CN109709496A - A kind of quantum sensor closed-loop control system and phase error compensation control method - Google Patents

A kind of quantum sensor closed-loop control system and phase error compensation control method Download PDF

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CN109709496A
CN109709496A CN201711016700.XA CN201711016700A CN109709496A CN 109709496 A CN109709496 A CN 109709496A CN 201711016700 A CN201711016700 A CN 201711016700A CN 109709496 A CN109709496 A CN 109709496A
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quantum sensor
sinusoidal signal
magnetic resonance
control system
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CN109709496B (en
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秦杰
汤恩琼
万双爱
郭宇豪
薛帅
刘建丰
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Beijing Automation Control Equipment Institute BACEI
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Abstract

The invention belongs to quantum field of sensing technologies, more particularly to a kind of quantum sensor closed-loop control system and phase error compensation control method, the system includes controller, digital direct frequency synthesizer DDS, quantum sensor, low-pass filter LPF, analog/digital converter A/D and phase resolve module;The two-way sinusoidal signal of digital direct frequency synthesizer DDS output, signal passes through low-pass filter LPF and analog/digital converter A/D link all the way, another way signal first passes through quantum sensor, then after passing through low-pass filter LPF and analog/digital converter A/D link again, it first passes through phase and resolves after module carries out dynamic compensation to the phase error that two-way sinusoidal signal generates and feed back to controller again, closed-loop control is carried out to magnetic resonance quantum sensor.The present invention reduces influence of the control system phase error to quantum sensor magnetic-field measurement precision, improves the measurement accuracy of quantum sensor, the present invention is especially suitable for the magnetic anomaly detection fields more demanding to measurement accuracy.

Description

A kind of quantum sensor closed-loop control system and phase error compensation control method
Technical field
The invention belongs to quantum field of sensing technologies, and in particular to a kind of quantum sensor closed-loop control system and phase are missed Poor compensating control method.
Background technique
Quantum sensor realizes the measurement to magnetic field using quantum spin effect, is a kind of magnetic field with hypersensitivity Test device has wide practical use in fields such as geological prospecting, biologic medical and far-reaching extra large magnetic anomaly detections.
Quantum sensor based on magnetic resonance effect realizes the precise measurement to magnetic field by measurement Quantum Spin frequency, can Reach higher accuracy of measurement.It may be implemented using the phase closed-loop control system based on related operation principle to Quantum Spin The stability contorting of frequency, and Quantum Spin is made to be in resonance state always, to achieve the purpose that accurately to measure magnetic field strength.
Summary of the invention
For the above-mentioned prior art, it is an object of the invention to propose a kind of quantum sensor closed-loop control system and phase Error compensation control method, the control deviation that real-time compensation phase error introduces, makes Quantum Spin frequency be more nearly magnetic resonance Frequency effectively improves measurement accuracy of the quantum sensor within the scope of its Measurement bandwidth.
In order to achieve the above object, the present invention uses following technical scheme.
A kind of magnetic resonance quantum sensor closed-loop control system of the present invention, which includes controller, direct digital frequency Synthesizer DDS, quantum sensor, low-pass filter LPF and analog/digital converter A/D;
The two-way sinusoidal signal of digital direct frequency synthesizer DDS output, signal passes through low-pass filter LPF and mould all the way Quasi-/digital quantizer A/D link feeds back to controller, and another way signal first passes through quantum sensor, then passes through low pass filtered again Wave device LPF and analog/digital converter A/D link feed back to controller, when the phase for the two-way sinusoidal signal that controller receives There are when deviation, controller can export sinusoidal letter to digital direct frequency synthesizer DDS for potential difference and the input of controller phase reference Number frequency be adjusted, and using after adjusting digital direct frequency synthesizer DDS export sinusoidal signal it is defeated as pumping signal Enter quantum sensor.
Further, the controller phase reference input is 90 °.
Further, which further includes that phase resolves module;The two-way sine letter of digital direct frequency synthesizer DDS output Number, for signal by low-pass filter LPF and analog/digital converter A/D link, another way signal first passes through quantum sensing all the way Device after then passing through low-pass filter LPF and analog/digital converter A/D link again, first passes through phase and resolves module to two-way The phase error that sinusoidal signal generates feeds back to controller after carrying out dynamic compensation again, carries out closed loop to magnetic resonance quantum sensor Control.
Further, the phase resolves module according to two-way input signal, the sinusoidal letter of real-time resolving quantum sensor output Number amplitude, then resolve current magnetic field environment under, phase error existing for magnetic resonance quantum sensor closed-loop control system mend Value is repaid, to resolve the phase error that obtained phase error compensation value complement repays magnetic resonance control system.
Further, the calculation formula of quantum sensor output sinusoidal signal amplitude are as follows:
In formula: AoThe amplitude of sinusoidal signal is exported for quantum sensor, T is magnetic resonance quantum sensor closed-loop control system The control period, VoIt (t) is quantum sensor voltage output, t is time variable;
Further, the phase error compensation value, which resolves, includes:
(1) variables A is setmax0WithInitial value be 0, execute following algorithm within first control period:
Amax0=Ao (4)
In formula: Amax0The maximum value of sinusoidal signal amplitude in all control periods in past is exported for quantum sensor, For the phase error in a control period in magnetic resonance quantum sensor closed-loop control system, AoQuantum sensor exports sinusoidal signal It is amplitude;
(2) since second control period, current period quantum sensor output sinusoidal signal is sought according to formula (3) Amplitude Ao, then sequence executes formula (5) described algorithm, and by current period phase error compensation valueWith the phase of controller Position reference input superposition, carries out the closed-loop control of magnetic resonance phase control system, after the operation in several control periods,It receives After holding back,Phase error compensation value existing for control system under current magnetic field environment as to be sought;
In formula: Amax1Sinusoidal signal is exported in all control periods including current control period for quantum sensor The maximum value of amplitude, Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroAmount Sub- sensor output sinusoidal signal is amplitude,For phase error compensation value, kpAnd kiFor constant, kpValue range is 0.1- 2, kiValue range is 0.01-0.2,Phase for a control period in magnetic resonance quantum sensor closed-loop control system is missed Difference, T are the control period of magnetic resonance quantum sensor closed-loop control system.
A kind of magnetic resonance quantum sensor phase error compensation control method, method includes the following steps:
Step 1: phase resolves the amplitude of module real-time resolving quantum sensor output sinusoidal signal;
It is resolved under current magnetic field environment Step 2: phase resolves module, magnetic resonance quantum sensor closed-loop control system is deposited Phase error compensation value;
Step 3: changing the magnetic field strength of stabilizing magnetic field environment locating for quantum sensor, step 1 and step 2 are repeated, is obtained Obtain the phase error of quantum sensor magnetic resonance control system under different magnetic resonance frequencies;To magnetic resonance frequency and phase error Discrete relationship carried out curve fitting using 1 yuan of n rank equation, obtain the fit correlation of phase error compensation value and magnetic resonance frequency Expression formula;
Step 4: in each control cycle, according to current quantum sensor sinusoidal signal frequency, real-time update phase is missed Poor offset, with the compensation magnetic resonance control system phase error of real-time update.
Further, in the step 1, quantum sensor voltage output sinusoidal signal in stabilizing magnetic field environment Expression formula are as follows:
In formula: VoIt (t) is quantum sensor voltage output, AoThe amplitude of sinusoidal signal is exported for quantum sensor, ω is frequency Rate,For phase, t is time variable;
The real time settlement of the amplitude of quantum sensor output sinusoidal signal in stabilizing magnetic field environment uses auto-correlation Algorithm, shown in the following formula of auto-correlation algorithm:
In formula: T is the control period of magnetic resonance quantum sensor closed-loop control system, VoIt (t) is quantum sensor voltage Output, t is time variable, AoThe amplitude of sinusoidal signal is exported for quantum sensor;
The calculation formula of quantum sensor output sinusoidal signal amplitude are as follows:
In formula: AoThe amplitude of sinusoidal signal is exported for quantum sensor, T is magnetic resonance quantum sensor closed-loop control system The control period, VoIt (t) is quantum sensor voltage output, t is time variable.
Further, in the step 2, phase error compensation value solution process the following steps are included:
(1) variables A is setmax0WithInitial value be 0, execute following algorithm within first control period:
Amax0=Ao (4)
In formula: Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroAmount Sub- sensor output sinusoidal signal is amplitude;
(2) since second control period, current period quantum sensor output sinusoidal signal is sought according to formula (3) Amplitude Ao, then sequence executes formula (5) described algorithm, and by current period phase error compensation valueWith the phase of controller Position reference input superposition, carries out the closed-loop control of magnetic resonance phase control system, after the operation by several control periods, After convergence,Phase error compensation value existing for control system under current magnetic field environment as to be sought;
In formula: Amax1Sinusoidal signal is exported in all control periods including current control period for quantum sensor The maximum value of amplitude, Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroAmount Sub- sensor output sinusoidal signal is amplitude,For phase error compensation value, kpAnd kiFor constant, kpValue range is 0.1- 2, kiValue range is 0.01-0.2,Phase for a control period in magnetic resonance quantum sensor closed-loop control system is missed Difference, T are the control period of magnetic resonance quantum sensor closed-loop control system.
Technical solution provided in an embodiment of the present invention has the benefit that
A kind of quantum sensor closed-loop control system of the present invention and phase error compensation control method, to magnetic resonance phase control Systematic phase error processed carries out real-time compensation, reduces control system phase error to the shadow of quantum sensor magnetic-field measurement precision It rings.
A kind of quantum sensor closed-loop control system of the present invention and phase error compensation control method, being capable of effective compensation magnetic Resonate phase error existing for phase control system, improves the measurement accuracy of quantum sensor.
A kind of quantum sensor closed-loop control system of the present invention and phase error compensation control method, are applied to nuclear magnetic resonance Gyro and atom magnetometer based on paramagnetic resonance effect, especially suitable for being led to the more demanding magnetic anomaly detection of measurement accuracy Domain.
Detailed description of the invention
Fig. 1 is magnetic resonance quantum sensor closed-loop control system structural schematic diagram of the present invention;
Fig. 2 is the relation schematic diagram between quantum sensor magnetic resonance frequency of the present invention and magnetic field strength;
Fig. 3 is present invention compensation front and back magnetic field strength measurement error contrast schematic diagram.
Specific embodiment
A kind of quantum sensor closed-loop control system of the present invention and phase are missed with attached drawing With reference to embodiment Poor compensating control method is described in detail.
As shown in Figure 1, a kind of magnetic resonance quantum sensor closed-loop control system of the present invention, including controller, number is directly Frequency synthesizer DDS, quantum sensor, low-pass filter LPF and analog/digital converter A/D;
Digital direct frequency synthesizer DDS output two-way sinusoidal signal, a-road-through cross low-pass filter LPF and simulation/ Digital quantizer A/D link feeds back to controller, and another way first passes through quantum sensor, then passes through low-pass filter LPF again Controller is fed back to analog/digital converter A/D link, phase difference and control when the two-way sinusoidal signal that controller receives There are when deviation, controller can export digital sinusoidal signal to digital direct frequency synthesizer DDS for device phase reference input processed Frequency is adjusted, and inputs quantum sensor as pumping signal.
When the frequency of the pumping signal is quantum sensor magnetic resonance frequency, two-way sinusoidal signal that controller receives Phase difference be 90 °, quantum sensor magnetic output signal amplitude also reaches maximum value at this time;Therefore setting controller phase reference Input is 90 °, and quantum sensor can work in magnetic resonance state, to realize the accurate measurement to magnetic field.
The two paths of signals of digital direct frequency synthesizer DDS output passes through low-pass filter LPF and analog/digital converter When A/D link, since these links realize upper and Non-completety symmetry in circuit, thus digital direct frequency synthesizer will lead to The phase difference of the two-way sinusoidal signal of DDS output can generate phase error after by these links, this phase error meeting When leading to magnetic resonance phase closed-loop control system stable state, the phase difference non-90 degree for the two-way sinusoidal signal that controller receives, finally Lead to Quantum Spin frequency departure resonant frequency, and then influences the magnetic-field measurement precision of quantum sensor.
Also, when the main field locating for the quantum sensor changes, Quantum Spin resonant frequency changes therewith, no The same corresponding control system phase error of resonant frequency is also different.
A kind of magnetic resonance quantum sensor closed-loop control system further includes that phase resolves module, number directly frequency The two-way sinusoidal signal of rate synthesizer DDS output, a-road-through cross low-pass filter LPF and analog/digital converter A/D link, Another way first passes through quantum sensor, after then passing through low-pass filter LPF and analog/digital converter A/D link again, first leads to It crosses phase and resolves after module carries out dynamic compensation to the phase error that two-way sinusoidal signal generates and feed back to controller again, realize magnetic The closed-loop control for the quantum sensor that resonates.
The invention also includes a kind of magnetic resonance quantum sensor phase error compensation control method, this method includes following step It is rapid:
Step 1: the amplitude of real-time resolving quantum sensor output sinusoidal signal;
The expression formula of quantum sensor voltage output sinusoidal signal in stabilizing magnetic field environment are as follows:
In formula: VoIt (t) is quantum sensor voltage output, AoThe amplitude of sinusoidal signal is exported for quantum sensor, ω is frequency Rate,For phase, t is time variable;
The real time settlement of the amplitude of quantum sensor output sinusoidal signal in stabilizing magnetic field environment is used certainly Related algorithm, shown in the following formula of auto-correlation algorithm:
In formula: T is the control period of magnetic resonance quantum sensor closed-loop control system, VoIt (t) is quantum sensor voltage Output, t is time variable, AoThe amplitude of sinusoidal signal is exported for quantum sensor;
The then calculation formula of quantum sensor output sinusoidal signal amplitude are as follows:
In formula: AoThe amplitude of sinusoidal signal is exported for quantum sensor, T is magnetic resonance quantum sensor closed-loop control system The control period, VoIt (t) is quantum sensor voltage output, t is time variable;
Step 2: resolving under current magnetic field environment, phase error existing for magnetic resonance quantum sensor closed-loop control system Offset;
Phase error compensation value solution process the following steps are included:
(1) variables A is setmax0WithInitial value be 0, execute following algorithm within first control period:
Amax0=Ao (4)
In formula: Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroAmount Sub- sensor output sinusoidal signal is amplitude;
(2) since second control period, current period quantum sensor output sinusoidal signal is sought according to formula (3) Amplitude Ao, then sequentially execute following algorithm, and by current period phase error compensation valueWith the phase reference of controller Input superposition, carries out the closed-loop control of magnetic resonance phase control system, after the operation by several control periods,It converges to After constant value, phase error compensation value existing for control system under current magnetic field environment as to be sought;
In formula: Amax1Sinusoidal signal is exported in all control periods including current control period for quantum sensor The maximum value of amplitude, Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroAmount Sub- sensor output sinusoidal signal is amplitude,For phase error compensation value, kpAnd kiFor constant, kpValue range is 0.1- 2, kiValue range is 0.01-0.2,Phase for a control period in magnetic resonance quantum sensor closed-loop control system is missed Difference, T are the control period of magnetic resonance quantum sensor closed-loop control system;
Step 3: changing the magnetic field strength of stabilizing magnetic field environment locating for quantum sensor, step 1 and step 2 are repeated, is obtained Obtain the phase error of quantum sensor magnetic resonance control system under different magnetic resonance frequencies;To magnetic resonance frequency and phase error Discrete relationship carried out curve fitting using 1 yuan of n rank equation, obtain phase error compensation valueWith magnetic resonance frequency frFitting Relational expression is denoted as
Step 4: in each control cycle, according to current quantum sensor sinusoidal signal frequency, real-time update phase is missed Poor offsetWith real-time updateMagnetic resonance control system phase error is compensated, the measurement accuracy of quantum sensor is promoted.
As shown in Figures 2 and 3, right using a kind of magnetic resonance quantum sensor phase error compensation control method of the present invention The magnetic field strength measurement range of certain known quantum sensor is 20000nT-80000nT.Magnetic field strength becomes in the measurement range When changing 1nT, quantum sensor magnetic resonance frequency changes 3.5Hz.It draws between quantum sensor magnetic resonance frequency and magnetic field strength Relation curve it is as shown in Fig. 2.
In order to measure influence of the magnetic resonance closed-loop control system phase error to magnetic-field measurement accuracy, quantum is passed first Sensor is placed in the stabilizing magnetic field, then continuously changes biography within the scope of 20000nT-80000nT with 1000nT fixed step size The magnetic field strength in magnetic field locating for sensor, real-time measurement quantum sensor magnetic resonance frequency.Magnetic resonance frequency and magnetic according to Fig.2, Field intensity relationship can obtain the measured value for currently giving magnetic field strength.The relationship drawn between magnetic field strength measured value and given value is bent It is shown in solid in line such as attached drawing 3.It is shown in solid it can be found that when there are phase errors for magnetic resonance closed-loop control system from Fig. 3 When, to the measurement of known magnetic field, there are errors, and the error can increase with the increase of magnetic field strength, thus the amount of seriously affecting The accuracy of measurement of sub- sensor.
Control is finally compensated to magnetic resonance control system using phase error compensation control method provided by the invention, After can must compensating between magnetic field strength measured value and given value relation curve as shown in dotted line in attached drawing 3.It is shown in solid from Fig. 3 It can be found that the compensating control method can improve the measurement accuracy of quantum sensor with effective compensation phase error.

Claims (9)

1. a kind of magnetic resonance quantum sensor closed-loop control system, it is characterised in that: the system includes controller, number directly frequency Rate synthesizer DDS, quantum sensor, low-pass filter LPF and analog/digital converter A/D;
Digital direct frequency synthesizer DDS output two-way sinusoidal signal, all the way signal by low-pass filter LPF and simulation/ Digital quantizer A/D link feeds back to controller, and another way signal first passes through quantum sensor, then passes through low-pass filter again LPF and analog/digital converter A/D link feed back to controller, when the phase difference for the two-way sinusoidal signal that controller receives And for the input of controller phase reference there are when deviation, controller can export sinusoidal signal to digital direct frequency synthesizer DDS Frequency is adjusted, and the sinusoidal signal that digital direct frequency synthesizer DDS after adjusting is exported is as pumping signal input quantity Sub- sensor.
2. a kind of magnetic resonance quantum sensor closed-loop control system according to claim 1, it is characterised in that: the control The input of device phase reference is 90 °.
3. a kind of magnetic resonance quantum sensor closed-loop control system according to claim 2, it is characterised in that: the system is also Module is resolved including phase;The two-way sinusoidal signal of digital direct frequency synthesizer DDS output, signal passes through low-pass filtering all the way Device LPF and analog/digital converter A/D link, another way signal first pass through quantum sensor, then pass through low-pass filter again After LPF and analog/digital converter A/D link, first passes through phase and resolve the phase error that module generates two-way sinusoidal signal Controller is fed back to again after carrying out dynamic compensation, and closed-loop control is carried out to magnetic resonance quantum sensor.
4. a kind of magnetic resonance quantum sensor closed-loop control system according to claim 3, it is characterised in that: the phase Module is resolved according to two-way input signal, real-time resolving quantum sensor exports the amplitude of sinusoidal signal, then resolves current magnetic Under the environment of field, phase error compensation value existing for magnetic resonance quantum sensor closed-loop control system is missed with resolving obtained phase The phase error of poor offset compensation magnetic resonance control system.
5. a kind of magnetic resonance quantum sensor closed-loop control system according to claim 4, it is characterised in that: quantum sensing The calculation formula of device output sinusoidal signal amplitude are as follows:
In formula: AoThe amplitude of sinusoidal signal is exported for quantum sensor, T is the control of magnetic resonance quantum sensor closed-loop control system Period processed, VoIt (t) is quantum sensor voltage output, t is time variable.
6. a kind of magnetic resonance quantum sensor closed-loop control system according to claim 5, it is characterised in that: the phase Error compensation value resolves
(1) variables A is setmax0WithInitial value be 0, execute following algorithm within first control period:
Amax0=Ao (4)
In formula: Amax0The maximum value of sinusoidal signal amplitude in all control periods in past is exported for quantum sensor,For magnetic The phase error in a control period, A in the quantum sensor closed-loop control system that resonatesoQuantum sensor exports sinusoidal signal Amplitude;
(2) since second control period, the width of current period quantum sensor output sinusoidal signal is sought according to formula (3) Value Ao, then sequence executes formula (5) described algorithm, and by current period phase error compensation valueJoin with the phase of controller Input superposition is examined, the closed-loop control of magnetic resonance phase control system is carried out, after the operation in several control periods,Convergence Afterwards,Phase error compensation value existing for control system under current magnetic field environment as to be sought;
In formula: Amax1Sinusoidal signal amplitude in all control periods including current control period is exported for quantum sensor Maximum value, Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroQuantum passes It is amplitude that sensor, which exports sinusoidal signal,For phase error compensation value, kpAnd kiFor constant, kpValue range is 0.1-2, ki Value range is 0.01-0.2,For the phase error in a control period in magnetic resonance quantum sensor closed-loop control system, T For the control period of magnetic resonance quantum sensor closed-loop control system.
7. the quantum sensor phase error of magnetic resonance quantum sensor closed-loop control system described in a kind of pair of claim 3 carries out The method for compensating control, which is characterized in that method includes the following steps:
Step 1: phase resolves the amplitude of module real-time resolving quantum sensor output sinusoidal signal;
It is resolved under current magnetic field environment Step 2: phase resolves module, existing for magnetic resonance quantum sensor closed-loop control system Phase error compensation value;
Step 3: changing the magnetic field strength of stabilizing magnetic field environment locating for quantum sensor, step 1 and step 2, acquisition amount are repeated The phase error of sub- sensor magnetic resonance control system under different magnetic resonance frequencies;To magnetic resonance frequency and phase error from The relationship of dissipating is carried out curve fitting using 1 yuan of n rank equation, and the fit correlation for obtaining phase error compensation value and magnetic resonance frequency is expressed Formula;
Step 4: in each control cycle, according to current quantum sensor sinusoidal signal frequency, real-time update phase error is mended Value is repaid, with the compensation magnetic resonance control system phase error of real-time update.
8. a kind of magnetic resonance quantum sensor phase error compensation control method according to claim 7, it is characterised in that: In the step 1, the expression formula of the quantum sensor voltage output sinusoidal signal in stabilizing magnetic field environment are as follows:
In formula: VoIt (t) is quantum sensor voltage output, AoThe amplitude of sinusoidal signal is exported for quantum sensor, ω is frequency,For phase, t is time variable;
The real time settlement of the amplitude of quantum sensor output sinusoidal signal in stabilizing magnetic field environment uses auto-correlation algorithm, Shown in the following formula of auto-correlation algorithm:
In formula: T is the control period of magnetic resonance quantum sensor closed-loop control system, VoIt (t) is quantum sensor voltage output, t For time variable, AoThe amplitude of sinusoidal signal is exported for quantum sensor;
The calculation formula of quantum sensor output sinusoidal signal amplitude are as follows:
In formula: AoThe amplitude of sinusoidal signal is exported for quantum sensor, T is the control of magnetic resonance quantum sensor closed-loop control system Period processed, VoIt (t) is quantum sensor voltage output, t is time variable.
9. a kind of magnetic resonance quantum sensor phase error compensation control method according to claim 8, it is characterised in that: In the step 2, phase error compensation value solution process the following steps are included:
(1) variables A is setmax0WithInitial value be 0, execute following algorithm within first control period:
Amax0=Ao (4)
In formula: Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroQuantum passes It is amplitude that sensor, which exports sinusoidal signal,;
(2) since second control period, the width of current period quantum sensor output sinusoidal signal is sought according to formula (3) Value Ao, then sequence executes formula (5) described algorithm, and by current period phase error compensation valueJoin with the phase of controller Input superposition is examined, the closed-loop control of magnetic resonance phase control system is carried out, after the operation by several control periods,Convergence Afterwards,Phase error compensation value existing for control system under current magnetic field environment as to be sought;
In formula: Amax1Sinusoidal signal amplitude in all control periods including current control period is exported for quantum sensor Maximum value, Amax0The maximum value of sinusoidal signal amplitude in all control periods in past, A are exported for quantum sensoroQuantum passes It is amplitude that sensor, which exports sinusoidal signal,For phase error compensation value, kpAnd kiFor constant, kpValue range is 0.1-2, ki Value range is 0.01-0.2,For the phase error in a control period in magnetic resonance quantum sensor closed-loop control system, T For the control period of magnetic resonance quantum sensor closed-loop control system.
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