represents the output generated by the cerebellum model neural network controller CMAC, U represents the input space, S represents the quantization space, AC represents the storage space, aj represents the activation state of the jth storage unit, AP represents the storage weight space, ω j Represents the weight of the j-th storage unit;

[0064] S23. Utilize the weight learning component in the output layer to obtain the corresponding output value y(t) at the completion of each control cycle of the parallel rotating mirror interferometer, compare it with the reference signal r(t), and update the weight value using the supervised δ learning algorithm according to the learning rate η to perform weighted learning. The weight value is updated using the following logic:

[0065]

[0066] Where η∈(0,1) represents the learning rate of the network.

[0067] The cerebellar model neural network controller (CMAC) employed in this invention stores information in a local structure, reducing weight corrections in the output layer and accelerating learning. The CMAC offers superior nonlinear approximation performance compared to existing neural network data processing methods and avoids the local minima problem inherent in neural network algorithms. This makes it superior to traditional models in nonlinear real-time control under complex dynamic conditions.

[0068] In a more specific technical solution, step S2 further includes:

[0069] S21′, using the inertia factor of the cerebellum model neural network controller CMAC to perform weight correction, wherein the inertia factor uses the following logic to correct the weight value:

[0070]

[0071] Where, α∈(0,1) represents the inertia factor;

[0072] S22', use the following logic to obtain the output u of the PID controller p (k) Output u of the cerebellum model neural network controller CMAC n (k):

[0073]

[0074] Where e(t) is the difference between the reference signal and the system output. p is the proportionality coefficient, T i is the integration time, T d is the differential time, a i is the binary selection vector, w is the weight value of CMAC;

[0075] S23', using the following logic, obtain the overall output of the CMAC-PID composite controller:

[0076] u(k)=u n (k)+up (k) (16)

[0077] S24', adjust and update the weight value ω using the following logic:

[0078]

[0079] This invention introduces an inertia factor into the weight calibration process to reduce weight perturbations. In CMAC, the inertia factor controls the weight update rate. A larger inertia factor slows down weight updates and provides a smoother response to system changes. A smaller inertia factor results in faster weight updates and a faster response to system changes.

[0080] The present invention combines PID with CMAC, enabling controller parameters to adjust based on system changes, thus optimizing system control performance. This invention incorporates CMAC into the PID controller for system identification. By leveraging CMAC's self-learning capabilities, PID parameters can adapt to system changes, achieving improved control performance and optimizing the controller's anti-interference performance and robustness.

[0081] In a more specific technical solution, the parallel rotating mirror interferometer system control system includes:

[0082] The interferometer modeling module is used to analyze the relationship between the angular velocity of the voice coil motor and the optical path difference speed, thereby establishing a mathematical model of the parallel rotating mirror interferometer. During the operation of parallel mirror rotation, the optical path difference (OPD) between the reflected light beam and the projected light beam on the detector is determined to generate optical interference. The optical path difference speed (OPDV) function is obtained to determine the relationship between the optical path difference speed and the speed of the voice coil motor. The dynamic voltage balance equation, dynamic force balance equation, and torque balance equation of the parallel rotating mirror interferometer are obtained to obtain the open-loop transfer function of the parallel rotating mirror interferometer and establish the interferometer mathematical model.

[0083] An interferometer control module is used to control a parallel rotating mirror interferometer using a CMAC-PID composite control strategy to suppress nonlinear disturbances in the mathematical model. The cerebellum model neural network controller (CMAC) in the CMAC-PID composite control strategy includes an input space segmentation component, a nonlinear mapping component from the input layer to the output layer, and a weight learning component in the output layer. The interferometer control module is connected to the interferometer modeling module.

[0084] The input space segmentation component and the input layer to output layer nonlinear mapping component are used to realize the nonlinear relationship between input and output by using nonlinear mapping and linear mapping, increase the number of network layers and generalization parameters of the cerebellum model neural network controller CMAC, and connect the input space segmentation component with the input layer to output layer nonlinear mapping component:

[0085] The weight learning component in the output layer is used to obtain the corresponding output value y(t) at the completion of each control cycle of the parallel rotating mirror interferometer, for comparison with the reference signal r(t). The weight value is updated using a supervised δ learning algorithm according to the learning rate η to perform weight learning. The cerebellar model neural network controller CMAC is used for self-learning, and the PID controller is used to adjust the PID parameters to obtain the overall output control signal to control the parallel rotating mirror interferometer. The weight learning component in the output layer is connected to the nonlinear mapping component from the input layer to the output layer.

[0086] This invention offers the following advantages over existing technologies: It proposes a control strategy for a parallel-mirror interferometer based on CMAC-PID composite control. The effectiveness of this controller has been verified through simulation, achieving high-performance control of the parallel-mirror interferometer system. The invention analyzes the relationship between the optical path velocity difference and the angular position of the voice coil motor and establishes a mathematical model of the parallel-mirror interferometer motion system. Based on this model, a CMAC-PID composite controller was designed, and a real-time control model for the voice coil motor (RT-VCM) was developed in MATLAB. Finally, simulation analysis verified the effectiveness of the CMAC-PID control strategy.

[0087] In the parallel mirror interferometer system of the present invention, the optical path difference velocity is controlled by the rotation speed of the VCM. The present invention realizes a stable optical path difference velocity OPDV in the interferometer system and improves the signal-to-noise ratio of the Fourier transform spectroscopy FTS interferometer.

[0088] The RT-VCM used in the present invention has the advantages of small size and good control performance. Based on the performance advantages of the RT-VCM, the response speed and steady-state accuracy requirements of the parallel mirror interferometer are met.

[0089] The cerebellar model neural network controller (CMAC) employed in this invention stores information in a local structure, reducing weight corrections in the output layer and accelerating learning. CMAC outperforms most neural networks in nonlinear approximation and avoids the local minima problem inherent in neural network algorithms. This makes it superior to traditional models in nonlinear real-time control under complex dynamic conditions.

[0090] This invention introduces an inertia factor into the weight calibration process to reduce weight perturbations. In CMAC, the inertia factor controls the weight update rate. A larger inertia factor slows down weight updates and provides a smoother response to system changes. A smaller inertia factor results in faster weight updates and a faster response to system changes.

[0091] The present invention combines PID with CMAC, enabling controller parameters to adjust based on system changes, thus optimizing system control performance. This invention incorporates CMAC into the PID controller for system identification. By leveraging CMAC's self-learning capabilities, PID parameters can adapt to system changes, achieving improved control performance and optimizing the controller's anti-interference performance and robustness.

[0092] The present invention solves the technical problems in the prior art that the spectral signal-to-noise ratio obtained by inversion is affected by the stability of the optical path difference (OPD) speed, and the existence of time-varying interference leads to low control accuracy and poor control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 Schematic diagram of the basic steps of the control method of the parallel rotating mirror interferometer system provided in Example 1 of the present invention;

[0094] Figure 2 Schematic diagram of the parallel mirror interferometer system components of Example 1 of the present invention;

[0095] Figure 3 Schematic diagram of the electrical model of the RT-VCM under ideal conditions according to Example 1 of the present invention;

[0096] Figure 4 Schematic diagram of the driving force of the voice coil motor according to embodiment 1 of the present invention;

[0097] Figure 5 This is a schematic diagram of the structure of a voice coil motor driven rotating platform according to Example 1 of the present invention;

[0098] Figure 6 This is a system driving diagram of the parallel mirror interferometer according to Example 1 of the present invention;

[0099] Figure 7 This is a schematic diagram of the nonlinear quantized CMAC network structure of Example 1 of the present invention;

[0100] Figure 8 This is a block diagram of the CMAC-PID composite control according to embodiment 1 of the present invention;

[0101] Figure 9a This is a schematic diagram of the optical path difference speed tracking effect of the PID controller of Example 2 of the present invention;

[0102] Figure 9b This is a schematic diagram of the optical path difference speed tracking effect of the CMAC-PID controller of Example 2 of the present invention;

[0103] Figure 10a This is a graph showing the optical path difference speed tracking curve of the PID controller according to Example 2 of the present invention;

[0104] Figure 10bThis is a CMAC-PID controller optical path difference speed tracking curve diagram of Example 2 of the present invention. DETAILED DESCRIPTION

[0105] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0106] Example 1

[0107] like Figure 1 As shown, the control method of the parallel rotating mirror interferometer system provided by the present invention includes the following basic steps:

[0108] S1. Analyze the relationship between the angular velocity of the rotary voice coil motor and the optical path difference velocity, and establish a mathematical model of the parallel rotating mirror interferometer;

[0109] like Figure 2 As shown in the figure, in this embodiment, the parallel mirror interferometer system includes: a voice coil motor (VCM), a rotating platform with a flexible pivot, an interferometer, a detector, a controller, a power driver, and a reference laser. The system uses a rotating VCM to drive the rotating platform, thereby changing the optical path difference and generating Michelson interference. In order to improve the signal-to-noise ratio of the Fourier transform spectroscopy (FTS) interferometer, it is necessary to achieve a stable optical path difference velocity (OPDV) in the interferometer system

[20] . In the parallel mirror interferometer system, the optical path difference velocity is controlled by the rotation speed of the VCM.

[0110] In the process of analyzing the relationship between the optical path difference speed and the voice coil motor speed in this embodiment, see Figure 1 , two parallel mirrors are fixed on the same rotating platform, and the two mirrors rotate simultaneously under the action of a bearing. The beam splitter is mounted on a fixed platform. The light incident at a 45° angle is split into two beams by the beam splitter. The reflected and transmitted light beams are reflected on the surface of the parallel mirror and return to the beam splitter along the original optical path, and finally converge on the detector. When the two mirrors rotate, an optical path difference (OPD) is introduced between the two beams on the detector, resulting in optical interference. The magnitude of the optical path difference is given by the following formula:

[0111]

[0112] Where ω is the angular velocity of the voice coil motor, R is the distance between the parallel mirrors, and t is the time within the motion cycle.

[0113] In this embodiment, a derivative operation is performed on time t to obtain an optical path difference velocity (OPDV) function:

[0114]

[0115] in,

[0116] α1=sin(π / 4-ωt)

[0117] α2=sin(π / 4+ωt)

[0118] β1=cos(2ωt)

[0119] β2=sin(2ωt)

[0120] ρ1=cos(π / 4+ωt)

[0121] ρ2=cos(π / 4-ωt)

[0122] In this embodiment, since the rotation angle is very small, that is, ωt approaches zero, the above equation (2) can be simplified to:

[0123] OPDV≈4R*ω / sin(π / 4+ωt) (3)

[0124] In this embodiment, according to the aforementioned formula (3), the motor angular velocity and the optical path difference velocity have a time-varying relationship. In this embodiment, for a given fixed optical path difference velocity, the system needs to achieve a time-varying motor angular velocity. Therefore, this nonlinear coupling effect between the optical path difference velocity and the RT-VCM angular velocity is considered a nonlinear perturbation of the interferometer system.

[0125] In the interferometer system modeling and operation described in this example, the RT-VCM is a key component of the parallel rotating mirror interferometer system, and its performance directly impacts spectral quality. Compared to stepper motors, the RT-VCM offers advantages such as compact size and excellent controllability. Based on these advantages, we selected the RT-VCM as the interferometer system's driver to meet the system's requirements for response speed and steady-state accuracy.

[0126] like Figure 3 As shown, in this embodiment, by considering the relationship between voltage and back electromotive force, a dynamic voltage balance equation can be derived, as shown in equation (4).

[0127]

[0128] Where u(t) is the armature voltage, i(t) is the coil current, R is the total resistance of the coil, L is the coil inductance, Ea is the back electromotive force generated by the coil winding under the action of the electromagnetic force, B is the magnetic field strength, l is the effective length of the RT-VCM coil, v is the angular velocity of the motor rotor, and Ke is the motor torque coefficient.

[0129] like Figure 4 As shown, in this embodiment, the dynamic force balance equation of RT-VCM is:

[0130]

[0131] Among them, N is the number of turns of the coil, and Km=NBl is the electromagnetic force coefficient.

[0132] like Figure 5 As shown, in this embodiment, the connection mechanism between the voice coil motor and the rotating platform uses a bearing. In this embodiment, the bearing connection is used to reduce friction. The charged coil is placed in a constant magnetic field generated by two permanent magnets. This generates an Ampere force on both sides, causing the rotating platform to rotate about its axis.

[0133] See also Figure 5 , the torque balance equation can be expressed as formula (6).

[0134]

[0135] Where r is the distance between the coil and the center of rotation, m(t) is the bearing friction torque, J is the moment of inertia of the rotating platform, and w(t) is the angular velocity

[0136] Since the speed of the RT-VCM is low, the back EMF Ea can be ignored, resulting in a very small back EMF. By using the Laplace transform, the time domain expressions of the above equations (4), (5) and (6) are converted into s-domain expressions, as shown in equation (7).

[0137]

[0138] therefore, Figure 6 The system drive diagram of the parallel rotating mirror interferometer is shown.

[0139] In this embodiment, if friction is regarded as an external nonlinear interference of the system and the external nonlinear interference is not considered when modeling the system, the open-loop transfer function of the system can be obtained, such as formula (8):

[0140] (8)

[0142] S2. In order to suppress the disturbance of the nonlinear factors of the system model, the CMAC-PID composite control strategy is used to control the parallel rotating mirror interferometer;

[0143] In this embodiment, the CMAC algorithm of the CMAC-PID composite control strategy uses a cerebellar model neural network controller (CMAC), a local approximation neural network. CMAC stores information in a local structure, reducing weight corrections in the output layer and accelerating learning. CMAC outperforms most neural networks in nonlinear approximation and avoids the local minima problem inherent in neural network algorithms. This makes CMAC highly effective for nonlinear real-time control in complex dynamic situations.

[0144] In this embodiment, the CMAC network structure includes, but is not limited to, partitioning the input space, implementing a nonlinear mapping from the input layer to the output layer, and implementing a weight learning algorithm in the output layer. In this embodiment, the two nonlinear relationships between input and output are implemented using two basic mappings: a U→AC nonlinear mapping and an AC→AP linear mapping.

[0145] like Figure 7 As shown, in this embodiment, U represents the input space, S represents the quantization space, AC represents the storage space, aj represents the activation state of the j-th storage unit, AP represents the storage weight space, and ωj represents the weight of the j-th storage unit. In this embodiment, if aj=1, the j-th storage unit is activated.

[0146] See also Figure 7 N is the parameter representing the number of network layers. Increasing the number of network layers can improve the richness and complexity of input features, but it also increases computational and storage complexity. The number of network layers should be adjusted based on the complexity of the problem and the importance of the input features.

[0147] Similarly, C is also a parameter called the generalization parameter. A larger generalization parameter can make the output of CMAC smoother, but may lose details. A smaller generalization parameter will approximate the input-output mapping more accurately, but may lead to unstable output.

[0148] In this embodiment, assuming that the input signal is u(t), the input signal U is quantized by a nonlinear function to obtain a quantized signal S. In this embodiment, the nonlinear function includes but is not limited to:

[0149] Signed power function:

[0150]

[0151] Signed Gaussian function:

[0152]

[0153] In this embodiment, the quantization space S is divided into N+2C quantization intervals, and the interval is [Smin, Smax], as shown in formula (9):

[0154]

[0155] In this embodiment, the activation state of the AC unit can be expressed using the following formula (10):

[0156]

[0157] In this embodiment, when the input variable Ui is nonlinearly quantized and converted to Si, the C units in the storage space AC are activated and multiplied with the weights in the storage AP to obtain the output of the network, as shown in formula (11);

[0158]

[0159] Among them, u n (k) represents the output generated by CMAC.

[0160] In this embodiment, after each control cycle is completed, the corresponding output value y(t) is calculated and compared with the reference signal r(t). Then, a supervised delta learning algorithm is used to adjust the weight value and start the learning process. The weight update process is shown in formula (12):

[0161]

[0162] Among them, η∈(0,1) represents the learning rate of the network.

[0163] In this embodiment, the magnitude of CMAC weight adjustments is determined by the learning rate η. A faster learning rate enables CMAC to adapt to system changes more quickly, but may also cause weight oscillation or instability. A slower learning rate delays weight adjustments but improves stability. The chosen learning rate should strike a balance between flexibility and stability.

[0164] In this embodiment, an inertia factor is introduced into the weight correction process to reduce weight disturbances. In CMAC, the inertia factor controls the update rate of the weights. A larger inertia factor will slow down the weight update and provide a smoother response to system changes. A smaller inertia factor will result in faster weight updates and a faster response to system changes. The method for adjusting the inertia factor on the weight value is shown in formula (13):

[0165]

[0166] Among them, α∈(0,1) represents the inertia factor.

[0167] In this embodiment, CMAC is introduced into the PID controller for system identification. By utilizing the self-learning ability of CMAC, the PID parameters can adapt to system changes, thereby achieving improved control effects.

[0168] like Figure 8 As shown, in this embodiment, the PID output and CMAC output are expressed by formula (14) and formula (15) respectively:

[0169]

[0170] where e(t) is the difference between the reference signal and the system output. p is the proportionality coefficient, T i is the integration time, T d is the differential time, a i is the binary selection vector, and w is the weight value of CMAC.

[0171] In this embodiment, the overall output of the CMAC-PID composite controller is expressed by formula (16).

[0172] u(k)=u n (k)+u p (k) (16)

[0173] In this embodiment, the updating and adjustment process of the weight value ω is as follows, which can be expressed by formula (17):

[0174]

[0175] When the system is initialized, the weight parameter w is set to 0. Therefore, u n is 0, and u takes u p Initially, the system is controlled by a traditional PID controller. Through the self-learning process of CMAC, the output u generated by the PID controller is p gradually approaches 0, and the output u of CMAC n Gradually converge to the entire system output u. This enables the CMAC network to identify the system model and use system information to optimize the control method.

[0176] Example 2

[0177] In this embodiment, a simulation experiment is conducted on the CMAC-PID composite control strategy.

[0178] To test the robustness and transient response of the CMAC-PID algorithm on a parallel mirror interferometer system, the system parameters were set to their actual values ​​and the control algorithm was simulated in the MATLAB / Simulink environment. The specific parameters are shown in Table 1.

[0179] Table 1. Interferometer system parameters

[0180] parameters Value N 200 B 0.5T L 0.001H l 0.01m R 20Ω r 0.1m J <![CDATA[0.05kg·m 2 ]]>

[0181] According to the given parameters and the mathematical model of the interferometer system, the open-loop transfer function of the interferometer system can be derived as shown in formula (18).

[0182]

[0183] The open-loop transfer function of the system given by formula (18) is converted into its discrete form through z-transformation to obtain the discrete function shown in formula (19).

[0184]

[0185] The control system is implemented in Matlab / Simulink environment, where Equation (19) is used as the system model. Two controllers, namely CMAC and PID, are implemented using M functions.

[0186] PID and CMAC-PID control strategies were simulated under various conditions to evaluate the effectiveness of the CMAC-PID controller (step response, square wave response with time-varying disturbances). First, the steady-state and dynamic characteristics of each controller were compared, and the controller performance was confirmed by evaluating the step response of each controller. Time-varying disturbances from an interferometer system were added to these controllers (PID and CMAC-PID) to test and evaluate the disturbance rejection and robustness of each controller, validating the superiority of the CMAC-PID controller.

[0187] In this embodiment, the step response is shown in Table 2 and Table 3 below. Table 2 and Table 3 respectively show the parameters of the PID controller and the CMAC-PID controller:

[0188] Table 2. PID parameters

[0189] parameters Value <![CDATA[K p ]]> 10 <![CDATA[K i ]]> 0.3 <![CDATA[K d ]]> 0

[0190] Table 3. CMAC-PID parameters

[0191]

[0192]

[0193] like Figure 9a and9b As shown, in this embodiment, a step response simulation of each controller is performed in MATLAB / Simulink.

[0194] according to Figure 9a and 9b The simulation results, rise time, overshoot, and steady-state values ​​of the calculated system are shown in Table 4. It can be seen from Table 4 that in the absence of time-varying disturbances, the step response results of the PID and CMAC-PID controllers are close, and both have good control performance.

[0195] Table 4. Step response results

[0196] Controller Rise time Overshoot Steady-state value PID 0.0432 0 1.00001 CMAC-PID 0.044 0 1.0001

[0197] Square wave response with time-varying disturbance

[0198] In this embodiment, internal interference is unavoidable within the parallel rotating mirror interferometer, primarily due to the nonlinear coupling between the optical path difference velocity and the motor angular velocity during the RT-VCM motion. In addition to internal interference, there is also external interference, primarily due to friction and other interferences that were ignored in the theoretical derivation. These interferences are time-varying functions that change with the continuous motion of the RT-VCM. According to formula (3), the time-varying function f(t) corresponding to the total interference can be assumed as follows:

[0199] f(t)=0.2sin(2πt) (20)

[0200] like Figure 10a and Figure 10b As shown, in this embodiment, while keeping the parameters of PID and CMAC-PID controllers unchanged, a time-varying disturbance function is added to the parallel rotating mirror system and simulated in MATLAB / Simulink.

[0201] Figure 10a and Figure 10b The simulation results in show that the rise time and overshoot are essentially the same. Due to the presence of nonlinear interference, the steady-state value of the system is constantly changing, especially the steady-state value output of the PID controller has changed significantly. To evaluate the anti-interference capability, the steady-state fluctuation error is introduced to analyze the robustness of the controller. The steady-state fluctuation calculation method is shown in formula (21):

[0202] SSF=∑|y out -y ideal | (21)

[0203] According to formula (21), the steady-state fluctuation error of the system is calculated, as shown in Table 5:

[0204] Table 5. Square wave response with time-varying disturbance

[0205]

[0206]

[0207] As shown in Table 5, after adding nonlinear perturbations to the system, the steady-state fluctuation error of the CMAC-PID is much smaller than that of the PID controller, reducing it by 90.1%. This effectively suppresses time-varying disturbances and improves the robustness of the system. In this example, a modeling and simulation study of a type of parallel rotating mirror interferometer was conducted. The simulation results show that compared with the PID controller, the steady-state fluctuation error of the CMAC-PID is reduced by 90.1%, successfully suppressing time-varying disturbances. This modeling and simulation study enhances our understanding of parallel rotating mirror interferometer systems and can provide a reference for optimizing the design of interferometer scanning control systems.

[0208] In summary, this paper presents a control strategy for a parallel-mirror interferometer based on CMAC-PID composite control. The effectiveness of this controller has been verified through simulation, achieving high-performance control of the parallel-mirror interferometer system. This paper analyzes the relationship between the optical path velocity difference and the angular position of the voice coil motor and establishes a mathematical model of the parallel-mirror interferometer motion system. Based on this model, we designed a CMAC-PID composite controller and developed a real-time control model for the voice coil motor (RT-VCM) in MATLAB. Finally, simulation analysis verified the effectiveness of the CMAC-PID control strategy.

[0209] In the parallel mirror interferometer system of the present invention, the optical path difference velocity is controlled by the rotation speed of the VCM. The present invention realizes a stable optical path difference velocity OPDV in the interferometer system and improves the signal-to-noise ratio of the Fourier transform spectroscopy FTS interferometer.

[0210] The RT-VCM used in the present invention has the advantages of small size and good control performance. Based on the performance advantages of the RT-VCM, the response speed and steady-state accuracy requirements of the parallel mirror interferometer are met.

[0211] The cerebellar model neural network controller (CMAC) employed in this invention stores information in a local structure, reducing weight corrections in the output layer and accelerating learning. CMAC outperforms most neural networks in nonlinear approximation and avoids the local minima problem inherent in neural network algorithms. This makes it superior to traditional models in nonlinear real-time control under complex dynamic conditions.

[0212] This invention introduces an inertia factor into the weight calibration process to reduce weight perturbations. In CMAC, the inertia factor controls the weight update rate. A larger inertia factor slows down weight updates and provides a smoother response to system changes. A smaller inertia factor results in faster weight updates and a faster response to system changes.

[0213] The present invention combines PID with CMAC, enabling controller parameters to adjust based on system changes, thus optimizing system control performance. This invention incorporates CMAC into the PID controller for system identification. By leveraging CMAC's self-learning capabilities, PID parameters can adapt to system changes, achieving improved control performance and optimizing the controller's anti-interference performance and robustness.

[0214] The present invention solves the technical problems in the prior art that the spectral signal-to-noise ratio obtained by inversion is affected by the stability of the optical path difference (OPD) speed, and the existence of time-varying interference leads to low control accuracy and poor control performance.

[0215] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for controlling a parallel rotating mirror interferometer system, characterized in that: The method comprises: S1. Analyze the relationship between the angular velocity of the voice coil motor and the optical path difference speed, and establish a mathematical model of a parallel rotating mirror interferometer based on the relationship. During the operation of the parallel mirror rotating, determine the optical path difference OPD between the reflected light beam and the projected light beam on the detector to generate the optical interference, and obtain an optical path difference speed OPDV function to determine the relationship between the optical path difference speed and the speed of the voice coil motor. Obtain a dynamic voltage balance equation, a dynamic force balance equation, and a torque balance equation of the parallel rotating mirror interferometer to obtain an open-loop transfer function of the parallel rotating mirror interferometer and establish a mathematical model of the interferometer. S2. Using a CMAC-PID composite control strategy to control a parallel rotating mirror interferometer to suppress nonlinear disturbances in the interferometer mathematical model, wherein the cerebellum model neural network controller (CMAC) in the CMAC-PID composite control strategy includes: an input space segmentation component, a nonlinear mapping component from the input layer to the output layer, and a weight learning component in the output layer; In the input space segmentation component and the input layer to output layer nonlinear mapping component, nonlinear mapping and linear mapping are used to realize the nonlinear relationship between input and output, thereby increasing the number of network layers and generalization parameters of the cerebellum model neural network controller CMAC: By utilizing the weight learning component in the output layer, a corresponding output value y(t) is obtained when each control cycle of the parallel rotating mirror interferometer is completed, and the corresponding output value y(t) is compared with the reference signal r(t). The weight value is updated according to the learning rate η using a supervised δ learning algorithm to perform weight learning. The cerebellar model neural network controller CMAC is used for self-learning, and the PID controller is used to adjust the PID parameters to obtain an overall output control signal to control the parallel rotating mirror interferometer.

2. The parallel rotating mirror interferometer system control method according to claim 1, characterized in that: The parallel mirror interferometer in step S1 includes: a voice coil motor (VCM), a rotating platform with a flexible pivot, an interferometer, a detector, a controller, a power driver, a reference laser, a parallel mirror, and a beam splitter. The voice coil motor (VCM) is rotated to drive the rotating platform to adjust the optical path difference and generate optical interference, and the optical path difference speed is controlled by adjusting the rotation speed of the voice coil motor (VCM); Fixing at least two parallel mirrors on the same rotating platform, wherein the rotating platform drives the parallel mirrors to rotate simultaneously via bearings; The beam splitter is installed on a pre-set fixed platform so that light incident at a specific angle is split by the beam splitter into a reflected light beam and a projected light beam. The reflected light beam and the transmitted light beam are reflected by the parallel mirror and return to the beam splitter along the original optical path and converge on the detector.

3. The parallel rotating mirror interferometer system control method according to claim 2, characterized in that: During the operation of the parallel mirror rotation, the optical path difference OPD between the reflected light beam and the projected light beam on the detector is determined using the following logic to generate the optical interference, wherein the optical interference includes: Michelson interference: Where ω is the angular velocity of the voice coil motor, R is the distance between the parallel mirrors, and t is the time within the motion cycle.

4. The parallel rotating mirror interferometer system control method according to claim 1, characterized in that: In step S1, the following logic is used to perform a derivative operation on the time t within the motion cycle of the parallel rotating mirror interferometer to obtain the optical path difference velocity OPDV function: in, α1=sin(π / 4-ωt) α2=sin(π / 4+ωt) β1=cos(2ωt) β2=sin(2ωt) ρ1=cos(π / 4+ωt) ρ2=cos(π / 4-ωt) Simplifying equation (2), we can obtain the simplified optical path difference velocity OPDV function: OPDV≈4R*ω / sin(π / 4+ωt) (3) According to the simplified optical path difference velocity OPDV function, the relationship between the optical path difference velocity and the speed of the voice coil motor is determined.

5. The parallel rotating mirror interferometer system control method according to claim 2, characterized in that: The voice coil motor VCM further comprises: a driving component RT-VCM; wherein the RT-VCM is a key component of the parallel rotating mirror interferometer system; Using the following logic, we analyze the relationship between voltage and back electromotive force and derive the dynamic voltage balance equation: Where u(t) is the armature voltage, i(t) is the coil current, R is the total resistance of the coil, L is the coil inductance, Ea is the back electromotive force generated by the coil winding under the action of the electromagnetic force, B is the magnetic field strength, l is the effective length of the RT-VCM coil, v is the angular velocity of the motor rotor, and Ke is the motor torque coefficient; The dynamic force balance equation of the driving component RT-VCM is expressed using the following logic: Where N is the number of turns of the coil, and Km=NBl is the electromagnetic force coefficient; The voice coil motor is connected to the rotating platform through a bearing, and the charged coil is placed in a constant magnetic field to generate an Ampere force to drive the rotating platform to rotate around the axis; The torque balance equation of the driving component RT-VCM is expressed using the following logic: Where r is the distance between the coil and the center of rotation, m(t) is the bearing friction torque, J is the moment of inertia of the rotating platform, and w(t) is the angular velocity; The following Laplace transform logic is used to transform the time domain expressions of the dynamic voltage balance equation (4), the dynamic force balance equation (5), and the torque balance equation (6) into s-domain expressions: The open-loop transfer function of the parallel rotating mirror interferometer is expressed using the following logic:

6. The parallel rotating mirror interferometer system control method according to claim 1, characterized in that: In step S2, a nonlinear relationship between input and output is realized by using nonlinear mapping and linear mapping, wherein the nonlinear mapping and the linear mapping are represented by the following logic: U→AC, AC→AP.

7. The parallel rotating mirror interferometer system control method according to claim 1, characterized in that: In step S2, assuming that the input signal is u(t), the input signal U of the parallel mirror interferometer is quantized by a nonlinear function using the following logic to obtain a quantization space S: Signed power function: Signed Gaussian function: The quantization space S is divided into N+2C sub-quantization intervals using the following logic:

8. The control method of the parallel rotating mirror interferometer system according to claim 1, wherein: The step S2 comprises: S21. Express the activation status of the storage space AC using the following logic: S22. When the input signal U is quantized into the quantization space S, the C units in the storage space AC are activated and multiplied by the weights in the storage weight space AP to obtain a CMAC network output: Where u n (k) represents the output generated by the cerebellum model neural network controller CMAC, U represents the input space, S represents the quantization space, AC represents the storage space, a j represents the activation state of the jth storage unit, AP represents the storage weight space, ω j Represents the weight of the j-th storage unit; S23. Utilizing the weight learning component in the output layer, upon completion of each control cycle of the parallel rotating mirror interferometer, obtain a corresponding output value y(t), compare it with a reference signal r(t), and update the weight value using a supervised delta learning algorithm according to a learning rate η to perform weighted learning. The weight value is updated using the following logic: Where η∈(0,1) represents the learning rate of the network.

9. The parallel rotating mirror interferometer system control method according to claim 1, characterized in that: The step S2 further includes: S21′, performing weight correction using the inertia factor of the cerebellum model neural network controller CMAC, wherein the inertia factor corrects the weight value using the following logic: Where, α∈(0,1) represents the inertia factor; S22', use the following logic to obtain the output u of the PID controller p (k), the output u of the cerebellar model neural network controller CMAC n (k): Where e(t) is the difference between the reference signal and the system output. p is the proportionality coefficient, T i is the integration time, T d is the differential time, a i is the binary selection vector, w is the weight value of CMAC; S23', using the following logic, obtain the overall output of the CMAC-PID composite controller: u(k)=u n (k)+u p (k) (16) S24', adjust and update the weight value ω using the following logic:

10. A parallel mirror interferometer system control system, characterized in that: The system comprises: An interferometer modeling module is used to analyze the relationship between the angular velocity of the voice coil motor and the optical path difference speed, thereby establishing a mathematical model of a parallel rotating mirror interferometer. During the operation of rotating the parallel mirror, the optical path difference OPD between the reflected light beam and the projected light beam on the detector is determined to generate the optical interference, and an optical path difference speed OPDV function is obtained to determine the relationship between the optical path difference speed and the speed of the voice coil motor. The dynamic voltage balance equation, dynamic force balance equation, and torque balance equation of the parallel rotating mirror interferometer are obtained to obtain the open-loop transfer function of the parallel rotating mirror interferometer to establish the interferometer mathematical model. An interferometer control module is used to control a parallel rotating mirror interferometer using a CMAC-PID composite control strategy to suppress nonlinear disturbances in the mathematical model, wherein the cerebellum model neural network controller (CMAC) in the CMAC-PID composite control strategy includes: an input space segmentation component, an input layer to output layer nonlinear mapping component, and an output layer weight learning component. The interferometer control module is connected to the interferometer modeling module; The input space segmentation component and the input layer to output layer nonlinear mapping component are used to realize the nonlinear relationship between input and output by using nonlinear mapping and linear mapping, increase the number of network layers and generalization parameters of the cerebellar model neural network controller CMAC, and the input space segmentation component is connected to the input layer to output layer nonlinear mapping component: The weight learning component in the output layer is used to obtain the corresponding output value y(t) when each control cycle of the parallel rotating mirror interferometer is completed, to compare it with the reference signal r(t), to update the weight value according to the learning rate η using the supervised δ learning algorithm to perform weight learning, to perform self-learning using the cerebellar model neural network controller CMAC, and to adjust the PID parameters using the PID controller to obtain the overall output control signal to control the parallel rotating mirror interferometer. The weight learning component in the output layer is connected to the input layer to output layer nonlinear mapping component.

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