CN113401366B - Strong anti-interference composite control method for overcoming influence of periodic moving parts - Google Patents

Strong anti-interference composite control method for overcoming influence of periodic moving parts Download PDF

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CN113401366B
CN113401366B CN202110674004.8A CN202110674004A CN113401366B CN 113401366 B CN113401366 B CN 113401366B CN 202110674004 A CN202110674004 A CN 202110674004A CN 113401366 B CN113401366 B CN 113401366B
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feedforward
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interference
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CN113401366A (en
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王佐伟
何刚
李建平
李乐尧
甘永
石恒
姚蘅
沈扬帆
王青
贾涛
于淑晶
高秀娟
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Beijing Institute of Control Engineering
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
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    • B64G1/00—Cosmonautic vehicles
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    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/244—Spacecraft control systems
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
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Abstract

The invention relates to a strong anti-interference composite control method for overcoming the influence of periodic moving parts, belonging to the field of spacecraft attitude control; the method comprises the steps of estimating periodic interference by comprehensively utilizing Fast Fourier Transform (FFT) and an Extended State Observer (ESO), designing an equivalent feedforward compensation law according to the angular momentum conservation principle on the basis, adjusting a feedforward compensation moment value of interference moment by utilizing a fuzzy logic system, and dynamically adjusting the gain of a PID controller according to whether the interference moment is in a feedforward compensation period or not. Compared with the prior art, the method does not need system identification and excessive model prior knowledge, and realizes better anti-interference effect by a simple control law; the invention is used for controlling the satellite attitude with periodic interference, and can effectively improve the attitude control precision and the attitude stability of the system. The whole method has strong systematicness, clear process and easy realization.

Description

Strong anti-interference composite control method for overcoming influence of periodic moving parts
Technical Field
The invention belongs to the field of spacecraft attitude control, and relates to a strong anti-interference composite control method for overcoming the influence of periodic moving parts.
Background
Large long-life satellites usually carry a large number of different types of loads, the dynamic characteristics of the satellites are complex, and the control requirements are high. For imaging loads, the attitude stability of the satellite platform is an important technical index. Under the influence of various interference factors such as flexible vibration, liquid shaking, component movement and the like, the improvement of the star attitude stability is difficult. Among the numerous sources of interference on the planet, low frequency motion disturbances of periodically moving parts are common and have significant effects. Common periodic moving parts on a satellite are a scanning camera, a scanning antenna, a solar panel driving mechanism (SADA), and the like. Especially the SADA, which is an important component required for almost all three-axis stable satellites. The SADA is typically driven by a stepper motor, with a step disturbance torque on stepping being significant. In the high-stability remote sensing satellite, a subdivision driving mode is mostly adopted to reduce single-step motion interference of the SADA. This requires special design in hardware, and the system cost is relatively high. Therefore, for the periodic motion disturbance, it is necessary to improve the control method to enhance the capability of resisting the motion disturbance as much as possible.
For unknown periodic interference, the existing control methods are mainly classified into 3 types: 1) when the interference cannot be measured, but the period is known, repeated control based on an internal model principle is generally adopted, which is feedback control, but when large unmodeled dynamics exist, the stability of the system is not easy to guarantee; 2) when the disturbance can be directly measured or is known in advance (the conditions are usually difficult to satisfy in engineering), a control method mainly based on feedforward is generally adopted, and the control method comprises an inverse dynamics method, a finite impulse response method and the like; 3) for satellite attitude control with unknown (cycle unknown or amplitude unknown) deterministic interference, the method of the existing document is mainly to establish an interference model by adopting a system identification method, and the uncertainty of model parameters is ensured by improving the robustness of a feedback control law.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, provides a strong anti-interference composite control method for overcoming the influence of periodic moving parts, is used for satellite attitude control with periodic interference, and can effectively improve the attitude control precision and attitude stability of a system. The whole method has strong systematicness, clear process and easy realization.
The technical scheme of the invention is as follows:
a strong anti-interference composite control method for overcoming the influence of a periodic moving part comprises the following steps:
step one, setting an angular velocity measurement period as h and recording a time sequence as t1,t2,…,tk…; the current angular velocity measurement is ω (k);
step two, taking the satellite angular velocity measurement sequences omega (k-N +1), … omega (k-1) and omega (k) as input, and outputting the first harmonic frequency f of the periodic motion interference by adopting a fast Fourier transform methoddAnd calculating the motion disturbance period Deltatd；
Step three, calculating the angular acceleration estimated value z of the current moment2(k) (ii) a Calculating the amplitude T of the periodic disturbance torqued(k) (ii) a And obtaining the maximum amplitude T of the periodic disturbance torqued,max；
Step four, the amplitude T of the periodic disturbance torqued(k) From 0 to 0.1 × Td,maxIs denoted as tsPeriod of same motion disturbance Δ tdAmplitude T of internal and periodic disturbance torqued(k) From Td,maxDown to 0.1 × Td,maxIs denoted as tf(ii) a Calculating each dynamic interference period delta tdInner feedforward compensation duration Δ tc(ii) a Number of sampling points N for calculating interference perioddAnd the number of sampling points N in the feedforward compensation durationc；
Step five, according to the sampling point number N of the interference perioddAnd the number of sampling points N in the feedforward compensation durationcCalculating feedforward control quantity Tc；
Step six, obtaining the maximum amplitude omega of the angular speed error by utilizing an extreme method according to the angular speed measurement sequences omega (k-N +1), … omega (k-1) and omega (k)max；
Step seven, according to the maximum amplitude T of the disturbance moment estimated valued,maxMaximum amplitude ω of the sum angular velocity errormaxCalculating the feedforward compensation time value delta t of the disturbance momentlead(ii) a And calculates a delay value deltat relative to the start time of the current calculation cyclelag；
Step eight, calculating the delay value delta t relative to the starting moment of the current calculation periodlagFeedforward compensation duration Δ tcFeedforward control amount TcThree parameters constitute the feedforward control rate, i.e. at after the start of the current calculation cyclelag～Δtlag+ΔtcIn a time period, a feedforward control quantity T is outputcAnd the feedforward compensation mark Sc1, placing; at Δ tlag～Δtlag+ΔtcAt a time outside the time interval, the feedforward control quantity T iscSet 0 and feed forward compensation flag ScSetting 0;
step nine, according to the feedforward compensation mark ScThe value of (3) is adjusted to the feedback control law;
and step ten, adding the control quantity output by the feedback control law and the control quantity output by the feedforward control rate to obtain a final composite control quantity, and controlling the satellite by using the composite control quantity.
In the above strong disturbance rejection complex control method for overcoming the influence of the periodically moving parts, in the second step, the fast fourier transform method is a radix-2 type fast fourier transform algorithm which is decimated according to time; period of motion disturbance Δ tdThe calculation method comprises the following steps:
Δtd＝1/fd。
in the above-mentioned strong disturbance rejection composite control method for overcoming the influence of periodically moving parts, in the third step, the angular acceleration estimated value z at the current moment2(k) The calculation method comprises the following steps:
Figure BDA0003120319280000031
in the formula, e (×) is observer error;
z1() is the observer first order state quantity;
h is an angular velocity measurement period;
ω (k-1) is the angular velocity measurement;
β1a first preset gain factor;
u (k) is a closed-loop control quantity;
j is the uniaxial moment of inertia of the star;
β2a second preset gain factor;
fal (x, α, δ) is a nonlinear function;
the nonlinear function fal (x, α, δ) is calculated by the formula:
Figure BDA0003120319280000041
in the formula, α and δ are both preset coefficients.
In the above-mentioned strong disturbance rejection composite control method for overcoming the influence of the periodically moving component, in the third step, the amplitude T of the periodically disturbing momentd(k) The calculation method comprises the following steps:
Td(k)＝u(k)-Jz2(k)
and obtaining the maximum amplitude T of the periodic disturbance torque by an extreme value judgment methodd,max。
In the above-mentioned strong disturbance rejection composite control method for overcoming the influence of the periodically moving part, in the fourth step, the feedforward compensation duration Δ tcThe calculation method comprises the following steps:
Δtc＝tf-ts。
in the above-mentioned strong anti-interference composite control method for overcoming the influence of the periodically moving part, in the fourth step, the number of sampling points N of the interference perioddThe calculation method comprises the following steps:
Figure BDA0003120319280000042
wherein Z (x) is rounded;
number of sampling points N within feedforward compensation durationcThe calculation method comprises the following steps:
Figure BDA0003120319280000043
in the above strong disturbance rejection composite control method for overcoming the influence of the periodically moving part, in the fifth step, the feedforward control quantity TcThe calculation method comprises the following steps:
Figure BDA0003120319280000044
in the above strong disturbance rejection composite control method for overcoming the influence of the periodically moving part, in the seventh step, the disturbance moment feedforward compensation time value delta tleadThe calculation method comprises the following steps: establishing a fuzzy logic system; the input variable of the fuzzy logic system is the maximum amplitude T of the periodic disturbance torqued,maxMaximum amplitude ω of the sum angular velocity errormaxThe output variable is the feedforward compensation time value delta t of the disturbance momentlead(ii) a The rules of fuzzy logic are shown in table 1:
TABLE 1
Figure BDA0003120319280000051
In the table, S represents Small; m represents in; b represents large; s1 indicates smaller; s2 indicates very small; b1 indicates larger; b2 denotes very large;
maximum amplitude T of periodic disturbance torqued,maxHas a discourse field of [0,0.15 ]]；
Maximum amplitude ω of angular velocity errormaxHas a discourse field of [0,0.01 ]]；
Disturbance moment feedforward compensation moment value delta tleadHas a discourse field of [0,4.3 ]]。
In the seventh step of the strong disturbance rejection composite control method for overcoming the influence of the periodically moving part, the current meter is compared with the current meterCalculating the delay value delta t of the starting moment of the cyclelagThe calculation method comprises the following steps:
Δtlag＝Δtd-Δtlead
in the formula,. DELTA.tdIs a motion disturbance period.
In the aforementioned strong disturbance rejection composite control method for overcoming the influence of the periodic moving part, in the ninth step, the feedback control law adopts a PID control rate, and the specific method for adjusting the PID control law is as follows:
when S iscWhen the value is equal to 0, namely during the non-feedforward compensation period, adopting a PID control law of normal gain; when S iscWhen the value is 1, namely during the feedforward torque compensation, a PID control law with higher gain is adopted, namely, the proportional coefficient and the differential coefficient of the PID control law are appropriately increased on the basis of a normal value.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method does not need system identification, and does not have excessive requirements on the prior knowledge of the model;
(2) the invention realizes the accurate compensation and inhibition of the periodic motion interference of the satellite moving parts and has better anti-interference effect.
Drawings
FIG. 1 is a flow chart of the strong anti-interference composite control of the present invention;
fig. 2 is a schematic structural diagram of a robust disturbance rejection complex control system according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples.
Aiming at the influence of on-satellite periodic moving parts, a novel feedforward and feedback composite control method with strong anti-interference capability is provided; the method comprehensively utilizes Fast Fourier Transform (FFT) and an Extended State Observer (ESO) to estimate periodic interference, on the basis, an equivalent feedforward compensation law is designed according to the angular momentum conservation principle, a fuzzy logic system is utilized to adjust the feedforward compensation time value of the interference moment, and the gain of a PID controller is dynamically adjusted according to whether the interference moment is in a feedforward compensation period or not. Compared with the existing method, the method does not need system identification and excessive model prior knowledge, and realizes better anti-interference effect by a simple control law.
As shown in fig. 1, the strong anti-interference composite control method for overcoming the influence of a periodic moving part specifically includes the following steps:
step one, setting an angular velocity measurement period as h and recording a time sequence as t1,t2…, tk, …; the current angular velocity measurement is ω (k).
Step two, taking the satellite angular velocity measurement sequences omega (k-N +1), … omega (k-1) and omega (k) as input, and outputting the first harmonic frequency f of the periodic motion interference by adopting a fast Fourier transform methoddAnd calculating the motion disturbance period Deltatd(ii) a The fast Fourier transform method is a radix-2 type fast Fourier transform algorithm which is selected according to time; period of motion disturbance Δ tdThe calculation method comprises the following steps:
Δtd＝1/fd。
step three, calculating the angular acceleration estimated value z at the current moment2(k) (ii) a Calculating the amplitude T of the periodic disturbance torqued(k) (ii) a And obtaining the maximum amplitude T of the periodic disturbance torqued,max(ii) a Angular acceleration estimate z at the present time2(k) The calculation method comprises the following steps:
Figure BDA0003120319280000061
in the formula, e (×) is observer error;
z1() is the observer first order state quantity;
h is an angular velocity measurement period;
ω (k-1) is the angular velocity measurement;
β1a first preset gain coefficient;
u (k) is a closed-loop control quantity;
j is the uniaxial moment of inertia of the star;
β2a second preset gain factor;
fal (x, α, δ) is a non-linear function;
the nonlinear function fal (x, α, δ) is calculated by the formula:
Figure BDA0003120319280000071
in the formula, both α and δ are predetermined coefficients.
Amplitude T of the periodic disturbance torqued(k) The calculation method comprises the following steps:
Td(k)＝u(k)-Jz2(k)
and obtaining the maximum amplitude T of the periodic disturbance torque by an extreme value judgment methodd,max。
Step four, the amplitude T of the periodic disturbance torqued(k) From 0 to 0.1 × Td,maxIs denoted as tsPeriod of same motion disturbance Δ tdAmplitude T of internal and periodic disturbance torqued(k) From Td,maxDown to 0.1 × Td,maxTime of (a) is recorded as tf(ii) a Calculating each dynamic interference period delta tdInner feedforward compensation duration Δ tc(ii) a Number of sampling points N for calculating interference perioddAnd the number of sampling points N in the feedforward compensation durationc(ii) a Feedforward compensation duration Δ tcThe calculation method comprises the following steps:
Δtc＝tf-ts。
number of sampling points N of interference perioddThe calculating method comprises the following steps:
Figure BDA0003120319280000072
wherein Z is rounded;
number of sampling points N within feedforward compensation durationcThe calculation method comprises the following steps:
Figure BDA0003120319280000081
step five, according to the sampling point number N of the interference perioddAnd feed forwardNumber of samples N within the compensated durationcCalculating feedforward control quantity Tc(ii) a Feedforward control quantity TcThe calculating method comprises the following steps:
Figure BDA0003120319280000082
step six, obtaining the maximum amplitude omega of the angular speed error by utilizing an extreme method according to the angular speed measurement sequences omega (k-N +1), … omega (k-1) and omega (k)max。
Step seven, according to the maximum amplitude T of the disturbance moment estimated valued,maxMaximum amplitude ω of the sum angular velocity errormaxCalculating the feedforward compensation time value delta t of the disturbance momentlead(ii) a And calculates a delay value deltat relative to the start time of the current calculation cyclelag(ii) a Disturbance moment feedforward compensation moment value delta tleadThe calculation method comprises the following steps: establishing a fuzzy logic system; the input variable of the fuzzy logic system is the maximum amplitude T of the periodic disturbance torqued,maxMaximum amplitude ω of the sum angular velocity errormaxThe output variable is the feedforward compensation time value delta t of the disturbance momentlead(ii) a The rules of fuzzy logic are shown in table 1:
TABLE 1
Figure BDA0003120319280000083
In the table, S represents Small; m represents in; b represents large; s1 indicates small; s2 indicates very small; b1 indicates larger; b2 denotes very large;
maximum amplitude T of periodic disturbance torqued,maxHas a discourse field of [0,0.15 ]]；
Maximum amplitude omega of angular velocity errormaxHas a discourse field of [0,0.01 ]]；
Disturbance moment feedforward compensation time value delta tleadHas a discourse field of [0,4.3 ]]。
Delay value delta t relative to the start time of the current calculation cyclelagThe calculating method comprises the following steps:
Δtlag＝Δtd-Δtlead
in the formula,. DELTA.tdIs a motion disturbance period.
Step eight, calculating the delay value delta t relative to the starting moment of the current calculation periodlagFeedforward compensation duration Δ tcFeedforward control amount TcThree parameters constitute the feedforward control rate, i.e. at after the start of the current calculation cyclelag～Δtlag+ΔtcIn a time period, a feedforward control quantity T is outputcAnd the feedforward compensation mark Sc1, placing; at Δ tlag～Δtlag+ΔtcAt the time outside the time interval, the feedforward control quantity T iscSet 0 and set the feedforward compensation flag ScSetting 0;
step nine, according to the feedforward compensation mark ScThe value of (3) is adjusted to the feedback control law; the feedback control law adopts PID control rate, and the specific method for adjusting the PID control law is as follows:
when S iscWhen the value is equal to 0, namely during the non-feedforward compensation period, adopting a PID control law of normal gain; when S iscWhen the value is 1, namely during the feedforward torque compensation, a PID control law with higher gain is adopted, namely, the proportional coefficient and the differential coefficient of the PID control law are appropriately increased on the basis of a normal value.
And step ten, adding the control quantity output by the feedback control law and the control quantity output by the feedforward control rate to obtain a final composite control quantity, and controlling the satellite by using the composite control quantity.
Examples
The embodiments of the present invention will be described by taking a satellite with a flywheel as an execution component. The satellite pitch axis control is taken as an example for explanation. Assuming that the inertia of the pitch axis of the satellite is 5000kg.m2, the maximum resultant moment of the flywheel set on the pitch axis is 0.2 Nm. The satellite movable part is SADA driven by a stepping motor through a reduction gear, and the motion period delta t of the satellite movable part isd4.32s, maximum moment T acting on stard,maxAbout 0.1Nm, and a dynamic course of single step motion of about 1 s. And the sampling period h of the controller is 0.1 s. The following technical points and calculation formulas are realized by satellite software and calculated in real time. FIG. 2 provides an embodiment of the present inventionThe structure of the strong anti-interference composite control system is shown schematically. In the present system, it is preferred that,
(1) the periodic interference frequency is estimated from the angular velocity measurement information using a fast fourier transform.
A conventional time-decimated radix-2 FFT algorithm is employed. The data length (number of sequence points) N is taken to be 128. The input of the FFT algorithm module is satellite angular velocity measurement information sequences omega (k-N +1), … omega (k-1) and omega (k), and the output is the first harmonic frequency (fundamental frequency) f of periodic motion interferenced. F is obtained by FFT algorithmdThen, the period value of the motion disturbance is obtained according to the following formula:
Δtd＝1/fd
(2) and designing a second-order extended state observer, obtaining a star acceleration estimated value from satellite angular velocity measurement information, and further calculating to obtain the amplitude of the periodic disturbance moment.
Designing a nonlinear discrete second-order extended state observer to obtain an angular acceleration estimated value z at the current moment2(k) The formula is as follows:
Figure BDA0003120319280000101
in the formula, e (×) is observer error;
z1() is the observer first order state quantity;
h is an angular velocity measurement period;
ω (k-1) is the angular velocity measurement;
β1a first preset gain coefficient;
u (k) is a closed-loop control quantity;
j is the uniaxial moment of inertia of the star;
β2a second preset gain factor;
fal (x, α, δ) is a non-linear function;
the relevant design factors are chosen as follows: beta is a1＝30，β2＝110。
Based on the output result of the extended state observer, further countingCalculating the amplitude T of the periodic disturbance torqued(k) The formula is as follows:
Td(k)＝Jz2(k)-u(k)
according to the accumulated time period (in this example, take 5 Δ t)d) The maximum amplitude T of the periodic disturbance torque is calculated by a conventional extreme value determination method (in this example, the simplest sequential comparison method is used)d,max。
(3) And calculating the equivalent disturbance moment feedforward compensation value in each compensation period.
3.1) will rise from 0 to 0.1Td,maxIs denoted as tsFrom Td,maxDown to 0.1 × Td,maxIs denoted as tf. Will be Δ tc＝tf-tsAs a period of each interference Δ tdThe feed forward compensation duration in. Respectively calculating the sampling points in the interference period and the compensation duration, wherein the formula is as follows:
Figure BDA0003120319280000111
Figure BDA0003120319280000112
in the formula, Z (×) represents a rounding operation.
3.2) calculating a feedforward control quantity, wherein the formula is as follows:
Figure BDA0003120319280000113
(4) and designing a two-dimensional fuzzy logic system for adjusting the feedforward compensation moment value of the disturbance moment.
The fuzzy logic system is designed by the following steps:
4-1) determining the discourse domain of input and output variables and defining corresponding fuzzy sets
The discourse domain of the input variable and the output variable is respectively as follows:
Td,max＝[0,0.15](Nm)，ωmax＝[0,0.01](°/s)，Δtlead＝[0,4.3](s)；
the fuzzy sets are respectively:
Td,max＝{S2,S1,M,B1,B2}
ωmax＝{S,M,B}
Δtlead＝{S2,S1,M,B1,B2}
4-2) establishing a fuzzy rule base
The fuzzy rule base is described in the form of a fuzzy rule table, as shown in table 1.
4-3) determining membership functions of variables
In the invention, the membership function of each variable has no special requirement, so the same membership function is adopted. The membership function adopts a triangular membership function. The expression is as follows:
Figure BDA0003120319280000121
in the formula, xiAs an input quantity, ciIs the value of the ith equipartition point in the domain of discourse, biIs an adjustable parameter.
4-4) establishing a fuzzy system adopting a single-value fuzzy machine, a Mamdani inference machine and a central average ambiguity resolver
In the fuzzy inference engine, the inference type adopts a Mamdani fuzzy implication minimum operation method, and (and) operation adopts an intersection method (a small method), or (also/or) operation adopts a union method (a large method), and a maximum-minimum method is used for synthesis.
(5) And performing feedforward torque compensation according to the disturbance torque feedforward compensation moment value.
Feed-forward compensation time value delta t given by fuzzy logic systemleadConverting the delay value relative to the starting moment of the current calculation cycle into a delay value, wherein the conversion formula is as follows:
Δtlag＝Δtd-Δtlead
(6) and dynamically adjusting the gain of the PID feedback control law according to whether the PID feedback control law is in the feedforward compensation period or not.
The feedback control law uses the most common PID control law.
During the non-feedforward compensation period, the PID control law of normal gain is adopted. For this example, the PID control law normal parameters are as follows: kp＝30、Ki＝0.3、Kd40. During the feedforward torque compensation, a PID control law with higher gain is adopted, namely the proportional coefficient and the differential coefficient of the PID control law are properly increased on the basis of a normal value. For this example, K is taken during the feed-forward torque compensationp＝50、Ki＝0.3、Kd＝65。
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (10)

1. A robust disturbance rejection composite control method for overcoming effects of periodically moving parts, comprising:
step one, setting an angular velocity measurement period as h and recording a time sequence as t1,t2,…,tk…; the current angular velocity measurement is ω (k);
step two, taking the satellite angular velocity measurement sequences omega (k-N +1), … omega (k-1) and omega (k) as input, and outputting the first harmonic frequency f of the periodic motion interference by adopting a fast Fourier transform methoddAnd according to said fdCalculating the motion disturbance period Deltatd；
Thirdly, calculating the angular acceleration estimated value z at the current moment according to the angular velocity measured value omega (k-1)2(k) (ii) a Calculating the amplitude T of the periodic disturbance torqued(k) (ii) a And obtaining the maximum amplitude T of the periodic disturbance torqued,max；
Step four, amplitude T of the periodic disturbance torqued(k)From 0 to 0.1 × Td,maxIs denoted as tsPeriod of same motion disturbance Δ tdAmplitude T of internal and periodic disturbance torqued(k) From Td,maxDown to 0.1 × Td,maxIs denoted as tf(ii) a Calculating each dynamic interference period delta tdInner feedforward compensation duration Δ tc(ii) a Number of sampling points N for calculating interference perioddAnd the number of sampling points N in the feedforward compensation durationc；
Step five, according to the sampling point number N of the interference perioddAnd the number of sampling points N in the feedforward compensation durationcCalculating feedforward control quantity Tc；
Step six, obtaining the maximum amplitude omega of the angular speed error by utilizing an extreme method according to the angular speed measurement sequences omega (k-N +1), … omega (k-1) and omega (k)max；
Step seven, according to the maximum amplitude T of the disturbance moment estimated valued,maxMaximum amplitude ω of the sum angular velocity errormaxCalculating the feedforward compensation time value delta t of the disturbance momentlead(ii) a And calculates a delay value deltat relative to the start time of the current calculation cyclelag；
Step eight, calculating the delay value delta t relative to the starting moment of the current calculation periodlagFeedforward compensation duration Δ tcFeedforward control amount TcThree parameters constitute the feedforward control law, namely delta t after the beginning of the current calculation cyclelag～Δtlag+ΔtcIn a time period, a feedforward control quantity T is outputcAnd the feedforward compensation mark Sc1, placing; at Δ tlag～Δtlag+ΔtcAt a time outside the time interval, the feedforward control quantity T iscSet 0 and set the feedforward compensation flag ScSetting 0;
step nine, according to the feedforward compensation mark ScThe value of (3) is adjusted to the feedback control law;
and step ten, adding the feedback control quantity output by the feedback control law and the feedforward control quantity to obtain a final composite control quantity, and controlling the satellite by using the composite control quantity.
2. The method according to claim 1, wherein in the second step, the fast fourier transform method is a radix-2 type fast fourier transform algorithm decimated in time; according to fdCalculating the motion disturbance period DeltatdThe method comprises the following steps:
Δtd＝1/fd。
3. the method as claimed in claim 1, wherein in step three, the angular acceleration at the current time z is estimated2(k) The calculation method comprises the following steps:
Figure FDA0003120319270000021
in the formula, e (×) is observer error;
z1() is the observer first order state quantity;
h is an angular velocity measurement period;
ω (k-1) is the angular velocity measurement;
β1a first preset gain coefficient;
u (k) is a closed-loop control quantity;
j is the uniaxial moment of inertia of the star;
β2a second preset gain factor;
fal (x, α, δ) is a non-linear function;
the nonlinear function fal (x, α, δ) is calculated by the formula:
Figure FDA0003120319270000031
in the formula, both α and δ are predetermined coefficients.
4. The method of claim 3, wherein: in the third step, the amplitude T of the periodic disturbance torqued(k) The calculation method comprises the following steps:
Td(k)＝u(k)-Jz2(k)
and obtaining the maximum amplitude T of the periodic disturbance torque by an extreme value judgment methodd,max。
5. The method of claim 4, wherein: in the fourth step, the feedforward compensation duration Δ tcThe calculating method comprises the following steps:
Δtc＝tf-ts。
6. the method of claim 5, wherein: in the fourth step, the number of sampling points in the interference period is NdThe calculation method comprises the following steps:
Figure FDA0003120319270000032
wherein Z (x) is rounded;
number of sampling points N within feedforward compensation durationcThe calculation method comprises the following steps:
Figure FDA0003120319270000033
7. the method of claim 6, wherein: in the fifth step, the control quantity T is fed forwardcThe calculation method comprises the following steps:
Figure FDA0003120319270000034
8. the method of claim 7, wherein: in the seventh step, the disturbance moment feedforward compensation time value delta tleadThe calculating method comprises the following steps: establishing a fuzzy logic system; the input variable of the fuzzy logic system is the maximum amplitude T of the periodic disturbance torqued,maxMaximum amplitude of sum angular velocity errorValue omegamaxThe output variable is the feedforward compensation time value delta t of the disturbance momentlead(ii) a The rules of fuzzy logic are shown in table 1:
TABLE 1
Figure FDA0003120319270000041
In the table, S represents Small; m represents in; b represents large; s1 indicates smaller; s2 indicates very small; b1 indicates larger; b2 denotes very large;
maximum amplitude T of periodic disturbance torqued,maxHas a discourse field of [0,0.15 ]]；
Maximum amplitude ω of angular velocity errormaxHas a discourse field of [0,0.01 ]]；
Disturbance moment feedforward compensation time value delta tleadHas a discourse field of [0,4.3 ]]。
9. The method of claim 8, wherein: in the seventh step, the delay value delta t relative to the starting time of the current calculation periodlagThe calculation method comprises the following steps:
Δtlag＝Δtd-Δtlead
in the formula,. DELTA.tdIs a motion disturbance period.
10. The method of claim 9, wherein: in the ninth step, the feedback control law adopts a PID control rate, and the specific method for adjusting the PID control law is as follows:
when S iscWhen the value is equal to 0, namely during the non-feedforward compensation period, adopting a PID control law of normal gain; when S iscWhen the value is equal to 1, namely the feedforward torque compensation period, a PID control law with higher gain is adopted, namely the proportional coefficient and the differential coefficient of the PID control law are appropriately increased on the basis of normal values.
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