Multi-anti-interference increment backstepping observer design method and device based on specified time

Abstract

The invention discloses a method and a device for designing a multi-anti-interference incremental backstepping observer based on specified time, and belongs to the technical field of signal tracking and processing. The method comprises the following steps: establishing a system dynamics model containing time-varying disturbance and model uncertainty items; scaling the tracking error and the estimation error by using a scaling function so as to realize the accurate convergence of the system state and the disturbance estimation within the specified time T; combining the scaled error, introducing an incremental backstepping control thought, and designing an incremental backstepping observer capable of processing model uncertainty and multiple disturbances at the same time; under the condition that the total disturbance and the derivative thereof are assumed to be bounded, stability analysis is carried out through a Lyapunov function, and constraint conditions of system stability convergence are deduced; and finally, verifying the effectiveness and superiority of the observer under various input and disturbance working conditions through simulation. The method is suitable for a high-dynamic and time-sensitive precision control system.

Description

Technical Field

[0001] This invention belongs to the field of signal tracking and processing technology, specifically relating to a design method and apparatus for a multi-disturbance-resistant incremental backstepping observer based on a specified time. Background Technology

[0002] With the rapid development of the aerospace industry, high-precision line-of-sight stabilization systems are increasingly widely used in Earth observation, space communication, and other fields. Their stabilization accuracy directly determines the success or failure of mission execution. However, when such systems operate in complex space environments, they are not only affected by external time-varying disturbance torques (such as friction and wind disturbances), but also face the coupled effects of various disturbance factors such as internal nonlinear dynamics and parameter uncertainties. These composite disturbances are characterized by high frequency, time-varying, and even mismatched features, posing severe challenges to the control accuracy and stability of the system.

[0003] In existing control strategies, traditional PID control struggles to handle strong nonlinearity and time-varying disturbances; while sliding mode control possesses good robustness, its inherent chattering phenomenon can affect system stability and may excite unmodeled dynamics; backstepping control, in its theoretical design, typically assumes that disturbances are constant or slowly varying, which is seriously inconsistent with the dynamic characteristics of rapidly time-varying disturbances in engineering practice. As a result, when facing mismatched disturbances and strong time-varying disturbances, its convergence speed heavily depends on the initial state of the system and often requires precise upper bound information on the disturbance. It is difficult to guarantee accurate convergence within the stringent time limits specified by the user, thus limiting its application in time-sensitive, highly dynamic scenarios.

[0004] To improve disturbance rejection performance, existing research often employs a hybrid architecture with separate observers and controllers. For example, extended state observers (ESOs) or disturbance observers (DOBs) are used to estimate disturbances, followed by feedforward compensation using traditional control laws. While these methods improve system performance to some extent, the inherent phase lag problem of their discrete structure and the complexity of observer and controller parameter tuning limit the system's dynamic response. More importantly, discrete schemes struggle to achieve coordinated and rapid convergence of system state and disturbance estimates within a specified time. When the disturbance frequency exceeds the system bandwidth or exhibits non-stationary characteristics, control performance and estimation accuracy significantly degrade.

[0005] Therefore, for line-of-sight stabilization systems with high dynamics and multiple disturbance coupling, it is of vital theoretical significance and engineering application value to study an integrated control method that can integrate disturbance estimation and control law design and achieve fast and accurate convergence within a user-preset time. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a design method and apparatus for a multi-disturbance-resistant incremental backstepping observer based on a specified time. By constructing a system dynamics model incorporating time-varying disturbances and model uncertainties, scaling the tracking and estimation errors using a scaling function, and introducing the concept of incremental backstepping control, a multi-disturbance-suppressing incremental backstepping observer with time-based convergence is designed to handle model uncertainties and disturbances. Control performance is optimized based on stability constraints. Simulation results show that this method can solve the problems of traditional backstepping methods, such as convergence speed depending on the initial state or requiring precise upper bound information on the disturbance when facing challenges like mismatched disturbances and strong time-varying interferences, and difficulty in guaranteeing precise convergence within user-specified strict time limits, thus limiting its application in time-sensitive, highly dynamic scenarios.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, the method comprising:

[0009] Step 1: For the photoelectric tracking system, establish a system dynamics model that includes time-varying disturbances and model uncertainties;

[0010] Step 2: Design a time-varying scaling function to scale the tracking error and disturbance estimation error of the system dynamics model.

[0011] Step 3: Using the tracking error and disturbance estimation error after the scaling transformation, and combining the incremental backstepping control concept, design a multi-disturbance suppression incremental backstepping observer with convergence based on a specified time.

[0012] Step 4: Set the assumption that the total perturbation of the backstepping observer and its derivative are bounded;

[0013] Step 5: Based on the aforementioned assumptions, design a Lyapunov function for stability analysis and derive the constraints for the system to achieve stable convergence within a specified time.

[0014] Step 6: When the system dynamics model satisfies the constraint conditions for stable convergence, determine whether the backstepping observer satisfies the design objective. If not, repeat steps 1-5. If it satisfies, end the design.

[0015] On the other hand, the present invention provides a design apparatus for a multiple disturbance-resistant incremental backstepping observer based on a specified time, comprising:

[0016] The modeling module is used to build a system dynamics model for photoelectric tracking systems that includes time-varying disturbances and model uncertainties.

[0017] The scaling module is used to design time-varying scaling functions to scale and transform the tracking error and disturbance estimation error of the system dynamics model.

[0018] The observer module is used to design a multi-disturbance-suppressed incremental backstepping observer with convergence based on a specified time by using the tracking error and disturbance estimation error after the scaling transformation, combined with the incremental backstepping control idea.

[0019] The assumption module is used to set the assumption that the total perturbation of the backstepping observer and its derivative are bounded.

[0020] The stability analysis module is used to design Lyapunov functions for stability analysis based on the aforementioned assumptions, and derive the constraints for the system to achieve stable convergence within a specified time.

[0021] The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the multi-disturbance suppression incremental backstepping observer that converges within a specified time when the system model meets the stability constraints, and to determine whether the design objectives are met. If not, the module re-enters the modeling module to start the design; if the objectives are met, the design ends.

[0022] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned design method for a multi-disturbance-resistant incremental backstepping observer based on a predetermined time.

[0023] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned design method for a multi-disturbance-resistant incremental backstepping observer based on a specified time.

[0024] The beneficial effects of this invention are as follows:

[0025] It achieves precise convergence and stability within a specified time: by introducing a time-varying scaling function to transform the system tracking error and estimation error, it strictly ensures that all signals can converge within a fixed time preset by the user. The convergence time is independent of the initial state of the system, which significantly improves the control timeliness and reliability in time-sensitive scenarios.

[0026] The system's disturbance rejection and robustness are significantly enhanced: an innovative combination of incremental feedback and backstepping observer structure is used to construct an integrated controller-observer framework. This design not only initially suppresses time-varying disturbances and model uncertainties through incremental control, but also accurately estimates and compensates for residual total disturbances in real time through the backstepping observer. Thus, it can maintain excellent tracking accuracy and robust stability even when facing complex operating conditions such as mismatched disturbances, strong time-varying interference, and model mismatch.

[0027] The integrated structure reduces design and implementation complexity: Compared with the traditional composite architecture that separates the observer and the controller, this invention realizes an integrated design of the controller and the disturbance observer, which effectively avoids the phase lag and complex parameter tuning problems caused by discrete structures, simplifies engineering implementation, and improves the dynamic response speed and control performance of the system. Attached Figure Description

[0028] Figure 1 This is a flowchart of the design method for a multiple disturbance rejection incremental backstepping observer based on a specified time according to the present invention;

[0029] Figure 2 This is a comparison chart of the convergence effects under different specified times in this invention, under the premise of composite input;

[0030] Figure 3 This is a comparison chart of the tracking performance of different control strategies under sinusoidal input in this invention;

[0031] Figure 4 This is a comparison chart of the disturbance estimation performance of different control strategies under zero input and step disturbance conditions in this invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] This invention proposes a design method and device for a multi-disturbance-resistant incremental backstepping observer based on a specified time. While fully considering time-varying disturbances and model uncertainties, it is constructed as a single system, successfully achieving an integrated design of the controller and observer. In complex environments, equipment faces disturbances and model uncertainties caused by numerous complex uncertainties. The incremental backstepping observer, based on a simple system dynamic model, is constructed through a step-by-step back-calculation method, enabling accurate estimation of the magnitude and direction of the total disturbance and real-time compensation in the control system. Simultaneously, under the control of the specified time, it can meet the convergence time requirements in different scenarios. This not only enhances the adaptability of the line-of-sight stabilization system to complex environments but also further improves positioning accuracy and motion control stability, ensuring reliable and efficient operation of the equipment under harsh conditions and providing strong support for various engineering tasks.

[0034] like Figure 1 The diagram shown is a control block diagram of the design method for a multiple disturbance rejection incremental backstepping observer based on a specified time according to the present invention. The method specifically includes:

[0035] Step 1: For the photoelectric tracking system (in this embodiment, a photoelectric turntable is selected), a system dynamics model including time-varying disturbances and model uncertainties is established as follows:

[0036] ,

[0037] Among them, state variables , Representing position and velocity respectively, To control the input, This represents an unknown time-varying disturbance term. To model uncertainty, the superscript · denotes the first derivative.

[0038] Step 2: Design a time-varying scaling function to scale the system's tracking error and disturbance estimation error; use the scaling function to scale the tracking error and disturbance estimation error. The scaling function is used to make the system converge within a specified time T. Represented as:

[0039] ,

[0040] in, Indicates the accuracy adjustment parameter (controls steady-state error). The transition rate parameter (controlling smoothness) is represented by t, time t represents time, and e represents the exponential function.

[0041] Step 3: Use the tracking error after the scaling transformation. and and the perturbation estimation error after scaling transformation Combining the incremental backstepping control concept, a multi-disturbance suppression incremental backstepping observer with convergence based on a specified time is designed, and its control variable... Expressed as:

[0042] ,

[0043] in, It is a time-varying scaling function used to specify time control. For backstepping control parameters that are greater than 0, It is a virtual control law, and also The expected trajectory express By tracking the value after the differentiator This represents the velocity tracking error before scaling transformation, for the total disturbance. The estimated term The derivative is designed as:

[0044] ,

[0045] in, Let represent the perturbation estimation factor and robustness factor, respectively, which are greater than 0. The original (before scaling) error is: Indicates total disturbance Perturbation estimation term , The reference input signal is represented as follows: The scaled error is expressed as:

[0046] .

[0047] Step 4: Set the assumption as follows: the total perturbation of the multi-perturbation suppression incremental backstepping observer based on convergence within a specified time. and its derivative Bounded, meaning there exist two constants. , making In practical engineering, disturbances encountered by equipment, such as load variations and environmental interference, are constrained by physical laws, and their parameter evolution exhibits time-varying smoothness. This determines that disturbances and their derivatives possess bounded physical characteristics. This assumption forms the theoretical basis for control system stability analysis and controller designability.

[0048] Step 5: Based on the aforementioned assumptions, design a Lyapunov function for stability analysis, derive the constraints for the system to achieve stable convergence within a specified time, and confirm whether the system satisfies the constraints.

[0049] The stability constraint is: When the assumptions hold, for a continuous-time nonlinear system, if there exists a condition for the stability of the system state... A scalar function with continuous first-order partial derivatives , And for the state space All non-zero values ​​in The following conditions must be met:

[0050] It is positive definite;

[0051] It is a semi-negative definite;

[0052] For any nonzero ;

[0053] when hour, ;

[0054] The system is asymptotically stable over a wide range when it is in equilibrium at the origin.

[0055] Step 6: When the system model meets the constraints of stable convergence, perform simulation verification analysis on the multi-disturbance suppression incremental backstepping observer based on convergence within a specified time to determine whether the design objective is met. If not, repeat steps 1-5. If the objective is met, end the design.

[0056] Under the premise of ensuring stability, the convergence error is analyzed and expressed as:

[0057] ,

[0058] Where M represents the radius of the convergence range circle. At this point, the design objective has been achieved, and the design process ends; otherwise, step 1 is repeated.

[0059] To more clearly illustrate the advantages of this invention, the following comparative explanation is provided:

[0060] First, a composite input signal is provided to the system, including a step signal, a ramp signal, and a sine wave signal. Three experimental groups are set up, with all settings identical except for the specified time. The specified time is set to 2 seconds, 3 seconds, and 4 seconds respectively. Figure 2 The results show that all three sets of data can achieve convergence and stabilization within the specified time, which is in full accordance with our expectations.

[0061] Secondly, a sinusoidal input signal is provided to compare the tracking performance of three different control strategies: PI-BSO, PI-IBSC, and PI-IBSO. The trajectory tracking results are as follows: Figure 3 As shown in the figure, the top figure shows the trajectory tracking, and the bottom figure shows the error. It can be clearly seen that PI-IBSO has a significant advantage in tracking sinusoidal signals.

[0062] Finally, a step disturbance is introduced with zero input signal to compare the disturbance handling effects of three different control strategies: PI-BSO, PI-IBSC, and PI-IBSO. The disturbance estimation results are as follows: Figure 4 As shown in the figure, the top figure represents the disturbance estimation, and the bottom figure represents the error. It can be clearly seen that PI-IBSO has a better ability to estimate disturbances than the other two methods.

[0063] On the other hand, the present invention provides a design device for a multi-perturbation suppression incremental backstepping observer based on convergence within a specified time. The various modules included in this device can implement the various steps of the aforementioned method. Specifically, it includes:

[0064] The modeling module is used to build a system dynamics model for photoelectric tracking systems that includes time-varying disturbances and model uncertainties.

[0065] The scaling module is used to design time-varying scaling functions to scale and transform the tracking error and disturbance estimation error of the system dynamics model.

[0066] The observer module is used to design a multi-perturbation suppression incremental backstepping observer that converges within a specified time.

[0067] The assumption module is used to set the assumption that the unknown total perturbation term and its derivative of the multi-perturbation suppression incremental backstepping observer based on convergence within a specified time are bounded.

[0068] The stability analysis module is used to perform stability analysis on the multi-perturbation suppression incremental backstepping observer that converges within a specified time based on the assumptions, obtain the constraints, and confirm whether the system model satisfies the constraints.

[0069] The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the multi-disturbance suppression incremental backstepping observer that converges within a specified time when the system model meets the stability constraints, and to determine whether the design objectives are met. If not, the module re-enters the modeling module to start the design; if the objectives are met, the design ends.

[0070] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned design method for a multi-disturbance-resistant incremental backstepping observer based on a predetermined time.

[0071] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned design method for a multi-disturbance-resistant incremental backstepping observer based on a specified time.

[0072] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, characterized in that, The method includes: Step 1: For the photoelectric tracking system, establish a system dynamics model that includes time-varying disturbances and model uncertainties; Step 2: Design a time-varying scaling function to scale the tracking error and disturbance estimation error of the system dynamics model. Step 3: Using the tracking error and disturbance estimation error after the scaling transformation, and combining the incremental backstepping control concept, design a multi-disturbance suppression incremental backstepping observer with convergence based on a specified time. Step 4: Set the assumption that the total perturbation of the backstepping observer and its derivative are bounded; Step 5: Based on the aforementioned assumptions, design a Lyapunov function for stability analysis and derive the constraints for the system to achieve stable convergence within a specified time. Step 6: When the system dynamics model satisfies the constraint conditions for stable convergence, determine whether the backstepping observer satisfies the design objective. If not, repeat steps 1-5. If it satisfies, end the design.

2. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 1, is characterized in that, In step 1, the system dynamics model is as follows: ， Among them, state variables , Representing position and velocity respectively, To control the input, This represents an unknown time-varying disturbance term. To model uncertainty, the superscript · denotes the first derivative.

3. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 2, is characterized in that... In step 2, the structure of the time-varying scaling function is determined by a predetermined convergence time set by the user. The steady-state error and smoothness of the transient process of the system are controlled by adjusting the parameters in the function.

4. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 3, is characterized in that... The time-varying scaling function Represented as: ， in, This indicates the precision adjustment parameter used to control steady-state error. The transition rate parameter is used to control smoothness, t represents time, e represents the exponential function, and T represents the specified time for convergence.

5. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 4, is characterized in that... In step 3, the control quantity of the backstepping observer Expressed as: ， in, For backstepping control parameters that are greater than 0, For virtual control laws, Indicates speed By tracking the value after the differentiator This represents the velocity tracking error before scaling transformation, for the total disturbance. The estimated term The derivative is designed as ,in, These represent the disturbance estimation factor and robustness factor, respectively, which are greater than 0. and These represent the position tracking error and the velocity tracking error after scaling transformation, respectively.

6. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 5, is characterized in that, In step 5, the constraint condition for stable convergence is derived by ensuring that the derivative of the designed Lyapunov function is semi-negative definite and that the function itself satisfies radial unboundedness, so as to ensure that the equilibrium state at the origin of the system is asymptotically stable over a wide range.

7. The design method for a multiple disturbance-resistant incremental backstepping observer based on a specified time, as described in claim 6, is characterized in that, In step 6, the design objective is to ensure that, while maintaining stability, the convergence error satisfies the following: ， Where M represents the radius of the convergence range circle.

8. A design device for a multiple disturbance-resistant incremental backstepping observer based on a specified time, characterized in that, include: The modeling module is used to build a system dynamics model for photoelectric tracking systems that includes time-varying disturbances and model uncertainties. The scaling module is used to design time-varying scaling functions to scale and transform the tracking error and disturbance estimation error of the system dynamics model. The observer module is used to design a multi-disturbance-suppressed incremental backstepping observer with convergence based on a specified time by using the tracking error and disturbance estimation error after the scaling transformation, combined with the incremental backstepping control idea. The assumption module is used to set the assumption that the total perturbation of the backstepping observer and its derivative are bounded. The stability analysis module is used to design Lyapunov functions for stability analysis based on the aforementioned assumptions, and derive the constraints for the system to achieve stable convergence within a specified time. The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the multi-disturbance suppression incremental backstepping observer that converges within a specified time when the system model meets the stability constraints, and to determine whether the design objectives are met. If not, the module re-enters the modeling module to start the design; if the objectives are met, the design ends.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the design method of the multiple disturbance rejection incremental backstepping observer based on a specified time as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the design method of a multi-disturbance-resistant incremental backstepping observer based on a specified time, as described in any one of claims 1-7.

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