A laser pointing preset performance sliding mode control method and a stability verification method thereof

Abstract

The application provides a laser pointing preset performance sliding mode control method and a stability verification method thereof, and belongs to the technical field of space control. The control method comprises the following steps: based on an exponential decay type preset performance function constructed by a laser pointing error, a smooth error transformation function is used to convert the laser pointing error into an unconstrained variable, and an unconstrained variable matrix is formed; a fractional order sliding mode surface is constructed according to the unconstrained variable matrix; equivalent control torque and switching control torque are obtained according to the fractional order sliding mode surface, and a total control law is obtained by synthesizing the equivalent control torque and the switching control torque; and sliding mode control is performed according to the total control law. Through the technical scheme provided by the application, the convergence time can be shortened by 77.3%, the vibration mode peak value can be suppressed by more than 90%, and the performance boundary can still be strictly met under strong thermal disturbance, thereby providing theoretical support and engineering implementation scheme for the laser energy transmission pointing control of the lunar surface of the lunar orbit solar power station.

Description

Technical Field

[0001] This invention relates to the field of space control technology, specifically to a sliding mode control method for laser pointing preset performance and its stability verification method. Background Technology

[0002] With the exploration and development of the lunar polar shadow region becoming a focus, providing a continuous and stable energy source for rovers performing long-term exploration missions in this area has become a core technological challenge. Lunar solar power stations supply power to lunar surface facilities via wireless laser energy transmission, but face significant challenges. Flexible truss solar arrays are prone to low-frequency vibrations and deformations under the non-spherical gravity of the moon, solar radiation pressure, and thermo-optical-mechanical coupling disturbances, directly affecting laser pointing accuracy and energy transmission efficiency.

[0003] Existing control technologies have significant shortcomings: traditional proportional-integral-derivative (PID) controllers struggle to meet micro-radian-level pointing accuracy requirements, exhibiting issues such as large overshoot, long convergence time, and weak disturbance rejection; while classical sliding mode control offers strong robustness, its inherent chattering problem easily excites high-frequency modes in flexible structures, and it lacks explicit constraints on transient performance; advanced methods such as fractional-order sliding mode and model predictive control are still in their early stages of on-orbit application, failing to consider the unique rigid-flexible coupling dynamics and multi-source disturbance coupling effects of lunar solar power stations. Therefore, a high-precision pointing control method that combines strict performance guarantees, strong robustness, and low chattering is urgently needed. Summary of the Invention

[0004] The purpose of this invention is to provide a laser pointing preset performance sliding mode control method and its stability verification method. By explicitly encoding the convergence speed, overshoot and steady-state accuracy of the laser pointing error as time-varying boundaries through a preset performance function, and integrating the adaptive robustness of fractional sliding mode, it achieves collaborative optimization management of uncertainties, strong environmental disturbances and performance constraints of large flexible structures.

[0005] To achieve the above objectives, the present invention provides a sliding mode control method for laser pointing preset performance, the control method comprising:

[0006] Step S1: Based on the exponentially decaying preset performance function constructed through the laser pointing error, a smooth error transformation function is used to convert the laser pointing error into an unconstrained variable and form an unconstrained variable matrix.

[0007] Step S2: Construct a fractional sliding surface based on the unconstrained variable matrix;

[0008] Step S3: Obtain the equivalent control torque and switching control torque based on the fractional-order sliding surface, and synthesize the total control law based on the equivalent control torque and switching control torque; Step S4: Perform sliding mode control based on the total control law.

[0009] The present invention also provides a stability verification method for a laser pointing preset performance sliding mode control method, which is used in the above laser pointing preset performance sliding mode control method. The stability verification method includes: based on the Lyapunov function, under the action of the total control law, if the fractional sliding surface converges to the neighborhood of the origin within a finite convergence time, then the laser pointing error satisfies the preset performance constraint.

[0010] The beneficial effects of this invention are as follows:

[0011] The technical solution provided by this invention enables high-precision laser energy transmission pointing control of lunar surface facilities at the micro-arc level by a lunar orbit solar power station, achieving collaborative optimization management of uncertainties, strong environmental disturbances, and performance constraints of large flexible structures, as detailed below:

[0012] (1) A high-fidelity, real-time computable rigid-flexible coupling dynamic model was established. The Craig-Bampton modal synthesis method was used to reduce the tens of thousands of degrees of freedom to the order of tens of orders, which greatly improved the computational efficiency while ensuring the key dynamic characteristics and met the real-time control requirements.

[0013] (2) An adaptive sliding mode control framework with preset performance guarantee is proposed. By using preset performance function, the engineering index is explicitly encoded as time-varying boundary, ensuring that the error of the entire control process is within the safe range, thus solving the problem of lack of transient performance guarantee in traditional methods.

[0014] (3) By integrating the memory characteristics of fractional calculus with the super-spiral algorithm to construct a continuous control law, the chattering problem of traditional sliding mode control is effectively suppressed, while the robustness to lumped disturbances is enhanced, and the convergence time is shortened by more than 70% compared with PID control.

[0015] (4) Even under extreme conditions such as strong thermal disturbance and lunar non-spherical gravity, the pointing error can still be strictly guaranteed to be within the preset boundary, and the peak suppression rate of vibration mode is over 90%, providing a highly reliable engineering solution for laser energy transmission in lunar solar power stations. Attached Figure Description

[0016] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0017] Figure 1 This is a flowchart of the laser pointing preset performance sliding mode control method provided by the present invention;

[0018] Figure 2 These are the simulation results of the torque control of the laser pointing joint provided by this invention;

[0019] Figure 3 This invention provides the laser pointing error under strong interference.

[0020] Figure 4 This invention provides a vibration response analysis of the solar panel during its deployment process. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0022] Figure 1 This is a flowchart of the laser pointing preset performance sliding mode control method provided by the present invention, as follows: Figure 1 As shown, the control method includes:

[0023] Step S1: Based on the exponentially decaying preset performance function constructed through the laser pointing error, a smooth error transformation function is used to convert the laser pointing error into an unconstrained variable and form an unconstrained variable matrix.

[0024] Step S2: Construct a fractional sliding surface based on the unconstrained variable matrix;

[0025] Step S3: Obtain the equivalent control torque and switching control torque based on the fractional-order sliding surface, and synthesize the total control law based on the equivalent control torque and switching control torque; Step S4: Perform sliding mode control based on the total control law.

[0026] Step S1 includes:

[0027] Based on laser pointing error Construct an exponentially decaying preset performance function as follows:

[0028] ;

[0029] in, Let be the initial boundary, representing the maximum allowable error at the initial time. The steady-state boundary represents the maximum allowable error at steady state. Here, is the convergence rate parameter, representing the decay rate of the control error boundary. For time, To control the degree of freedom index. In one embodiment of the invention, the initial boundary... steady-state boundary , In this case, the laser pointing error converges to the steady-state boundary within 170 seconds, and the overshoot is less than 1%.

[0030] Step S1 also includes:

[0031] A smooth error transformation function is used to convert the laser pointing error into an unconstrained variable. Unconstrained variables The calculation is as follows:

[0032] ;

[0033] in, Let be the smoothing error transformation function. unconstrained variables Construct an unconstrained variable matrix , The value range is 1 to Unconstrained variables Let be any unconstrained variable in the unconstrained variable matrix.

[0034] Convert laser pointing error into an unconstrained variable This makes the original constraints This is transformed into an equivalent unconstrained stabilization problem.

[0035] The smooth error transformation function will constrain the laser pointing error. Mapping to unconstrained real space ,in When the error approaches the performance boundary, the transformation variable tends to infinity. The stabilization of the unconstrained space indirectly ensures that the original error always meets the preset performance constraints. Let be the value of the preset performance function at time t, where In the case of Indicates the laser pointing error at time t The maximum allowed boundary value satisfies .

[0036] The fractional sliding surface in step S2 is calculated as follows:

[0037] ;

[0038] Where s is a fractional-order sliding surface. This is the proportional gain matrix, used to adjust the instantaneous response under error conditions. This is the fractional-order gain matrix, used to control the memory effect and damping characteristics of the fractional derivative. Both can be designed independently and determined through pole placement, optimization algorithms, or trial-and-error methods. for Caputo-type fractional derivative, ,in The order of the fractional-order sliding surface. , For gamma function, Let be the unconstrained variable matrix at time t. For integration variables The corresponding unconstrained variable matrix, , For integration variables The corresponding unconstrained variable matrix The derivative of This is the first positive definite gain matrix. This is the second positive definite gain matrix. , , , , , , , All of these are preset values. Represents a diagonal matrix. and It can be determined through trial and error or optimization algorithms, and is used to enhance system robustness. For symbolic functions, Defined as follows: In In the case of ,exist In the case of , In the case of .

[0039] The order of the fractional-order sliding surface in step S2 The value is 0.8, representing the first positive definite gain matrix. The second positive definite gain matrix To balance convergence speed and robustness.

[0040] Step S3 includes:

[0041] Step S31, calculate the equivalent control torque as follows:

[0042] ;

[0043] in, For equivalent control torque, Generalized coordinates The inertia matrix at that location, To be based on generalized coordinates The obtained generalized velocity vector, To represent the generalized coordinates of the laser's direction, The matrix of Coriolis force and centrifugal force. Let q be the gravitational gradient torque vector at the generalized coordinate q. It is an unconstrained variable matrix. Unconstrained variable matrix The first derivative matrix, Unconstrained variable matrix The second derivative matrix, The order of the fractional-order sliding surface. ; for Caputo-type fractional derivative, , For symbolic functions, Defined as follows: In In the case of ,exist In the case of , In the case of .

[0044] Step S32, calculate the switching control torque based on the superspiral algorithm:

[0045] ;

[0046] in, To switch control torque, The value is an adaptive estimate, where s is a fractional-order sliding surface. Let be the Euclidean norm of the fractional sliding surface s. It is a positive definite adaptive gain matrix and , As a proportional term, finite-time convergence is achieved through nonlinear gain. This is the integral term, used to eliminate steady-state error and enhance robustness. For symbolic functions, Defined as follows: In In the case of ,exist In the case of The proportional and integral terms work together to form a superspiral algorithm, which effectively suppresses the chattering problem of traditional sliding mode control.

[0047] Step S33: The total sliding mode control law is obtained by combining the equivalent control torque and the switching control torque.

[0048] The total sliding mode control law is obtained by adding the equivalent control torque and the switching control torque: .

[0049] In step S32, In this case, ,exist In this case, ;in, For adaptive estimates The preset upper bound value, For adaptive estimates The Euclidean norm, It is a positive definite adaptive gain matrix and .

[0050] Accordingly, the present invention also provides a stability verification method for a laser pointing preset performance sliding mode control method, which is used in the laser pointing preset performance sliding mode control method of the present invention. The stability verification method includes, based on the Lyapunov function, under the action of the total control law, if the fractional sliding surface converges to the neighborhood of the origin within a finite convergence time, then the laser pointing error satisfies the preset performance constraint.

[0051] The Lyapunov function is constructed as follows:

[0052] ;

[0053] in, The Lyapunov function value is used to measure the energy of the system. The generalized mass matrix after order reduction. To estimate the error, This represents the deviation between the adaptive estimate and the true value of the upper bound of the perturbation. For adaptive estimates, Let be the true value of the upper bound of the perturbation, and s be the fractional-order sliding surface. It is a positive definite adaptive gain matrix and The order reduction in this invention involves using the Craig-Bampton mode synthesis method to reduce the order of the flexible solar array and flexible laser antenna array of the solar power station, reducing the system with tens of thousands of degrees of freedom to retain the q-order fixed interface canonical mode.

[0054] Finite convergence time The calculation is as follows:

[0055] ;

[0056] in, Let be the finite convergence time for the fractional sliding surface s to converge to the neighborhood of the origin. Let be the initial value of the Lyapunov function at the initial time t=0, reflecting the energy deviation between the initial state of the system and the sliding surface. To take the square root of the initial value of the Lyapunov function at the initial time t=0, To be related to the first positive definite gain matrix Second positive definite gain matrix and positive definite adaptive gain matrix Related positive numbers, Used to adjust the convergence speed. The larger the value, the shorter the convergence time, specifically... , Represents the first positive definite gain matrix Minimum eigenvalue, Represents the second positive definite gain matrix Minimum eigenvalue, Represents the adaptive gain matrix Minimum eigenvalue.

[0057] The present invention will be further described below through specific embodiments.

[0058] This invention can be used in a low lunar orbit solar power station system, in which a rigid central truss is connected to a laser antenna array via a J1 rotary joint and to a flexible solar array via a J2 rotary joint, and the laser transmitter is pointed at a lunar surface receiving station, operating in a 100km lunar orbit.

[0059] Figure 2 These are the simulation results of the torque control of the laser pointing joint provided by this invention. Figure 2 The diagram shows the overall control law for the J2 rotary joint. The component at the J1 rotary joint, from Figure 2 It can be seen that adaptive compensation during thermal disturbance significantly reduces chattering compared to traditional sliding mode. Figure 2 The red line represents the control torque of the sliding mode control provided by this invention, while the blue line represents the control torque of the traditional sliding mode control. It can be seen that the method of this invention significantly reduces chattering. Figure 2 The traditional sliding mode control shown is PID (Proportional Integral Derivative) control.

[0060] Figure 3 This invention provides laser pointing error under strong interference. Figure 3 The figure shows the laser pointing error under strong interference: the vertical axis is in units of laser pointing error, i.e., microradians (μrad, 1μrad=10). -6 rad). Figure 3It contains four curves: the red solid line represents the laser pointing error under the preset performance finite-time sliding mode control provided by this invention; the blue solid line represents the laser pointing error under PID control; and the red dashed line represents the upper and lower boundaries of the preset performance, where the upper boundary is... The lower boundary is The gray area represents the region affected by strong interference. From Figure 3 As can be seen, the technical solution of this invention has a convergence time of about 170s (77.3% shorter than PID), no overshoot, a steady-state error of ±2μrad, and remains within the safety boundary of 80μrad during strong thermal disturbance (t=1500s-1700s), strictly meeting the preset performance constraints.

[0061] Figure 4 This invention provides a vibration response analysis of the solar panel during its deployment process, such as... Figure 4 As shown, Figure 4 The vibration response of the first mode coordinates during the deployment of the solar array is shown: the horizontal axis is time (unit: seconds), and the vertical axis is the modal coordinates (normalized amplitude, dimensionless). Figure 4 It contains two curves: the red solid line represents the modal coordinate response under the preset performance finite-time sliding mode control provided by this invention, and the blue solid line represents the modal coordinate response under traditional PID control. From Figure 4 As can be seen, during the deployment maneuver of the solar array (0-3000 seconds), the peak value of the first-order modal coordinates under traditional PID control is approximately 65 (normalized amplitude), while the peak value under the preset performance finite-time sliding mode control provided by this invention is approximately 0.08 (normalized amplitude), achieving a vibration modal peak suppression rate of over 96% (calculation formula: (65-2) / 65×100%=96.9%). Simultaneously, the modal coordinate convergence time under the preset performance finite-time sliding mode control provided by this invention is significantly shortened, significantly outperforming the PID control method, thus verifying the effective suppression capability of this invention for flexible structure vibration.

[0062] In this embodiment, the physical parameters of the lunar solar power station system can be set as follows: mass of the rigid central truss B0. Inertial tensor The total mass of the flexible solar array B1 Its first two fixed interface natural frequencies are 0.05Hz and 0.12Hz; the total mass of the flexible laser antenna array B2 is... The first two natural frequencies of the flexible laser antenna array B2 are 0.08Hz and 0.15Hz. The lunar solar power station operates in a lunar circular orbit at an altitude of h=100km, with an orbital angular velocity... .

[0063] During the execution of each control cycle, the laser pointing error is calculated. ;in For the actual generalized coordinate vector of the system, The rigid body coordinates of the interface nodes (including spacecraft attitude angles and laser pointing mechanism joint angles) These are flexible modal coordinates (modal amplitudes retained after order reduction by the Craig-Bampton modal synthesis method). The desired generalized coordinate vector is obtained by the Craig-Bampton coordinate transformation of the desired trajectory planned by the laser pointing task. The technical solution provided by the present invention is verified by simulation, and a simulation platform is constructed. The following multi-task simulation scenarios are designed: (1) Solar array deployment and solar pointing task: complete a 60° rotation within 3000 seconds, with an overshoot of less than 5%; (2) High-precision tracking task of laser antenna: track a sinusoidal signal with an amplitude of 50μrad and a period of 500s, with an error constraint of ±100μrad and a steady-state error of less than 5μrad; (3) Strong disturbance composite maneuver task: inject a 200-second continuous thermal disturbance at t=1500 seconds, and simultaneously command a 2° attitude step adjustment. The simulation is compared with that of the traditional PID controller to verify the superiority of the technical solution of the present invention in terms of convergence time, vibration suppression and anti-disturbance performance.

[0064] Simulation results show that the PID controller has a convergence time of approximately 749 s, an overshoot of 85 μrad, and a steady-state oscillation of ±8 μrad. The proposed solution has a convergence time of approximately 170 s, no overshoot, and a steady-state error of ±2 μrad. Compared to PID control, the proposed solution reduces laser pointing convergence time by 77.3%, suppresses vibration mode peak values ​​by over 90%, maintains pointing error within a safe margin of 80 μrad under strong thermal disturbances, and reduces chattering to ±2. Within this range, the preset performance constraints are strictly met.

[0065] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0066] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0067] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A sliding mode control method for preset laser pointing performance, characterized in that, The control method includes: Step S1: Based on the exponentially decaying preset performance function constructed through the laser pointing error, a smooth error transformation function is used to convert the laser pointing error into an unconstrained variable and form an unconstrained variable matrix. Step S2: Construct a fractional sliding surface based on the unconstrained variable matrix; Step S3: Obtain the equivalent control torque and switching control torque based on the fractional-order sliding surface, and synthesize the total control law based on the equivalent control torque and switching control torque. Step S4: Perform sliding mode control according to the overall control law.

2. The laser pointing preset performance sliding mode control method according to claim 1, characterized in that, Step S1 includes: Based on laser pointing error Construct an exponentially decaying preset performance function as follows: ； in, Let be the initial boundary, representing the maximum allowable error at the initial time. The steady-state boundary represents the maximum allowable error at steady state. Here, is the convergence rate parameter, representing the decay rate of the control error boundary. For time, To control the degree of freedom index.

3. The laser pointing preset performance sliding mode control method according to claim 2, characterized in that, Step S1 further includes: A smooth error transformation function is used to convert the laser pointing error into an unconstrained variable. Unconstrained variables The calculation is as follows: ； in, For smooth error transformation function, unconstrained variables Construct an unconstrained variable matrix , The value range is 1 to .

4. The laser pointing preset performance sliding mode control method according to claim 3, characterized in that, The fractional sliding surface calculation in step S2 is as follows: ； Where s is a fractional-order sliding surface, and where... This is the gain matrix for the proportional term; The gain matrix is ​​a fractional term. for Fractional derivative of the Cabot type, ,in The order of the fractional-order sliding surface. , For gamma function, Let be the unconstrained variable matrix at time t. For integration variables The corresponding unconstrained variable matrix, , For integration variables The corresponding unconstrained variable matrix The derivative of This is the first positive definite gain matrix. This is the second positive definite gain matrix. , , , , , , , All of these are preset values. Represents a diagonal matrix. For symbolic functions, Defined as follows: In In the case of ,exist In the case of , In the case of .

5. The laser pointing preset performance sliding mode control method according to claim 4, characterized in that, The order of the fractional-order sliding surface in step S2 The value is 0.8, representing the first positive definite gain matrix. The second positive definite gain matrix .

6. The laser pointing preset performance sliding mode control method according to claim 4, characterized in that, Step S3 includes: Step S31, calculate the equivalent control torque: ； in, For equivalent control torque, Generalized coordinates The inertia matrix at that location, To be based on generalized coordinates The obtained generalized velocity vector, To represent the generalized coordinates of the laser's direction, The matrix of Coriolis force and centrifugal force. Let q be the gravitational gradient torque vector at the generalized coordinate q. It is an unconstrained variable matrix. Unconstrained variable matrix The first derivative matrix, Unconstrained variable matrix The second derivative matrix, The order of the fractional-order sliding surface. , for Fractional derivative of the Cabot type, , For symbolic functions, Defined as follows: In In the case of ,exist In the case of , In the case of ; Step S32, calculate the switching control torque based on the superspiral algorithm: ； in, To switch control torque, The value is an adaptive estimate, where s is a fractional-order sliding surface. Let be the Euclidean norm of the fractional sliding surface s. It is a positive definite adaptive gain matrix and , For the proportion term, For integration, For symbolic functions, Defined as follows: In In the case of ,exist In the case of The proportional term and the integral term work together to form the superspiral algorithm; Step S33: The total sliding mode control law is obtained by combining the equivalent control torque and the switching control torque.

7. The laser pointing preset performance sliding mode control method according to claim 6, characterized in that, In step S32, In this case, ,exist In this case, ;in, For adaptive estimates The preset upper bound value, For adaptive estimates The Euclidean norm.

8. A stability verification method for a laser pointing preset performance sliding mode control method, used in the laser pointing preset performance sliding mode control method of claim 7, characterized in that, The stability verification method includes: Based on the Lyapunov function, under the action of the total control law, if the fractional sliding surface converges to the neighborhood of the origin within a finite convergence time, then the laser pointing error satisfies the preset performance constraints.

9. The stability verification method of the laser pointing preset performance sliding mode control method according to claim 8, characterized in that, The Lyapunov function is constructed as follows: ； in, M is the Lyapunov function value, used to measure the energy of the system. a The generalized mass matrix after order reduction. To estimate the error, , Let be the true value of the upper bound of the perturbation, and s be the fractional-order sliding surface. It is a positive definite adaptive gain matrix and .

10. The stability verification method of the laser pointing preset performance sliding mode control method according to claim 9, characterized in that, Finite convergence time The calculation is as follows: ； in, Let be the finite convergence time of the fractional sliding surface s to the neighborhood of the origin, and V(0) be the initial value of the Lyapunov function at the initial time t=0. To take the square root of the initial value of the Lyapunov function at the initial time t=0, To be related to the first positive definite gain matrix Second positive definite gain matrix and positive definite adaptive gain matrix The relevant positive numbers are, specifically , Represents the first positive definite gain matrix Minimum eigenvalue, Represents the second positive definite gain matrix Minimum eigenvalue, Represents the adaptive gain matrix Minimum eigenvalue.

Images