Smart control method for hemispherical resonator gyro under input saturation

Abstract

The application relates to a kind of intelligent control methods of hemispherical resonator gyro under input saturation, belong to intelligent instrument and meter technical field.The method gives the dynamic equation of amplitude, quadrature, speed, frequency phase control variable according to Lynch's random average method theory;For the uncertainty caused by environmental factors such as temperature, a parallel estimation model of real dynamics is constructed, the prediction error is given, the neural network weight updating law is designed combined with the prediction error and tracking error, and the composite learning of system uncertainty is realized;For the problem that control input cannot be executed as expected under input saturation, an auxiliary system is introduced to compensate the input saturation error;Finally, the composite controller is designed combined with the uncertain estimation feedforward compensation and PI feedback control to realize the stable control of hemispherical resonator gyro.The intelligent control strategy of hemispherical resonator gyro under input saturation designed by the application can realize high-precision estimation of system uncertainty and realize the stable control of gyro.

Description

TECHNICAL FIELD

[0001] The application relates to an intelligent control technology of a hemispherical resonator gyro under input saturation, and belongs to the technical field of intelligent instruments. BACKGROUND

[0002] The hemispherical resonator gyro is one of mainstream high-precision inertial devices and has been widely applied in the fields of spaceflight and navigation due to high precision, high reliability, long service life, and radiation resistance. In the full-angle mode, the standing wave of the hemispherical resonator freely precesses with the rotation input of the gyro, the azimuth of the standing wave is the rate integration output, and the angle information can be directly obtained by detecting the azimuth of the standing wave. At this time, the gyro has a large dynamic range and is suitable for carriers with large maneuverability. However, the driving force has a saturation phenomenon due to the physical characteristics of the torque transducer, and the control input becomes constant once the controller calculated in theory exceeds the upper and lower limits of saturation. Meanwhile, in the full-angle mode, the gyro is easily affected by environmental factors such as temperature, resulting in uncertainty of the control system and degradation of the control performance.

[0003] In view of the problem of the decline of the gyro measurement accuracy caused by environmental factors such as temperature, the paper 'Design of Temperature Control System for Hemispherical Resonator Gyroscope' (Qin Qian, Jiang Jingke, Chen Zhenyu, Lv Qiyuan, Li Qiang, Electronic Technology Application, 2021) designs a hemispherical resonator gyro temperature control system to provide a constant temperature environment for the gyro and reduce the influence of temperature changes; the paper 'Self-compensation of Hemispherical Resonator Gyroscope Zero-bias Temperature Drift' (Liu Jili, Li Jianpeng, Wu Zhizhong, Li Kai, Space Control Technology and Application, 2018) establishes a nonlinear model of the resonant frequency and temperature, and realizes temperature error compensation by adjusting the resonant frequency. However, the environmental temperature control increases the hardware complexity of the gyro, and the resonant frequency modeling compensation depends on large test equipment such as temperature control boxes, which is difficult to popularize. In view of the input saturation problem, the current engineering method is to simplify the controller so that it does not exceed the upper and lower limits of saturation, but this is an engineering test method and lacks theoretical support. SUMMARY

[0004] Technical problem: In view of the system uncertainty and input saturation problem caused by environmental factors such as temperature, the application proposes an intelligent control strategy for a hemispherical resonator gyro under input saturation in the full-angle mode. In the application, a compound learning strategy is designed based on the parallel estimation model to estimate the system uncertainty, an auxiliary system is introduced to compensate for the control error caused by input saturation, and a compound controller is designed by combining the uncertain estimation feedforward compensation and PI feedback control to realize stable control of the hemispherical resonator gyro.

[0005] Technical solution: The technical solution adopted by the application to solve the technical problem is: an intelligent control method for a hemispherical resonator gyro under input saturation, comprising the following steps:

[0006] Step 1: Considering the uncertainty caused by temperature and other environmental factors, the dynamic equations of the amplitude, quadrature, velocity, and frequency phase control variables of the hemispherical resonator gyroscope are given according to the random average method theory of Lynch;

[0007] Step 2: Construct a parallel estimation model of real dynamics, give a prediction error, combine the prediction error and the tracking error to design a neural network weight update law, and realize the compound learning of system uncertainty;

[0008] Step 3: Introduce an auxiliary system to compensate for input saturation error;

[0009] Step 4: Combine the uncertain estimation feedforward compensation and PI feedback control to design a compound controller, and realize the stable control of the hemispherical resonator gyroscope.

[0010] The specific process is as follows:

[0011] Considering the uncertainty caused by temperature and other environmental factors, the dynamic equations of the amplitude, quadrature, velocity, and frequency phase control variables are

[0012]

[0013] In the formula:

[0014]

[0015] Where E, Q, θ, δφ are the control variables of the amplitude, quadrature, velocity, and frequency phase control loops, f as , f qc , f qs , f ac , are the controllers to be designed, f E , f Q , f θ , f δφ are the uncertainties caused by temperature and other environmental factors on each control variable, θ τ and θ ω are the angles between the damping and stiffness main axes, Ω is the input angular velocity, k is the angle gain, τ1 and τ2 are the decay times of the two split modes, ω1 and ω2 are the resonance frequencies of the two split modes, ω and Δω are the mean and variance of ω1 and ω2, φ = δφ + φ r and φ r are the initial phases of the signal demodulation reference signal.

[0016] Set f ac = 0. f as = sat(u as ), f qc = sat(u qc ), fqs = sat(u qs ), is a controller to be designed with saturation property, and

[0017]

[0018] where, is the upper bound of saturation of the control input u i , u i is the lower bound of saturation of the control input u i .

[0019] The system uncertainty is approximated by a neural network, and

[0020]

[0021] where, is the n-dimensional optimal neural network weight parameter vector, is the n-dimensional neural network basis function vector, ε E , ε Q , ε θ , ε δφ is the neural network approximation error.

[0022] Define are the estimates of ρ E , ρ Q , ρ θ , ρ δφ , respectively, and the estimate of the system uncertainty is

[0023]

[0024] where, are the estimates of f E , f Q , f θ , f δφ , respectively.

[0025] Define the tracking errors of the amplitude, quadrature, and velocity control loops as

[0026] e E = E - E r , e Q = Q - Q r , e θ = θ - θ r (4)

[0027] where E r is the reference signal of the amplitude control loop, Q r is the reference signal of the quadrature control loop, and θ r is the reference signal of the velocity control loop.

[0028] Considering the dynamic equation (1) of the control variable u as , u qc , u qs , u φ is designed as

[0029]

[0030] where K P1 , K P2 , K P3 , K P4 , K I1 , K I2 , K I3 , K I4 , is a normal number to be designed; is obtained by the weight adaptive updating law of the following formula (7); η as , η qc , η qs , η φ is an auxiliary variable for compensating saturation effect, which is obtained by the following auxiliary system

[0031]

[0032] where c i , is a normal number to be designed, f i (e j ) is a feedback function and e φ = δφ, Δu i = sat(u i )-u i .

[0033] The weight adaptive updating law is designed as

[0034]

[0035] where r E1 , r E2 , r E3 , r Q1 , r Q2 , r Q3 , r θ1 , r θ2 , r θ3 , r δφ1 , r δφ2 , r δφ3 is a normal number to be designed, z E , z Q , z θ , z φ is a prediction error, and ​

[0036]

[0037] wherein, is obtained from the following parallel estimation model

[0038]

[0039] wherein, α E , α Q , α θ , α φ is a normal number to be designed.

[0040] Advantages: The advantages of the present application compared with the prior art are:

[0041] (1) For the dynamic change of the system uncertainty in the hemispherical resonator gyro dynamic model caused by environmental factors such as temperature, a parallel estimation model of the dynamic model is introduced, a compound learning strategy is designed, and high-precision estimation of the system dynamic uncertainty is realized.

[0042] (2) For the problem that the control input cannot be executed as expected due to the limited execution ability of the gyro transducer under input saturation, an auxiliary system is introduced to compensate for the control error caused by input saturation, so that the gyro controller can quickly escape from the influence of input saturation.

[0043] (3) For the problem of control performance degradation caused by environmental factors such as temperature, the uncertainty estimated by the compound learning is fed forward to the control system, and a compound controller is designed by combining the saturation compensation system and the PI feedback control, which realizes the saturation compensation and high-precision control under the influence of temperature and other environmental factors. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is the intelligent control scheme diagram of the hemispherical resonator gyro under input saturation.

[0045] Figure 2 is the compound learning strategy diagram for system uncertainty caused by temperature and other environments. DETAILED DESCRIPTION

[0046] Example 1: The specific implementation of the intelligent control scheme of the hemispherical resonator gyro under input saturation proposed by the present application is as follows:

[0047] Figure 1 is the intelligent control scheme diagram of the hemispherical resonator gyro under input saturation designed by the present application, which includes the following steps:

[0048] Step 1: Hemispherical resonator gyro dynamic modeling.

[0049] Considering the system uncertainty caused by temperature variations, based on Lynch's stochastic averaging method, the dynamic equations for the amplitude, orthogonality, velocity, and frequency-phase control variables of the hemispherical resonant gyroscope are as follows:

[0050]

[0051] In the formula:

[0052]

[0053] Where E, Q, θ, and δφ are the control variables of the amplitude, quadrature, velocity, and frequency phase control loops, respectively, and f as f qc f qs f ac , For the controller to be designed, f E f Q f θ f δφ θ represents the uncertainty caused by environmental factors such as temperature for each control variable. τ and θ ω Let ω1 and ω2 be the angles between the damping principal axes and the stiffness principal axes, respectively; Ω be the input angular velocity; k be the angular gain; τ1 and τ2 be the decay times of the two broken modes; ω1 and ω2 be the resonant frequencies of the two broken modes; ω and Δω be the mean and variance of ω1 and ω2, respectively; and φ = δφ + φ r And φ r This is the initial phase of the reference signal for signal demodulation. In this embodiment, θ is set to... τ =45.1°, θ ω =49.9°, k=1.0001, τ1=0.15s, τ2=0.16s, ω1=10rad / s, ω2=10.2rad / s, φ r =0 rad.

[0054] Set f ac =0. f as =sat(u as ), f qc =sat(u qc ), f qs =sat(u qs ), For the controller to be designed, which has saturation characteristics, and

[0055]

[0056] In the formula, It is the control input u i The upper bound of saturation, u i It is the control input u ithe saturation lower bound. In this embodiment, we set u i = -10000.

[0057] Step 2: Intelligent learning design for system uncertainty.

[0058] Neural network approximation is used to approximate system uncertainty, and

[0059]

[0060] where, is the n-dimensional unknown optimal neural network weight parameter vector, is the n-dimensional neural network basis function vector, and ε E , ε Q , ε θ , ε δφ is the unknown neural network approximation error.

[0061] Define are the estimates of ρ E , ρ Q , ρ θ , ρ δφ , and the estimate of system uncertainty is

[0062]

[0063] where, are the estimates of f E , f Q , f θ , f δφ .

[0064] Step 3: Input saturation compensation and compound controller design for the HSG based on the auxiliary system.

[0065] Define the tracking errors of the amplitude, quadrature, and velocity control loops as

[0066] e E = E - E r , e Q = Q - Q r , e θ = θ - θ r (4)

[0067] where E r is the reference signal of the amplitude control loop, generally selected as a constant; Q r is the reference signal of the quadrature control loop, generally selected as zero; and θ r is the reference signal of the velocity control loop, generally selected as a constant. In this embodiment, we set E r = 1.2, Q r= 0, θ r = 0.5.

[0068] Considering the dynamic equation (1) of control variable, u as , u qc , u qs , u φ is designed as

[0069]

[0070] where K P1 , K P2 , K P3 , K P4 , K I1 , K I2 , K I3 , K I4 , is a normal number to be designed. In this embodiment, K P1 = 10, K P2 = 10, K P3 = 10, K P4 = 10, K I1 = 12, K I2 = 12, K I3 = 12, K I4 = 12, is obtained from the weight adaptive updating law of formula (7) in the following; η as , η qc , η qs , η φ is an auxiliary variable for compensating saturation effect, which is obtained from the following auxiliary system

[0071]

[0072] where c i , is a normal number to be designed, f i (e j ) is a feedback function and e φ = δφ, Δu i = sat(u i )-u i . In this embodiment, c i = 0.5,

[0073] Step 4: Composite learning strategy design.

[0074] The specific idea of composite learning design for system uncertainty is shown in Figure 2 The weight adaptive updating law of neural network is designed as

[0075]

[0076] wherein r E1 , r E2 , r E3 , r Q1 , r Q2 , r Q3 , r θ1 , r θ2 , r θ3 , r δφ1 , r δφ2 , r δφ3 are normal numbers to be designed, in the embodiment, r E1 =1.2, r E2 =60, r E3 =0.5, r Q1 =1, r Q2 =70, r Q3 =0.5, r θ1 =1, r θ2 =70, r θ3 =0.5, r δφ1 =1.6, r δφ2 =65, r δφ3 =0.5; z E , z Q , z θ , z φ are prediction errors, and

[0077]

[0078] wherein, is obtained from the following parallel estimation model

[0079]

[0080] wherein, α E , α Q , α θ , α φ are normal numbers to be designed. In the embodiment, α E =0.8, α Q =0.8, α θ =0.8, α φ =0.8.

[0081] For the dynamic equation (1) of the control variable, the controller (5), the saturation compensation auxiliary system (6), and the weight updating law (7) are adopted, so that the system uncertainty compound learning, input saturation compensation, and gyro stable control of the hemispherical resonator gyro can be realized.

[0082] It should be noted that the above examples do not limit the scope of the present application, and equivalent substitutions or replacements made on the basis of the above all belong to the protection scope of the claims of the present application.

Claims

1. A method for intelligent control of a hemispherical resonator gyro under input saturation, characterized in that, The method comprises the following steps: Step 1: considering the uncertainty caused by temperature environment factors, dynamic equations of amplitude, quadrature, velocity, frequency and phase control variables are given according to the random average method theory of Lynch; Step 2: a parallel estimation model of real dynamics is constructed, prediction errors are given, neural network weight updating law is designed combining the prediction errors and tracking errors, and composite learning of system uncertainty is realized; Step 3: an auxiliary system is introduced to compensate input saturation errors; Step 4: a composite controller is designed combining feedforward compensation of uncertainty estimation and PI feedback control to realize stable control of the hemispherical resonator gyro; In step 1, hemispherical resonator gyro dynamics modeling is as follows: Considering the uncertainty caused by temperature environment factors, dynamic equations of amplitude, quadrature, velocity, frequency and phase control variables are as follows according to the random average method theory of Lynch In the formula: Wherein, E, Q, θ, δφ are control variables of amplitude, quadrature, velocity, frequency phase control loop respectively, f as , f qc , f qs , f ac , is the controller to be designed, f E , f Q , f θ , f δφ are uncertainties caused by temperature environment factors on each control variable, θ τ and θ ω are the included angle of the damping spindle and the stiffness spindle, Ω is the input angular velocity, k is the angle gain, τ1 and τ2 are the decay time of the two split modes, ω1 and ω2 are the resonance frequencies of the two split modes respectively, ω and Δω are the mean and variance of ω1 and ω2 respectively, φ = δφ + φ r and φ r is the initial phase of the signal demodulation reference signal; Set f ac = 0, f as = sat(u as ), f qc = sat(u qc ), f qs = sat(u qs ), is a controller with saturation characteristics to be designed, and wherein is a saturation upper bound for the control input u i , u i is a saturation lower bound for the control input u i ; In step 3, hemispherical resonator gyro input saturation compensation and composite controller design based on the auxiliary system are as follows: Define the tracking errors of amplitude, quadrature and velocity control loops as e E = E - E r ,e Q = Q - Q r ,e θ = Θ - Θ r (4) where E r is the reference signal of the amplitude control loop, Q r is the reference signal of the quadrature control loop, and Θ r is the reference signal of the speed control loop. Considering the dynamic equation of the control variable (1), u as , u qc , u qs , u φ is designed as where K P1 , K P2 , K P3 , K P4 , K I1 , K I2 , K I3 , K I4 , l1, l2, l3, l4 are normal numbers to be designed; is obtained from the weight adaptive update law of the following formula (7); η as , η qc , η qs , η φ is an auxiliary variable for compensating saturation effect, which is obtained from the following auxiliary system φ where c i , is a constant to be designed, f i (e j ) is a feedback function and e φ = δφ, Δu i = sat(u i )-u i ; In step 4, composite learning strategy design is as follows: Neural network weight adaptive updating law is designed as where r E1 , r E2 , r E3 , r Q1 , r Q2 , r Q3 , r θ1 , r θ2 , r θ3 , r δφ1 , r δφ2 , r δφ3 are design constants, z E , z Q , z θ , z φ is a prediction error, and wherein, is obtained from the following parallel estimation model wherein α E , α Q , α θ , α φ are real numbers to be designed; For the dynamic equation (1) of the control variable, the controller (5), the auxiliary system (6) and the neural network weight updating law (7) can realize hemispherical resonator gyro input saturation compensation and stable control.

2. The input-saturation-under semi-gyroscopic smart control method according to claim 1, wherein, In step 2, intelligent learning design of system uncertainty is as follows: The system uncertainty caused by temperature environment factors is approximated by a neural network, and there are wherein, is the n-dimensional optimal weight parameter vector of the neural network, is the n-dimensional basis function vector of the neural network, ε E , ε Q , ε θ , ε δφ is the approximation error of the neural network; Definitions respectively, and the estimate of the system uncertainty is E respectively, and the estimate of the system uncertainty is Q respectively, and the estimate of the system uncertainty is θ respectively, and the estimate of the system uncertainty is δφ respectively, and the estimate of the system uncertainty is wherein, are the estimates of f E , f Q , f θ , f δφ , respectively.

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