Design method of drag-free control system based on test mass acceleration PSD index

Abstract

The present invention provides a design method for a drag-free control system based on a proof mass acceleration PSD index, comprising the following steps: designing PID parameters, controlling the refresh rate, and the time constant of the inertial link connected in series with the differential link in the PID controller based on the supremum frequency of the frequency band specified by the proof mass acceleration PSD index requirement of the drag-free control system; calculating whether the proof mass acceleration PSD design value of the drag-free control system meets the index requirement in the specified frequency band, reducing the propulsion time constant and / or reducing the noise envelope parameter, and adjusting the PID parameters and the control refresh rate accordingly until the stability margin of the drag-free control system meets the index requirement and the proof mass acceleration PSD design value meets the index requirement in the specified frequency band; and outputting the design parameters that meet the requirements. The present invention establishes a proof mass acceleration PSD index expression based on the external disturbance force noise acceleration PSD envelope, and provides a systematic design method for a displacement drag-free control system.

Description

Technical Field

[0001] The invention relates to the technical field of satellite drag-free control, in particular to a design method of a drag-free control system based on a proof mass acceleration PSD index. Background Art

[0002] Drag-free control technology is a key technology in the field of control technology for gravity field measurement satellites, gravitational wave detection satellites and equivalent principle verification satellites. According to the different state variables controlled, drag-free control is divided into two categories: acceleration mode drag-free control and displacement mode drag-free control. Displacement mode drag-free control can make the test mass in the inertial sensor almost unaffected by any conservative and non-conservative forces other than the gravity of celestial bodies, so it can be regarded as a space inertial reference. It is one of the major key technologies for space gravitational wave detection spacecraft.

[0003] Displacement mode drag-free control requires that the test mass in the onboard inertial sensor be controlled within a small range of variation near its nominal position in the electrode cage by a thruster with continuously adjustable thrust. The displacement of the test mass relative to the nominal position is the result of the negative stiffness force of the electrostatic bias and the satellite being subjected to sunlight pressure, atmospheric drag and thrust of the thruster. The negative stiffness coefficient of the inertial sensor along the drag-free control channel is The essential characteristics of the displacement-drag-free controlled object are to make the displacement-drag-free controlled object have positive real eigenvalues ​​and open-loop instability.

[0004] At present, there are no reports in the public literature on the design method of displacement drag-free control system. my country has a space inertial reference technology test satellite displacement drag-free control system that integrates ready-made inertial sensors and cold air propulsion system. There is no clear proof mass acceleration PSD index requirement, only an easily achievable time domain index requirement. The displacement drag-free control system uses space gravitational wave detection as the application scenario. In the future space gravitational wave detection scientific mission model, there will inevitably be clear proof mass acceleration PSD index requirements from the top level. Summary of the invention

[0005] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a displacement drag-free control system design method based on the test mass acceleration PSD index, which lays a systematic theoretical foundation for the design of such drag-free control systems, the determination of propulsion system index requirements and the adjustment of PID control parameters.

[0006] The technical solution of the present invention is:

[0007] The design method of the drag-free control system based on the inspection mass acceleration PSD index includes the following steps:

[0008] (1) Construct a drag-free control system, which is a forward loop including a PID controller with an inertial link in series with a differential link, a propulsion system and an inertial sensor. There is a unit negative feedback closed-loop system with external disturbance force acceleration noise between the propulsion system and the inertial sensor. The displacement of the test mass in the spacecraft inertial sensor is controlled by driving the propulsion system with a PID controller. The design parameters include PID parameters, the time constant T of the inertial link in series with the differential link of the PID controller, and the time constant T of the inertial link in series with the differential link of the PID controller. d , control refresh rate f s , the noise envelope parameters of the external disturbance force acceleration noise, the propulsion time constant of the propulsion system;

[0009] (2) The supremum frequency ω of the specified frequency band based on the PSD index requirement of the test mass acceleration of the drag-free control system h Design PID parameters and determine f according to PID parameters s , and according to f s Determine T d ;

[0010] (3) Preset the noise envelope parameters and propulsion time constant, combined with the PID parameters designed in (2), f s and T d , calculate the stability margin of the drag-free control system. If the stability margin index is met, go to step (4). Otherwise, adjust the PID parameters to make the bandwidth of the drag-free control system ω c Reduce until the stability margin meets the index requirements and go to step (4);

[0011] (4) Calculate whether the design value of the test mass acceleration PSD of the drag-free control system in the frequency band specified by the test mass acceleration PSD index requirement meets the requirement. If so, proceed to step (6); otherwise, proceed to step (5);

[0012] (5) Reduce the propulsion time constant and / or reduce the noise envelope parameters, and adjust the PID parameters, f accordingly. s and T d , until the stability margin of the drag-free control system meets the index requirements and the design value of its test mass acceleration PSD meets the test mass acceleration PSD index requirements in the specified frequency band;

[0013] (6) Output the design parameters that meet the requirements.

[0014] Preferably, in step (2), the supremum frequency ω of the specified frequency band based on the test mass acceleration PSD index of the drag-free control system is h Design PID parameters, specifically:

[0015] Take the drag-free control system bandwidth ω cThe upper bound frequency ω of the specified frequency band of the test mass acceleration PSD indicator h One order of magnitude larger, select the PID parameters according to the following expression:

[0016]

[0017]

[0018]

[0019] In the formula, k p is the proportionality coefficient, k i is the integration coefficient, k d is the differential coefficient, is the negative stiffness coefficient of the test mass and ξ is the damping coefficient.

[0020] Preferably, in step (2), f is determined according to the PID parameters s , specifically:

[0021] f s Satisfies the following expression:

[0022] Where π is the ratio of a circle to its circumference.

[0023] Preferably, in step (2), according to f s Determine T d , specifically:

[0024]

[0025] Preferably, the noise envelope parameter includes the PSD value S of the medium and high frequency white noise. m and the standard deviation of low frequency pink noise driving white noise σ l .

[0026] Preferably, the standard deviation σ of the low-frequency pink noise driving white noise is l Determined by: PSD envelope curve of low frequency pink noise Take any frequency point f=f0 and the corresponding coordinate point (f0, S1(f0)), and calculate it according to the following formula:

[0027] Preferably, the propulsion system adopts cold air propulsion, and the design value of the proof mass acceleration PSD of the drag-free control system is calculated by the following expression:

[0028]

[0029]

[0030] In the formula, Sx1 (ω) is the design value of the test mass acceleration PSD of the drag-free control system when the propulsion system adopts cold gas propulsion, ω is the circular frequency independent variable, τ1 is the cold gas propulsion delay time, and τ2 is the time constant of the cold gas propulsion inertia link.

[0031] Preferably, the propulsion system adopts electric propulsion, and the design value of the proof mass acceleration PSD of the drag-free control system is calculated by the following expression:

[0032]

[0033]

[0034] In the formula, S x2 (ω) is the design value of the test mass acceleration PSD of the drag-free control system when the propulsion system adopts electric propulsion, τ3 is the electric propulsion delay time, τ4 is the time constant of the electric propulsion inertia link, and ζ is the damping coefficient of the second-order oscillation link of the electric propulsion.

[0035] Preferably, in step (5), the propulsion time constant is adjusted and / or the noise envelope parameter is reduced, and the PID parameters, f s and T d , until the stability margin of the drag-free control system meets the index requirements and the PSD value of its test mass acceleration meets the index requirements, specifically:

[0036] Shorten the push time constant and / or reduce the noise envelope parameters; when shortening the push time constant, expand ω c As the goal, increase the PID parameters and increase the control refresh rate f s , and by f s Determine T d .

[0037] Preferably, in step (3), the PID parameters are adjusted so that the system bandwidth ω c Reduce until the stability margin meets the index requirements, specifically: reduce the value of PID parameters as little as possible while meeting the stability margin index.

[0038] The advantages of the present invention compared with the prior art are:

[0039] (1) The present invention provides an initial value range for PID controller parameter tuning, so that the iterative search and determination process of PID parameters can be carried out;

[0040] (2) The present invention provides an analytical expression for the acceleration PSD index that the proof mass is expected to achieve by taking into account the displacement no-drag control system sensor, actuator, combined external disturbance force noise envelope and PID controller, making the process of determining whether the acceleration PSD index requirement of the displacement no-drag control system can be met simple and convenient, and also facilitating the formulation of index requirements for the propulsion system;

[0041] (3) The present invention provides specific steps for designing a displacement drag-free control system based on the inspection mass acceleration PSD index requirements, which is convenient for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the design method of a drag-free control system based on the inspection mass acceleration PSD index of the present invention;

[0043] Figure 2 It is a block diagram of the displacement drag-free control system of the present invention. DETAILED DESCRIPTION

[0044] In order to make the objectives, technical solutions and advantages of the present invention more clear, the specific implementation methods of the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0045] Drag-free control technology is a key technology in the field of control technology for gravity field measurement satellites, gravitational wave detection satellites and equivalent principle verification satellites. The concepts of the test mass, negative stiffness system, test mass acceleration PSD, etc. described in the present invention can refer to the invention patent CN111638643B "A method for determining the dynamic coordination conditions of a displacement mode drag-free control" and the literature "Canuto E, Massotti L. All-propulsion design of the drag-free and attitude control of the European satellite GOCE[J]. Acta Astronautica, 2009, 64(2-3): 325-344".

[0046] like Figure 2 As shown, the drag-free control system includes a PID controller link C, a propulsion system link T, an external disturbance force acceleration noise link n and an inertial sensor link I, x is the displacement of the inspection mass in the inertial sensor in the displacement drag-free control system relative to the negative stiffness force zero position, and the negative stiffness force zero position is generally located at the geometric center of the electrode cage in the inertial sensor; r x is the instruction displacement, usually specified as r x =0; e is the control deviation; I represents the inertial sensor link, which is a second-order link without zero point, and its transfer function is:

[0047]

[0048] In the formula, s is the differential operator, It is called the negative stiffness coefficient. This parameter reflects the essential characteristics of the displacement drag-free control system: open-loop instability. The test mass is placed in the inertial sensor electrode cage and is not affected by non-conservative external interference forces such as solar pressure, propulsion system thrust and atmospheric resistance. It is mainly affected by the negative stiffness force corresponding to the negative stiffness coefficient. Therefore, the residual acceleration of the test mass is:

[0049]

[0050] In the displacement mode drag-free control, when x = 0, the test mass in the inertial sensor is not affected by any conservative or non-conservative forces other than the gravity of the celestial body, and is thus regarded as a space inertial reference. Therefore, the displacement mode drag-free control technology is one of the key technologies for space gravitational wave detection spacecraft.

[0051] PID controller link C is a series correction controller link, which outputs the acceleration control quantity, and its transfer function is:

[0052]

[0053] Among them, k p is the proportionality coefficient, k i is the integration coefficient, k d is the differential coefficient, T d It is the time constant of the inertia link connected in series with the differential link.

[0054] The propulsion system link T generally has two options: a continuously variable thrust cold air propulsion system and a continuously variable thrust electric propulsion system, which outputs the real acceleration control amount. Among them, the continuously variable thrust drag-free cold air propulsion system has a transfer function of:

[0055]

[0056] Among them, τ1 is the first time lag parameter, and τ2 is the time constant of the inertia link.

[0057] The transfer function of the continuously variable thrust drag-free electric propulsion system is:

[0058]

[0059] Among them, τ3 is the second time lag parameter, τ4 is the time constant of the second-order oscillation link, and ζ is the damping coefficient of the second-order oscillation link of electric propulsion.

[0060] The external disturbance force acceleration noise link n corresponds to the synthetic external disturbance force of all non-conservative forces such as sunlight pressure and drag-free control thrust acting on the spacecraft. Displacement drag-free spacecraft are generally far away from the atmosphere and are not affected by atmospheric drag. However, when conducting displacement drag-free control tests in low-Earth medium orbit, atmospheric drag is also part of the synthetic external disturbance force. According to engineering experience, thrust noise generally dominates the synthetic external disturbance force acceleration noise.

[0061] The external disturbance force acceleration noise component n is low-frequency pink noise N l With medium and high frequency white noise N m The result of synthesis, low frequency pink noise N l The transfer function is:

[0062]

[0063] Its noise envelope parameter is the standard deviation of its envelope noise driving white noise σ l The method for determining this parameter is: in the low frequency pink noise PSD envelope curve

[0064]

[0065] The coordinate point (f0, S l (f0)) and calculate it as follows:

[0066]

[0067] Medium and high frequency white noise N m The transfer function is:

[0068] N m (s)=1

[0069] Its noise envelope parameter is the PSD value S of its envelope white noise. m .

[0070] The power spectrum density of the external disturbance acceleration noise n is:

[0071]

[0072] Where ω is the circular frequency independent variable.

[0073] The control object transfer function between the closed-loop inertial sensor link and the propulsion system link, which represents the mass of the untowed spacecraft, is Incorporated into the PID controller and synthesized external disturbance force acceleration noise.

[0074] The transfer function from the synthetic external disturbance acceleration noise to the control output is:

[0075]

[0076] Thus, in the case of cold air propulsion:

[0077]

[0078] In case of electric propulsion:

[0079]

[0080] Assuming that there is a measurement of the relative speed of the test mass, there is no need to connect the inertia link in series in the differential link of the PID controller. Therefore, without considering the transfer function of the propulsion system link, the transfer function from the synthetic external disturbance acceleration noise to the control deviation is simplified to:

[0081]

[0082] The displacement-free drag control of the spacecraft is mainly controlled by the k p The coefficient provides the restoring force acceleration to offset the negative stiffness force and establishes the approximate closed-loop control bandwidth ω c The closed-loop control bandwidth generally needs to be larger than the control refresh rate f corresponding to the sampling control period. s The corresponding Nyquist frequency is more than one order of magnitude smaller. Applying the Routh-Hurwitz criterion to the denominator of the above equation, the necessary conditions that the PID parameter values ​​should meet are:

[0083]

[0084]

[0085]

[0086] In the formula, ξ is the damping coefficient introduced by PID control, which is generally 0.707 and takes a value in the interval (0,1). In order to ensure that the closed-loop system of various links such as the propulsion link, the inertial link connected in series with the differential link of the PID controller, and even the anti-aliasing filter link after the inertial sensor output has sufficient stability margin, it is generally taken as:

[0087]

[0088] According to the random control system theory, the mass residual acceleration PSD index S is tested. x Satisfies the relationship:

[0089]

[0090] Where j is the imaginary unit.

[0091] When the transfer function from the synthetic external disturbance acceleration noise to the control deviation is taken as a simplified expression, the PSD expression of the residual acceleration of the test mass is derived as follows:

[0092]

[0093] In engineering practice, there is generally no dedicated test mass relative speed measurement link, so the differential link in the PID controller must be connected in series with an inertia link. In the case of displacement drag-free control, the time constant of the inertia link is T d Generally, it is taken as the sampling control period:

[0094]

[0095] Or take a value near this period, usually On this basis, when cold gas propulsion is used as the displacement drag-free control actuator, the PSD expression of the residual acceleration of the test mass is derived as follows:

[0096]

[0097] In the formula, the denominator is expressed as follows:

[0098]

[0099] When electric propulsion is used as the displacement drag-free control actuator, the PSD expression of the residual acceleration of the test mass is derived as follows:

[0100]

[0101] In the formula, the denominator is expressed as follows:

[0102]

[0103] Taking the case of using electric propulsion as the displacement drag-free control actuator as an example, the following understanding can be obtained from the PSD expression of the residual acceleration of the inspection mass:

[0104] As the circular frequency independent variable tends to zero, the residual acceleration PSD of the test mass also tends to zero, that is:

[0105]

[0106] If there is a gravitational wave signal in the ultra-low frequency band, no matter how weak the signal is, as long as the frequency band is low enough and the observation time is long enough, the gravitational wave signal can always be detected;

[0107] Increase k p It is beneficial to make S x2 (ω) decreases, which is conducive to the highlighting of gravitational wave signals;

[0108] The basic parameter σ corresponding to the low-frequency pink noise + medium-high frequency white noise envelope of the combined external disturbance acceleration noise PSD l With S m The smaller the S x2 (ω) is also smaller. Since thrust noise plays a dominant role in external disturbance force, this actually requires that thrust noise be reduced as much as possible.

[0109] Increasing the PID parameters will directly lead to a wider bandwidth of the displacement drag-free control closed-loop system. In order to ensure the stability of the closed-loop system, the bandwidth of the propulsion system is required to be wide enough, so that the two time constants τ3 and τ4 in the propulsion model should be small enough. Without considering the engineering implementation constraints, the smaller τ3 and τ4 are, the better.

[0110] The above understanding is also valid for the case where cold air propulsion is used as the displacement drag-free control actuator, and is also valid for the ideal propulsion case where τ3 and τ4 are both zero.

[0111] Based on the above derivation, a drag-free control system design method based on the inspection mass acceleration PSD index is proposed, and its flow chart is as follows: Figure 1 As shown,

[0112] Assume that the displacement drag-free control system has the following index requirements for the residual acceleration PSD of the test mass:

[0113] S x1 (ω) r (ω∈[ω l ,ω h ])

[0114] Among them, S r is the upper limit of the displacement drag-free control system test mass residual acceleration PSD index, ω l is the lower limit frequency required by the displacement drag-free control system to test the residual acceleration PSD index, ω h It is the upper limit frequency required for verifying the mass residual acceleration PSD index of the displacement drag-free control system.

[0115] The design parameters of the system include the PID parameters of the PID controller, the time constant T of the inertia link connected in series with the differential link, and the time constant T d , control refresh rate f s , the noise envelope parameters of the external disturbance acceleration noise, the propulsion time constant of the propulsion system; the noise envelope parameters include σ l With S m When the propulsion system adopts cold air propulsion, the propulsion time constants are τ1 and τ2. When the propulsion system adopts electric propulsion, the propulsion time constants are τ3 and τ4.

[0116] The steps to design a drag-free control system based on this indicator are as follows:​

[0117] S1: Take the displacement no-drag control bandwidth ω c The upper limit frequency ω required by the index h About one order of magnitude larger, without considering the propulsion transfer function, the PID parameters are preliminarily calculated under the guidance of the PID parameter value range, and based on and engineering implementation constraints, and in turn preliminarily select the control refresh rate f of the displacement no-drag control s The time constant T of the inertia link connected in series with the differential link in the PID controller d ;

[0118] S2: Introduce the propulsion system transfer function into the open-loop transfer function to calculate the stability margin of the unit negative feedback closed-loop system; if the stability margin index is insufficient, appropriately reduce the control bandwidth ω by reducing the PID parameters c , until the stability margin index is met;

[0119] S3: Calculate whether the residual acceleration PSD index of the inspection mass is satisfied. If so, go to step S7; if not, go to step S4;

[0120] S4: Adjust the design index of the control system to improve the index requirements of the propulsion system within the acceptable range of the propulsion system product, shorten the propulsion time constant (τ1 and τ2 or τ3 and τ4) and / or reduce the noise envelope parameter σ l With S m , in the case where the propulsion time constant is shortened, in order to expand the closed-loop system bandwidth ω c As the goal, increase the PID parameters and increase the control refresh rate f s , and by f s Determine the time constant T of the inertia link connected in series with the differential link in the PID controller d ;

[0121] S5: Calculate the stability margin of the unit negative feedback closed-loop system. If the stability margin index is insufficient, appropriately reduce the control bandwidth ω c , until the stability margin index is met;

[0122] S6: Calculate whether the residual acceleration PSD index of the inspection mass is satisfied. If so, go to step S7; if not, go to step S4;

[0123] S7: The design of the displacement mode drag-free control system is completed.

[0124] Finally, the drag-free propulsion system is put into production with the final control component model and its noise parameters as the index requirements to determine the control refresh rate f s Back-calculation of the sampling control period T of the drag-free control system for spacecraft displacementc , thereby guiding the development, testing and application of drag-free control systems.

[0125] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A drag-free control system design method based on the inspection mass acceleration PSD index is characterized by: The following steps are involved: (1) Construct a drag-free control system, which is a forward loop including a PID controller with an inertial link in series with a differential link, a propulsion system and an inertial sensor. There is a unit negative feedback closed-loop system with external disturbance force acceleration noise between the propulsion system and the inertial sensor. The displacement of the test mass in the spacecraft inertial sensor is controlled by driving the propulsion system with a PID controller. The design parameters include PID parameters, the time constant T of the inertial link in series with the differential link of the PID controller, and the time constant T of the inertial link in series with the differential link of the PID controller. d , control refresh rate f s , the noise envelope parameters of the external disturbance force acceleration noise, the propulsion time constant of the propulsion system; (2) The supremum frequency ω of the specified frequency band based on the PSD index requirement of the test mass acceleration of the drag-free control system h Design PID parameters and determine f according to PID parameters s , and according to f s Determine T d ; (3) Preset the noise envelope parameters and propulsion time constant, combined with the PID parameters designed in (2), f s and T d , calculate the stability margin of the drag-free control system. If the stability margin index is met, go to step (4). Otherwise, adjust the PID parameters to make the bandwidth of the drag-free control system ω c Reduce until the stability margin meets the index requirements and go to step (4); (4) Calculate whether the design value of the test mass acceleration PSD of the drag-free control system in the frequency band specified by the test mass acceleration PSD index requirement meets the requirement. If so, proceed to step (6); otherwise, proceed to step (5); (5) Reduce the propulsion time constant and / or reduce the noise envelope parameters, and adjust the PID parameters, f accordingly. s and T d , until the stability margin of the drag-free control system meets the index requirements and the design value of its test mass acceleration PSD meets the test mass acceleration PSD index requirements in the specified frequency band; (6) Output the design parameters that meet the requirements.

2. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 1 is characterized in that: In step (2), the supremum frequency ω of the specified frequency band based on the test mass acceleration PSD index of the drag-free control system h Design PID parameters, specifically: Take the drag-free control system bandwidth ω c The upper bound frequency ω of the specified frequency band of the test mass acceleration PSD indicator h One order of magnitude larger, select the PID parameters according to the following expression: In the formula, k p is the proportionality coefficient, k i is the integration coefficient, k d is the differential coefficient, is the negative stiffness coefficient of the test mass and ξ is the damping coefficient.

3. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 2 is characterized in that: In step (2), f is determined according to the PID parameters s , specifically: f s Satisfies the following expression: Where π is the ratio of a circle to its circumference.

4. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 3 is characterized in that: In the step (2), according to f s Determine T d , specifically:

5. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 4 is characterized in that: The noise envelope parameters include the PSD value S of the medium and high frequency white noise m and the standard deviation of low frequency pink noise driving white noise σ l .

6. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 5 is characterized in that: The standard deviation of the low-frequency pink noise driving the white noise is σ l Determined by: PSD envelope curve of low frequency pink noise Take any frequency point f=f0 and the corresponding coordinate point (f0, S1(f0)), and calculate it according to the following formula:

7. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 6 is characterized in that: The propulsion system adopts cold air propulsion, and the design value of the test mass acceleration PSD without drag control system is calculated by the following expression: In the formula, S x1 (ω) is the design value of the test mass acceleration PSD of the drag-free control system when the propulsion system adopts cold gas propulsion, ω is the circular frequency independent variable, τ1 is the cold gas propulsion delay time, and τ2 is the time constant of the cold gas propulsion inertia link.

8. The drag-free control system design method based on the proof mass acceleration PSD index according to claim 6 is characterized in that: The propulsion system adopts electric propulsion, and the design value of the test mass acceleration PSD without drag control system is calculated by the following expression: In the formula, S x2 (ω) is the design value of the test mass acceleration PSD of the drag-free control system when the propulsion system adopts electric propulsion, τ3 is the electric propulsion delay time, τ4 is the time constant of the electric propulsion inertia link, and ζ is the damping coefficient of the second-order oscillation link of the electric propulsion.

9. The drag-free control system design method based on the test mass acceleration PSD index according to any one of claims 1 to 8, wherein in step (5), the propulsion time constant is adjusted and / or the noise envelope parameter is reduced, and the PID parameters, f s and T d , until the stability margin of the drag-free control system meets the index requirements and the PSD value of its test mass acceleration meets the index requirements, specifically: Shorten the push time constant and / or reduce the noise envelope parameters; when shortening the push time constant, expand ω c As the goal, increase the PID parameters and increase the control refresh rate f s , and by f s Determine T d .

10. The drag-free control system design method based on the proof mass acceleration PSD index according to any one of claims 1 to 8, characterized in that: In step (3), the PID parameters are adjusted so that the system bandwidth ω c Reduce until the stability margin meets the index requirements, specifically: reduce the PID parameter values ​​as little as possible while meeting the stability margin index.

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