CN113074711B - Noise spectrum analysis and signal-to-noise ratio optimization method of fiber-optic gyroscope - Google Patents
Noise spectrum analysis and signal-to-noise ratio optimization method of fiber-optic gyroscope Download PDFInfo
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Abstract
The invention discloses a noise spectrum analysis and signal-to-noise ratio optimization method of a fiber-optic gyroscope, which comprises the following steps: firstly, demodulating by using a sine wave modulation technology to obtain a closed-loop error of a closed-loop fiber optic gyroscope system; step two, establishing a dynamic equation of the fiber-optic gyroscope by considering parameter uncertainty based on a closed-loop error model; step three, designing a feedback control matrix Kc of the closed-loop fiber-optic gyroscope system to ensure that the fiber-optic gyroscope has the required H ∞ On the premise of performance, the method meets the exponential stability under the conditions of uncertain parameters, nonlinearity and disturbance so as to optimize the linearity and the detection precision of the fiber-optic gyroscope system. The invention modulates the closed-loop error to high frequency to eliminate the influence of interference light intensity and stray light interference, considers nonlinear interference effect, light intensity fluctuation and inevitable noise, and establishes a dynamic model of the closed-loop fiber-optic gyroscope system. Then, a robust control algorithm is designed to optimize the performance of the fiber optic gyroscope system.
Description
Technical Field
The invention belongs to the field of analysis and optimization of a noise spectrum of a fiber-optic gyroscope, and relates to a performance optimization method of fiber-optic gyroscope closed-loop control by adopting sine wave modulation.
Background
Fiber optic gyroscopes currently play an important role in various fields such as inertial navigation, seismic surveillance and vehicle safety systems. In recent years, fiber optic gyroscopes have been considered to be one of the most promising technological directions in the field of inertial navigation, due to their advantages of high theoretical accuracy, small size and inherent immunity to electromagnetic interference. However, the optical weak signal of the fiber-optic gyroscope is susceptible to various noises and uncertainties of optical parameters, which poses a challenge to obtain a theoretically high-precision signal of the fiber-optic gyroscope.
The fiber optic gyroscope is an angular velocity measuring device based on the Sagnac effect, under the action of the Sagnac effect, the angular velocity of a fiber optic gyroscope system is converted into the change of resonant frequency of a resonant cavity, and frequency change information is extracted through a signal detection system so as to calculate the angular velocity of the system.
In the past decades, signal detection schemes for fiber optic gyroscopes have been studied much. Due to the nonlinear optical effect, the dynamic range and linearity of the fiber-optic gyroscope are difficult to improve. Closed loop detection techniques are used in fiber optic gyroscopes to meet the requirements of engineering practice. A feedback system is introduced into a fiber-optic gyroscope closed-loop detection system to improve the dynamic range. However, the interference light intensity is a weak signal containing a Sagnac phase, and a weak closed-loop error signal submerged by noise needs to be extracted with high precision, so that the noise level of the closed-loop fiber-optic gyroscope needs to be optimized so as to adapt to the application of the high-precision fiber-optic gyroscope in engineering practice. In particular, the closed-loop error signal is difficult to be accurately extracted due to the fluctuation of the optical power and the interference of stray light, so that the noise spectrum analysis and the signal-to-noise ratio optimization are very important for improving the detection precision of the fiber-optic gyroscope. It can be seen that how to analyze the noise spectrum of the closed-loop error and optimize the signal-to-noise ratio is an important issue for achieving high performance of the fiber-optic gyroscope.
Disclosure of Invention
In order to solve the technical problems, the invention provides a noise spectrum analysis and signal-to-noise ratio optimization method of a fiber-optic gyroscope, wherein a novel fiber-optic gyroscope closed-loop control method adopting a sine wave modulation technology is adopted to accurately extract closed-loop errors related to angular velocity and improve the detection precision and linearity of the fiber-optic gyroscope; firstly, the invention modulates the closed-loop error of the fiber-optic gyroscope into high frequency to eliminate the direct current component existing in the interference light intensity and irrelevant stray light, and transmits the modulated signal to the PSD and the demodulation filter, thereby improving the signal-to-noise ratio of the closed-loop fiber-optic gyroscope system. In addition, the invention designs a robust controller of the fiber-optic gyroscope system to ensure that the system has the specified H ∞ Mean square index stability of performance level. Finally, the effectiveness of the closed-loop control method adopting the sine wave modulation technology is proved through experimental results.
The invention provides a noise spectrum analysis and signal-to-noise ratio optimization method of a fiber-optic gyroscope, wherein a novel fiber-optic gyroscope closed-loop control method adopting a sine wave modulation technology is adopted, and a robust controller of a fiber-optic gyroscope system is designed: the method comprises the following specific steps:
firstly, the invention provides a sine wave modulation and demodulation method to accurately obtain a closed-loop error signal. Fig. 1 is a schematic diagram of the signal detection principle of the closed-loop fiber-optic gyroscope system of the present invention. The sine wave modulation technique includes modulating the signal, demodulating the signal, and low pass filtering. All the modules are realized by an FPGA chip, the modulation signal and the reference signal have the same frequency, and simultaneously, sinusoidal modulation is designed to inhibit 1/f noise of a circuit detection system and eliminate direct current components of interference light signals and irrelevant stray light. The modulation signal and the feedback signal are added together and applied to the integrated optical phase modulator through a D/a converter so that the low frequency closed loop error signal is passed through a sine wave to a high frequency. According to Jacobi-Anger, the detected signal is written as:
wherein, J n Representing an n-order Bessel function of the first kind (n =1,2,3 … …), R 1 Denotes the transimpedance of the photodetector, alpha denotes the optical path loss, I in Indicating the light intensity of the light source output, K D Representing the feedback path gain, and Δ x (t) represents the closed loop error signal. It can be seen that the modulated closed loop error signal ax (t) shifts to a frequency n ω 0 Wherein component J 1 (K D )sin(ω 0 Tk + - Δ x (k)) is in U p There is a maximum energy of the closed loop error signal in (t). Thus, the present invention can pass this frequency ω 0 The component extracts the closed loop error signal. Can be realized by converting a digital signal U in an FPGA digital system p (k) And a modulated signal k de cosω 0 Tk to obtain this closed loop error signal. Thus, there are:
where T is the sampling period, U d (k) Is a demodulated signal, k de Is the demodulation gain, k qd Is the gain, k, of the detector and preamplifier circuit ad Is the gain of the a/D converter. The component J can be seen in the present invention 1 (K D )sin(ω 0 t ± Δ x (k)) again to zero frequency. Other frequency components n ω 0 (n =1,2,3 … …) may be considered as an unwanted entry. The closed loop error signal is then obtained through a low pass filter. In the demodulation process, the designed low-pass filter is H (z) = H (0) + H (1) z -1 +…+h(m)z -m Where h (0), h (1) … h (m) are coefficients of a low pass filter, z = e jwT And T represents the sampling period of the A/D.
Since the system bandwidth of the fiber-optic gyroscope is expected to be 100Hz in practical application, in order to expand the closed-loop bandwidth as much as possible and simultaneously extract the closed-loop error accurately, the invention designs the FIR digital filter with the bandwidths of 32 orders and 1 kHz. The corresponding filtering and demodulation results can be described as:
the theory of the demodulated closed loop error signal U (k) can be derived. Considering the light intensity fluctuation affected by the actual temperature environment, (3) may be rewritten as:
U(k)＝(k 1 +Δk 1 )sin[Δx(k)] (4)
wherein, the first and the second end of the pipe are connected with each other,
is the gain of the forward channel in the closed loop fiber-optic gyroscope system, including the interference light intensity, the detector gain, the preamplifier circuit gain, the A/D converter gain and the demodulation gain, delta k 1 Is the gain uncertainty caused by the variation of light intensity with temperature.
In turn, although closed loop detection schemes bring some significant performance improvements, the design of the controller still needs to overcome some difficult problems. It can be seen that there are uncertainties in parameters such as optical interference intensity, nonlinearity and noise in the demodulation result of the actual system. Therefore, the invention further provides a robust H based on the design of the modulation and demodulation method ∞ And controlling an algorithm to improve the detection precision of the fiber-optic gyroscope.
Considering parameter uncertainty, optical effect nonlinearity and disturbance, the dynamic equation of the fiber-optic gyroscope can be deduced as follows:
x(k+1)＝Px(k)+Q(k 1 +Δk 1 )sin(K C x(k))+Qw(k) (5)
wherein x (k) is ∈ R n Is a state variable, K c ∈R 1×n Is a feedback control matrix of control, expressed as a controllability specification form according to an automatic control theory
And
where w (t) represents white noise.
Definition of
In the present invention, the parameter Δ k 1 Is bounded in a real system, so the bounded matrix Q Δ k 1 Can be converted into Q delta k 1 = R Δ (k) S, where R and S are constant matrices of appropriate dimensions describing the change in forward channel gain due to temperature drift, Δ (k) is an indeterminate matrix, of appropriate order, and satisfies Δ (k) T And delta (k) is less than or equal to I, and I is a unit matrix.
Furthermore, in order to improve the noise suppression level of signal processing and the linearity of a closed-loop fiber-optic gyroscope system, the invention provides a feedback control matrix K c The method ensures that the optical fiber gyroscope has the required H ∞ On the premise of performance, the method also meets the exponential stability under the conditions of uncertain parameters, nonlinearity and disturbance. Consider the following theorem:
theorem 1 for a given scalar 0 < α < 1, if there is a matrix X = X T >0,T∈R n×n Feedback control matrix K c ∈R 1×n And the positive scalar ε satisfies the inequality that the equation of motion (5) with parametric uncertainty, nonlinearity and perturbation describes a system that is exponentially stable and has a specified H ∞ The performance index γ.
And (3) proving that: the invention constructs the Lyapunov function V (k) = x T (k)X --1 X (k), where X is defined by theorem 1. Then, for the system (5),
V(k+1)-αV(k)+x T (k)x(k)-γ 2 w T (k)w(k)≤x T (k)x(k)-αV(k)-γ 2 w T (k)w(k)+V(k+1)-2sin T (K c x(k))(sin(K c x(k)-K c x(k)))＝η T (k)[ξ T X -1 ξ+Y]η(k)
wherein, eta [ k]＝[x T (k) sin T (K c x(k)) w T (k)] T ，
And is
Wherein r is the constructed r (k) = x T (k)x(k)-γ 2 w T (k)w(k)。
Introduction of introduction 1: for the form D = [ D ] ij ]Is equal to 1,2.D 11 ∈R r×r ，D 12 ∈R r×(n-r) ，D 22 ∈R (n-r)×(n-r) . If and only if D 11 <0,D 22 -D 21 D 11 -1 D 12 <0 or D 22 <0,D 11 -D 12 D 22 -1 D 21 <D is less than 0 when 0 is used.
According to the introduction 1, xi T X -1 A sufficient condition of ξ + Y < 0 is that if and only if the following inequality holds,
left and right of equation (7) are multiplied by diag { T T Ii I } and transposes thereof. Due to-T T X -1 T≤X-T T -T, having:
it can be seen that M<0 is equivalent to (6) of theorem 1. The present invention may define (6)
And solving by linear matrix inequality
Then, the present invention can obtain a feedback gain matrix
If (6) is true, the invention can obtain:
V(k+1)-αV(k)+x T (k)x(k)-γ 2 w T (k)w(k)≤0 (8)
structure r (k) = x T (k)x(k)-γ 2 w T (k) w (k) is
V(k+1)≤α 3 V(k-2)-α 2 r(k-2)-αr(k-1)-r(k) (9)
Rewriting (9) as
Since the scalar α satisfies 0 < α < 1 and the Lyapunov function is positive when k = ∞, there are:
due to the fact that
Therefore, the first and second electrodes are formed on the substrate,
from theorem 1, it follows that the system described by equation (5) is at a specified H ∞ The performance index gamma is stable.
Furthermore, the three functions realized by the FPGA of the invention comprise phase demodulation, digital filtering and feedback control. The demodulation method is realized by modulating the modulation signal from the modulation frequency omega 0 =5kHz shifted to zero frequency to accurately extract the closed-loop error. The digital filtering in the demodulation process eliminates stray light and simultaneously inhibits the interference of a light path and a circuit. In the system designed by the invention, the feedback control matrix K obtained by theorem 1 c = (0.625,0.315) make fiber optic gyroscope system have H-satisfaction in presence of gain uncertainty, nonlinearity and noise ∞ Index stability of performance index. Moreover, theorem 1 is a linear matrix inequality that can be easily solved in existing software (e.g., matlab LMI toolbox). Although the interference light intensity of the fiber optic gyroscope is a nonlinear function with angular velocity information and a weak signal with a large amount of noise and parameter uncertainty, the invention can extract closed-loop errors with high precision by the proposed sine wave modulation and feedback control method and improve the linearity and detection precision of the fiber optic gyroscope system.
Based on the derivation and analysis processes, the technical scheme of the invention is as follows: a noise spectrum analysis and signal-to-noise ratio optimization method of a fiber-optic gyroscope comprises the following steps:
firstly, demodulating by using a sine wave modulation technology to obtain a closed-loop error of a closed-loop fiber optic gyroscope system;
step two, establishing a dynamic equation of the fiber-optic gyroscope by considering parameter uncertainty based on a closed-loop error model;
step three, designing feedback control of a closed-loop fiber optic gyroscope systemMatrix K c So as to ensure that the optical fiber gyroscope has the required H ∞ On the premise of performance, the exponential stability is satisfied under the conditions of uncertain parameters, nonlinearity and disturbance.
Further, in the first step, the modulation signal and the feedback signal are added together and loaded on the integrated optical phase modulator through a D/A converter, so that the low-frequency closed-loop error signal is transmitted to the high frequency through a sine wave; according to Jacobi-Anger, the detected signal is written as:
wherein, J n Representing a Bessel function of order n, n =1,2,3 … …, R 1 Denotes the transimpedance of the photodetector, a denotes the optical path loss, I in Indicating the light intensity of the light source output, K D Represents the feedback channel gain, Δ x (t) represents the closed-loop error signal; the modulated closed-loop error signal Deltax (t) shifts to a frequency n omega 0 Wherein component J 1 (K D )sin(ω 0 Tk + - Δ x (k)) is in U p (t) maximum energy of closed-loop error signal, passing frequency ω 0 Component extraction of closed-loop error signal by converting the digital signal U in FPGA digital system p (k) And a modulated signal k de cosω 0 Tk to obtain this closed loop error signal, and therefore:
where T is the sampling period, U d (k) Is a demodulated signal, k de Is the demodulation gain, k qd Is the gain, k, of the detector and preamplifier circuit ad Is the gain of the A/D converter, thereby dividing the component J 1 (K D )sin(ω 0 t + - Δ x (k)) is shifted to zero frequency again, and the other frequency components n ω are shifted to zero frequency 0 N =1,2,3 … … is considered as an unwanted term, and then a closed loop error signal is obtained by a low pass filter designed to low pass filter during demodulationThe wave filter is H (z) = H (0) + H (1) z -1 +…+h(m)z -m Where h (0), h (1) … h (m) are coefficients of a low pass filter, z = e jwT And T represents the sampling period of the A/D.
Further, in the second step, under the condition of considering parameter uncertainty, optical effect nonlinearity and disturbance, the dynamic equation of the fiber-optic gyroscope is established as follows:
x(k+1)＝Px(k)+Q(k 1 +Δk 1 )sin(K c x(k))+Qw(k)
wherein x (k) is E.R n Is a state variable, R n Is a real number set of n dimensions, K c ∈R 1×n Is a feedback control matrix expressed in a controllability normative form according to an automatic control theory
And
wherein w (t) represents white noise;
will be bounded by the matrix Q Δ k 1 Conversion to Q Δ k 1 = R Δ (k) S, where R and S are constant matrices of appropriate dimensions describing the change in forward channel gain due to temperature drift, Δ (k) is an indeterminate matrix of an appropriate order and satisfies Δ (k) T And delta (k) is less than or equal to I, and I is a unit matrix.
Further, the third step is to design a feedback control matrix K of the closed-loop fiber-optic gyroscope system c To ensure that the optical fiber gyroscope has the required H ∞ On the premise of performance, the method also meets the index stability under the conditions of uncertain parameters, nonlinearity and disturbance, and specifically comprises the following steps:
for a given scalar 0 < α < 1, if there is a matrix X = X T >0,n order matrix T ∈ R n×n Feedback control matrix K c ∈R 1×n And the positive scalar ε satisfies the inequality that a dynamic equation with parametric uncertainty, nonlinearity and perturbation describes a stable system index with a specified H ∞ Performance index γ:
has the beneficial effects that:
(1) By adopting the novel fiber optic gyroscope closed-loop control method of the sine wave modulation technology, the closed-loop error related to the angular velocity can be accurately extracted, and the detection precision and the linearity of the fiber optic gyroscope are further improved. By modulating the closed-loop error of the fiber-optic gyroscope to high frequency, the direct-current component in the interference light intensity and irrelevant stray light can be eliminated, and the modulated signal is transmitted to the PSD and the demodulation filter, so that the signal-to-noise ratio of the closed-loop fiber-optic gyroscope system is improved.
(2) Through the proposed closed-loop detection scheme with the sine wave modulation technology, the closed-loop fiber optic gyroscope system can work near an optimal point and has the advantages of good linearity and wide measurement range.
(3) In order to improve the noise suppression level of signal processing and the linearity of a closed-loop fiber-optic gyroscope system, the invention provides a feedback control matrix K c The method ensures that the optical fiber gyroscope has the required H ∞ On the premise of performance, the method also meets the index stability under the conditions of uncertain parameters, nonlinearity and disturbance.
Drawings
FIG. 1 is a schematic diagram of the signal detection principle of a closed-loop fiber optic gyroscope system according to the present invention;
FIG. 2 is the output of the closed loop fiber optic gyroscope system of the present invention before optimization;
FIG. 3 shows the output of the optimized closed-loop fiber-optic gyroscope system of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
According to the embodiment of the invention, the noise spectrum analysis and signal-to-noise ratio optimization method of the fiber-optic gyroscope specifically comprises the following steps:
firstly, demodulating by utilizing a sine wave modulation technology to obtain a closed-loop error of a closed-loop fiber optic gyroscope system; the method specifically comprises the following steps:
the sinusoidal modulation is designed to suppress the 1/f noise of the circuit detection system and to eliminate the dc component of the interfering light signal and extraneous stray light. According to Jacobi-Anger, the signals are written as follows:
wherein, J n Representing an n-order Bessel function of the first kind (n =1,2,3 … …), R 1 Denotes the transimpedance of the photodetector, alpha denotes the optical path loss, I in Indicating the light intensity of the light source output, K D Representing the feedback channel gain, and deltax (t) representing the closed loop error signal. The invention can see that the modulated closed loop error signal delta x (t) shifts to the frequency n omega 0 Wherein component J 1 (K D )sin(ω 0 Tk + - Δ x (k)) is in U p There is a maximum energy of the closed loop error signal in (t). Therefore, the present invention can pass the frequency ω 0 The component extracts a closed loop error signal. Can be realized by converting a digital signal U in an FPGA digital system p (k) And a modulated signal k de cosω 0 Tk to obtain this closed loop error signal.
Further passing frequency omega 0 The component extracts the closed loop error signal. The closed loop error signal is then obtained through a low pass filter. Then, based on the purpose of widening the closed-loop bandwidth, the invention further designs the FIR digital filter with 32-order and 1kHZ bandwidth. Considering the case where the light intensity is affected by temperature, rewriting is further performed, that is,
wherein T isSampling period, U d (k) Is a demodulated signal, k de Is the demodulation gain, k qd Is the gain, k, of the detector and preamplifier circuit ad Is the gain of the a/D converter. The component J can be seen in the present invention 1 (K D )sin(ω 0 t ± Δ x (k)) is shifted again to zero frequency. Other frequency components n ω 0 (n =1,2,3 … …) may be considered as an unwanted entry. The closed loop error signal is then obtained through a low pass filter. In the demodulation process, the designed low-pass filter is H (z) = H (0) + H (1) z -1 +…+h(m)z -m Where h (0), h (1) … h (m) are coefficients of a low pass filter, z = e jwT And T represents the sampling period of the A/D. Since the system bandwidth of the fiber-optic gyroscope is expected to be 100Hz in practical application, in order to expand the closed-loop bandwidth as much as possible and simultaneously extract the closed-loop error accurately, the invention designs the FIR digital filter with the bandwidths of 32 orders and 1 kHz. The corresponding filtering and demodulation results can be described as:
the above formula is further rewritten as:
U(k)＝(k 1 +Δk 1 )sin[Δx(k)]
the closed loop error Δ x can be obtained by demodulation. In addition, the feedback phase Δ x f (t) is typically designed to counteract the phase change Δ x caused by the input angular velocity s (t), with Δ x (t) ≈ 0. Therefore, by the proposed closed-loop detection scheme with the sine wave modulation technology, the closed-loop fiber optic gyroscope system can work near an optimal point and has the advantages of good linearity and wide measurement range.
Secondly, establishing a dynamic equation of the fiber-optic gyroscope by considering parameter uncertainty based on a closed-loop error model; the method specifically comprises the following steps:
based on a closed-loop error model, considering parameter uncertainty, optical effect nonlinearity and disturbance, the dynamic equation of the fiber-optic gyroscope can be deduced by the method:
x(k+1)＝Px(k)+Q(k 1 +Δk 1 )sin(K C x(k))+Qw(k)；
thirdly, designing a feedback control matrix K of the closed-loop fiber-optic gyroscope system c So as to ensure that the optical fiber gyroscope has the required H ∞ On the premise of performance, the exponential stability is satisfied under the conditions of uncertain parameters, nonlinearity and disturbance. The method comprises the following specific steps:
using the proposed robust H ∞ Control algorithm, using feedback control matrix K c To ensure that the fiber optic gyroscope has the required H ∞ On the premise of performance, the method also meets the exponential stability under the conditions of uncertain parameters, nonlinearity and disturbance. On the basis of considering the nonlinearity and the disturbance of the optical effect, the invention introduces constant matrixes R and S to describe the change intensity of the forward channel gain caused by temperature drift, and guarantees delta (k) T Delta (k) is less than or equal to I. The following theorem 1 holds:
theorem 1. For a given scalar 0 < α < 1, if there is a matrix X = X T >0,T∈R n×n Feedback gain matrix K c ∈R 1×n And the positive scalar ε satisfies the following inequality, the dynamic system (5) with parametric uncertainty, nonlinearity and perturbation is exponentially stable with a specified H ∞ Performance index γ:
from theorem 1, the present invention can see that the closed loop system is at a specified H ∞ The performance index gamma is stable. The invention can easily obtain the feedback control matrix K through the existing software c The invention can extract the closed-loop error with high precision by the proposed sine wave modulation and feedback control method, and improve the linearity and detection precision of the fiber-optic gyroscope system.
Three functions implemented by the FPGA include phase demodulation, digital filtering and feedback control. The demodulation method is realized by modulating signal from modulation frequency omega 0 Shift of 5kHz to zero frequency to accurately extract the closed-loop error. Digital filtering in the demodulation process eliminates stray light and inhibits stray lightInterference of the optical path and the electric circuit is made.
And fourthly, solving parameters by adopting the method provided by the invention.
For the fiber optic gyroscope experimental setup used. The digital part of the signal detection system is realized by a high-speed sampling platform, and the platform consists of a reconfigurable Virtex-5 SX95T FPGA, a high-speed PCI and a PXI-e bus. The high-speed sampling platform not only monitors nanosecond state variables of the fiber-optic gyroscope, but also analyzes the frequency spectrum of key signals, and executes phase demodulation, digital filtering and control algorithm processing.
The light source is a wide-spectrum light source with wavelength of lambda (1550 nm) and output power of I in (2 mW), optical path loss of alpha (3.2 dB), feedback channel gain
Demodulation gain k de The gain k of the A/D converter can be obtained by setting the number of bits of the A/D converter to be 15, setting the reference voltage of the A/D converter to be 2V ad Is composed of
The photoelectric conversion efficiency obtained by the detector is 0.88A/W and the transimpedance R 1 At 200K, the preamplifier circuit gain was 31.34, and K was obtained qd Is 5.53X 10 6 According to the known parameters of the fiber optic gyroscope and the order number n =2 of the system state variable, it can be known that:
the lag times of the states are d =1, respectively.
It is desirable to design a suitable memoryless state feedback control law such that the closed loop system is asymptotically stable, the closed loop performance index is bounded, and a minimum upper bound on the closed loop performance index is given for all allowed uncertainties.
The solver feasp in the LMI toolbox can be applied to judge the feasibility problem of the linear matrix inequality. Find System H ∞ Minimum value of performance index gamma. This is a convex optimization problem with linear matrix inequality constraints, and therefore the problem is solved according to the theorem and applying the solver mincx in the LMI toolbox.
Obtaining by solution:
with this feasible solution of the optimization problem, the control law of the system under consideration can be constructed:
K c ＝[-6.67 -1.22]
the matrix equation determining the state equation according to the fiber-optic gyroscope modulation and demodulation mode and the parameter distribution is as follows:
when the order n =3 of the state variable,
the lag times of the state and control are d =1, respectively.
It is desirable to design a suitable memoryless feedback control law so that the closed loop system is asymptotically stable for all allowed uncertainties and gives a minimum upper bound on the closed loop performance index. For this purpose, the response optimization problem is solved by a solver mincx in the LMI toolbox, and the optimal solution of the problem can be obtained as follows:
ε＝1.1213
with this feasible solution to the optimization problem, the control law of the system under consideration can be constructed:
K c ＝[-0.2085 -0.2250 -0.5055]
and fifthly, verifying the optimization effect through experiments. As shown in fig. 2-3, the output of the system before and after the improvement is performed in the fourth step, and experimental data show that the optimization system improves the detection accuracy of the system. According to the test data, the loop gain and the control algorithm are reasonably distributed, and the noise suppression capability of the system can be improved.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the embodiment of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A noise spectrum analysis and signal-to-noise ratio optimization method of a fiber-optic gyroscope is characterized by comprising the following steps:
firstly, demodulating by using a sine wave modulation technology to obtain a closed-loop error of a closed-loop fiber optic gyroscope system;
step two, establishing a dynamic equation of the fiber-optic gyroscope by considering parameter uncertainty based on a closed-loop error model;
step three, designing a feedback control matrix K of the closed-loop fiber-optic gyroscope system c So as to ensure that the optical fiber gyroscope has the required H ∞ On the premise of performance, the exponential stability is met under the conditions of uncertain parameters, nonlinearity and disturbance;
in the first step, a modulation signal and a feedback signal are added together and loaded on an integrated optical phase modulator through a D/A converter, so that a low-frequency closed-loop error signal is transmitted to a high frequency through a sine wave; according to Jacobi-Anger, the detected signal is written as:
wherein, J n Representing a Bessel function of order n, n =1,2,3 … …, R 1 Denotes the transimpedance of the photodetector, alpha denotes the optical path loss, I in Indicating the light intensity of the light source output, K D Represents the feedback path gain, Δ x (t) represents the closed loop error signal; modulated closed loop error signal Deltax (t) transitionTo frequency n omega 0 Wherein the component J 1 (K D )sin(ω 0 Tk + - Δ x (k)) is in U p (t) maximum energy of closed-loop error signal, passing frequency ω 0 Component extraction of closed-loop error signal, in particular by converting the digital signal U in an FPGA digital system p (k) And a modulated signal k de cosω 0 Tk to obtain this closed loop error signal, and therefore:
where T is the sampling period, U d (k) Is a demodulated signal, k de Is the demodulation gain, k qd Is the gain, k, of the detector and preamplifier circuit ad Is the gain of the A/D converter, thereby dividing the component J 1 (K D )sin(ω 0 t + - Δ x (k)) is shifted again to zero frequency, the other frequency components n ω 0 N =1,2,3 … … is regarded as an unwanted term, and then a closed-loop error signal is obtained by a low-pass filter designed to be H (z) = H (0) + H (1) z during demodulation -1 +…+h(m)z -m Where h (0), h (1) … h (m) are coefficients of a low pass filter, z = e jwT T represents the sampling period of A/D;
in the second step, under the condition of considering parameter uncertainty, optical effect nonlinearity and disturbance, the dynamic equation of the fiber-optic gyroscope is established as follows:
x(k+1)＝Px(k)+Q(k 1 +Δk 1 )sin(K c x(k))+Qw(k)
wherein x (k) is E.R n Is a state variable, R n Is a real number set of n dimensions, K c ∈R 1×n Is a feedback gain matrix of control expressed as a controllability specification form according to an automatic control theory
And
wherein w (t) represents white noise;
is the gain of the forward channel in the closed loop fiber-optic gyroscope system, including the interference light intensity, the detector gain, the preamplifier circuit gain, the A/D converter gain and the demodulation gain, delta k 1 Is the gain k caused by the variation of light intensity with temperature 1 Uncertainty of (d);
will be bounded by the matrix Q Δ k 1 Conversion to Q Δ k 1 = R Δ (k) S, where R and S are constant matrices of appropriate dimensions describing the change in forward channel gain due to temperature drift, Δ (k) is an indeterminate matrix of an appropriate order and satisfies Δ (k) T Delta (k) is less than or equal to I, and I is a unit matrix;
thirdly, designing a feedback control matrix K of the closed-loop fiber optic gyroscope system c To ensure that the optical fiber gyroscope has the required H ∞ On the premise of performance, the method also meets the index stability under the conditions of uncertain parameters, nonlinearity and disturbance, and specifically comprises the following steps:
for a given scalar 0 < α < 1, if there is a matrix X = X T >0,n order matrix T ∈ R n×n Feedback control matrix K c ∈R 1 ×n And the positive scalar ε satisfies the inequality that a dynamic equation with parametric uncertainty, nonlinearity and perturbation describes a stable system index with a specified H ∞ Performance index γ:
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