Backstepping observer design method and device based on observer visual angle

Abstract

The invention discloses a backstepping observer design method and device based on an observer visual angle, and belongs to the technical field of signal tracking and processing. The method comprises the following steps: firstly, establishing a system dynamics model containing time-varying disturbance; then designing a backstepping observer with a disturbance estimation function, and constructing a control law through a step-by-step backstepping mode; on the premise of assuming that disturbance and derivatives thereof are bounded, Lyapunov stability analysis is carried out, and constraint conditions are deduced; finally, the design effect is verified through disturbance suppression performance analysis. The method can accurately estimate and compensate various forms of disturbances such as sine, variable frequency and composite disturbances in real time, has better disturbance suppression capability and tracking precision, and is suitable for a photoelectric tracking system with complex environmental interference.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal tracking and processing, and particularly relates to a backstepping observer design method and device based on an observer perspective. Background Art

[0002] As a key component of modern precision measurement and control, optoelectronic tracking systems are widely used in fields such as space observation, laser communications, marine navigation, and industrial automation. As applications become increasingly complex, these systems face multi-source, time-varying, and nonlinear environmental interference, including but not limited to complex interference factors such as strong wind disturbances, mechanical vibration, and temperature drift. These disturbances severely impact the tracking accuracy and stability of the system, becoming a major bottleneck restricting system performance.

[0003] Traditional control methods have significant limitations when addressing such problems: PID control struggles to adapt to nonlinear, time-varying systems; sliding mode control, while highly robust, suffers from inherent chattering; and conventional backstepping control (BPC) typically assumes constant or slowly varying disturbances in its theoretical derivation, which is inconsistent with the characteristics of fast, time-varying disturbances in real-world engineering. Existing solutions often employ discrete observer and controller architectures, such as the extended state observer (ESO) or a combination of a disturbance observer (DOB) and a controller. This architecture not only increases system complexity but also introduces phase lag due to the cascaded structure, limiting the system's dynamic response performance.

[0004] Of particular note, in extreme environments such as aerospace, systems often need to simultaneously cope with the coupled effects of multiple disturbances. Existing literature indicates that when the disturbance frequency exceeds the system bandwidth or exhibits non-stationary characteristics, the disturbance estimation accuracy of traditional methods significantly decreases. Furthermore, discrete architectures present practical challenges such as complex parameter tuning and high computational burden. Therefore, developing an integrated control method that can achieve accurate disturbance estimation and real-time compensation is a pressing need to improve the performance of electro-optical tracking systems. Summary of the Invention

[0005] To address these technical issues, the present invention provides a backstepping observer design method and device based on the observer's perspective. By constructing a system model containing time-varying disturbances, a backstepping observer is designed to estimate and compensate for disturbances, and then optimize control performance based on stability constraints. Experiments have shown that this method can effectively suppress disturbances in complex environments, improving the stability and tracking accuracy of optoelectronic tracking systems, particularly in scenarios with variable-frequency sinusoidal disturbances and complex disturbances.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A backstepping observer design method based on an observer perspective, the method comprising:

[0008] Step 1: Construct a system model including time-varying disturbances for the optoelectronic tracking system;

[0009] Step 2: Design a backstepping observer with time-varying disturbance suppression effect from the observer perspective;

[0010] Step 3: Set the assumption that the unknown time-varying disturbance term and its derivative of the backstepping observer are bounded;

[0011] Step 4: Based on the assumptions, perform stability analysis on the backstepping observer to obtain constraints and confirm whether the system model satisfies the constraints.

[0012] Step 5: When the system model satisfies the stability constraint conditions, the disturbance rejection performance of the backstepping observer is analyzed to determine whether the design goal is met. If not, steps 1 to 4 are re-executed. If so, the design is terminated.

[0013] In another aspect, the present invention provides a backstepping observer design apparatus based on an observer perspective, comprising:

[0014] A modeling module for building a system model including time-varying disturbances for an optoelectronic tracking system;

[0015] The observer module is used to design a backstepping observer with time-varying disturbance suppression effect from the observer perspective;

[0016] An assumption module is used to set an assumption condition that the unknown time-varying disturbance term of the backstepping observer and its derivative are bounded;

[0017] A stability analysis module is used to perform stability analysis on the backstepping observer based on the assumptions, obtain constraints, and confirm whether the system model satisfies the constraints;

[0018] The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the backstepping observer when the system model meets the stability constraint conditions, and determine whether the design goal is met. If not, re-enter the modeling module to start the design; if so, end the design.

[0019] In a third aspect, 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 backstepping observer design method based on the observer perspective.

[0020] In a fourth aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned backstepping observer design method based on the observer perspective.

[0021] The beneficial effects of the present invention are:

[0022] This invention innovatively integrates time-varying disturbance estimation into the backstepping control framework, achieving an integrated controller and observer design, fundamentally overcoming the phase lag and system complexity issues inherent in traditional discrete architectures. Compared to existing technologies, this method achieves breakthroughs in disturbance suppression performance. It not only accurately estimates a variety of time-varying disturbances, including sinusoidal, variable-frequency, and compound disturbances, but also implements real-time dynamic compensation, enabling the system to maintain excellent tracking accuracy even in high-disturbance environments. Of particular note, this method overcomes the traditional backstepping control assumption of constant-valued disturbances. By introducing bounded conditions for the disturbance derivative, it significantly improves the system's adaptability to rapidly time-varying disturbances. In practical applications, this method can effectively suppress multi-source interference in complex environments, reducing the steady-state error of the optoelectronic tracking system to less than 30% of traditional methods while avoiding the chattering issues associated with methods such as sliding mode control. Furthermore, the integrated design simplifies the system structure, streamlines the parameter tuning process, and improves computational efficiency by approximately 40%, facilitating engineering implementation. These technical advantages make this method particularly suitable for fields such as aerospace and ocean exploration that have extremely high requirements for control accuracy and reliability, and provide an innovative solution to solving precision control problems in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of a backstepping observer design method based on the observer perspective of the present invention;

[0024] Figure 2 The disturbance estimation and error are obtained when the disturbance is sinusoidal and there is noise under the premise of 0 input in the present invention, where (a) is the disturbance estimation and (b) is the error.

[0025] Figure 3 This is the trajectory tracking under the premise of 0 input when the disturbance is sinusoidal and there is noise in the present invention, where (a) is the trajectory tracking and (b) is the disturbance estimation error histogram;

[0026] Figure 4 The disturbance estimation and error are obtained when the disturbance is a variable frequency sinusoidal signal with noise under the premise of zero input in the present invention, where (a) is the disturbance estimation and (b) is the error.

[0027] Figure 5The disturbance estimation and error are obtained when the disturbance is a composite signal and there is noise under the premise of 0 input in the present invention, where (a) is the disturbance estimation and (b) is the error. DETAILED DESCRIPTION

[0028] The present invention will be further described below with reference to the accompanying drawings and examples.

[0029] The present invention proposes a backstepping observer design method based on the observer's perspective. While fully considering time-varying disturbances, it is constructed as a type-one system, successfully realizing the integrated design of the controller and observer. In complex environments, equipment faces disturbances caused by numerous complex and uncertain factors. The backstepping observer is based on the system dynamic model and is constructed in a step-by-step backstepping manner. It can accurately estimate the size and direction of the disturbance and compensate for it in real time in the control system. This not only improves the adaptability of the optoelectronic turntable to complex environments, but also further improves the positioning accuracy and motion control stability, ensuring that the equipment can operate reliably and efficiently under harsh conditions, and providing strong support for various tasks in the engineering field.

[0030] like Figure 1 FIG. 1 is a control block diagram of a backstepping observer design method based on an observer perspective according to the present invention, wherein the method specifically includes:

[0031] Step 1: Construct a system model including time-varying disturbance for the optoelectronic tracking system:

[0032] ,

[0033] Among them, the state quantity , , , Represent position, velocity and unknown time-varying disturbance terms respectively . , ,in To control the gain, , is the control input. The goal of backstepping observer design is to make the state Tracking the desired trajectory state , disturbance estimation term Approaching the unknown time-varying disturbance term , the superscript · indicates the first-order derivative.

[0034] Step 2: From the observer's perspective, design a backstepping observer with time-varying disturbance suppression effect as follows:

[0035] ,

[0036] Among them, the expected state quantity , To track the desired trajectory state, is the state of tracking the desired speed, represents the unknown time-varying disturbance term The disturbance estimate of , the error is , the superscript T indicates transposition, , , is a backstepping control parameter greater than 0, Represent the disturbance estimation factor and robust factor greater than 0 respectively.

[0037] Step 3: Propose a hypothesis: unknown time-varying disturbance term and its derivatives Bounded, that is, there are two constants , making In practical engineering, disturbances encountered by equipment, such as load fluctuations and environmental interference, are subject to physical constraints, and their parameter evolution exhibits time-varying smoothness. This dictates that the disturbance and its derivative possess the physical characteristic of being bounded. This assumption forms the theoretical foundation for control system stability analysis and controller designability.

[0038] Step 4: Perform stability analysis on the backstepping observer to obtain constraints and confirm whether the system model satisfies the constraints.

[0039] The stability constraint condition is: for the constructed continuous system model containing time-varying disturbances and the backstepping observer, when the assumptions in step 3 are established, if it is possible to construct A scalar function with continuous first-order partial derivatives , , and an attraction region around the origin of the state space , so that all non-zero states The following conditions are met:

[0040] ,

[0041] ,

[0042] For any non-zero state vector ;

[0043] and The estimated derivative value satisfies , then the original system is in equilibrium exist The domain is exponentially stable.

[0044] Step 5: When the tracking system satisfies the stability constraints, analyze the disturbance rejection performance of the backstepping observer and determine whether it meets the design objectives. If not, repeat steps 1 to 4. If so, end the design.

[0045] Under the premise of ensuring stability, the disturbance rejection error is analyzed and expressed as:

[0046] ,

[0047] in, represents the backstepping observer observation The steady-state error, represents the Laplace factor, Indicates the current sampling time, represents the previous sampling moment, represents the error function, and for The superscript · represents the first-order derivative, and the superscript ·· represents the second-order derivative. Judging from the disturbance suppression error formula, when a constant is used as the disturbance input, the disturbance estimation term With zero steady-state error, when the disturbance input contains a velocity function, the boundary error is , when the disturbance contains higher-order functions such as parabolic functions, the disturbance estimate There is infinite error, which means that the design goal is achieved and the design is completed. Otherwise, repeat step 1.

[0048] In order to more clearly illustrate the advantages of the present invention, the following comparative description is made:

[0049] First, in a complex environment with zero input signal, a sinusoidal disturbance with amplitude 1, and noise, we focus on comparing the disturbance processing effects of different control strategies. The control strategies for comparison are traditional backstepping control (BSC), backstepping control combined with disturbance observer (BSC+DOB), and backstepping control combined with extended state observer (BSC+ESO). The disturbance estimation results are shown in the figure below. Figure 2 As shown, (a) is the disturbance estimation, (b) is the error, the trajectory tracking results and error distribution histogram are shown in Figure 3 As shown in the figure, (a) is trajectory tracking, and (b) is the disturbance estimation error histogram. It can be seen that the backstepping observer has the best disturbance estimation effect among several control strategies. At the same time, the trajectory tracking performance is also better than other control strategies. It can more effectively resist the influence of disturbances and noise and maintain stable operation of the system.

[0050] Secondly, in a complex environment with zero input signal, variable frequency sinusoidal disturbance with amplitude 1 and noise, the disturbance processing effects of different control strategies are compared. Figure 4As shown, (a) is the disturbance estimation and (b) is the error. It can be clearly seen that the backstepping observer has a great advantage in estimating the variable frequency sinusoidal disturbance signal.

[0051] Finally, in a complex environment with zero input signal, compound disturbances composed of step, ramp, and sine, and noise, the effects of different control strategies on disturbance processing are compared. Figure 5 As shown, (a) is the disturbance estimation and (b) is the error. It can be clearly seen that the backstepping observer has better estimation ability for composite disturbances than the other three methods.

[0052] On the other hand, the present invention provides a backstepping observer design device based on the observer perspective, wherein the modules included in the device can implement the various steps of the aforementioned method, specifically including: A modeling module for building a system model including time-varying disturbances for an optoelectronic tracking system;

[0053] The observer module is used to design a backstepping observer with time-varying disturbance suppression effect from the observer perspective;

[0054] An assumption module is used to set an assumption condition that the unknown time-varying disturbance term of the backstepping observer and its derivative are bounded;

[0055] A stability analysis module is used to perform stability analysis on the backstepping observer based on the assumptions, obtain constraints, and confirm whether the system model satisfies the constraints;

[0056] The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the backstepping observer when the system model meets the stability constraint conditions, and determine whether the design goal is met. If not, re-enter the modeling module to start the design; if so, end the design.

[0057] In a third aspect, 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 backstepping observer design method based on the observer perspective.

[0058] In a fourth aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned backstepping observer design method based on the observer perspective.

[0059] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only 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 in the scope of protection of the present invention.

Claims

1. A backstepping observer design method based on the observer perspective, characterized in that: The method comprises: Step 1: Construct a system model including time-varying disturbances for the optoelectronic tracking system; Step 2: Design a backstepping observer with time-varying disturbance suppression effect from the observer perspective; Step 3: Set the assumption that the unknown time-varying disturbance term and its derivative of the backstepping observer are bounded; Step 4: Based on the assumptions, perform stability analysis on the backstepping observer to obtain constraints and confirm whether the system model satisfies the constraints. Step 5: When the system model satisfies the stability constraint conditions, the disturbance rejection performance of the backstepping observer is analyzed to determine whether the design goal is met. If not, steps 1 to 4 are re-executed. If so, the design is terminated.

2. The backstepping observer design method based on the observer perspective according to claim 1, characterized in that: The system model containing time-varying disturbances in step 1 is: ， Among them, the state quantity , , , Represent position, velocity and unknown time-varying disturbance terms respectively , , ,in, To control the gain, , is the control input, represents the unknown time-varying disturbance term, and the superscript · represents the first-order derivative.

3. The backstepping observer design method based on the observer perspective according to claim 2, characterized in that: The goal of the backstepping observer design in step 2 is to make the position Tracking the desired trajectory state , disturbance estimation term Approaching the unknown time-varying disturbance term .

4. The backstepping observer design method based on the observer perspective according to claim 3, characterized in that: The backstepping observer in step 2 is: ， Among them, the expected state quantity , To track the desired trajectory state, is the state of tracking the desired speed, represents the unknown time-varying disturbance term The disturbance estimate of , the error is , the superscript T indicates transposition, , , is a backstepping control parameter greater than 0, Represent the disturbance estimation factor and robust factor greater than 0 respectively.

5. The backstepping observer design method based on the observer perspective according to claim 4, characterized in that: The step 3 includes the existence of two constants , making .

6. The backstepping observer design method based on the observer perspective according to claim 5, characterized in that: In step 4, the stability constraint condition is: construct A scalar function with continuous first-order partial derivatives , , and an attraction region around the origin of the state space , so that all non-zero states The following conditions are met: ， ， For any non-zero state vector ; When the time-varying disturbance term is unknown The estimated derivative value satisfies , then the original system is in equilibrium exist The domain is exponentially stable.

7. The backstepping observer design method based on the observer perspective according to claim 6, characterized in that: In step 5, under the premise of ensuring stability, the disturbance rejection error is analyzed and expressed as: ， in, represents the backstepping observer observation The steady-state error, represents the Laplace factor, Indicates the current sampling time, represents the previous sampling moment, represents the error function, and for For a constant as disturbance input, the disturbance estimation term With zero steady-state error, when the disturbance input contains a velocity function, the boundary error is , when the disturbance contains higher-order functions such as parabolic functions, the disturbance estimate With infinite error, the superscript · represents the first-order derivative, and the superscript ·· represents the second-order derivative.

8. A backstepping observer design device based on the observer perspective, characterized in that: include: A modeling module for building a system model including time-varying disturbances for an optoelectronic tracking system; The observer module is used to design a backstepping observer with time-varying disturbance suppression effect from the observer perspective; An assumption module is used to set an assumption condition that the unknown time-varying disturbance term of the backstepping observer and its derivative are bounded; A stability analysis module is used to perform stability analysis on the backstepping observer based on the assumptions, obtain constraints, and confirm whether the system model satisfies the constraints; The disturbance performance analysis module is used to perform disturbance suppression performance analysis on the backstepping observer when the system model meets the stability constraint conditions, and determine whether the design goal is met. If not, re-enter the modeling module to start the design; if so, end the design.

9. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the backstepping observer design method based on the observer perspective according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that Executable instructions are stored thereon, and when the instructions are executed by a processor, the processor can implement a backstepping observer design method based on an observer perspective as described in any one of claims 1 to 7.

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