Resonant fiber-optic gyroscope frequency locking method based on active disturbance rejection control

Abstract

The invention discloses a resonant fiber-optic gyroscope frequency locking method based on active-disturbance-rejection control, which comprises the following steps: firstly, establishing a mathematical model of output signals of a resonant fiber-optic gyroscope according to the working principle of the resonant fiber-optic gyroscope, and then establishing an active-disturbance-rejection controller structure model suitable for the resonant fiber-optic gyroscope; and finally, building a complete simulation system model in Simulink, and setting partial parameters in the active disturbance rejection controller, thereby obtaining the optimal control effect of the system. Compared with an existing PI control frequency locking method, the active-disturbance-rejection control method has the advantages that the same frequency locking time and gyroscope dynamic range can be obtained, the contradiction between overtonality and rapidity existing in traditional PI control can be balanced, a better tracking effect and angular velocity detection precision can be achieved, and a further thought can be provided for engineering application.

Description

Technical Field

[0001] The present invention belongs to the technical field of fiber optic gyroscopes, and in particular relates to a resonant fiber optic gyroscope frequency locking method based on active anti-disturbance control. Background Art

[0002] A resonant fiber gyroscope (RFG) is a high-precision inertial sensor device that uses the Saganc effect to detect angular velocity. Its core sensor is a fiber ring resonator (FNR). Light waves propagate in clockwise and counterclockwise directions within the FNR. The angular velocity of a RFG is reflected as the resonant frequency difference between the two beams of light propagating in opposite directions. Because the resonant frequency difference is a weak signal and difficult to detect directly, the center frequency of the laser's output light waves is locked to the resonant frequency of one of the beams. The output signal of the other beam reflects the resonant frequency difference between the two beams, thereby enabling the gyroscope's angular velocity to be detected.

[0003] Currently, the frequency tracking and locking methods commonly used in frequency-locked servo loops include PI control and PID control. These use a linear control method for the error signal, which has problems such as slow adjustment, large steady-state error, and a contradiction between overshoot and rapidity. In addition, the differential link will introduce redundant high-frequency noise into the optical path. Summary of the Invention

[0004] In response to the problems existing in the prior art, the present invention provides a frequency locking method for a resonant fiber optic gyroscope based on active disturbance rejection control. According to the working principle of the resonant fiber optic gyroscope, a mathematical model of the resonant fiber optic gyroscope is established; an active disturbance rejection controller is introduced into the frequency locking servo loop. Since the active disturbance rejection controller does not need to know the accurate system model, it can adapt to complex nonlinear systems and uncertain environments, expand all internal and external uncertainties of the system into a new state quantity, and estimate the internal state and uncertain factors of the system through input and output information. When applied to a nonlinear gyroscope system, better control effect can be achieved; a corresponding simulation model is established in Simulink, and parameter tuning is performed to obtain an optimal control effect, thereby improving the tracking capability and locking accuracy of the gyroscope angular velocity detection.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A frequency locking method for a resonant fiber optic gyroscope based on active disturbance rejection control comprises the following steps:

[0007] Step 1: Based on the working principle of the resonant fiber gyroscope, a mathematical model of the output signal of the resonant fiber gyroscope is established;

[0008] Step 2: Based on the mathematical model of the resonant fiber gyroscope output signal established in step 1, establish an active disturbance rejection controller structure model suitable for the resonant fiber gyroscope;

[0009] Step 3: Based on the mathematical model of the resonant fiber gyroscope output signal established in step 1 and the active disturbance rejection control structure model suitable for the resonant fiber gyroscope established in step 2, build a complete simulation system model in Simulink and adjust the parameters in step 2 to obtain the optimal control effect of the active disturbance rejection controller.

[0010] Furthermore, the output signal of the resonant fiber gyroscope in step 1 is expressed as:

[0011]

[0012] Where c is the speed of light in vacuum, ε0 is the dielectric constant of vacuum, R v is the responsivity of the photodetector 1, α PM is the insertion loss of phase modulator 1, E0 is the output light field of the laser, J n is the Bessel expansion coefficient, h n is the transfer function of the resonant cavity output amplitude.

[0013] Furthermore, in step 2, the active disturbance rejection controller structure model applicable to the resonant fiber optic gyroscope includes an extended state observer and a nonlinear state error feedback control law; the output V of the lock-in amplifier 1 LIA The system output is input into the extended state observer to obtain the discrete expressions of the observation value z1 of the demodulated signal, the observation value z2 of the differential of the demodulated signal and the total disturbance z3 of the system; the nonlinear state error feedback control law combines the error -z1 and the error differential -z2 into a nonlinear PD controller, and feeds back the total disturbance z3 of the system to the control quantity u0, thereby obtaining the actual control quantity u of the laser voltage tuning, and feeding it back to the laser end to realize the tracking and locking of the laser center frequency to the resonant frequency of the counterclockwise optical path.

[0014] Furthermore, the discrete form of the extended state observer is expressed as follows:

[0015]

[0016] Where z1 is the observed value of the demodulated signal, z2 is the observed value of the differential of the demodulated signal, z3 is the total disturbance of the system, h is the integration step size, β1, β2, and β3 are the correction gains of the extended state observer, fal(·) is a continuous power function, α1 and α2 are tracking factors, b0 is the compensation factor, u is the control variable of the system, and δ is the limit for distinguishing the size of the error ε;

[0017] The discrete form of the nonlinear state error feedback control law is expressed as follows:

[0018] u0(k)=kp fal(-z1(k),α1,δ)+k d fal(-z2(k),α2,δ)

[0019] Among them, k p is the proportional adjustment coefficient, k d is the differential adjustment coefficient;

[0020] The actual control quantity u of laser voltage tuning is expressed as follows:

[0021] u(k)=u0(k)-z3(k) / b0.

[0022] Furthermore, the resonant fiber gyroscope frequency locking method based on active disturbance rejection control is implemented based on a resonant fiber gyroscope system using an active disturbance rejection controller, and the resonant fiber gyroscope system using an active disturbance rejection controller includes: a laser, an optical isolator, a splitter, a phase modulator 1, a phase modulator 2, a circulator 1, a circulator 2, a coupler, a fiber ring resonator, a photodetector 1, a photodetector 2, a lock-in amplifier 1, a lock-in amplifier 2, and an active disturbance rejection controller;

[0023] The laser, optical isolator and optical splitter are connected in sequence. The output end of the optical splitter is connected to phase modulator 1 and phase modulator 2 respectively. The output ends of phase modulator 1 and phase modulator 2 are connected to end 1 of circulator 1 and end 2 of circulator 2 respectively. Ends 2 of circulator 1 and end 2 of circulator 2 are connected to a coupler. The coupler is connected to a fiber ring resonator. End 3 of circulator 1 is connected to photodetector 2 and lock-in amplifier 2 in sequence. End 3 of circulator 2 is connected to photodetector 1, lock-in amplifier 1 and active interference rejection controller in sequence. Active interference rejection controller outputs control signal to the laser.

[0024] Furthermore, the active disturbance rejection controller includes an extended state observer and a nonlinear state error feedback control law.

[0025] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0026] This invention applies an active disturbance rejection control method, more suitable for nonlinear systems, to the frequency-locked servo loop of a resonant fiber-optic gyroscope (FOG). This method improves the tracking capability and frequency-locking accuracy of the gyro's angular velocity detection, providing a reference for its application in engineering. Compared with existing PI control frequency-locking methods, it achieves the same frequency-locking time and gyro dynamic range, balances the overshoot and rapidity inherent in traditional PI control, and achieves better tracking and angular velocity detection accuracy, providing further insights for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1This is a structural diagram of the resonant fiber optic gyroscope system based on active disturbance rejection control provided by the present invention.

[0028] Figure 2 Schematic diagram of the normalized demodulation curve of the resonant fiber gyroscope output.

[0029] Figure 3 The present invention discloses an active disturbance rejection controller structure suitable for a resonant fiber optic gyroscope system.

[0030] Figure 4 This is a schematic diagram of the gyro locking process using the active disturbance rejection control frequency locking method of the present invention. DETAILED DESCRIPTION

[0031] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0032] like Figure 1 The figure shows the system architecture of a resonant fiber gyroscope using the active disturbance rejection control frequency locking method. The structure includes: a laser, an optical isolator, a splitter, phase modulator 1, phase modulator 2, circulator 1, circulator 2, a coupler, a fiber ring resonator, photodetector 1, photodetector 2, lock-in amplifier 1, lock-in amplifier 2, and an active disturbance rejection controller. Laser light from a tunable semiconductor laser is first input to the splitter through the optical isolator, where it is split into two beams of equal intensity and frequency. These two beams are then transmitted to phase modulator 1 and phase modulator 2, respectively, where they are modulated by sinusoidal waves and transmitted to circulator 1 and circulator 2, respectively. These beams then pass through the circulator's input port 1 and output port 2, respectively, and are then transmitted to the coupler. After this, they travel around the fiber ring resonator in both clockwise and counterclockwise directions. They are then transmitted by the coupler to circulator 2 and circulator 1, respectively. The light beam transmitted in the counterclockwise direction is input from the 2nd end and output from the 3rd end of the circulator 2, and is converted into an electrical signal by the photodetector 1, and input into the phase-locked amplifier 1 for signal demodulation, low-pass filtering and signal amplification. The obtained voltage signal is transmitted to the active interference rejection controller to obtain a control signal, and is input into the laser for frequency tuning of the laser, thereby locking the center frequency of the laser to the resonant frequency point of the counterclockwise light wave; the light beam transmitted in the clockwise direction is input from the 2nd end and output from the 3rd end of the circulator 1, and is converted into an electrical signal by the photodetector 2, and input into the phase-locked amplifier 2 for signal demodulation, low-pass filtering and signal amplification. The obtained voltage output can represent the resonant frequency difference between the two light waves transmitted clockwise and counterclockwise in the fiber ring resonator, and thus represent the angular velocity output of the gyroscope.

[0033] For example Figure 1 The system shown in FIG. 1 is a resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control provided by the present invention, which specifically includes the following steps:

[0034] Step 1: Based on the working principle of the resonant fiber gyroscope, a mathematical model of the resonant fiber gyroscope system is established.

[0035] Assume that the laser output light field is E0 and the initial phase of the light field is The center frequency of the laser is f0, and the insertion loss of phase modulator 1 is α PM , the sine wave modulation frequency is f1, then the counterclockwise light field output by the fiber ring resonator can be expressed as:

[0036]

[0037] Among them, J n (M) is the Bessel expansion coefficient, h n is the transfer function of the resonant cavity output amplitude, φ n is the transfer function of the resonant cavity output phase. n and φ n It can be expressed as follows:

[0038]

[0039] Where Δf is the resonant frequency difference, α C is the loss coefficient of the coupler, FSR is the free spectral width of the fiber ring resonator, ρ is the resonance depth of the resonance spectrum, T is the transmission coefficient of the through-end of the fiber ring resonator, R is the transmission coefficient of the light wave after passing through the cross-end of the coupler and returning to the through-end, and Q is the transmission coefficient of the light wave after one cycle of transmission in the fiber ring resonator, which can be expressed as follows:

[0040]

[0041] Among them, κ C is the coupling coefficient of the coupler, α L It is the loss coefficient of light wave propagating one circle in the optical fiber ring resonator.

[0042] Assume that the responsivity of photodetector 1 is R v , the propagation speed of light in a vacuum is c, the dielectric constant of a vacuum is ε0, and the output voltage of the photodetector 1 is related to the optical power at the input end and the square of the optical wave field scalar. According to the time relationship, the output voltage of the photodetector 1 can be expressed as:

[0043]

[0044] Where n and n' are both positive integers, then according to the synchronous demodulation principle, the output of the phase-locked amplifier 1 and the output V of the photodetector 1 PD With the same frequency and phase, V PDThe first harmonic component is extracted from the output, and the remaining high-frequency components are filtered out by a low-pass filter. The output of the lock-in amplifier 1 is:

[0045]

[0046] The derivation process of the output of the phase-locked amplifier 2 after the clockwise light field is output is the same as above, thereby obtaining the mathematical model of the resonant fiber optic gyroscope system.

[0047] Step 2: Based on the mathematical model of the resonant fiber gyroscope output signal established in step 1, establish an active disturbance rejection controller structure model suitable for the resonant fiber gyroscope.

[0048] The normalized demodulation curve of the output of the lock-in amplifier 1 obtained by the mathematical model established in step 1 is as follows: Figure 2 As shown in the figure, the resonant frequency point is where the difference Δf = 0 between the laser center frequency and the fiber ring resonator resonant frequency, and the demodulation curve is zero at this point. Furthermore, the demodulation curve exhibits a linear variation range within a certain resonant frequency difference, representing the linear operating region of the resonant fiber gyroscope. By feeding the demodulation curve output as an error signal back into a frequency-locked servo loop formed by an active disturbance rejection controller, the laser center frequency can be locked at the resonant frequency point.

[0049] Active disturbance rejection controllers typically consist of a tracking differentiator, an extended state observer, and a nonlinear state error feedback control law. Their core principle is to achieve control by estimating and canceling system disturbances. They can offset both external and internal disturbances, thereby improving system stability and accuracy. They can quickly respond to system changes, reducing adjustment time and increasing system response speed. They do not require an accurate system model, exhibit good robustness, and are adaptable to complex nonlinear systems and uncertain environments.

[0050] Since the tracking differentiator usually takes the set value as input and arranges the transition output for the system, thus obtaining the tracking output and the tracking output differential. When the system is at the resonant frequency point, the demodulated output is zero, so the input set value of the tracking differentiator can be set to 0, thereby obtaining the tracking output and the tracking output differential to be 0. Therefore, in the active disturbance rejection controller suitable for the resonant fiber optic gyroscope system, the tracking differentiator structure can be omitted, thus obtaining the following Figure 3 The active disturbance rejection controller structure suitable for the resonant fiber optic gyroscope system shown in the figure mainly includes two parts: an extended state observer and a nonlinear state error feedback control law.

[0051] The extended state observer expands all the uncertain models and external disturbances of the system into new state variables, without the need for an accurate mathematical model of the system. LIAAs the system output and input to the extended state observer, the discrete expressions of the observation value z1 of the demodulated signal, the observation value z2 of the differential of the demodulated signal and the total disturbance z3 of the system are obtained:

[0052]

[0053] Where h is the integration step size, u is the control variable of the system, β1, β2, and β3 are the correction gains of the extended state observer, α1 and α2 are tracking factors, δ is the limit for distinguishing the size of the error ε, b0 is the compensation factor, and fal(·) is a continuous power function, which can be expressed as:

[0054]

[0055] The nonlinear state error feedback control law can effectively control the system error and suppress the uncertain disturbance in the system, thereby improving the efficiency of system information processing. The control law applied to the resonant fiber optic gyroscope can be expressed as:

[0056] u0(k)=k p fal(-z1(k),α1,δ)+k d fal(-z2(k),α2,δ)

[0057] Among them, the error -z1 and the error differential -z2 form a nonlinear PD controller, k p is the proportional adjustment coefficient, k d is the differential adjustment coefficient. In order to realize the disturbance compensation of the system, the total disturbance z3 of the system is fed back to the control quantity u0, thereby obtaining the actual control quantity u of the laser voltage tuning:

[0058] u(k)=u0(k)-z3(k) / b0

[0059] By feeding back the laser voltage tuning control value u to the laser end, the laser center frequency can be tracked and locked to the counterclockwise optical path resonant frequency.

[0060] Step 3: Based on the mathematical model of the resonant fiber gyroscope established in step 1 and the active disturbance rejection control structure model for the resonant fiber gyroscope established in step 2, build a complete simulation system model in Simulink and adjust the parameters β1, β2, β3, α1, α2, δ, b0, k in step 2. p and k d Tuning is performed to obtain the best control effect of the active disturbance rejection controller.

[0061] The gyro output of the phase-locked amplifier 2 is obtained as Figure 4As shown in the figure, compared with the existing PI control frequency locking method, the active disturbance rejection control method can obtain the same frequency locking time and gyro dynamic range, and can also balance the contradiction between overshoot and rapidity in traditional PI control, and can achieve better tracking effect and angular velocity detection accuracy, which can provide further ideas for engineering applications.

[0062] It should be noted that the above content merely illustrates the technical idea of ​​the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A frequency locking method for a resonant fiber optic gyroscope based on active disturbance rejection control, characterized in that: The steps include: Step 1: Based on the working principle of the resonant fiber gyroscope, a mathematical model of the output signal of the resonant fiber gyroscope is established; Step 2: Based on the mathematical model of the resonant fiber gyroscope output signal established in step 1, establish an active disturbance rejection controller structure model suitable for the resonant fiber gyroscope; Step 3: Based on the mathematical model of the resonant fiber gyroscope output signal established in step 1 and the active disturbance rejection control structure model suitable for the resonant fiber gyroscope established in step 2, build a complete simulation system model in Simulink and adjust the parameters in step 2 to obtain the optimal control effect of the active disturbance rejection controller.

2. The resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control according to claim 1, characterized in that: The output signal expression of the resonant fiber gyroscope in step 1 is: Where c is the speed of light in vacuum, ε0 is the dielectric constant of vacuum, R v is the responsivity of the photodetector 1, α PM is the insertion loss of phase modulator 1, E0 is the output light field of the laser, J n is the Bessel expansion coefficient, h n is the transfer function of the resonant cavity output amplitude.

3. The resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control according to claim 1, characterized in that: In step 2, the active disturbance rejection controller structure model suitable for the resonant fiber optic gyroscope includes an extended state observer and a nonlinear state error feedback control law; the output V of the phase-locked amplifier 1 LIA The system output is input into the extended state observer to obtain the discrete expressions of the observation value z1 of the demodulated signal, the observation value z2 of the differential of the demodulated signal and the total disturbance z3 of the system; the nonlinear state error feedback control law combines the error -z1 and the error differential -z2 into a nonlinear PD controller, and feeds back the total disturbance z3 of the system to the control quantity u0, thereby obtaining the actual control quantity u of the laser voltage tuning, and feeding it back to the laser end to realize the tracking and locking of the laser center frequency to the resonant frequency of the counterclockwise optical path.

4. The resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control according to claim 3, characterized in that: The discrete form of the extended state observer is expressed as follows: Where z1 is the observed value of the demodulated signal, z2 is the observed value of the differential of the demodulated signal, z3 is the total disturbance of the system, h is the integration step size, β1, β2, and β3 are the correction gains of the extended state observer, fal(·) is a continuous power function, α1 and α2 are tracking factors, b0 is the compensation factor, u is the control variable of the system, and δ is the limit for distinguishing the size of the error ε; The discrete form of the nonlinear state error feedback control law is expressed as follows: u0(k)=k p fal(-z1(k),α1,δ)+k d fal(-z2(k),α2,δ) Among them, k p is the proportional adjustment coefficient, k d is the differential adjustment coefficient; The actual control quantity u of laser voltage tuning is expressed as follows: u(k)=u0(k)-z3(k) / b0.

5. The resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control according to claim 1, characterized in that: The invention is realized based on a resonant fiber gyroscope system using an active disturbance rejection controller, wherein the resonant fiber gyroscope system using an active disturbance rejection controller comprises: a laser, an optical isolator, a splitter, a phase modulator 1, a phase modulator 2, a circulator 1, a circulator 2, a coupler, a fiber ring resonator, a photodetector 1, a photodetector 2, a lock-in amplifier 1, a lock-in amplifier 2 and an active disturbance rejection controller; The laser, optical isolator, and optical splitter are connected in sequence. The output end of the optical splitter is connected to the phase modulator 1 and the phase modulator 2 respectively. The output ends of the phase modulator 1 and the phase modulator 2 are connected to the 1 end of the circulator 1 and the 2 end of the circulator 1 and the circulator 2 respectively. The 2 ends of the circulator 1 and the circulator 2 are connected to the coupler, and the coupler is connected to the fiber ring resonator; the 3 ends of the circulator 1 are connected to the photodetector 2 and the phase-locked amplifier 2 in sequence. The 3 ends of the circulator 2 are connected to the photodetector 1, the phase-locked amplifier 1, and the active interference rejection controller in sequence. The active interference rejection controller outputs a control signal to the laser.

6. The resonant fiber optic gyroscope frequency locking method based on active disturbance rejection control according to claim 1, characterized in that: The active disturbance rejection controller includes an extended state observer and a nonlinear state error feedback control law.

Images