Satellite attitude system preset performance tracking control method based on second-order disturbance observer

Abstract

The application discloses a satellite attitude system preset performance tracking control method based on a second-order disturbance observer, first, combining the rigid body satellite dynamics and kinematics equation, the state prediction error is introduced into the structure of the traditional second-order disturbance observer, the improved second-order disturbance observer is designed, the influence of high-frequency noise is weakened while the disturbance is estimated and compensated under the condition of low gain; secondly, the tunnel type performance function is introduced in the error conversion process, the transient and steady state performance of the attitude tracking error is improved; then, combined with the disturbance estimation result, a disturbance fault-tolerant auxiliary system is constructed, the performance boundary is flexibly adjusted by generating a disturbance non-negative correction signal, the influence of strong mutation disturbance is reduced, and the robustness of the system is guaranteed; finally, a preset performance anti-disturbance controller is designed for the satellite system, and high-precision attitude tracking control is realized. The application has higher efficient estimation performance and more accurate control precision, and effectively improves the anti-interference ability of the satellite system.

Description

Technical Field

[0001] This invention belongs to the field of satellite attitude system control, and specifically relates to a satellite attitude system preset performance tracking control method based on a second-order interference observer. Background Technology

[0002] Satellites are celestial bodies that orbit planets, stars, and other celestial bodies periodically. Based on their formation, they can be divided into natural satellites and artificial satellites. Artificial satellites are launched into space by launch vehicles and orbit the Earth to perform various space missions. In recent years, satellites, relying on their high-precision attitude pointing and rapid attitude maneuvering capabilities, have been widely used in military and civilian fields. To maintain these core performance characteristics, satellite attitude control technology plays a crucial role. Specifically, in deep space exploration missions, precise attitude control ensures that the probe achieves sub-arcsecond pointing accuracy; in remote sensing observation and positioning missions, sensitive attitude control enables the satellite to achieve high dynamic response, thereby quickly switching observation targets. Therefore, as a core subsystem of a satellite, the attitude control system needs to possess higher control precision, faster convergence speed, and stronger anti-interference capabilities.

[0003] Compared to the terrestrial climate environment, the space environment exhibits more significant time-varying characteristics and strong disturbances. Typical disturbances include gravity gradients, solar radiation pressure, aerodynamic drag, and geomagnetic interference. During their operation in orbit, satellites are inevitably subjected to these continuous, minute disturbances. It is important to note that, in addition to the aforementioned continuous disturbance torques, the space environment also contains strong abrupt impact torques caused by meteorite fragments or space debris. These disturbances are applied to the satellite in pulse form, significantly disrupting the stable operation of the satellite system. Therefore, developing a controller with strong disturbance immunity is a core task in satellite attitude system design. Because disturbance observers can accurately estimate and compensate for external disturbances and are easily integrated with other control strategies, rigid body satellite attitude control system schemes based on disturbance observers have been proposed in recent years. For example, designs have been developed to achieve satellite rendezvous and docking functions without relying on the upper bounds of the first and second derivatives of disturbances; and disturbance-resistant and fault-tolerant control schemes based on multiple observers have been proposed to simultaneously address external disturbances, measurement errors, actuator failures, and input constraints. However, existing interference observers in these methods only focus on improving the accuracy of interference estimation, neglecting the convergence rate and the dynamic characteristics of interference evolution over time. Based on the above analysis, developing an estimation strategy that can simultaneously guarantee the steady-state and transient performance of interference estimation response is crucial to meeting the performance indicators of satellite systems.

[0004] Furthermore, in practical engineering applications, to ensure high-precision tracking and control, satellite systems must also meet multi-dimensional performance requirements such as window time, pointing accuracy, and maximum overshoot. This necessitates that the satellite system's attitude trajectory strictly conform to preset transient and steady-state performance specifications. The aforementioned control strategies can only ensure the convergence of the closed-loop system; the dynamic behavior of its tracking error over time and the allowable residual set are uncontrollable. Based on the above analysis, embedding preset performance technologies into satellite attitude control strategies is crucial for the high-quality completion of space missions. In recent years, many satellite attitude control schemes based on preset performance technologies have achieved phased results. For example, a predefined time performance control scheme has been proposed, enabling the tracking error to converge to a small neighborhood within a preset time; another scheme combines preset performance technologies to design an exponentially corrected differential tracker, enabling a space robot to meet predetermined performance indicators in scenarios where velocity information is lacking. However, the above schemes only use exponential functions or functions with similar properties as relatively loose funnel-shaped performance boundaries. Under these circumstances, it is difficult for the system to accurately control transient performance such as overshoot. Meanwhile, when encountering rapid and dynamic environmental changes such as strong abrupt disturbances, satellite actuators may be unable to output sufficient torque in a timely manner to ensure that tracking errors remain within performance boundaries. In summary, balancing mission requirements and performance indicators under strong abrupt disturbances is a core challenge in satellite attitude system control design. Summary of the Invention

[0005] Purpose of the invention: In view of the problems of insufficient stability and reduced control accuracy of satellites when they are in orbit and are subjected to strong sudden interference, the present invention proposes a satellite attitude system preset performance tracking control method based on a second-order interference observer.

[0006] Technical Solution: The satellite attitude system preset performance tracking control method based on a second-order interference observer described in this invention is implemented as follows:

[0007] (1) Based on the satellite attitude dynamics and kinematic equations, establish a rigid body satellite attitude maneuver control model;

[0008] (2) Based on the rigid body satellite attitude maneuver control model, considering the influence of state prediction error on the rigid body satellite attitude maneuver process, an improved second-order disturbance observer is designed to estimate the total disturbance of the satellite attitude system and output the estimated value of the external disturbance.

[0009] (3) Based on the rigid body satellite attitude maneuver control model, an asymmetric tunnel-type preset performance function is designed to ensure that the attitude tracking error meets the expected transient and steady-state performance indicators.

[0010] (4) Based on the estimated value of the external disturbance output by the improved second-order disturbance observer described in step (2), a disturbance tolerance auxiliary system is designed to improve the sensitivity of the boundary compensation mechanism while relaxing the boundary of the preset performance function, thereby enhancing the robustness of the closed-loop system.

[0011] (5) Based on the estimated value of the external interference output by the improved second-order interference observer described in step (2), the asymmetric tunneling performance function described in step (3), and the boundary correction signal output by the disturbance tolerance auxiliary system described in step (4), a preset performance anti-disturbance controller is designed to realize the attitude safety tracking control of rigid body satellite.

[0012] Furthermore, the attitude maneuver control model for rigid-body satellites described in step (1) is as follows:

[0013] (1);

[0014] In the formula, and For collective terms, This indicates external interference caused by multiple factors; The attitude angles of a rigid satellite in its body coordinate system relative to its inertial coordinate system include yaw, pitch, and roll. This represents the measured angular velocity of a rigid satellite relative to its body coordinate system. These are the control moments acting on the rigid satellite, corresponding to the roll, pitch, and yaw moments, respectively. Representing vectors The skew-symmetric matrix has the following specific form:

[0015] (2);

[0016] The rotation matrix for the satellite is expressed as:

[0017] (3);

[0018] In the formula, ,therefore reversible; Let be the rotational inertia matrix of the rigid satellite in its body coordinate system, and its expression is:

[0019] (4);

[0020] For the rotational motion of a satellite, define Let be the desired attitude angle of the satellite in the reference coordinate system relative to the inertial coordinate system, and then the attitude tracking error and its derivative are expressed as:

[0021] (5);

[0022] Based on the above analysis, the following satellite attitude tracking error system is derived:

[0023] (6);

[0024] In the formula, , , , They are respectively , , , The derivative with respect to time.

[0025] Furthermore, the implementation process of step (2) is as follows:

[0026] First, the state predictor is designed as follows:

[0027] (7);

[0028] In the formula, , These are the predicted state value and the estimated disturbance value, respectively. The Hurwitz matrix to be determined; state prediction error is introduced. Interference estimation error and interference derivative estimation error ;

[0029] Furthermore, combined with state prediction error Design an improved second-order interference observer, specifically in the following form:

[0030] (8);

[0031] In the formula, It is an intermediate auxiliary variable. represent The derivative with respect to time; The observer gain matrix is... The state prediction gain matrix contains unknown constants. , , Make , , .

[0032] Furthermore, the interference estimation error and interference derivative estimation error The dynamic system is:

[0033] (9);

[0034] about , , The state-space equations can be expressed in the following form:

[0035] (10);

[0036] in, , , ,definition , , They are respectively , , The Laplace transform of the above-mentioned improved second-order disturbance observer is used to define the system matrix. ,matrix Given sufficiently small positive constants Positive definite matrix , make the inequality when If this holds true, then the interference estimation error and interference derivative estimation error signals of the improved second-order interference observer are both uniformly bounded.

[0037] Furthermore, the implementation process of step (3) is as follows:

[0038] The tunnel-type performance function in the asymmetric case is:

[0039] (18);

[0040] In the formula, , , These are the upper and lower bounds of the performance boundary, respectively. , and These are the parameters to be designed; , Let be the initial and steady-state values ​​of the performance boundary, respectively, and satisfy . , Represents attitude tracking error The initial value; Represents a symbolic function;

[0041] To ensure that the attitude tracking error meets the preset performance constraints, an error transformation function is introduced. There will be constrained error Convert to unconstrained error The specific form is as follows:

[0042] (19);

[0043] In the formula, The limit value satisfies and ; and thus the conversion error is obtained. The expression:

[0044] (20).

[0045] Furthermore, the disturbance fault-tolerant auxiliary system in step (4) is:

[0046] (twenty one);

[0047] In the formula, the perturbation non-negative correction signal Used for dynamically adjusting performance boundaries This indicates the information related to interference estimation used for generating... The disturbance deviation signal. The external disturbance estimate is obtained from the improved second-order disturbance observer. This represents the interference threshold set by the user based on prior data; at this point, the asymmetric tunneling performance function is reconstructed as follows:

[0048] (twenty two);

[0049] Differentiating the above equation, we get:

[0050] (twenty three);

[0051] In the formula, , All are scale parameters. Used to adjust the non-negative correction signal for perturbation The convergence rate, express Sensitivity to changes in the magnitude of external disturbances; If and only if Disturbance deviation signals will only be generated at this time. ;and, ,therefore Nonnegative and bounded.

[0052] Furthermore, the implementation process of step (5) is as follows:

[0053] Design virtual control law It can be expressed as follows:

[0054] (32);

[0055] Therefore, a pre-defined performance disturbance rejection controller is designed, expressed by the following formula:

[0056] (34);

[0057] In the formula, for The derivative with respect to time, , The gain matrix of the controller to be designed, and the angular velocity tracking error. ,matrix ,matrix .

[0058] Furthermore, the aforementioned , Must meet:

[0059] (35);

[0060] in, , yes The smallest eigenvalue, yes The largest eigenvalue; considering the rigid body satellite system, if a matrix exists... and If equation (35) holds, then all tracking signals in the closed-loop system are uniformly bounded, and the attitude tracking error meets the predetermined performance constraints, and the satellite system achieves the control objective under the influence of dynamic interference.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0062] 1. In order to cope with the negative impact of external interference in the space environment, this invention utilizes an improved second-order interference observer to estimate disturbances in the satellite attitude system. By introducing the state prediction error into the design of the second-order interference observer, the closed-loop system can improve the accuracy and speed of interference estimation under low gain conditions, while avoiding the introduction of high-frequency noise due to high gain, reducing the instantaneous overshoot of the estimation error response in the initial stage, thereby improving the steady-state and transient performance of interference estimation.

[0063] 2. In order to balance the relationship between high-precision tracking control and system stability, and considering the shortcomings of the classic exponential function form, this invention introduces a tunnel-type performance function to strengthen the performance constraints on attitude trajectory. Compared with the loose funnel-shaped constraint boundary of the traditional performance function, the same-side boundary distribution characteristics of the tunnel-type performance function enable it to more accurately control the dynamic behavior of the error signal, avoid the peak phenomenon caused by excessive overshoot in the initial stage, and improve the transient performance of the closed-loop system.

[0064] 3. Based on the estimation results of the improved second-order interference observer, this invention designs a disturbance tolerance auxiliary system to reduce the impact of strong abrupt disturbances on the satellite attitude system. Using a user-defined disturbance threshold as a benchmark, when a strong abrupt disturbance causes tracking errors that may violate performance boundaries, the auxiliary system generates a disturbance correction signal to flexibly relax the performance envelope, prioritizing system stability by reducing performance requirements. When the strong abrupt disturbance disappears, the correction signal can also quickly converge to zero, restoring the system to the originally specified performance requirements. This adaptive boundary compensation mechanism can improve the boundary disturbance immunity of the satellite attitude system and enhance system robustness. Attached Figure Description

[0065] Figure 1 This is a flowchart of the present invention;

[0066] Figure 2 This is a graph showing the interference estimation of the present invention.

[0067] Figure 3 This is a graph showing the attitude tracking of the present invention;

[0068] Figure 4 This is a graph showing the angular velocity tracking error of the present invention.

[0069] Figure 5 This is a graph showing the attitude tracking error of the present invention;

[0070] Figure 6 This is a graph of the disturbance deviation signal of the present invention;

[0071] Figure 7 This is a graph of the disturbance correction signal of the present invention;

[0072] Figure 8 This is a control torque curve diagram of the present invention. Detailed Implementation

[0073] The invention will now be further described with reference to the accompanying drawings.

[0074] like Figure 1 As shown, this invention proposes a satellite attitude system preset performance tracking control method based on a second-order interference observer, specifically including the following steps:

[0075] Step 1: Combine satellite attitude dynamics and kinematic equations to establish a model for rigid body satellite attitude maneuver control.

[0076] In this embodiment, a rigid satellite is taken as the research object, and an attitude maneuver control model for rigid satellites is established. Considering the advantages of the Euler angle representation method, such as its intuitiveness and few computational parameters, this invention adopts the Euler angle method to represent the attitude motion of the satellite. Therefore, the attitude kinematics and dynamic equations of the satellite are derived using the Euler angle representation method, which can be presented in the following form:

[0077]

[0078] In the formula, and For collective terms, This indicates external interference caused by multiple factors; The attitude angles of a rigid satellite in its body coordinate system relative to its inertial coordinate system include yaw, pitch, and roll. This represents the measured angular velocity of a rigid satellite relative to its body coordinate system. These are the control moments acting on the rigid satellite, corresponding to the roll, pitch, and yaw moments, respectively. Representing vectors The skew-symmetric matrix has the following specific form:

[0079]

[0080] at the same time, The rotation matrix for the satellite is expressed as:

[0081]

[0082] In the formula, ,therefore reversible; Let be the rotational inertia matrix of the rigid satellite in its body coordinate system, and its expression is:

[0083]

[0084] in , , For the satellite's moment of inertia, , , Let be the inertial product of the satellite. For the satellite's rotational motion, define... Let be the desired attitude angle of the satellite in the reference coordinate system relative to the inertial coordinate system. Therefore, the attitude tracking error and its derivative can be expressed as:

[0085]

[0086] Based on the above analysis, the following satellite attitude tracking error system can be derived:

[0087]

[0088] In the formula, , , , They are respectively , , , The derivative with respect to time.

[0089] like Figure 1 As shown, in this embodiment, the attitude maneuver control of a rigid body satellite is taken as the research object, and the current attitude is used to control the attitude maneuver. and target posture Obtain attitude tracking error Combined with asymmetric tunnel-type performance function , Error transformation will have constrained errors. Convert to equivalent unconstrained error According to the error The virtual control torque is obtained by designing the backstepping control law. and expected output torque Since external disturbances can reduce the accuracy of satellite attitude maneuvers, an improved second-order disturbance observer is designed to estimate and compensate for the amount of external disturbance. At the same time, a disturbance tolerance auxiliary system is designed to cope with the negative impact of strong sudden disturbances and improve the accuracy of satellite attitude maneuvers.

[0090] Step 2: Based on the rigid body satellite attitude maneuver control model established in Step 1, consider external disturbances. To address the impact of attitude maneuvers on rigid body satellites, an improved second-order disturbance observer is designed to estimate the total system disturbance. The total disturbance of the original control system is treated as a state variable of the new control system, and the estimated value of the external disturbance is obtained by observing these state variables. The convergence of the proposed improved second-order disturbance observer is proved using Lyapunov functions.

[0091] In this embodiment, for a second-order system oriented towards a rigid satellite attitude maneuver control model, the state predictor is first designed as follows:

[0092]

[0093] In the formula, , These are the predicted state value and the estimated disturbance value, respectively. Let be the Hurwitz matrix to be determined. State prediction error is introduced here. Interference estimation error and interference derivative estimation error Furthermore, this is combined with the state prediction error. Design an improved second-order interference observer, specifically in the following form:

[0094]

[0095] In the formula, It is an intermediate auxiliary variable. represent The derivative with respect to time; The observer gain matrix is... This is the state prediction gain matrix. There are unknown constants. , , Make , , From the formula and The following can be derived about and Dynamic systems:

[0096]

[0097] Combined - ,about , , The state-space equations can be expressed in the following form:

[0098]

[0099] in, , , .definition , , They are respectively , , Laplace transform, system matrix , .

[0100] In this embodiment, the convergence of the improved second-order disturbance observer designed in step (2) is proved using Lyapunov functions; the specific process is as follows:

[0101] First, define the state vector. , by formula It can be known that:

[0102]

[0103] For the state vector Construct the Lyapunov function:

[0104]

[0105] In the formula Let be the positive definite matrix to be designed. Next, calculate... It can be deduced that:

[0106]

[0107] for From Young's inequality, we can obtain:

[0108]

[0109] in Let it be a sufficiently small positive integer. Then the expression... Substitution We can obtain:

[0110]

[0111] Define matrix Given positive constants If a positive definite matrix exists Make hour, The following inequalities must be satisfied:

[0112]

[0113] In the formula, , , yes The smallest eigenvalue, yes The largest eigenvalue. At this time, the system It satisfies uniform bounded stability, and:

[0114]

[0115] in, yes The smallest eigenvalue. Therefore, when When established, the disturbance estimation error and interference derivative estimation error All are uniformly bounded and stable, and the convergence proof is complete.

[0116] By Combined with the design of a second-order interference observer, and with appropriate selection With a small gain, the closed-loop system can effectively suppress interference estimation and its derivative error, and improve the transient and steady-state performance of interference estimation over time.

[0117] Step 3: Based on the rigid-body satellite attitude maneuver control model established in Step 1, an asymmetric tunnel-type preset performance function is designed to ensure that the attitude tracking error meets the expected transient and steady-state performance indicators. Furthermore, compared to the relatively loose funnel-shaped performance limits of traditional performance functions, the tunnel-type performance function establishes a tighter performance constraint range, thus enabling more precise control of overshoot, improving transient performance, resulting in a smoother error tracking trajectory, and significantly enhancing the robustness of the closed-loop system.

[0118] In this embodiment, an asymmetric tunnel-type performance function is first designed, expressed by the following formula:

[0119]

[0120] In the formula, , , These are the upper and lower bounds of the performance boundary, respectively. , and These are the parameters to be designed; , Let be the initial and steady-state values ​​of the performance boundary, respectively, and satisfy . , Represents attitude tracking error The initial value; Represents a symbolic function.

[0121] At this point, the performance boundary of the tunnel type is asymmetric, making the original error transformation form unusable. This invention introduces a new error transformation function. There will be constrained errors. Equivalent transformation to unconstrained error The specific form is as follows:

[0122]

[0123] In the formula, The limit value satisfies and This leads to the conversion error. The expression:

[0124]

[0125] Step 4: Based on the estimated value of the external disturbance output by the improved second-order disturbance observer, design a disturbance tolerance auxiliary system. While relaxing the boundary of the preset performance function, improve the sensitivity of the boundary compensation mechanism and enhance the robustness of the closed-loop system.

[0126] In this embodiment, a disturbance fault-tolerant auxiliary system is first designed, expressed by the following formula:

[0127]

[0128] In the formula, the perturbation non-negative correction signal Used for dynamically adjusting performance boundaries This indicates the information related to interference estimation used for generating... The disturbance deviation signal. The external interference estimate obtained by the improved second-order interference observer described in step (2) is... This represents the interference threshold set by the user based on prior data. At this point, the asymmetric tunneling performance function described in step 3 is reconstructed as follows:

[0129]

[0130] Differentiating the above equation, we get:

[0131]

[0132] In the formula, , All are scale parameters. Used to adjust the non-negative correction signal for perturbation The convergence rate, express Sensitivity to changes in the magnitude of external disturbances; That is, if and only if Disturbance deviation signals will only be generated at this time. ;and, ,therefore Nonnegative and bounded.

[0133] In this embodiment, the Lyapunov function is used to prove the formula. All auxiliary signals are non-negative and bounded; the specific process is as follows:

[0134] This invention will address the perturbation correction signal. Prove the nonnegativity and boundedness separately.

[0135] ① Nonnegativity: According to the formula It can be solved The expression:

[0136]

[0137] because It can be seen Each term is non-negative, therefore The proof of its nonnegativity is now complete.

[0138] ② Boundedness: for Construct the following Lyapunov function:

[0139]

[0140] Differentiating the above equation, we get:

[0141]

[0142] because ,thereby satisfy:

[0143]

[0144] when hour:

[0145]

[0146] From the monotonicity of the function, we know that when hour, , Monotonically increasing; when hour, , It will be suppressed to no more than Within that range. Therefore There exists a maximum value, that is Furthermore, if initial value , Final satisfaction Therefore, the non-negative perturbation correction signal Subject to the upper realm Constraints are imposed to ensure the performance function of the perturbed tunnel-type flexible structure. and It will not grow indefinitely; its boundedness has been proven.

[0147] The design of the disturbance-tolerant auxiliary system establishes a connection between dynamic disturbances and constraint boundaries. This is achieved by using a second-order disturbance observer... Greater than The auxiliary system will generate and This temporarily relaxes the performance limits to ensure that the attitude error tracking trajectory remains within the performance envelope, avoiding potential singularity issues. When the strong abrupt disturbance disappears... and It converges rapidly to zero, making and Restore to the original form to ensure the system meets predefined performance metrics.

[0148] Step 5: Based on the rigid body satellite attitude maneuver control model, design the virtual control torque and preset performance disturbance rejection control law using the backstepping control method. Prove the closed-loop stability of the proposed preset performance control method using Lyapunov functions.

[0149] In this embodiment, firstly, the formula... In Differentiation yields:

[0150]

[0151] The formula Substitution Further results were obtained:

[0152]

[0153] In the formula, Let it be a diagonal matrix, and then define the matrix. for:

[0154]

[0155] At the same time, define the matrix Based on the backstep control method, select As a virtual control law:

[0156]

[0157] In the formula, This represents the gain matrix of the controller to be designed. (For...) Define the angular velocity error and its derivative:

[0158]

[0159] Based on the above analysis, the pre-set performance disturbance rejection controller for rigid body satellites is designed as follows:

[0160]

[0161] In the formula, This is also the gain matrix of the controller to be designed.

[0162] In this embodiment, the closed-loop stability of the backstepping control method is proved using Lyapunov functions. According to Lyapunov stability analysis, when designing the above control law, if the following conditions are met:

[0163]

[0164] Then all tracking signals in the closed-loop system are uniformly bounded, and the attitude tracking error meets the predetermined performance constraints. At this time, the satellite system can achieve the control objective under the influence of dynamic disturbances. , yes The smallest eigenvalue, yes The largest eigenvalue. Considering a rigid body satellite system, if there exists a matrix... and If the above inequality holds, then all tracking signals in the closed-loop system are uniformly bounded, and the attitude tracking error satisfies the predetermined performance constraints. Therefore, the satellite system can achieve the control objective under the influence of dynamic disturbances.

[0165] The specific analysis process is as follows: based on the conversion error... Angular velocity tracking error and interference estimation error Choose the following Lyapunov function:

[0166]

[0167] In the formula, First, let's look at the formula. In Substitution From this, we can obtain:

[0168]

[0169] Combined and Further obtained The expression is:

[0170]

[0171] On the other hand, the formula In Substitution In Derivation:

[0172]

[0173] Will Substituting the form into the above equation, we obtain The form is expressed by the following formula:

[0174]

[0175] Therefore, differentiating the Lyapunov function yields:

[0176]

[0177] In the formula, Perform a symmetry operation on the matrix. Based on the formula , and We can obtain the following inequalities:

[0178]

[0179] for Using Young's inequality, we can obtain:

[0180]

[0181] Therefore, combined and From this, we can deduce that:

[0182]

[0183] At the same time, according to the formula Analysis of the convergence of the improved second-order disturbance observer shows that the disturbance estimation error... Bounded, meaning there exists an unknown positive constant. , making Based on all the above analyses, the final conclusion is... The following inequalities must be satisfied:

[0184]

[0185] In the formula:

[0186]

[0187] At this point, all tracking error signals in the closed-loop system are uniformly bounded, and the stability has been proven.

[0188] The proposed satellite attitude system preset performance tracking control method based on a second-order disturbance observer was verified through simulation experiments in Matlab to demonstrate the feasibility of the proposed preset performance disturbance rejection control scheme. First, the satellite's inertial matrix was selected as follows:

[0189]

[0190] During the simulation, the initial state of the satellite system is set as follows: , The desired tracking signal is selected as follows: Furthermore, the continuous interference settings for the satellite system are as follows:

[0191]

[0192] Meanwhile, in order to simulate the scenario of a satellite being impacted by a meteorite or attacked by an enemy satellite in space, this invention... Strong mutation interference was introduced. :

[0193]

[0194] To evaluate the effectiveness of the proposed satellite attitude system preset performance tracking control method based on a second-order interference observer, this invention selects a method that ensures all tracking signals in the closed-loop system are consistently bounded and that the tracking error remains within a preset performance envelope. First, to guarantee the estimation speed and accuracy of the improved second-order interference observer, the observer gain is selected... , , Secondly, for tunnel-type performance functions, setting scale parameters. Convergence rate initial error steady-state error Next, to ensure that the disturbance-tolerant auxiliary system can maintain a balance between performance indicators and system stability, a scale parameter is also selected. , And set the interference threshold based on prior data. Finally, select the preset performance disturbance rejection controller gain. , .

[0195] Figure 2 The estimation curves of external interference were plotted, and it can be clearly observed that the improved second-order interference observer designed in this invention can respond quickly to sudden changes in interference, and can maintain good speed and accuracy in interference estimation even with a small observer gain. Figure 3 The satellite system attitude angles were displayed. By tracking the trajectory, it can be observed that the system state experiences slight fluctuations under the influence of external disturbances, but under the control of the controller, the actual signal... It can still accurately track the desired signal. . Figure 4 The angular velocity error signal can quickly converge to a sufficiently small limit within a short period of time. Figure 5 This demonstrates the attitude tracking error. The response curves of the flexible performance function of the disturbed tunnel type show that... It can quickly converge to the design performance limits with almost no overshoot in the initial response phase. When strong abrupt disturbances are introduced (where dynamic disturbance estimation is performed...), it achieves this. Greater than the interference threshold The disturbance-tolerant auxiliary system can generate Figure 6 and Figure 7 Disturbance deviation signal in and disturbance correction signal This allows for flexible relaxation of performance boundaries, ensuring... It remains within the performance envelope. When the mutation interference disappears... and It can also quickly converge to zero to ensure that the system meets the preset performance indicators. Finally, the control torque required to achieve high-precision tracking control. like Figure 8 As shown. Overall, despite the influence of external interference, the satellite system is still able to meet the required control requirements and ensure its stability under complex interference, thus verifying the effectiveness of the control method proposed in this invention.

[0196] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A satellite attitude system preset performance tracking control method based on a second-order interference observer, characterized in that, Includes the following steps: (1) Based on the satellite attitude dynamics and kinematic equations, establish a rigid body satellite attitude maneuver control model; (2) Based on the rigid body satellite attitude maneuver control model, considering the influence of state prediction error on the rigid body satellite attitude maneuver process, an improved second-order disturbance observer is designed to estimate the total disturbance of the satellite attitude system and output the estimated value of the external disturbance. (3) Based on the rigid body satellite attitude maneuver control model, an asymmetric tunnel-type preset performance function is designed to ensure that the attitude tracking error meets the expected transient and steady-state performance indicators. (4) Based on the estimated value of the external disturbance output by the improved second-order disturbance observer described in step (2), a disturbance tolerance auxiliary system is designed to improve the sensitivity of the boundary compensation mechanism while relaxing the boundary of the preset performance function, thereby enhancing the robustness of the closed-loop system. (5) Based on the estimated value of the external interference output by the improved second-order interference observer described in step (2), the asymmetric tunneling performance function described in step (3), and the boundary correction signal output by the disturbance tolerance auxiliary system described in step (4), a preset performance anti-disturbance controller is designed to realize the attitude safety tracking control of rigid body satellite.

2. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 1, characterized in that, The attitude maneuver control model for rigid body satellites described in step (1) is as follows: (1)； In the formula, and For collective terms, This indicates external interference caused by multiple factors; The attitude angles of a rigid satellite in its body coordinate system relative to its inertial coordinate system include yaw, pitch, and roll. This represents the measured angular velocity of a rigid satellite relative to its body coordinate system. These are the control moments acting on the rigid satellite, corresponding to the roll, pitch, and yaw moments, respectively. Representing vectors The skew-symmetric matrix has the following specific form: (2)； The rotation matrix for the satellite is expressed as: (3)； In the formula, ,therefore reversible; Let be the rotational inertia matrix of the rigid satellite in its body coordinate system, and its expression is: (4)； For the rotational motion of a satellite, define Let be the desired attitude angle of the satellite in the reference coordinate system relative to the inertial coordinate system, and then the attitude tracking error and its derivative are expressed as: (5)； Based on the above analysis, the following satellite attitude tracking error system is derived: (6)； In the formula, , , , They are respectively , , , The derivative with respect to time.

3. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 1, characterized in that, The implementation process of step (2) is as follows: First, the state predictor is designed as follows: (7)； In the formula, , These are the predicted state value and the estimated disturbance value, respectively. The Hurwitz matrix to be determined; state prediction error is introduced. Interference estimation error and interference derivative estimation error ; Furthermore, combined with state prediction error Design an improved second-order interference observer, specifically in the following form: (8)； In the formula, It is an intermediate auxiliary variable. represent The derivative with respect to time; The observer gain matrix is... The state prediction gain matrix contains unknown constants. , , Make , , .

4. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 3, characterized in that, The interference estimation error and interference derivative estimation error The dynamic system is: (9)； about , , The state-space equations can be expressed in the following form: (10)； in, , , ,definition , , They are respectively , , The Laplace transform of the above-mentioned improved second-order disturbance observer is used to define the system matrix. ,matrix Given sufficiently small positive constants Positive definite matrix , make the inequality when If this holds true, then the interference estimation error and interference derivative estimation error signals of the improved second-order interference observer are both uniformly bounded.

5. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 1, characterized in that, The implementation process of step (3) is as follows: The tunnel-type performance function in the asymmetric case is: (18)； In the formula, , , These are the upper and lower bounds of the performance boundary, respectively. , and These are the parameters to be designed; , Let be the initial and steady-state values ​​of the performance boundary, respectively, and satisfy . , Represents attitude tracking error The initial value; Represents a symbolic function; To ensure that the attitude tracking error meets the preset performance constraints, an error transformation function is introduced. There will be constrained error Convert to unconstrained error The specific form is as follows: (19)； In the formula, The limit value satisfies and ; and thus the conversion error is obtained. The expression: (20)。 6. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 1, characterized in that, The disturbance fault-tolerant auxiliary system mentioned in step (4) is: (21)； In the formula, the perturbation non-negative correction signal Used for dynamically adjusting performance boundaries This indicates the information related to interference estimation used for generating... The disturbance deviation signal. The external disturbance estimate is obtained from the improved second-order disturbance observer. This represents the interference threshold set by the user based on prior data; at this point, the asymmetric tunneling performance function is reconstructed as follows: (22)； Differentiating the above equation, we get: (23)； In the formula, , All are scale parameters. Used to adjust the non-negative correction signal for perturbation The convergence rate, express Sensitivity to changes in the magnitude of external disturbances; If and only if Disturbance deviation signals will only be generated at this time. ; and, ,therefore Nonnegative and bounded.

7. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 1, characterized in that, The implementation process of step (5) is as follows: Design virtual control law It can be expressed as follows: (32)； Therefore, a pre-defined performance disturbance rejection controller is designed, expressed by the following formula: (34)； In the formula, for The derivative with respect to time, , The gain matrix of the controller to be designed, and the angular velocity tracking error. ,matrix ,matrix .

8. The satellite attitude system preset performance tracking control method based on a second-order interference observer according to claim 7, characterized in that, The , Must meet: (35)； in, , yes The smallest eigenvalue, yes The largest eigenvalue; considering the rigid body satellite system, if a matrix exists... and If equation (35) holds, then all tracking signals in the closed-loop system are uniformly bounded, and the attitude tracking error meets the predetermined performance constraints, and the satellite system achieves the control objective under the influence of dynamic interference.

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