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

Attitude control method for flexible satellite with high stability based on frequency domain analysis

technical field

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

Background technique

In today's era, the increasingly fierce competition in comprehensive national strength will inevitably promote the rapid development of science and technology. Due to its outstanding contributions and important roles in the military and civilian fields, aerospace technology continues to advance and has always been closely watched by the country and scientific researchers. As a product of aerospace technology, satellites have been widely used today, including communication, meteorological observation, navigation, etc.

With the gradual maturity of technology and the increasing demand for space exploration, the satellite has a larger size and a very complex structure. It is usually equipped with accessories for various functions, such as solar panels, sports antennas, etc. This puts higher demands on the control. At the same time, indicators such as accuracy, stability, response speed, and service life have become the key elements in the design of the attitude control system.

What the flexible satellite attitude control system is facing is a nonlinear system with parameter and dynamic uncertainties and interference effects. At the same time, the control performance index of the satellite is greatly improved, and the attitude is required to have high pointing accuracy and stability. On this basis, how to Designing a reasonable and effective control method has always been a problem that needs to be solved.

Similar to the development process of control theory, the attitude control methods of flexible satellites can also be divided into classical control methods, modern control methods and intelligent control methods, as well as the comprehensive control methods produced by the combination and penetration of them. The literature "Improved satellite attitude control Using a disturbance compensator” adopts the control method of PD plus disturbance compensator, which realizes the suppression of the influence of flexibility and disturbance, and achieves stable attitude. At the same time, a low-pass filter is introduced to deal with the influence of high-frequency modes; "Design" designed a PID controller based on a single-axis decoupling model for a flexible aircraft controlled by a flywheel, and gave a parameter tuning method. The simulation verified that its good control effect is good; Anti-disturbance control" adopts the active disturbance rejection control method, through the nonlinear error feedback law and the expansion observer, effectively compensates the influence of uncertain factors such as disturbance, and meets the high stability requirements after attitude maneuvering; the literature "Optimal attitude control For three-axis stabilized flexible spacecraft" for three-axis stabilized flexible spacecraft with flywheel as the actuator, the LQR method was used to design the optimal controller, and satisfactory results were obtained in vibration suppression and attitude control; the literature "Low-order robust attitude control of an earth observation satellite” uses H∞ theory to design a low-order robust controller. Compared with the satellites in the previous SPOT system, the control effect has been greatly improved. The document "Adaptive fuzzy sliding mode control for flexible satellite" considers the combination of fuzzy control and sliding mode control and introduces an adaptive method to control the attitude of a flexible satellite, and obtains high attitude control accuracy. The document "Time-varying sliding mode variable structure and active vibration control of three-axis stable flexible satellite attitude maneuver" aimed at the problem of flexible satellite attitude maneuvering, considering the limited control torque, the sliding mode control method was adopted, and the piezoelectric The element actively controls the vibration. The literature "Adaptive sliding mode control of flexible spacecraft based on input shaping" combines the input shaping method and adaptive sliding mode control method to design the control law, so that the system can complete the nominal system under the influence of parameter uncertainty and external disturbance. tracking while suppressing flexural vibrations.

Contents of the invention

The present invention proposes a high-stability attitude control method for flexible satellites based on frequency-domain analysis, aiming to realize high-stability attitude control for flexible satellites by reducing the amplitude-frequency response from interference input to angular velocity output.

The high-stability attitude control method of the flexible satellite based on frequency domain analysis includes a roll axis control method, a pitch axis control method and a yaw axis control method, and the pitch axis control method includes the following steps:

Step 1. Establish the dynamic model of the flexible satellite, make a small-angle assumption and simplify it, take a single attachment to the simplified dynamic model, and obtain the frequency domain equation;

Step 2. Obtain the transfer function relationship between the actual pitch angle θ and the total moment T according to the frequency domain equation, and obtain a simplified model of the pitch axis of the flexible satellite according to the relationship between the actual pitch angle θ and the total moment T;

Step 3. In the simplified model of the flexible satellite pitch axis, the controller part is omitted and the influence of the flexible mode is included in the disturbance to obtain the expression of the disturbance compensator Z;

Step 4. Carry out frequency domain analysis on the simplified model of the flexible satellite pitch axis after adding the interference compensator, and obtain the analysis results of the generalized interference of the flexible impact and the non-generalized interference analysis of the flexible impact;

Step 5. Obtain the filtering parameters and PD control parameters of the disturbance compensator Z according to the analysis results of the generalized disturbance of the flexible influence and the analysis results of the non-generalized disturbance of the flexible influence;

Step 6, adding a disturbance compensator Z to the pitch channel system, adopting PD control on the pitch channel, and realizing the attitude control of the pitch axis of the flexible satellite;

Step 7. Control the attitude of the roll axis and the attitude of the yaw axis respectively through the processes described in steps 1 to 6, so as to realize the attitude control of the flexible satellite.

Beneficial effects: the flexible satellite attitude control method proposed by the present invention considers the influence of interference and uncertainty, and proposes an attitude control solution for the large inertia characteristics and high stability control requirements of the satellite. The traditional PD controller Based on this, the interference compensator is designed by using the principle of robust model matching; the transfer function models when the flexible influence is transformed into generalized interference and not transformed into generalized interference are respectively given, and the frequency domain method is used to analyze the interference compensator performance, and provide a reference for the selection of PD parameters and compensator parameters. The method can effectively suppress the vibration of the sailboard, greatly improve the accuracy and stability of attitude control, and is suitable for engineering applications.

Description of drawings

Fig. 1 is the flowchart of the flexible satellite high stability attitude control method based on the frequency domain analysis described in the first embodiment;

Fig. 2 is a schematic diagram of a traditional satellite attitude control system;

Fig. 3 is the schematic diagram of robust model matching method;

Fig. 4 is a block diagram of the pitch channel system when the disturbance compensator is introduced and the flexural influence is regarded as generalized disturbance;

Fig. 5 is a block diagram of the pitch channel system when the disturbance compensator is introduced and the influence of flexibility is considered;

Fig. 6 is a curve diagram of the system open-loop frequency characteristic when the PD parameter is constant and the interference compensator parameter changes;

Fig. 7 is the amplitude-frequency characteristic curve of the system from disturbance to angular velocity output when the PD parameter is constant and the disturbance compensator parameter changes;

Fig. 8 is a curve diagram of the system open-loop frequency characteristic when the disturbance compensator parameter is constant and the proportional parameter k _py of the PD controller changes;

Fig. 9 is a system closed-loop frequency characteristic curve when the disturbance compensator parameter is constant and the PD controller proportional parameter k _py changes;

Fig. 10 is a graph of amplitude-frequency characteristics from disturbance to angular velocity output when the disturbance compensator parameter is constant and the proportional parameter _kpy of the PD controller changes;

Figure 11 is the system attitude angle curve when no disturbance compensator is introduced;

Figure 12 is the system attitude angular velocity curve when the disturbance compensator is not introduced;

Fig. 13 is the system control torque curve when no disturbance compensator is introduced;

Figure 14 is the total environmental moment curve of the system when no disturbance compensator is introduced;

Figure 15 is the four environmental disturbance torque curves of the system when the disturbance compensator is not introduced. The four environmental disturbance torques include gravity gradient torque, aerodynamic torque, sunlight pressure torque and residual magnetic torque;

Fig. 16 is the modal coordinate curve of the sailboard in the positive direction of the pitch axis (Y axis) of the system when the interference compensator is not introduced;

Figure 17 is the modal coordinate curve of the sailboard in the negative direction of the pitch axis (Y axis) of the system when no interference compensator is introduced;

Fig. 18 is the system attitude angle curve when introducing the disturbance compensator;

Figure 19 is the system attitude angular velocity curve when the disturbance compensator is introduced;

Figure 20 is the system control torque curve when the disturbance compensator is introduced;

Fig. 21 is the modal coordinate curve of the sailboard in the positive direction of the pitch axis (Y axis) of the system when the interference compensator is introduced;

Fig. 22 is the modal coordinate curve of the sailboard in the negative direction of the pitch axis (Y axis) of the system when the disturbance compensator is introduced.

detailed description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT One, in conjunction with Fig. 1, illustrate this specific embodiment, the flexible satellite high stability attitude control method based on frequency domain analysis described in this specific embodiment comprises the following steps:

Step 1. Establish the dynamic model of the flexible satellite, make a small-angle assumption and simplify it, take a single attachment to the simplified dynamic model, and obtain the frequency domain equation;

Step 2. Obtain the transfer function relationship between the actual pitch angle θ and the total moment T according to the frequency domain equation, and obtain a simplified model of the pitch axis of the flexible satellite according to the relationship between the actual pitch angle θ and the total moment T;

Step 3. In the simplified model of the flexible satellite pitch axis, the controller part is omitted and the influence of the flexible mode is included in the disturbance to obtain the expression of the disturbance compensator Z;

Step 4. Carry out frequency domain analysis on the simplified model of the flexible satellite pitch axis after adding the interference compensator, and obtain the analysis results of the generalized interference of the flexible impact and the non-generalized interference analysis of the flexible impact;

Step 5. Obtain the filtering parameters and PD control parameters of the disturbance compensator Z according to the analysis results of the generalized disturbance of the flexible influence and the analysis results of the non-generalized disturbance of the flexible influence;

Step 6, adding a disturbance compensator Z to the pitch channel system, adopting PD control on the pitch channel, and realizing the attitude control of the pitch axis of the flexible satellite;

Step 7. Control the attitude of the roll axis and the attitude of the yaw axis respectively through the processes described in steps 1 to 6, so as to realize the attitude control of the flexible satellite.

In this embodiment, the steps and principles of the roll axis control method, the pitch axis control method and the yaw axis control method are the same, and the method of the present invention is also applicable to the roll axis control and yaw axis control, by controlling the three axes respectively , so as to realize the control of the attitude of the flexible satellite with high stability.

The satellite attitude control system is the core part of the satellite system. It can keep the satellite in a specific orientation with respect to the inertial reference frame in space, and is the key to the stability and mission execution of the satellite. A complete attitude control system is usually composed of controllers, actuators and sensors, as shown in Figure 2.

According to different task requirements of satellites, attitude control can be divided into two situations, attitude maneuvering and attitude stability. Among them, attitude stability refers to the control task of overcoming internal and external disturbance torques to keep the satellite attitude oriented to a certain reference orientation. Control torque, the attitude control method is divided into passive control and active control. Passive control is to use the environmental disturbance torque to control and adjust the attitude of the satellite. It does not need to consume the energy carried by the star to achieve the control effect. Today, satellites mainly use It is an active control method, that is, it relies on the measured attitude information to control according to the control law, which belongs to the closed-loop negative feedback control.

The actuators of satellite attitude control mainly include flywheel, thruster and magnetic torquer. The flywheel actuator uses angular momentum exchange to convert satellite momentum deviation into flywheel momentum control. The actuator considered in this invention is the flywheel. The active attitude control system with the flywheel as the main actuator can continuously obtain energy supply from the solar panel , especially suitable for satellites that work for a long time. The flywheel is a continuous rotation type, and its control accuracy is relatively high. However, because the jet device works in the form of pulses, the control accuracy is limited, and the output torque of the magnetic torque device is small. It is usually used as a flywheel uninstall and backup.

According to the different working methods of the flywheel, it can be divided into two categories. If the flywheel speed direction is variable and the average angular momentum is zero, it is called a reaction wheel or zero momentum wheel; if the flywheel speed does not exceed zero, the average angular momentum is a bias The set value is called the bias momentum wheel.

To study the control of flexible satellites, the first thing to consider is the vibration effect of flexible accessories. From a structural point of view, vibration will increase the stress on accessories, and if it exists for a long time, it will cause structural fatigue and reduce the service life of the satellite. In terms of the results of vibration, it will affect the steady-state performance index of attitude control. There are two basic vibration suppression methods, namely passive vibration control and active vibration control; in principle, passive control methods can be divided into energy splitting And energy dissipation, the basic principle is to separate the vibration source from the main body or transfer the energy generated by the vibration to other structures and consume it. From the early days to the present, a commonly used and effective method of flexible vibration suppression is the frequency isolation method, namely When designing the control system, its bandwidth is controlled to be five or ten times lower than the fundamental frequency of the flexible mode, so as to achieve the effect of isolating the vibration of the flexible structure, so that the modal vibration will not cause great damage to the control system influence, and can rely on its own damping to gradually attenuate. The frequency isolation method is easier to implement when the modal fundamental frequency is high, and will not increase the complexity of the control system, so it is widely used in engineering.

The active suppression control of vibration includes component force synthesis, input molding, and control methods combined with intelligent materials. Considering that active suppression control of vibration will inevitably increase energy consumption, and the introduction of piezoelectric elements will increase the complexity of the system. The present invention The control method adopts a frequency isolation method for vibration suppression.

As a classic attitude control method, PID control is still a precise and advanced control law. Based on the analysis and design of the automatic control principle, the PID controller can consider the system dynamic characteristics and bandwidth and other factors when designing, and reflect the robust performance of the system through the amplitude margin and phase margin. Three-axis stabilized satellites are used.

In PID control, the proportional signal can increase the passband of the system, but it will reduce the stability of the system. The differential signal provides damping to the system, thereby improving stability, but it also makes the system more sensitive to noise and interference. The integral signal improves the steady state of the system. Accuracy, the physical meaning of each control parameter is clear, simple and reliable, after proper selection, it can ensure that the satellite has high control accuracy and good dynamic performance.

Embodiment 2. The difference between this embodiment and the high-stability attitude control method for flexible satellites based on frequency domain analysis described in Embodiment 1 is that the dynamic model of the flexible satellite established in step 1 is The expression is:

Among them, ω _s =[ω ₁ ω ₂ ω ₃ ] ^T ∈ R ³ The body coordinate system relative to the inertial system and the attitude angular velocity vector projected and decomposed in the body coordinate system; I _s ∈ R ^3×3 is the satellite moment of inertia matrix; T _c ∈ R ³ is the control torque vector of the three channels of the flexible satellite; T _d ∈ R ³ is the disturbance torque suffered by the flexible satellite; the value of i is 1 or 2, which means two solar panels; F _si ∈ R ^3×n is the coupling coefficient of vibration and satellite rotation, η _i ∈ R ⁿ is the coordinate of the flexible mode; ξ _i and Ω _i are n-dimensional diagonal arrays, ξ _i is the damping ratio, Ω _i is the modal frequency, n is the mode order, is the first derivative of the attitude angular velocity, is the first derivative of η _i , is the second order derivative of η _i ,

When studying satellite attitude problems, the earth-centered inertial coordinate system, orbital coordinate system, satellite inertial reference coordinate system and body coordinate system are often used for research.

Specific Embodiment 3. The difference between this specific embodiment and the high-stability attitude control method for flexible satellites based on frequency domain analysis described in specific embodiment 2 is that the dynamic model of orbiting satellites is assumed to be small-angle and simplified to obtain The expression of the dynamic model of is:

Among them, Θ is the three-axis attitude angle, is the three-axis attitude angular acceleration, T=T _c +T _d ,

Taking a single attachment to the simplified dynamic model, the expression of the frequency domain equation is obtained as:

Among them, I _y is the moment of inertia of the pitch axis, F _sj is the coupling coefficient of the vibration of the pitch axis corresponding to the jth order mode and the rotation of the flexible satellite, η _j is the coordinate of the flexible mode of the pitch axis corresponding to the jth order mode, ξ _j is the damping ratio of the pitch axis corresponding to the jth mode, Ω _j is the modal frequency of the pitch axis corresponding to the jth mode,

The relationship between the modal coordinate η _j and the attitude angle θ is derived through the modal equation, and then brought into the attitude equation to eliminate the modal quantity, and then:

Embodiment 4. The difference between this embodiment and the flexible satellite high stability attitude control method based on frequency domain analysis described in Embodiment 3 is that in step 3, in the simplified model of the pitch axis of the flexible satellite, omit In the controller part, all the influence of the flexible mode is included in the disturbance, and the process of obtaining the expression of the disturbance compensator Z is:

Step 31. Obtain the observed value of disturbance q according to the angular velocity output in the simplified model of the flexible satellite pitch axis and the controlled object in, is the pitch rate, u _t is the output signal of the actuator;

Step 32: Apply an external control signal to the simplified model of the flexible satellite pitch axis The external control signal z _t is the output signal of the actuator, and the external drive signal of the actuator is obtained according to the model W(s) of the actuator u _c is the driving signal of the flywheel actuator;

Step 33: Use the filter F _r (s) to limit the interference suppression bandwidth, and then obtain the expression of the interference compensator Z.

In this embodiment, a robust model matching method is used to obtain the disturbance compensator Z, as shown in Figure 3, the robust model matching method takes factors such as disturbance and uncertainty into consideration, and is based on the principles and methods of classical control theory Yes, the design goal is to make the output transfer function from the disturbance to the concerned output equal to or approximately zero. By observing the output y and the inverse transfer function of the control object, the magnitude of the external disturbance can be obtained, and then introduced into the control system for compensation. In theory, the influence of interference is eliminated.

In Figure 3, M(s) represents the observer of the interference q, which is used to estimate the size of the interference; It is used to ensure the correctness of interference compensation; F _r (s) is a filter, which is used to select specific frequency interference for suppression. In the control system, there are: W _qy (s)=[1-F _r (s)] W′ _qy (s), where W′ _qy (s) represents the transfer function of the original system from the disturbance to the output. In an ideal case, if F _r (s) is equal to 1, then the closed-loop transfer The function W _qy (s) is always zero, which satisfies the original intention of the design, but it is unrealizable in practice, because at this time the system may introduce many uncertain factors and eventually lead to system instability. Therefore, when applying the disturbance compensator, The bandwidth of the filter F _r (s) needs to be designed with emphasis.

Since the filter F _r (s) plays a decisive role in the interference suppression of the interference compensator, its form and parameters must be reasonably designed. In the present invention, the filter F _r (s) is selected as:

Among them, α, β and γ are the parameters to be designed, and the filter is composed of three low-pass filters with α, β and γ as the cut-off frequency in series, so the selection of the above three parameters will determine the interference compensation It can be seen that the larger the value of α, β and γ, the closer the value of F _r (s) is to 1. When the value of α, β and γ is smaller, the filter F _r (s) cannot Effectively suppress interference in the desired frequency domain.

Embodiment 5. The difference between this embodiment and the flexible satellite high-stability attitude control method based on frequency domain analysis described in Embodiment 4 is that a filter F _r (s) is added in steps 3 and 3 to limit interference The suppressed bandwidth, and then the expression of the interference compensator Z is obtained as:

in, is the pitch rate.

Embodiment 6. This embodiment is described in conjunction with FIG. 4. The difference between this embodiment and the flexible satellite high stability attitude control method based on frequency domain analysis described in Embodiment 5 is that the flexible satellite is controlled in step 4. The simplified model of the satellite pitch axis is analyzed in the frequency domain, and the process of obtaining the results of the generalized interference analysis of the flexible effect is as follows:

The pitch channel system model is established when the disturbance compensator is introduced and the flexibility effect is regarded as the generalized disturbance, the flywheel is used as the actuator, and W(s) is taken as the form of the first-order inertial link:

According to the system model, the open-loop transfer function of the system is obtained as:

The closed-loop transfer function of the system is:

The transfer function from disturbance input to angular velocity output is:

Among them, τ _y is the flywheel time constant of the pitch axis, k _py is the proportional parameter of the PD controller of the pitch axis, and k _dy is the differential parameter of the PD controller of the pitch axis.

In this embodiment, C(s)=k _py +k _dy s is the transfer function of the PD controller. At this time, the open-loop and closed-loop transfer functions are exactly the same as those without the interference compensator, which are related to the parameters τ _y , I _y , k _py and k _dy are related, but have nothing to do with the filter parameters α, β and γ. Therefore, the system stability and other performances will not be affected after adding the interference compensator, and it can be seen that the transfer function at this time is the same as that without interference compensation The closed-loop transfer function of the filter has more [1-F _r (s)], so not only by changing the parameters τ _y , I _y , k _py and k _dy to control the bandwidth to achieve the suppression of interference, but also to design the filter reasonably The device F _r (s) plays an important role in improving the interference suppression effect.

Embodiment 7. This embodiment is described in conjunction with FIG. 5. The difference between this embodiment and the flexible satellite high stability attitude control method based on frequency domain analysis described in Embodiment 6 is that in step 4, the flexible The simplified model of the satellite pitch axis is analyzed in the frequency domain, and the process of obtaining the analysis results of the non-generalized interference of the flexible effect is as follows:

The pitching channel system model is established when the disturbance compensator is introduced and the flexibility effect is not regarded as the generalized disturbance. The transfer function of the superposition of the flexibility effect is denoted as ∑, and the open-loop transfer function of the system without the disturbance compensator is obtained as:

The closed-loop transfer function of the system when no disturbance compensator is introduced is:

When the disturbance compensator is not introduced, the transfer function from disturbance input to angular velocity output is:

The open-loop transfer function of the system when the disturbance compensator is introduced is:

The closed-loop transfer function of the system when the disturbance compensator is introduced is:

When the disturbance compensator is introduced, the transfer function from disturbance input to angular velocity output is:

By not introducing disturbance compensator and introducing disturbance compensator system open-loop transfer function and closed-loop transfer function, it can be seen that when flexibility is considered, the introduction of disturbance compensator can weaken the impact of flexibility on system performance, [1-F _r (s) ] If it is small enough, the effect of flexibility can be neglected. From the transfer function from the disturbance input to the angular velocity output, it can be seen that the disturbance can be suppressed effectively after the introduction of the disturbance compensator.

Embodiment 8. The difference between this embodiment and the flexible satellite high-stability attitude control method based on frequency domain analysis described in Embodiment 7 is that in step 5, according to the analysis results of the generalized interference of the flexibility and the flexibility The process of obtaining the filter parameters and PD control parameters of the disturbance compensator Z by affecting the non-generalized disturbance analysis results is as follows:

When the PD control parameters are constant, by changing the filter parameters of the disturbance compensator Z, the open-loop frequency characteristics of the system, the system closed-loop The frequency characteristics and the amplitude-frequency characteristics of the system interference to the angular velocity output, and determine the filter parameters of the interference compensator Z through the above characteristics;

When the filter parameters of the disturbance compensator Z are constant, the open-loop frequency characteristics of the system, the closed-loop frequency characteristics of the system, and the amplitude-frequency characteristics of the system disturbance to the angular velocity output can be obtained by changing the PD control parameters, and obtained by changing the PD control parameters. The open-loop frequency characteristics of the system, the closed-loop frequency characteristics of the system, and the amplitude-frequency characteristics of the system interference to the angular velocity output determine the PD control parameters.

The following is the verification of the control method of the present invention and the effectiveness analysis of the disturbance compensator, and the influence of flexibility is considered in the analysis and simulation process. The control effect of the system can be improved by adjusting the PD parameters or the F _r (s) filter parameters. Next, the pitch channel is analyzed in the frequency domain, and the adjustment of the compensator parameters and the PD parameters are considered respectively.

(1) Analysis of the impact of disturbance compensator parameter changes on the system when PD parameters are constant

PD parameters take k _py =15/500*I _y , k _dy =130/500*I _y , filter parameters α=β=γ, take 0.1Hz, 0.29Hz, 0.55Hz, 1Hz and 10Hz respectively, intercept the flexible For the first 5 modes, other parameters are as follows, and the parameters of the two sailboards are the same:

Satellite pitch axis inertia: I _y =6000(kg·m ² );

Flywheel time constant: τ _y = 0.1;

Mode frequency of sailboard: Ω＝diag(0.290; 0.740; 1.492; 1.865; 3.798)×2π(rad/s);

Damping ratio: ξ=diag(0.0262 0.0267 0.0397 0.0259 0.0178);

Pitch axis rotation 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 settings, the frequency characteristic curves of the open loop of the system and the closed loop from disturbance to angular velocity are obtained when the disturbance compensator is not introduced, the disturbance compensator is introduced, and the filter parameters in the disturbance compensator are changed, as shown in Figure 6 and Figure 7, from Figure 6 It can be seen that no matter whether the interference compensator is introduced or not, the open-loop frequency response curve of the system basically coincides in the low frequency band and the high frequency band, and the curve changes in the middle and high frequency parts, and with the increase of the filter parameters, the curve tends to be inflexible time situation. Similar conclusions can be drawn from the closed-loop properties of the system. It can be seen from Figure 7 that after the introduction of the interference compensator, the closed-loop amplitude-frequency characteristic from the interference to the angular velocity tends to move downward in the low frequency band, and with the increase of the filtering parameters, the downward shift of the curve becomes larger. It can be seen that the interference compensation The device has a suppression effect on interference, and the larger the parameter, the better the effect. At the same time, it can be seen that the bandwidth of the system is much smaller than the first-order frequency of the flexible mode, which meets the frequency isolation requirements.

(2) Analysis of the influence of the change of the PD controller proportional parameter k _py on the system when the disturbance compensator parameter is constant

When the parameters α, β and γ of the filter in the disturbance compensator are 0.55Hz at the same time, the effect of changing the value of k _py in the PD controller on the system is analyzed. k _py respectively 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 _y , according to the above parameters, obtain the frequency characteristic curves of the system's open-loop, closed-loop and interference to the angular velocity output, as shown in Figure 8-Figure 10, from the open-loop response in Figure 8 It can be seen from the figure that when the parameters of the interference compensator are constant, with the increase of k _py , the amplitude-frequency characteristic curve in the low frequency range will move up slightly, and the phase-frequency characteristic curve will move down, and the system stability margin will gradually decrease. At the same time, the system’s The closed-loop frequency response shows that the system bandwidth has increased. It can be seen from Figure 10 that with the increase of k _py , before a certain frequency in the low frequency band, the suppression effect on interference is gradually enhanced, and after this frequency, the suppression effect on interference weakened.

In summary, the introduction of the disturbance compensator can reduce the impact of flexibility on system performance, and as the filtering parameters increase, the system characteristics tend to be less flexible; the suppression of disturbance after the introduction of the disturbance compensator It has an obvious effect, and with the increase of the filter parameters, the suppression effect is enhanced; increasing the value of the parameter k _py in the PD controller can increase the bandwidth of the closed-loop system and enhance the suppression of interference below a certain frequency, but at the same time It will reduce the system phase angle margin and weaken the system stability. Therefore, in practical applications, it is enough to set the filtering parameters to be around the first-order vibration frequency of the flexible attachment. Considering the requirements of the stability margin, the k _py parameter is set to be 0.03 times the inertia value.

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

Satellite main inertia: I _x ＝15000(kg·m ² ), I _y ＝6000(kg·m ² ), I _z ＝13000(kg·m ² );

Flywheel time constant: τ _x = 0.1, τ _y = 0.1, τ _z = 0.1;

Mode frequency of sailboard: Ω＝diag(0.290; 0.740; 1.492; 1.865; 3.798)×2π(rad/s);

Damping ratio: ξ=diag(0.0262 0.0267 0.0397 0.0259 0.0178);

Rotational coupling coefficient:

Vibration coupling coefficient:

Initial pose: θ=0.1°, ψ=0.1°,

Computer sampling period: T=0.2s;

PD control parameters: k _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.

According to the above simulation parameters, simulate the flexible satellite without the introduction of the interference compensator and the introduction of the interference compensator. The simulation results without the introduction of the interference compensator are shown in Figure 11-Figure 17. The system attitude angle curve when the compensator is used; Figure 12 is the system attitude angular velocity curve when the disturbance compensator is not introduced; Figure 13 is the system control torque curve when the disturbance compensator is not introduced; Figure 14 is the system total environmental torque curve when the disturbance compensator is not introduced ; Figure 15 is the four environmental disturbance torque curves of the system when no disturbance compensator is introduced. The modal coordinate curve of the sailboard in the positive direction of the pitch axis (Y axis); Figure 17 is the modal coordinate curve of the sailboard in the negative direction of the pitch axis (Y axis) of the system when no interference compensator is introduced.

The simulation results when the disturbance compensator is introduced and the filtering parameter α=β=γ=0.1Hz are shown in Figure 18-22. Figure 18 is the system attitude angle curve when the disturbance compensator is introduced; Figure 19 is the system attitude angle curve when the disturbance compensator is introduced. Attitude angular velocity curve; Figure 20 is the system control torque curve when the disturbance compensator is introduced; Figure 21 is the modal coordinate curve of the sailboard in the positive direction of the pitch axis (Y axis) of the system when the disturbance compensator is introduced; Figure 22 is the time when the disturbance compensator is introduced The modal coordinate curve of the sailboard in the negative direction of the pitch axis (Y axis) of the system.

From the above simulation results, it can be seen that the attitude of the satellite in the two cases eventually tends to be stable, the suppression effect on the modal vibration is good, and the control index required by the project is reached. The control accuracy of the simple ^PD control reaches the 10 The stability is on the order of 10 ^-8 degrees/second; after the introduction of the disturbance compensator, the control accuracy and stability have reached the order of 10 ^-7 degrees and 10 ^-10 degrees/second respectively, which is better than the control effect when the compensator is not introduced There is a great improvement.

The following table shows the accuracy and stability when the filtering parameters are changed:

It can be seen from the table that with the increase of the filter parameters of the disturbance compensator, the control performance of the system is gradually enhanced. Considering that the increase of the filter parameters will increase the required control torque, in practical applications, after comprehensive consideration of various factors , set the value of the filter parameters to about the first-order frequency of the flexural 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.