A method for stabilizing the pumping rate of an atomic gyroscope based on a phase-reformatted extended state observer and a power approaching sliding mode control

Abstract

A kind of atomic gyroscope pumping rate stable composite control method based on phase reshaping extended state observer and power approaching sliding mode control.Aiming at the problems that standard linear extended state observer has steady-state estimation error under the action of ramp disturbance, disturbance estimation phase lag and it is difficult to balance between observation bandwidth improvement and noise sensitivity, a composite corrector composed of lead network and lag network is cascaded at the output end of disturbance estimation of extended state observer, the disturbance estimation channel is shaped in frequency domain, phase lead is provided in mid-frequency band to reduce compensation delay, amplitude lag characteristic is used to suppress high-frequency noise, and parameter constraint design is used to realize zero-error estimation of ramp disturbance;At the same time, a power approaching sliding mode controller is constructed to improve the adaptability to the nonlinear, internal and external coupling and parameter uncertainty of atomic gyroscope system, and the phase reshaping extended state observer is combined to effectively estimate and feed forward compensate the lumped disturbance, so as to improve the stability and accuracy of pumping rate control.The present application can balance dynamic anti-disturbance performance, steady-state control accuracy, convergence speed and noise robustness without significantly improving the observation bandwidth, and is suitable for atomic gyroscope precision control system affected by ultra-low frequency slowly varying disturbance.

Description

Technical Field

[0001] This invention relates to a composite control method based on a phase reshaping extended state observer and a power-approaching sliding mode control law, applicable to the field of pump rate stabilization control of spin-free exchange-relaxed atomic gyroscopes. Background Technology

[0002] With the development of quantum precision measurement technology, high-precision angular velocity sensors based on atomic spin have shown significant application potential in inertial navigation, geophysical exploration, and fundamental physics experiments. Atomic gyroscopes, due to their potential for high sensitivity and low drift, have promising application prospects. Among them, atomic gyroscopes without spin exchange relaxation conditions can significantly extend the spin coherence lifetime in low magnetic field environments, thereby achieving ultra-high sensitivity, making them particularly suitable for applications such as high-precision attitude control and geophysical measurement.

[0003] However, the long-term output consistency and repeatability of atomic gyroscopes are limited by their internal spin dynamics, particularly the steady-state maintenance of the longitudinal polarization of the electron spin. The longitudinal polarization not only determines the amplitude of the transverse signal and the equivalent angular velocity resolution but also directly affects the long-term consistency of the gyroscope's scaling factor, making it a core variable influencing the long-term stable operation of the system. In atomic systems, the steady-state of the longitudinal polarization is highly dependent on the pump rate of the pump laser, which is susceptible to ultra-low frequency, slowly varying disturbances such as temperature drift, optical component aging, and polarization noise. These disturbances typically exhibit ultra-low frequency, slowly varying trends and can induce unsteady fluctuations in the longitudinal polarization through spin dynamics, leading to scaling factor drift and zero-bias changes, adversely affecting long-term measurement performance. Therefore, achieving long-term stable control of the pump rate is a prerequisite for the practical engineering application of atomic gyroscopes.

[0004] To achieve high-precision closed-loop stable control of the pump rate of an atomic gyroscope, it is crucial to address key technical challenges in the control process. At the control level, the primary factor affecting the long-term stability of the pump rate is the ultra-low frequency disturbance caused by polarization noise. Linear active disturbance rejection control (ADRC) can uniformly attribute external disturbances, parameter drift, and unmodeled dynamics to a total disturbance, and perform real-time estimation and compensation through an extended state observer. This allows for effective suppression of disturbances without relying on a high-precision model of the controlled object, making it well-suited for long-term stable pump rate control scenarios.

[0005] Under ultra-low frequency slowly varying disturbance conditions, existing linear extended state observers are prone to steady-state errors and phase lag during disturbance estimation, leading to insufficient disturbance compensation and delayed dynamic response. Although increasing the observation bandwidth can improve these problems to some extent, it also enhances the effects of measurement noise and unmodeled high-frequency dynamics, and may even cause system jitter, making it difficult to balance disturbance estimation accuracy and noise robustness.

[0006] Furthermore, atomic gyroscope systems are characterized by nonlinearity, internal and external coupling, and parameter uncertainty. When relying solely on conventional linear feedback control, it is often difficult to simultaneously meet the control requirements of fast convergence, high steady-state accuracy, and strong robustness. In the case of lag or deviation in disturbance estimation, the control input may also experience problems such as untimely compensation and decreased error convergence speed, which further restricts the improvement of pump rate stability control performance.

[0007] Therefore, to improve the disturbance rejection performance, steady-state accuracy, and dynamic response capability of the pump rate stability control system under long-term operating conditions, it is necessary to synergistically improve the disturbance estimation channel and control law of the linear extended state observer. Considering that the ultra-low frequency slowly varying disturbance dominated by polarization noise can usually be approximated as a ramp-type trend term within a finite observation time, it is urgent to propose a control method that, while maintaining noise suppression capability, can achieve high-precision estimation and timely compensation of ramp disturbances, reduce phase lag in the dominant frequency band of the disturbance, and improve the control law's adaptability to system nonlinearity, coupling characteristics, and parameter perturbations, in order to obtain faster error convergence speed and higher pump rate stability control accuracy. Summary of the Invention

[0008] The technical problem solved by this invention is: addressing the difficulty in suppressing ultra-low frequency slowly varying disturbances during the long-term stable control of the pump rate of an atomic gyroscope. Without significantly increasing the observer bandwidth or amplifying noise, a stable control method based on a phase reshaping extended state observer and power-approaching sliding mode control is proposed. Through a cascaded composite corrector, the disturbance estimation channel is frequency-domain shaped to achieve zero steady-state error estimation of ramp disturbances. Simultaneously, a power-approaching sliding mode variable structure controller is constructed to handle the nonlinearity, internal and external coupling, and parameter uncertainties of the atomic gyroscope system, thereby improving the disturbance rejection performance, steady-state accuracy, and dynamic response capability of the pump rate control system under long-term operating conditions.

[0009] The technical solution of the present invention is as follows:

[0010] (1) Dynamic model of the controlled object

[0011]

[0012] in, The lumped disturbance term uniformly includes both internal uncertainties and external disturbances. To control the gain;

[0013] To achieve effective estimation and compensation for ultra-low frequency slowly varying disturbances, an extended state observer is constructed to estimate the system output and lumped disturbances. The extended state observer is defined as follows:

[0014]

[0015] in This is the estimated value output by the system. This is an estimate of the lumped disturbance. , For observer gain;

[0016] To address the steady-state error and phase lag issues of standard linear extended state observers when estimating ultra-low frequency ramp disturbances, a phase-reforming extended state observer is designed. By introducing a composite correction network with phase reshaping function into the disturbance estimation channel, the steady-state error-free estimation and phase lead compensation of ramp disturbances are achieved without excessively increasing the observation bandwidth and amplifying high-frequency noise, thereby improving the accuracy and response speed of disturbance estimation.

[0017] Output of the composite correction network Transfer function of composite correction network They are respectively:

[0018]

[0019]

[0020] in , It is the dominant time constant. It is a gain adjustment factor, and , ;

[0021] The composite correction network locally shapes the phase and amplitude in the mid-frequency band while keeping the low-frequency and high-frequency gains basically unchanged. By reasonably setting the network parameters, the corrected disturbance estimate can meet the condition of zero steady-state error estimation for slope disturbance, thereby reducing the phase lag of the disturbance estimate and improving the disturbance estimation accuracy.

[0022] (2) To address the nonlinearity, internal and external coupling, and parameter uncertainty of the atomic gyroscope system, a power-approaching sliding mode variable structure controller is constructed to improve the system's error convergence speed, steady-state accuracy, and robustness.

[0023] The power-approaching sliding mode variable structure control law Tracking error Sliding surface and power-order approach term They are respectively:

[0024]

[0025]

[0026]

[0027]

[0028] in, For reference input; , The controller gain is given by the condition that the ... , ; , are positive integers and satisfy ; The saturation function is the boundary layer thickness parameter; the saturation function satisfies:

[0029]

[0030] Corrected disturbance estimate The power-order approximation sliding mode variable structure control law is introduced as a feedforward compensation term; the power-order term... Used to enhance the nonlinear approach effect and improve the sliding surface arrival speed when the error is large; saturation function This is used to construct a boundary layer in the neighborhood of the sliding surface to replace the sign function switching term and reduce chattering in sliding mode control, thereby improving the engineering feasibility of the control law.

[0031] The advantages of this invention compared to the prior art are:

[0032] (1) This invention introduces a composite correction network with phase reshaping function into the disturbance estimation output channel of a standard extended state observer, and through parameter design, makes it meet specific constraints to achieve zero steady-state error estimation of ramp-type ultra-low frequency slowly varying disturbances, thereby reducing the steady-state error of the observer in this type of disturbance estimation. At the same time, the composite correction network provides phase lead compensation in the effective frequency band, which can reduce the phase lag in the original observer disturbance estimation, so that the corrected disturbance estimation value tracks the real disturbance change more timely, thereby improving the feedforward compensation accuracy and reducing the impact of ultra-low frequency slowly varying disturbances on the long-term stability of the system;

[0033] (2) This invention constructs a power-law approach sliding mode control law to replace the traditional linear state error feedback form. The power-law approach term enhances the nonlinear approach capability of the system error, which can improve the error convergence speed and improve the transient response characteristics and setpoint tracking performance of the system. At the same time, by introducing a saturation function to construct a boundary layer, the chattering phenomenon caused by the switching of the sign function in the traditional sliding mode control is reduced while maintaining a fast approach performance, thereby improving the stability and engineering feasibility of the control system.

[0034] (3) The improvements of this invention are mainly reflected in the disturbance estimation post-processing channel of the extended state observer and the nonlinear feedback structure of the control law. Performance improvement can be achieved without significantly changing the original active disturbance rejection control framework, which is convenient for integration and application in existing control systems. At the same time, the newly added parameters have clear division of roles and clearer tuning basis, which is beneficial to engineering implementation. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the overall control structure of the composite control method;

[0037] Figure 2 Comparison of disturbance estimation and control response between standard linear extended state observer and phase reshaping extended state observer under step disturbance;

[0038] Figure 3 A comparison of disturbance estimation and control response between the standard linear extended state observer and the phase-reformed extended state observer under slope disturbance conditions;

[0039] Figure 4 A comparison of disturbance estimation and control response between a standard linear extended state observer and a phase-reformed extended state observer under sinusoidal disturbance conditions;

[0040] Figure 5 A comparison of the control responses of the power-approaching sliding mode control law and the linear feedback control law under sinusoidal disturbance. Detailed Implementation

[0041] (1) Constructing an extended state observer for phase reshaping

[0042] like Figure 1 As shown, the specific implementation of the present invention is as follows:

[0043] Dynamic model of the controlled object

[0044]

[0045] in, The lumped disturbance term uniformly includes both internal uncertainties and external disturbances. To control the gain;

[0046] To achieve effective estimation and compensation for ultra-low frequency slowly varying disturbances, an extended state observer is constructed to estimate the system output and lumped disturbances. The extended state observer is defined as follows:

[0047]

[0048] in This is the estimated value output by the system. This is an estimate of the lumped disturbance. , For observer gain; through appropriate selection , , can make Approximating the system output and make Approaching the total disturbance;

[0049] To facilitate bandwidth tuning, let , , Indicates the observer bandwidth;

[0050] To address the steady-state error and phase lag issues of standard linear extended state observers when estimating ultra-low frequency ramp disturbances, a phase-reforming extended state observer is designed. By introducing a composite correction network with phase reshaping function into the disturbance estimation channel, the steady-state error-free estimation and phase lead compensation of ramp disturbances are achieved without excessively increasing the observation bandwidth and amplifying high-frequency noise, thereby improving the accuracy and response speed of disturbance estimation.

[0051] Output of the composite correction network Transfer function of composite correction network They are respectively:

[0052]

[0053]

[0054] in , It is the dominant time constant. It is a gain adjustment factor, and , ;

[0055] The composite correction network locally shapes the phase and amplitude in the mid-frequency band while keeping the low-frequency and high-frequency gains basically unchanged.

[0056] Its low-frequency and high-frequency asymptotic gains satisfy the following:

[0057] ,

[0058] In addition, the corrected disturbance estimate It can be represented as:

[0059]

[0060] The second-order linear extended state observer satisfies:

[0061]

[0062] Under zero initial conditions, the Laplace domain has The following formula can be obtained.

[0063]

[0064] From the above formula, we can see that Equivalent to in On top of that, a term is added due to observation error. The second-order low-pass compensation term is driven, thereby avoiding explicit differentiation of the measurement signal;

[0065] To facilitate discrete implementation, intermediate variables are introduced. , ,make

[0066]

[0067] This can be achieved using a two-stage first-order filter.

[0068]

[0069]

[0070] And by

[0071] ,

[0072] The corrected perturbation estimate is obtained. This implementation relies only on the observation error and the observer's internal variables, avoiding the risk of high-frequency noise amplification caused by directly introducing the differential element, while retaining the degree of freedom of mid-frequency phase shaping.

[0073] Furthermore, by appropriately setting the network parameters, the corrected disturbance estimate can satisfy the condition of zero steady-state error estimation for slope disturbances, thereby reducing the phase lag of the disturbance estimate and improving its accuracy; the steady-state error of the disturbance estimate under the influence of slope disturbances can also be considered. Take the slope disturbance as

[0074]

[0075] in, Let be the slope of the disturbance, and ,but

[0076]

[0077] The steady-state error of the perturbation estimate after phase reshaping under slope perturbation can be obtained as follows:

[0078]

[0079] Therefore, when satisfied At that time, you can get That is, the corrected disturbance estimate. It can achieve zero steady-state error estimation of slope disturbances;

[0080] The total perturbation observation channel of the phase reshaping extended state observer can be regarded as a series corrector performing amplitude and phase shaping based on the total perturbation observation channel of the linear extended state observer; when the corrector is in unit form, the phase reshaping extended state observer degenerates into a standard linear extended state observer.

[0081] For fixed observer bandwidth Its observation performance is mainly determined by the corrector parameters. Furthermore, after satisfying the condition of zero steady-state error in the total slope disturbance observation, the degrees of freedom of the corrector parameters can be further reduced. The main parameters affect the mid-frequency phase compensation strength and high-frequency noise immunity. Primarily used to determine the position of the shaping window and adjust the setup speed. In engineering applications, it can be used within the observer bandwidth. Under the premise of fixed values, first select based on the allowable phase lag and noise level within the dominant frequency band of the disturbance. Adjust The shaping window is matched with the dominant frequency band of the disturbance, and the remaining parameters are calculated by means of no steady-state error constraint. This improves the timeliness and accuracy of the total disturbance estimation without increasing the observer bandwidth, while maintaining acceptable high-frequency noise resistance.

[0082] (2) To address the nonlinearity, internal and external coupling, and parameter uncertainty of the atomic gyroscope system, a power-approaching sliding mode variable structure controller is constructed to improve the system's error convergence speed, steady-state accuracy, and robustness.

[0083] The power-approaching sliding mode variable structure control law Tracking error Sliding surface and power-order approach term They are respectively:

[0084]

[0085]

[0086]

[0087]

[0088] in, For reference input; , The controller gain is given by the condition that the ... , ; , are positive integers and satisfy ; The saturation function is the boundary layer thickness parameter; the saturation function satisfies:

[0089]

[0090] Corrected disturbance estimate The power-order approximation sliding mode variable structure control law is introduced as a feedforward compensation term; the power-order term... Used to enhance the nonlinear approach effect and improve the sliding surface arrival speed when the error is large; saturation function Used to construct a boundary layer in the neighborhood of the sliding surface to replace the sign function switching term and reduce chattering in sliding mode control, thereby improving the engineering feasibility of the control law;

[0091] To analyze the convergence mechanism of this control law, we first consider the ideal power-law approaching term:

[0092]

[0093] In the corrected disturbance estimate Under the condition that the lumped disturbance can be accurately estimated and compensated, the system error dynamics can be written as:

[0094]

[0095] Right now

[0096]

[0097] Under the action of the ideal power-law approaching term, when the disturbance is accurately estimated and compensated, the closed-loop error dynamics satisfy the finite-time stability condition, that is, there exists a finite-time stability condition. This makes all :

[0098]

[0099] The aforementioned finite-time convergence conclusion corresponds to an ideal power-law approaching term; in engineering implementation, to reduce chattering caused by sign function switching, a saturation function is used. By making an alternative, the actual control system can maintain fast error convergence performance while converging the system state to the neighborhood of the sliding surface, thus balancing control stability and engineering feasibility; controller parameters , , , and The selection of the appropriate type can be tuned based on the system's desired bandwidth, allowable jitter level, and noise sensitivity. Determines the nonlinear reaching characteristics, Used to adjust the linear convergence rate. Used to enhance the nonlinear approach capability when the error is large. Used to determine the boundary layer thickness.

[0100] (3) Control Simulation Examples

[0101] To verify the effectiveness of the phase reshaping extended state observer and the power-approaching sliding mode control law proposed in this invention, comparative simulations were performed on the standard linear extended state observer and the phase reshaping extended state observer, as well as the linear feedback control law and the power-approaching sliding mode control law, under the same controlled object, sampling conditions, reference input, and observer bandwidth settings. Figure 1 A schematic diagram of the overall control structure of the present invention is provided.

[0102] Figure 2 Comparison results between the standard linear extended state observer and the phase reshaping extended state observer under step perturbation are presented. Figure 3 Comparison results between the standard linear extended state observer and the phase reshaping extended state observer under the effect of slope disturbance are presented; Figure 4 Comparison results between the standard linear extended state observer and the phase-reformed extended state observer under sinusoidal perturbation are presented. Figure 5 The comparison results between the power-approaching sliding mode control law and the linear feedback control law under sinusoidal disturbance are presented.

[0103] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for stable pump rate control of a spin-free exchange relaxation (SERF) atomic gyroscope based on a phase renormalization extended state observer and power-approaching sliding mode control, characterized in that... Implement the following steps: (1) For the dynamic model of the controlled object, in, The lumped disturbance term uniformly includes both internal uncertainties and external disturbances. To control the gain; To achieve effective estimation and compensation for ultra-low frequency slowly varying disturbances, an extended state observer is constructed to estimate the system output and lumped disturbances. The extended state observer is defined as follows: in This is an estimated value output by the system. This is an estimate of the lumped disturbance. , For observer gain; To address the steady-state error and phase lag issues of standard linear extended state observers when estimating ultra-low frequency ramp disturbances, a phase-reforming extended state observer is designed. A composite correction network with phase reshaping function is introduced into the disturbance estimation channel to achieve zero steady-state error estimation and phase lead compensation of ramp disturbances without excessively increasing the observation bandwidth and amplifying high-frequency noise, thereby improving the accuracy and response speed of disturbance estimation. Output of the composite correction network Transfer function of composite correction network They are respectively in , It is the dominant time constant. It is a gain adjustment factor, and , ; (2) To address the nonlinearity, internal and external coupling, and parameter uncertainty of the atomic gyroscope system, a power-approaching sliding mode variable structure controller is constructed to improve the system's error convergence speed, steady-state accuracy, and robustness. The power-approaching sliding mode variable structure control law Tracking error Sliding surface and power-order approach term They are respectively: in, For reference input; , The controller gain is given by the condition that the ... , ; , are positive integers and satisfy ; The saturation function is the boundary layer thickness parameter; the saturation function satisfies:

Images