CN104267732B - Flexible satellite high stability attitude control method based on frequency-domain analysis - Google Patents

Abstract

Flexible satellite high stability attitude control method based on frequency-domain analysis, is related to Flexible Satellite Attitude control field.Purpose is by reducing the amplitude-frequency response exported from exogenous disturbances to angular speed, so as to realize the high stability gesture stability to flexible satellite.Attitude control method proposed by the present invention is under the influence of interference and uncertainty is considered, large inertia characteristic and high stability control for satellite requires to propose attitude control method, based on traditional PD control device, interference inverter is devised with robust Model matching principle；Transfer function model when flexible influence is turned into broad sense interference and is not turned into broad sense interference is sets forth, the performance of interference inverter is analyzed using frequency domain method, while providing reference for the selection of PD parameters and compensator parameter.This method effectively inhibits the vibration of windsurfing, improves attitude control accuracy and stability, suitable for engineer applied.

Description

Flexible satellite high-stability attitude control method based on frequency domain analysis

Technical Field

The invention relates to the field of flexible satellite attitude control.

Background

In the modern times, the increasingly fierce comprehensive national competition inevitably promotes the rapid development of science and technology. With outstanding contributions and important roles in the military and civilian areas, aerospace technology continues to advance and has always received much attention from both the nation and researchers. Satellites are now widely used as products of aerospace technology, including communications, meteorological observations, navigation, and the like.

With the gradual technical maturity and the increasing demand for space exploration, satellites have a larger size and a very complex structure, and are usually equipped with accessories for implementing various functions, such as solar panels, sports antennas, etc., which put high demands on control. Meanwhile, the indexes such as precision, stability, response speed and service life become important factors in the design of the attitude control system.

A flexible satellite attitude control system is faced with a nonlinear system with parameters, uncertain dynamics and interference influence, meanwhile, the control performance index of a satellite is greatly improved, the attitude is required to have high pointing accuracy and stability, and how to design a reasonable and effective control method is a problem which needs to be solved all the time on the basis.

The attitude control method of the flexible satellite can be divided into a classical control method, a modern control method, an intelligent control method and a comprehensive control method generated by mutual combination and penetration among the classical control method, the Improved satellite attitude control using a disturbance compensator adopts a control method of PD plus disturbance compensator, the suppression of flexibility influence and disturbance is realized, the attitude stabilization is achieved, and a low-pass filter is introduced to process high-frequency modal influence; in the literature, "design of a flywheel attitude control system of a flexible aircraft", a PID (proportion integration differentiation) controller is designed and a parameter setting method is provided for the flexible aircraft controlled by a flywheel based on a single-axis decoupling model, and good control effect is verified through simulation; the document 'spacecraft attitude maneuver and stable active disturbance rejection control' adopts an active disturbance rejection control method, effectively compensates the influence of uncertain factors such as disturbance and the like through a nonlinear error feedback law and an extended observer, and meets the requirement of high stability after the attitude maneuver; the document "Optimal attitude control for three-axis stabilized flexible spacecraft" designs an Optimal controller by applying an LQR method aiming at a three-axis stabilized flexible spacecraft with a flywheel as an actuating mechanism, and obtains satisfactory effects on vibration suppression and attitude control; the document "Low-order robust implementation of an earth observation satellite" adopts an H-infinity theory to design a Low-order robust controller, and compared with a satellite in the prior SPOT system, the control effect is greatly improved. The literature, "Adaptive fuzzy sliding mode control for flexible satellite" considers that fuzzy control and sliding mode control are combined and an Adaptive method is introduced for controlling the attitude of the flexible satellite, so that high attitude control precision is obtained. The document 'variable sliding mode variable structure and active vibration control during attitude maneuver of a three-axis stable flexible satellite' aims at the problem of attitude maneuver of the flexible satellite, considers the situation that the control moment is limited, adopts a sliding mode control method, and simultaneously utilizes a piezoelectric element to actively control vibration. The literature, "flexible spacecraft adaptive sliding mode control based on input shaping" combines an input shaping method and an adaptive sliding mode control method to carry out control law design, so that a system can complete tracking of a nominal system under the influence of parameter uncertainty and external disturbance, and flexible vibration is restrained.

Disclosure of Invention

The invention provides a high-stability attitude control method of a flexible satellite based on frequency domain analysis, and aims to realize high-stability attitude control of the flexible satellite by reducing amplitude-frequency response from interference input to angular speed output.

The flexible satellite high-stability attitude control method based on frequency domain analysis comprises a rolling axis control method, a pitching axis control method and a yawing axis control method, wherein the pitching axis control method comprises the following steps:

step one, establishing a dynamic model of a flexible satellite, performing small-angle assumption and simplification, and taking a single accessory for the simplified dynamic model to obtain a frequency domain equation;

obtaining a transfer function relation between an actual pitch angle theta and a total moment T according to a frequency domain equation, and obtaining a simplified model of a pitch axis of the flexible satellite according to the relation between the actual pitch angle theta and the total moment T;

step three, in the flexible satellite pitch axis simplified model, omitting a controller part and putting all flexible modal influences into interference to obtain an expression of an interference compensator Z;

performing frequency domain analysis on the simplified model of the pitch axis of the flexible satellite after the interference compensator is added to obtain a flexible influence generalized interference analysis result and a flexible influence non-generalized interference analysis result;

fifthly, obtaining a filtering parameter and a PD control parameter of the interference compensator Z according to the flexible influence generalized interference analysis result and the flexible influence non-generalized interference analysis result;

adding an interference compensator Z into the pitch channel system, and adopting PD control on a pitch channel to realize the attitude control of the pitch axis of the flexible satellite;

and step seven, respectively controlling the rolling shaft attitude and the yaw shaft attitude through the processes from the step one to the step six, and realizing the attitude control of the flexible satellite.

Has the advantages that: the attitude control method of the flexible satellite provided by the invention provides an attitude control solution aiming at the large inertia characteristic and high stability control requirement of the satellite under the influence of interference and uncertainty, and designs an interference compensator by applying a robust model matching principle on the basis of a traditional PD controller; transfer function models of flexible influence and non-flexible influence during generalized interference are respectively given, the performance of the interference compensator is analyzed by adopting a frequency domain method, and meanwhile, reference is provided for selection of PD parameters and compensator parameters. The method can effectively inhibit the vibration of the sailboard, greatly improve the accuracy and stability of attitude control, and is suitable for engineering application.

Drawings

Fig. 1 is a flowchart of a method for controlling a high stability attitude of a flexible satellite based on frequency domain analysis according to a first embodiment;

FIG. 2 is a schematic diagram of a conventional satellite attitude control system;

FIG. 3 is a schematic diagram of a robust model matching method;

FIG. 4 is a block diagram of a pitch channel system incorporating a disturbance compensator and having the effect of flexibility as a generalized disturbance;

FIG. 5 is a block diagram of a pitch channel system incorporating a disturbance compensator and taking into account the effect of flexibility;

FIG. 6 is a graph of open-loop frequency characteristics of the system with a constant PD parameter and a varying disturbance compensator parameter;

FIG. 7 is a graph of amplitude-frequency characteristics of the system from interference to angular velocity output when the PD parameters are constant and the parameters of the interference compensator are changed;

FIG. 8 shows the interference compensator with constant parameters and the PD controller with proportional parameter k_pyA system open loop frequency characteristic curve graph during variation;

FIG. 9 shows the interference compensator with constant parameters and the PD controller with proportional parameter k_pyA closed-loop frequency characteristic curve graph of the system during variation;

FIG. 10 shows the interference compensator with constant parameters and the PD controller with proportional parameter k_pyAn amplitude-frequency characteristic curve graph from interference to angular speed output in variation;

FIG. 11 is a plot of attitude angle of the system without the introduction of an interference compensator;

FIG. 12 is a plot of system attitude angular velocity without the introduction of an interference compensator;

FIG. 13 is a plot of system control torque without the introduction of disturbance compensators;

FIG. 14 is a plot of the total ambient torque of the system without the introduction of a disturbance compensator;

FIG. 15 is a graph of four environmental disturbance moments of the system without introducing a disturbance compensator, including a gravity gradient moment, a aerodynamic moment, a solar pressure moment, and a remanence moment;

FIG. 16 is a modal coordinate plot of a system pitch axis (Y-axis) positive direction windsurfing board without the introduction of a disturbance compensator;

FIG. 17 is a modal coordinate plot of a system pitch axis (Y-axis) negative direction windsurfing board without the introduction of disturbance compensators;

FIG. 18 is a plot of the attitude angle of the system with the introduction of a disturbance compensator;

FIG. 19 is a plot of system attitude angular velocity with the introduction of a disturbance compensator;

FIG. 20 is a plot of system control torque with the introduction of a disturbance compensator;

FIG. 21 is a modal coordinate curve of a system pitch axis (Y-axis) positive direction windsurfing board with the introduction of a disturbance compensator;

FIG. 22 is a modal coordinate plot of a system pitch axis (Y-axis) negative direction windsurfing board with the introduction of a disturbance compensator.

Detailed Description

First embodiment, the present embodiment is described with reference to fig. 1, and the method for controlling a high stability attitude of a flexible satellite based on frequency domain analysis according to the present embodiment includes the following steps:

step one, establishing a dynamic model of a flexible satellite, performing small-angle assumption and simplification, and taking a single accessory for the simplified dynamic model to obtain a frequency domain equation;

obtaining a transfer function relation between an actual pitch angle theta and a total moment T according to a frequency domain equation, and obtaining a simplified model of a pitch axis of the flexible satellite according to the relation between the actual pitch angle theta and the total moment T;

step three, in the flexible satellite pitch axis simplified model, omitting a controller part and putting all flexible modal influences into interference to obtain an expression of an interference compensator Z;

performing frequency domain analysis on the simplified model of the pitch axis of the flexible satellite after the interference compensator is added to obtain a flexible influence generalized interference analysis result and a flexible influence non-generalized interference analysis result;

fifthly, obtaining a filtering parameter and a PD control parameter of the interference compensator Z according to the flexible influence generalized interference analysis result and the flexible influence non-generalized interference analysis result;

adding an interference compensator Z into the pitch channel system, and adopting PD control on a pitch channel to realize the attitude control of the pitch axis of the flexible satellite;

and step seven, respectively controlling the rolling shaft attitude and the yaw shaft attitude through the processes from the step one to the step six, and realizing the attitude control of the flexible satellite.

In the embodiment, the step principle of the rolling axis control method, the pitch axis control method and the yaw axis control method is the same, the method is also suitable for rolling axis control and yaw axis control, and the three axes are respectively controlled, so that the control of the high-stability attitude of the flexible satellite is realized.

The satellite attitude control system is the core part of the satellite system, and can keep the satellite at a specific position in space relative to the inertial reference frame, which is the key to the stabilization and the execution of the satellite. A complete attitude control system is generally composed of a controller, an actuator and a sensor, as shown in fig. 2.

The attitude control can be divided into two conditions according to different task requirements of the satellite, namely attitude maneuver and attitude stabilization, wherein the attitude stabilization refers to a control task of overcoming internal and external interference moments to enable the attitude of the satellite to keep orientation to a certain reference azimuth, the attitude control mode is divided into passive control and active control according to whether the control moment is required to be generated by the satellite, the passive control is to control and adjust the attitude of the satellite by utilizing the environmental interference moment, the control effect can be achieved without consuming energy carried by the satellite, the satellite mainly adopts the active control mode at present, namely, the control is carried out according to the control rule by means of measured attitude information, and the control belongs to closed-loop negative feedback control.

The executing mechanism for controlling the satellite attitude mainly comprises a flywheel, a thruster, a magnetic torquer and the like. The flywheel actuating mechanism applies angular momentum exchange to convert satellite momentum deviation into flywheel momentum control, the actuating mechanism considered in the invention is a flywheel, an active attitude control system taking the flywheel as a main actuating mechanism can continuously obtain energy supply from a solar sailboard, and is particularly suitable for a satellite working for a long time, the flywheel is of a continuous rotation working type, the control precision of the flywheel is relatively high, and an air injection device is limited in control precision due to the fact that the working mode of the air injection device is a pulse mode, and the output torque of a magnetic torquer is small and is usually used for unloading and backup of the flywheel.

The flywheel can be divided into two types according to different working modes of the flywheel, and if the rotating speed direction of the flywheel is variable and the average angular momentum is zero, the flywheel is called a reaction wheel or a zero momentum wheel; if the flywheel speed does not cross zero, the average angular momentum is an offset value, called offset momentum wheel.

The control problem of the flexible satellite is researched, firstly, the vibration influence of a flexible accessory is considered emphatically, from the structural point of view, the vibration can increase the stress born by the accessory, the structural fatigue can be caused when the accessory exists for a long time, so that the service life of the satellite is reduced, and from the result of vibration generation, the steady-state performance index of attitude control can be influenced; the passive control method can be divided into energy shunting and energy dissipation in principle, the basic principle is that a vibration source is separated from a main body or energy generated by vibration is transferred to other structures and consumed, a common and effective flexible vibration suppression method from early to present is a frequency isolation method, namely, when a control system is designed, the bandwidth of the flexible vibration suppression method is controlled to be five times or ten times lower than the flexible mode fundamental frequency, the vibration isolation effect of the flexible structure is achieved, so that the mode vibration cannot cause great influence on the control system, the damping of the flexible vibration suppression method can be gradually attenuated by means of the damping of the flexible vibration suppression method, the frequency isolation method is easy to realize when the mode fundamental frequency is higher, the complexity of the control system is not increased, and the passive control method is widely applied in engineering.

The active suppression control of the vibration comprises component force synthesis, input molding, a control method combining an intelligent material and the like, considering that the active suppression control of the vibration inevitably increases energy consumption, and meanwhile, the introduction of a piezoelectric element increases the complexity of a system, and the control method adopts a frequency isolation method to suppress the vibration.

As a classical attitude control method, PID control is still an accurate and advanced control law. The PID controller can consider the factors such as the dynamic characteristic and bandwidth of the system during design and reflect the robust performance of the system through amplitude margin and phase margin, so that the PID controller is still adopted by most triaxial stable satellites.

In PID control, a proportional signal can increase the system common frequency band, but the system stability is reduced, a differential signal provides damping for the system, so that the stability is improved, but the system is sensitive to noise and interference, an integral signal improves the system steady-state precision, each control parameter has definite physical significance, is simple and reliable, and a satellite can be ensured to have higher control precision and good dynamic performance after proper selection.

The difference between the second embodiment and the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis in the first embodiment is that the expression of the dynamic model of the flexible satellite established in the first step is as follows:

wherein, ω is_s＝[ω₁ω₂ω₃]^T∈R³The body coordinate system is relative to the inertial system and projects and decomposes attitude angular velocity vectors in the body coordinate system; i is_s∈R^3×3A satellite rotational inertia matrix is obtained; t is_c∈R³Controlling moment vectors for three channels of the flexible satellite; t is_d∈R³The disturbance moment borne by the flexible satellite; the value of i is 1 or 2, which represents two solar sailboards; f_si∈R^3×nη for vibration and satellite rotation coupling coefficient_i∈RⁿIs a flexible mode coordinate ξ_iAnd Ω_iAre all n-dimensional diagonal arrays, ξ_iTo the damping ratio, Ω_iIs the modal frequency, n is the modal order,is the first derivative of the attitude angular velocity,is η_iThe first derivative of (a) is,is η_iThe second derivative of (a) is,

when the satellite attitude problem is researched, a geocentric inertial coordinate system, an orbit coordinate system, a satellite inertial reference coordinate system and a body coordinate system are often adopted for research.

The third embodiment, the present embodiment and the second embodiment of the method for controlling a high stability attitude of a flexible satellite based on frequency domain analysis are different in that the expressions of the dynamic model obtained by performing small angle assumption on the dynamic model of the orbiting satellite and simplifying the dynamic model are as follows:

wherein theta is a three-axis attitude angle,for three-axis attitude angular acceleration, T ═ T_c+T_d，

Taking a single accessory for the simplified dynamic model, and obtaining an expression of a frequency domain equation as follows:

wherein, I_yMoment of inertia of pitch axis, F_sjCoefficient of coupling between vibration and flexural satellite rotation for the pitch axis corresponding to the j-th order mode, η_jFlexible mode coordinates for pitch axis corresponding to j-th order mode, ξ_jDamping ratio, Ω, for pitch axis to jth order mode_jFor the modal frequency of the pitch axis corresponding to the j-th order mode,

deriving the modal coordinates η from the modal equations_jThe relationship with the attitude angle θ is then substituted into the attitude equation to cancel the modal quantity, which is given by:

the difference between the fourth embodiment and the method for controlling the attitude of the flexible satellite based on the frequency domain analysis in the third embodiment is that, in the step three, in the simplified model of the pitch axis of the flexible satellite, a controller is omitted and the flexible modal influence is totally included in the disturbance, and the process of obtaining the expression of the disturbance compensator Z is as follows:

step three, outputting and obtaining an observed value of the interference q according to the angular speed in the flexible satellite pitching axis simplified model and the controlled objectWherein,for pitch angle rate, u_tOutputting a signal for an actuator;

step three, applying an external control signal in the simplified model of the flexible satellite pitch axisThe additional control signal z_tFor the output signal of the actuator, an additional drive signal of the actuator is obtained from a model W(s) of the actuatoru_cIs a driving signal of the flywheel actuating mechanism;

step three, adopting a filter F_r(s) define the bandwidth of interference suppression, and then obtain an expression for the interference compensator Z.

In this embodiment, a robust model matching method is used to obtain the interference compensator Z, as shown in fig. 3, the robust model matching method considers factors such as interference and uncertainty, and is based on the principle and method of the classical control theory, and the design goal is to make the transfer function of the output concerned equal to or approximately zero, and by observing the transfer function of the output y and the inverse transfer function of the control object, the magnitude of the external interference can be obtained, and then the external interference is introduced into the control system for compensation, so that the influence caused by the interference is theoretically eliminated.

In fig. 3, m(s) represents an observer of the disturbance q for estimating the magnitude of the disturbance;for ensuring the correctness of interference compensation; f_r(s) is a filter for selecting and suppressing interference of a specific frequency, and the control system includes: w_qy(s)＝[1-F_r(s)]W′_qy(s), wherein, W'_qy(s) represents the transfer function from interference to output of the original system, in an ideal case, if let F_r(s) equals 1, then the closed loop transfer function W after the interference compensator is added_qy(s) is constant zero, which satisfies the design objectives, but is not practical because the system may introduce many uncertainties and eventually cause system instability, and thus, when applying the interference compensator, the filter F_rThe bandwidth of(s) is designed with emphasis.

Due to the filter F_r(s) dryingThe interference suppression of the interference compensator plays a decisive role, and therefore its form and parameters must be reasonably designed, in the present invention, the filter F is used_r(s) is selected as follows:

wherein α, β and gamma are all parameters to be designed, the filter is composed of three low-pass filters with α, β and gamma as cut-off frequencies in series, therefore, the selection of the three parameters determines the performance of the interference compensator, and it can be seen that the larger the values of α, β and gamma are, the larger the F is_rThe closer the value of(s) is to 1, the smaller the values of α, β, and γ, the filter F_r(s) interference in the desired frequency domain cannot be suppressed effectively.

The difference between the fifth embodiment and the fourth embodiment of the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis is that a filter F is added in the third step_r(s) defining the bandwidth of interference suppression, and then obtaining the expression of the interference compensator Z as:

wherein,is the pitch angle rate.

In a sixth specific embodiment, the specific embodiment is described with reference to fig. 4, and the difference between the specific embodiment and the flexible satellite high-stability attitude control method based on frequency domain analysis in the fifth specific embodiment is that, in the fourth step, frequency domain analysis is performed on the simplified model of the pitch axis of the flexible satellite, and a process of obtaining a flexible influence generalized perturbation analysis result is as follows:

establishing a pitch channel system model when introducing a disturbance compensator and taking a flexible influence as generalized disturbance, using a flywheel as an actuating mechanism, and taking W(s) as a first-order inertia link:

the open-loop transfer function of the system obtained according to the system model is as follows:

the closed loop transfer function of the system is:

the transfer function of the disturbance input to the angular velocity output is:

wherein, tau_yIs the time constant of the flywheel of the pitch axis, k_pyIs a proportional parameter, k, of the PD controller of the pitch axis_dyIs a pitch axis PD controller differential parameter.

In the present embodiment, c(s) ═ k_py+k_dys is the PD controller transfer function, where the open and closed loop transfer functions are identical to those without the disturbance compensator, and are equal to the parameter τ_y、I_y、k_pyAnd k_dyIndependent of the filter parameters α, β and gamma, and therefore, the addition of the interference compensator does not affect the system stability and other performance, and it can be seen that the transfer function is andthe closed loop transfer function without adding interference compensator is more than 1-F_r(s)]This term, therefore, not only by changing the parameter τ_y、I_y、k_pyAnd k_dyThe bandwidth is controlled to realize the suppression of interference, and the filter F is reasonably designed_r(s) has an important role in enhancing the interference suppression effect.

Seventh embodiment, the present embodiment is described with reference to fig. 5, and the difference between the present embodiment and the flexible satellite high-stability attitude control method based on frequency domain analysis described in the sixth embodiment is that, in the fourth step, frequency domain analysis is performed on the simplified model of the pitch axis of the flexible satellite, and a process of obtaining a flexible influence non-generalized interference analysis result is as follows:

establishing a pitching channel system model when the disturbance compensator is introduced and the flexibility influence is not taken as generalized disturbance, recording the transfer function of the flexibility influence superposition as sigma, and obtaining the open-loop transfer function of the system when the disturbance compensator is not introduced as follows:

the closed loop transfer function of the system without introducing an interference compensator is:

without the introduction of the disturbance compensator, the transfer function of the disturbance input to the angular velocity output is:

the open loop transfer function of the system when introducing the interference compensator is:

the closed loop transfer function of the system when introducing the interference compensator is:

with the introduction of the disturbance compensator, the transfer function of the disturbance input to the angular velocity output is:

by not introducing the disturbance compensator and introducing the disturbance compensator system open-loop transfer function and closed-loop transfer function, it can be seen that when flexibility is taken into account, the introduction of the disturbance compensator can diminish the impact of flexibility on system performance, [1-F ]_r(s)]If small enough, the flexibility effect can be neglected. The transfer function from the interference input to the angular velocity output shows that the interference can be effectively suppressed after the interference compensator is introduced.

The difference between the eighth specific embodiment and the seventh specific embodiment in the method for controlling a high stability attitude of a flexible satellite based on frequency domain analysis is that, in the fifth step, the process of obtaining the filter parameter and the PD control parameter of the interference compensator Z according to the analysis result of the flexible influence generalized interference and the analysis result of the flexible influence non-generalized interference is as follows:

when the PD control parameter is fixed, the open loop frequency characteristic of the system, the closed loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output are obtained by changing the filter parameter of the interference compensator Z when the interference compensator is not introduced, the interference compensator is introduced and the filter parameter in the interference compensator is changed, and the filter parameter of the interference compensator Z is determined through the characteristics;

when the filter parameter of the interference compensator Z is fixed, the open-loop frequency characteristic of the system, the closed-loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output are obtained by changing the PD control parameter, and the PD control parameter is determined by obtaining the open-loop frequency characteristic of the system, the closed-loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output when the PD control parameter is changed.

The following is verification of the control method of the present invention and analysis of the effectiveness of the disturbance compensator, taking into account the effect of flexibility in the analysis and simulation process. The control effect of the system can be realized by the parameters of PD or F_r(s) the adjustment of the filtering parameters is improved, the frequency domain analysis is performed on the pitch channel, the conditions of adjusting the compensator parameters and the PD parameters are respectively considered,

(1) influence analysis of PD parameter timing interference compensator parameter change on system

PD parameter k_py＝15/500*I_y、k_dy＝130/500*I_yThe filter parameters α ═ β ═ γ, 0.1Hz, 0.29Hz, 0.55Hz, 1Hz and 10Hz respectively, and the first 5 order modes of flexibility are intercepted, and other parameters are as follows, wherein the parameters of the two sailboards are the same:

satellite pitch axis inertia: i is_y＝6000(kg·m²)；

Flywheel time constant: tau is_y＝0.1；

And modal frequency of the sailboard: omega ═ diag (0.290; 0.740; 1.492; 1.865; 3.798). times.2 pi (rad/s);

damping ratio: ξ ═ diag (0.02620.02670.03970.02590.0178);

pitch axis rotational coupling coefficient: f_sy1＝(0.00002 25.6652 0.0024 -0.0001 3.2438)；

Pitch axis vibration coupling coefficient: f_sy2＝(-0.00002 24.7348 0.0023 0.0001 -3.2820)；

According to the above parameter setting, the frequency characteristic curves of the open loop of the system and the closed loop of the interference to the angular velocity when the interference compensator is not introduced, introduced and the filter parameter in the interference compensator is changed are obtained, as shown in fig. 6 and 7, it can be seen from fig. 6 that the open loop frequency response curve of the system is basically overlapped in the low frequency band and the high frequency band, the curve is changed in the middle and high frequency band, and the curve approaches to the situation when there is no flexibility as the filter parameter is increased. Similar conclusions can be drawn from the closed loop behavior of the system. Fig. 7 shows that the amplitude-frequency characteristic of the closed loop from the interference to the angular velocity after the interference compensator is introduced has a downward moving trend in a low frequency band, and the downward moving amplitude of the curve becomes larger as the filter parameter increases, so that the interference compensator has a suppression effect on the interference, and the larger the parameter is, the better the effect is, and meanwhile, it can be seen that the bandwidth of the system is far smaller than the first-order frequency of the flexible mode, and the frequency isolation requirement is met.

(2) Interference compensator parameter-timing PD controller proportional parameter k_pyAnalysis of the impact of changes on a System

When parameters α, β and gamma of a filter in the interference compensator simultaneously take 0.55Hz, k in the PD controller is changed_pyThe influence effect of the value of (1) on the system is analyzed. k is a radical of_pyRespectively take k_py1＝15/500*I_y、k_py2＝35/500*I_y、k_py3＝55/500*I_y、k_py4＝75/500*I_y、k_py5＝95/500*I_y，k_dy＝130/500*I_yThe frequency characteristics of the open loop, closed loop and disturbance to angular velocity output of the system are obtained from the above parameters, as shown in fig. 8-10, and it can be seen from the open loop response in fig. 8 that the disturbance compensator parameter is timed to follow k_pyThe amplitude-frequency characteristic curve of the low frequency band slightly moves upwards, the phase-frequency characteristic curve moves downwards, the stability margin of the system is gradually reduced, meanwhile, the closed loop frequency response of the system shows that the bandwidth of the system is increased, as can be seen from fig. 10, along with the increase of k_pyIs increasedIn addition, the suppression effect on the interference is gradually increased before a certain frequency in the low frequency band, and the suppression effect on the interference is reduced after the certain frequency.

In summary, the influence of flexibility on the system performance can be reduced after the interference compensator is introduced, and the system characteristics tend to be free of flexibility along with the larger filtering parameter; after the interference compensator is introduced, the interference suppression effect is obvious, and the suppression effect is enhanced along with the increase of filter parameters; increasing parameter k in PD controller_pyThe value of (2) can increase the bandwidth of a closed-loop system, enhance the suppression of interference below a certain frequency, but also reduce the phase angle margin of the system and weaken the stability of the system. Therefore, in practical application, the filtering parameter is only about the first-order vibration frequency of the flexible accessory, and k is taken into consideration of the requirement of stability margin_pyThe parameter is taken as an inertia value of 0.03 times.

According to the control method, the PD controller and the interference compensator are respectively designed for three axes and are applied to a complete flexible satellite model provided with two sailboards, the satellite is a large inertia satellite, the first 5-order mode of the sailboards is considered in simulation, the environmental interference is considered, and simulation parameters are as follows:

satellite main inertia: i is_x＝15000(kg·m²),I_y＝6000(kg·m²),I_z＝13000(kg·m²)；

Flywheel time constant: tau is_x＝0.1,τ_y＝0.1,τ_z＝0.1；

And modal frequency of the sailboard: omega ═ diag (0.290; 0.740; 1.492; 1.865; 3.798). times.2 pi (rad/s);

damping ratio: ξ ═ diag (0.02620.02670.03970.02590.0178);

coefficient of rotational coupling:

vibration couplerThe sum coefficient is:

initial attitude:θ＝0.1°,ψ＝0.1°，

computer sampling period: t is 0.2 s;

PD control parameters: k is a radical of_px＝15/500×I_x,k_py＝15/500×I_y,k_pz＝15/500×I_z；

k_dx＝130/500×I_x,k_dy＝130/500×I_y,k_dz＝130/500×I_z；

Filter parameters: α ═ β ═ γ ═ 0.1 Hz.

Respectively simulating the flexible satellites when the interference compensator is not introduced and when the interference compensator is introduced according to the simulation parameters, wherein the simulation results when the interference compensator is not introduced are shown in fig. 11-17, and fig. 11 is a system attitude angle curve when the interference compensator is not introduced; FIG. 12 is a plot of system attitude angular velocity without the introduction of an interference compensator; FIG. 13 is a plot of system control torque without the introduction of disturbance compensators; FIG. 14 is a plot of the total ambient torque of the system without the introduction of a disturbance compensator; FIG. 15 is a graph of four environmental disturbance moments of the system without introducing a disturbance compensator, including a gravity gradient moment, a aerodynamic moment, a solar pressure moment, and a remanence moment; FIG. 16 is a modal coordinate plot of a system pitch axis (Y-axis) positive direction windsurfing board without the introduction of a disturbance compensator; FIG. 17 is a modal coordinate plot of a system pitch axis (Y-axis) negative direction windsurfing board without the introduction of disturbance compensators.

Fig. 18-22 show simulation results when an interference compensator is introduced and a filter parameter α ═ β ═ γ ═ 0.1Hz, where fig. 18 is a system attitude angle curve when the interference compensator is introduced; FIG. 19 is a plot of system attitude angular velocity with the introduction of a disturbance compensator; FIG. 20 is a plot of system control torque with the introduction of a disturbance compensator; FIG. 21 is a modal coordinate curve of a system pitch axis (Y-axis) positive direction windsurfing board with the introduction of a disturbance compensator; FIG. 22 is a modal coordinate plot of a system pitch axis (Y-axis) negative direction windsurfing board with the introduction of a disturbance compensator.

From the simulation results, the satellite attitude finally tends to be stable under two conditions, the suppression effect on modal vibration is good, the control index required by a subject is achieved, and the control precision of pure PD control reaches 10^-4Degree of order and stability of 10^-8In the order of degrees/second; after the interference compensator is introduced, the control precision and the stability respectively reach 10^-7Degree and 10^-10The degree/second order is greatly improved compared with the control effect when the compensator is not introduced.

The following table gives the accuracy and stability when the filter parameters change:

it can be seen from the table that as the filtering parameter of the interference compensator increases, the control performance of the system gradually increases, and the required control torque increases in consideration of the increase of the filtering parameter, so in practical application, after various factors are comprehensively considered, the filtering parameter is taken to be about the first order frequency of the flexible vibration.

Claims (6)

1. The method for controlling the high-stability attitude of the flexible satellite based on frequency domain analysis is characterized by comprising the following steps of:

step one, establishing a dynamic model of a flexible satellite, performing small-angle assumption and simplification, and taking a single accessory for the simplified dynamic model to obtain a frequency domain equation;

obtaining a transfer function relation between an actual pitch angle theta and a total moment T according to a frequency domain equation, and obtaining a simplified model of a pitch axis of the flexible satellite according to the relation between the actual pitch angle theta and the total moment T;

step three, in the flexible satellite pitch axis simplified model, a controller part is omitted, the flexible modal influence is totally included in the interference, and a filter F is adopted_r(s) defining the bandwidth of interference suppression, obtaining an expression for an interference compensator Z;

performing frequency domain analysis on the simplified model of the pitch axis of the flexible satellite after the interference compensator is added to obtain a flexible influence generalized interference analysis result and a flexible influence non-generalized interference analysis result;

fifthly, obtaining a filtering parameter and a PD control parameter of the interference compensator Z according to the flexible influence generalized interference analysis result and the flexible influence non-generalized interference analysis result;

adding an interference compensator Z into the pitch channel system, and adopting PD control on a pitch channel to realize the attitude control of the pitch axis of the flexible satellite;

step seven, respectively controlling the rolling shaft attitude and the yaw shaft attitude through the processes from the step one to the step six, and realizing the attitude control of the flexible satellite;

in the fourth step, the frequency domain analysis is carried out on the simplified model of the pitch axis of the flexible satellite, and the process of obtaining the analysis result of the generalized interference of the flexible influence is as follows:

establishing a pitch channel system model when introducing a disturbance compensator and taking a flexible influence as generalized disturbance, using a flywheel as an actuating mechanism, and taking W(s) as a first-order inertia link:

$W\left(s\right)=\frac{1}{{\mathrm{\τ}}_{y}s+1},$

wherein W(s) is a model of the actuator;

the open-loop transfer function of the system obtained according to the system model is as follows:

$G\left(s\right)=\frac{k_{py}+k_{dy}s}{{\mathrm{\τ}}_y{I}_y{s}^3+I_y{s}^2},$

wherein, I_yMoment of inertia for the pitch axis;

the closed loop transfer function of the system is:

$\mathrm{\φ}\left(s\right)=\frac{k_{py}+k_{dy}s}{{\mathrm{\τ}}_y{I}_y{s}^3+I_y{s}^2+k_{dy}s+k_{py}},$

the transfer function of the disturbance input to the angular velocity output is:

${\mathrm{\φ}}_{\stackrel{\·}{y}q}\left(s\right)=\[1-F_r\left(s\right)\]\frac{(1+{\mathrm{\τ}}_{y}s)s}{{\mathrm{\τ}}_y{I}_y{s}^3+I_y{s}^2+k_{dy}s+k_{py}},$

wherein, tau_yIs the time constant of the flywheel of the pitch axis, k_pyIs a proportional parameter, k, of the PD controller of the pitch axis_dyFor the differential parameter of the pitch axis PD controller, F_r(s) is an expression for the filter;

in the fourth step, the frequency domain analysis is carried out on the simplified model of the pitch axis of the flexible satellite, and the process of obtaining the analysis result of the non-generalized interference of the flexible influence is as follows:

establishing a pitching channel system model when the disturbance compensator is introduced and the flexibility influence is not taken as generalized disturbance, recording the transfer function of the flexibility influence superposition as sigma, and obtaining the open-loop transfer function of the system when the disturbance compensator is not introduced as follows:

$G\left(s\right)=\frac{k_{py}+k_{dy}s}{(I_y-\mathrm{\Σ})({\mathrm{\τ}}_{y}s+1)s^2},$

the closed loop transfer function of the system without introducing an interference compensator is:

$\mathrm{\φ}\left(s\right)=\frac{k_{py}+k_{dy}s}{(I_y-\mathrm{\Σ})({\mathrm{\τ}}_{y}s+1)s^2+k_{dy}s+k_{py}},$

without the introduction of the disturbance compensator, the transfer function of the disturbance input to the angular velocity output is:

${\mathrm{\φ}}_{\stackrel{\·}{y}q}\left(s\right)=\frac{(1+{\mathrm{\τ}}_{y}s)s}{\[I_y-\mathrm{\Σ}\]({\mathrm{\τ}}_{y}s+1)s^2+k_{dy}s+k_{py}},$

the open loop transfer function of the system when introducing the interference compensator is:

$G_{RMM}\left(s\right)=\frac{k_{py}+k_{dy}s}{\[I_y-(1-F_r)\mathrm{\Σ}\]({\mathrm{\τ}}_{y}s+1)s^2},$

the closed loop transfer function of the system when introducing the interference compensator is:

${\mathrm{\φ}}_{RMM}\left(s\right)=\frac{k_{py}+k_{dy}s}{\[I_y-(1-F_r)\mathrm{\Σ}\]({\mathrm{\τ}}_{y}s+1)s^2+k_{dy}s+k_{py}},$

with the introduction of the disturbance compensator, the transfer function of the disturbance input to the angular velocity output is:

${\mathrm{\φ}}_{\stackrel{\·}{y}qRMM}\left(s\right)=\frac{\[1-F_r\left(s\right)\](1+{\mathrm{\τ}}_{y}s)s}{\[I_y-(1-F_r)\mathrm{\Σ}\]({\mathrm{\τ}}_{y}s+1)s^2+k_{dy}s+k_{py}}.$

2. the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis according to claim 1, wherein the expression of the established dynamic model of the flexible satellite is as follows:

$\begin{array}{c}{I}_s{\stackrel{\·}{\mathrm{\ω}}}_s+{\mathrm{\ω}}_s^{\×}{I}_s{\mathrm{\ω}}_s+\underset{i}{\mathrm{\Σ}}{F}_{si}{\stackrel{\·\·}{\mathrm{\η}}}_i+{\mathrm{\ω}}_s^{\×}{F}_{si}{\stackrel{\·}{\mathrm{\η}}}_i=T_c+T_d\\ {\stackrel{\·\·}{\mathrm{\η}}}_i+2{\mathrm{\ξ}}_i{\mathrm{\Ω}}_i{\stackrel{\·}{\mathrm{\η}}}_i+{\mathrm{\Ω}}_i^2{\mathrm{\η}}_i+F_{si}^T{\stackrel{\·}{\mathrm{\ω}}}_s=0\end{array},$

wherein, ω is_s＝[ω₁ω₂ω₃]^T∈R³The body coordinate system is relative to the inertial system and projects and decomposes attitude angular velocity vectors in the body coordinate system; i is_s∈R^3×3A satellite rotational inertia matrix is obtained; t is_c∈R³Controlling moment vectors for three channels of the flexible satellite; t is_d∈R³Is a flexible satelliteThe disturbance torque of (2); the value of i is 1 or 2, which represents two solar sailboards; f_si∈R^3×nη for vibration and satellite rotation coupling coefficient_i∈RⁿIs a flexible mode coordinate ξ_iAnd Ω_iAre all n-dimensional diagonal arrays, ξ_iTo the damping ratio, Ω_iIs the modal frequency, n is the modal order,is the first derivative of the attitude angular velocity,is η_iThe first derivative of (a) is,is η_iThe second derivative of (a) is,

${\mathrm{\ω}}_s^{\×}=\left[\begin{array}{ccc}0& -{\mathrm{\ω}}_3& {\mathrm{\ω}}_2\\ {\mathrm{\ω}}_3& 0& -{\mathrm{\ω}}_1\\ -{\mathrm{\ω}}_2& {\mathrm{\ω}}_1& 0\end{array}\right].$

3. the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis as claimed in claim 2, wherein the expressions of the dynamic models obtained by performing small angle hypothesis on the dynamic models of the orbiting satellites and simplifying the dynamic models are as follows:

$\left\{\begin{array}{c}{I}_s\stackrel{\·\·}{\mathrm{\Θ}}+\underset{i}{\Σ}{F}_{si}{\stackrel{\·\·}{\mathrm{\η}}}_i=T,\\ {\stackrel{\·\·}{\mathrm{\η}}}_i+2{\mathrm{\ξ}}_i{\mathrm{\Ω}}_i{\stackrel{\·}{\mathrm{\η}}}_i+{\mathrm{\Ω}}_i^2{\mathrm{\η}}_i+F_{si}^T\stackrel{\·\·}{\mathrm{\Θ}}=0\end{array}\right.,$

wherein theta is a three-axis attitude angle,for three-axis attitude angular acceleration, T ═ T_c+T_d，

Taking a single accessory for the simplified dynamic model, and obtaining an expression of a frequency domain equation as follows:

$\left\{\begin{array}{c}{I}_y{s}^2\mathrm{\θ}+\underset{j}{\Σ}{F}_{sj}{s}^2{\mathrm{\η}}_j=T\\ s^2{\mathrm{\η}}_j+2{\mathrm{\ξ}}_j{\mathrm{\Ω}}_{j}s{\mathrm{\η}}_j+{\mathrm{\Ω}}_j^2{\mathrm{\η}}_j+F_{sj}{s}^2\mathrm{\θ}=0\end{array}\right.,$

wherein, F_sjCoefficient of coupling between vibration and flexural satellite rotation for the pitch axis corresponding to the j-th order mode, η_jFlexible mode coordinates for pitch axis corresponding to j-th order mode, ξ_jDamping ratio, Ω, for pitch axis to jth order mode_jFor the modal frequency of the pitch axis corresponding to the j-th order mode,

deriving the modal coordinates η from the modal equations_jThe relationship with the attitude angle θ is then substituted into the attitude equation to cancel the modal quantity, which is given by:

$I_s{s}^2\mathrm{\θ}\left(s\right)+\underset{j}{\Σ}\frac{-F_{sj}^2{s}^2\mathrm{\θ}\left(s\right)}{s^2+2{\mathrm{\ξ}}_j{\mathrm{\Ω}}_{j}s+{\mathrm{\Ω}}_j^2}{s}^2=T\left(s\right).$

4. the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis according to claim 3, wherein in the simplified model of the pitch axis of the flexible satellite in step three, the controller part is omitted and the influence of the flexible mode is totally included in the model

While disturbing, and using a filter F_r(s) defining the bandwidth of interference suppression, the process of obtaining the expression of the interference compensator Z is:

step three, outputting and obtaining an observed value of the interference q according to the angular speed in the flexible satellite pitching axis simplified model and the controlled objectWherein,for pitch angle rate, u_tOutputting a signal for an actuator;

step three, applying an external control signal in the simplified model of the flexible satellite pitch axisThe additional control signal z_tFor the output signal of the actuator, an additional drive signal of the actuator is obtained from a model W(s) of the actuatoru_cIs a driving signal of the flywheel actuating mechanism;

step three, adopting a filter F_r(s) define the bandwidth of interference suppression, and then obtain an expression for the interference compensator Z.

5. The method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis as claimed in claim 4, wherein a filter F is adopted in the third step_r(s) defining the bandwidth of interference suppression, and then obtaining the expression of the interference compensator Z as:

$Z=F_r\left(s\right)\×z_c=F_r\left(s\right)\[u_c-\frac{I_{y}s}{W\left(s\right)}\stackrel{\·}{\mathrm{\θ}}\].$

6. the method for controlling the attitude of the flexible satellite with high stability based on the frequency domain analysis as claimed in claim 1, wherein the process of obtaining the filter parameter and the PD control parameter of the interference compensator Z according to the analysis result of the flexible influence generalized interference and the analysis result of the flexible influence non-generalized interference in the step five is as follows:

when the PD control parameter is fixed, the open loop frequency characteristic of the system, the closed loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output are obtained by changing the filter parameter of the interference compensator Z when the interference compensator is not introduced, the interference compensator is introduced and the filter parameter in the interference compensator is changed, and the filter parameter of the interference compensator Z is determined through the characteristics;

when the filter parameter of the interference compensator Z is fixed, the open-loop frequency characteristic of the system, the closed-loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output are obtained by changing the PD control parameter, and the PD control parameter is determined by obtaining the open-loop frequency characteristic of the system, the closed-loop frequency characteristic of the system and the amplitude-frequency characteristic of the system interference to angular speed output when the PD control parameter is changed.