A design method for disturbance rejection backstepping control of virtual composite axis based on error

Abstract

The present invention discloses a design method for disturbance suppression backstepping control of a virtual composite axis based on error, which belongs to the field of signal tracking and processing. The technical method proposed in the present invention does not rely on input signals and additional sensors, but only uses error information to operate, and can equivalently simulate the function of a composite axis mechanism. Its error suppression characteristics integrate the dual-axis suppression characteristics, effectively improving the tracking performance. At the same time, combined with the backstepping control strategy with disturbance suppression, the trajectory tracking performance is further improved, and the disturbance and uncertainty problems existing in the virtual composite axis are solved. The tracking accuracy is improved by 31.89%, and the disturbance suppression performance of the improved backstepping control is improved by 73.87%, so that it can meet the application in the actual engineering single physical axis system.

Description

Technical Field

[0001] The invention belongs to the field of signal tracking and processing, and specifically provides a virtual composite axis disturbance suppression backstepping control design method based on error. Background Art

[0002] Since the target position, velocity and acceleration are unknown and cannot be directly measured, the tracking accuracy of the system cannot be improved through the composite axis structure. In addition, the physical composite axis system relies on the physical dual-axis drive mechanism, which has a large volume inertia and does not meet the lightweight requirements of shipborne, airborne, satellite-borne and other motion platforms. Therefore, it is necessary to study the high-precision tracking control method of the single-stage drive optoelectronic tracking system that meets the lightweight requirements. Without adding hardware facilities, one solution is to superimpose a tracking system simulated by a model to form a virtual composite axis system. There are also studies that call the virtual composite axis secondary tracking control. Its control principle is the same as that of the general composite axis system. Its essence is also a two-dimensional correlation control system. It can improve the tracking accuracy well without adding hardware facilities and meeting the lightweight requirements.

[0003] At present, the realization of virtual composite axis system depends on both error information and input signal information. However, in optoelectronic tracking system, image-based method can only obtain tracking error, but not r signal. Moreover, due to the complex combination of methods, the calculation of the whole system may become complicated. In order to further improve the performance, it is necessary not only to pay attention to the accuracy of trajectory tracking, but also to deal with uncertainty and disturbance. Backstepping control (BSC) has the characteristics of easy design and implementation, and can measure the system state in real time, adjust the input according to the difference between the target output and the actual output, so as to achieve high-precision tracking, and effectively eliminate the uncertainty of the system. However, simple backstepping control cannot effectively eliminate uncertainty and disturbance, and can only be achieved by combining other control methods. The superposition of these methods will make the system more complicated. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a design method of virtual composite axis disturbance suppression backstepping control (DRBSC) based on error, which improves the efficiency of the algorithm and reduces the complexity of the system. The disturbance terms that can be suppressed include model uncertainty terms and internal and external disturbances. The method does not rely on input signals and additional sensors, and only uses error information to operate, which can equivalently simulate the function of the composite axis system. Its error suppression characteristics integrate the dual-axis suppression characteristics, effectively improving the tracking performance. At the same time, combined with the backstepping control strategy with disturbance suppression, the trajectory tracking performance is further improved, and the disturbance and uncertainty problems existing in the virtual composite axis are solved. Its tracking accuracy is improved by 31.89%, and the disturbance suppression performance of the improved backstepping control is improved by 73.87%.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A virtual composite axis disturbance suppression backstepping control design method based on error includes the following steps:

[0007] Step (1): Design a virtual composite axis structure for the tracking system where the target position, velocity and acceleration are unknown and cannot be directly measured, which makes it impossible to use the composite axis structure;

[0008] Step (2): using the improved backstepping control method to estimate and eliminate the total disturbance existing in the virtual composite shaft structure;

[0009] Step (3): Analyze the stability of the physical axis and the virtual axis of the virtual composite axis structure to obtain a first constraint condition, and confirm whether the tracking system satisfies the first constraint condition;

[0010] Step (4): Analyze the stability of the improved backstepping control method, obtain the second constraint condition, and confirm whether the tracking system satisfies the second constraint condition;

[0011] Step (5): When the tracking system satisfies both the first constraint and the second constraint, the tracking error characteristics and disturbance suppression characteristics of the virtual composite axis structure are calculated to determine whether the tracking error transfer function and the total disturbance of the tracking system are satisfied. If not, re-execute steps (1) to (4). If satisfied, end the design.

[0012] The beneficial effects of the present invention are:

[0013] (1) Compared with the existing virtual composite axis, the present invention does not rely on additional sensors, only uses error information to operate, and does not require input signals.

[0014] (2) The virtual composite axis system of the present invention can be used as a plug-in control and flexibly integrated into an already designed system without the need to redesign the entire system.

[0015] (3) The error suppression characteristics of the present invention integrate the dual-axis suppression characteristics, effectively improving the tracking performance.

[0016] (4) The backstepping control method with disturbance suppression of the present invention can effectively solve the model uncertainty and internal and external disturbance problems existing in the virtual composite axis, and it is not a simple superposition of different methods, and will not make the system more complicated. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A control block diagram of a virtual composite shaft disturbance suppression backstepping control design method based on error in the present invention;

[0018] Figure 2It is a schematic diagram of the structure of the error-based virtual composite axis servo system in the present invention;

[0019] Figure 3 The trajectory tracking comparison curves of the error-based virtual composite axis PID in the present invention and the existing virtual composite axis PID at 0.5Hz-20Hz variable frequency input, where (a) is the trajectory tracking curve, (b) is the trajectory tracking error curve, and (c) is the control amount curve;

[0020] Figure 4 The trajectory tracking comparison curves of the single-axis PID, the error-based virtual composite axis PID and the error-based virtual composite axis DRBSC when the input is a ramp signal + a sine signal in the present invention, wherein (a) is the trajectory tracking curve, (b) is the trajectory tracking error curve, and (c) is the control amount curve;

[0021] Figure 5 1 is a disturbance suppression comparison curve based on the error virtual composite axis PID, based on the error virtual composite axis BSC and based on the error virtual composite axis DRBSC when the disturbance is a ramp signal + a sine signal in the present invention, wherein (a) is a disturbance suppression error curve, (b) is a control amount curve, (c) is a disturbance estimation curve, and (d) is a disturbance estimation error curve;

[0022] Figure 6 These are the disturbance suppression comparison curves of the error virtual composite axis PID, the error virtual composite axis BSC and the error virtual composite axis DRBSC when the disturbance is a step signal in the present invention, wherein (a) is the disturbance suppression error curve, (b) is the control quantity curve, (c) is the disturbance estimation curve, and (d) is the disturbance estimation error curve. DETAILED DESCRIPTION

[0023] The specific implementation modes of the present invention are described in detail below with reference to the accompanying drawings.

[0024] Based on the basic theory of composite axis servo system and the relevant conclusions of engineering practice, a virtual composite axis disturbance suppression backstepping control design method based on error is proposed for ordinary tracking systems that cannot use composite axis structure. This method does not rely on additional sensors, does not require input signal information, and does not increase hardware cost. In addition, the disturbance suppression backstepping control method achieves further improvement of disturbance suppression performance and tracking accuracy. Figure 1 FIG. 1 is a control block diagram of the virtual composite axis disturbance suppression backstepping control based on error proposed by the present invention, wherein: The controlled plant model representing the physical axis, represents the controller of the physical axis, represents the controlled plant model of the virtual axis, represents the controller of the virtual axis, represents the reference trajectory input, represents the off-target amount, Indicates the physical axis control input, represents an estimate of the external disturbance and modeling uncertainty, represents the external disturbance, Represents the system output, represents the virtual axis tracking error, Indicates the virtual axis control input, Indicates the output of the virtual axis.

[0025] Figure 2 The figure shows the structure diagram of the error-based virtual composite axis servo system, where Indicates the reduced tracking error of the physical axis. To design a virtual composite axis structure, the controlled object model of the virtual composite axis structure needs to meet the following requirements:

[0026] ,

[0027] in, Represents the controlled object of the virtual axis structure, Indicates the spindle controlled object, , Represents the uncertainty difference between the controlled object of the virtual axis structure and the controlled object of the main axis.

[0028] make , assuming there is the following system.

[0029] ,

[0030] in, , , is the state quantity, and the input is , the output is ,in is a constant, Represents internal uncertainty and disturbance, and considers the whole as a total disturbance, whose estimated value is The control rate is finally obtained by backstepping control with disturbance estimation and compensation for:

[0031] ,

[0032] Among them, the parameters , represents the tracking error required in the backstepping design process, and the estimated value of the disturbance derivative is:

[0033] ,

[0034] in, , define the residual disturbance estimation error as :

[0035] ,

[0036] Construct the state vector A scalar function with continuous first-order partial derivatives , , and an attraction region Ω around the origin of the state space makes all non-zero states The following conditions must be met:

[0037] ,

[0038] ,

[0039] For any non-zero ;

[0040] And the derivative of the total disturbance The estimated value satisfies , The third derivative of satisfies: The original system equilibrium state It is asymptotically stable in the Ω domain, where is the tracking error, is the disturbance estimation error, represents the Lyapunov function, represents the time derivative of the Lyapunov function along the trajectory of the system, is an adjustable parameter, For non-zero states In the attraction area The derivative of the Lyapunov function is not always equal to zero, which means that the system state will not remain stationary in a non-zero state.

[0041] Tracking transfer function for virtual composite axis system for:

[0042] ,

[0043] in, represents the Laplace operator, represents the system transfer function output, Represents the system transfer function input.

[0044] According to the characteristic polynomial of the system tracking transfer function can be written as:

[0045] ,

[0046] like is the system tracking transfer function If the value is the extreme point of , then at least one of the following two formulas will hold:

[0047] ,

[0048] ,

[0049] It is easy to know that the eigenvalue polynomial of the tracking transfer function in a single physical axis closed-loop system is , and the original single physical axis closed-loop system is stable, so according to the small gain theorem, The constraint that all the eigenvalues ​​of are located in the left half plane of the s plane, that is, the constraint on the tracking transfer function stability of the virtual composite axis system is: All characteristic roots of have negative real parts, as shown in the following formula:

[0050] ,

[0051] in, Is plural The real part of , representing the position on the complex plane.

[0052] On the basis of ensuring the stability of the system, the tracking characteristics of the virtual composite axis design method based on error are analyzed. It is expressed as:

[0053] ,

[0054] When the system is a single-axis drive, its tracking error transfer function is: , the tracking error transfer function of the virtual composite axis Less than , achieving improved tracking accuracy. The disturbance suppression characteristic is expressed as: the total disturbance derivative The estimated value satisfies .

[0055] In order to more clearly illustrate the advantages of the error-based virtual composite axis disturbance suppression backstepping control method of the present invention, the following comparative description is now made:

[0056] The coefficients of the controlled plant model are: .

[0057] Since the existing virtual composite axis structure requires the use of input signals that cannot be directly measured, it is impossible to conduct experimental verification on the experimental platform. First, the effect of the error-based virtual composite axis of the present invention is illustrated by simulation comparison. The input amplitude is 1000 arcsec, and the frequency is a variable frequency sinusoidal signal from 0.5Hz to 20Hz. The results are as follows: Figure 3As shown in (a)-(c) of FIG. 1 . It can be clearly seen from the trajectory tracking diagram that as the frequency increases, the tracking effect of the existing virtual composite axis structure based on the input signal and the error signal is poorer than that of the virtual composite axis structure based on the error proposed in the present invention, and there is a downward trend. And from the ISU index given in Table 1, it can be seen that the virtual composite axis based on the error of the present invention has better stability and can eliminate errors more effectively.

[0058] Table 1 Comparison of ISU indicators

[0059]

[0060] In practical applications, the motion trajectories of the tracked targets are not necessarily of the same type. Therefore, the present invention conducts trajectory tracking experiments in the experimental platform under the condition of combining ramp signals and sinusoidal signals. The results are as follows: Figure 4 As shown in (a)-(c). Figure 4 From (a) to (c), it can be seen that under different input signal conditions, the virtual composite axis can still improve the trajectory tracking accuracy, and the backstepping control can also play a role in further improving the tracking accuracy. Figure 4 The comparison of the index values ​​in Table 2 shows that the virtual composite axis DRBSC based on error has the best control accuracy, the fastest convergence speed and the smallest average error compared with the single-axis PID and the virtual composite axis PID based on error.

[0061] Table 2 Comparison of virtual composite axis working parameters under different input signal conditions

[0062]

[0063] Secondly, in practical applications, disturbances are not always single disturbances. Therefore, the present invention analyzes the anti-disturbance when the sine signal and the ramp signal act together. The experimental results are as follows: Figure 5 As shown in (a)-(d). Figure 5 (a)-(d) show that when the disturbances are different and changing, the BSC based on the error virtual composite axis has disturbance suppression performance, but cannot estimate the disturbance well. However, the DRBSC based on the error virtual composite axis can achieve better disturbance suppression throughout the process.

[0064] In practical applications, there may also be sudden disturbances. The present invention analyzes step disturbances. Figure 6The results shown in (a)-(d) show that the error-based virtual composite axis PID can suppress step disturbances within a certain period of time, but it takes a long time. Compared with the previous set of control experiments, the BSC based on the error virtual composite axis can suppress step disturbances faster, but it will produce larger overshoots. Compared with the first two sets of control experiments, the disturbance suppression backstepping control based on the error virtual composite axis can achieve fast disturbance suppression without causing large overshoots.

[0065] 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 description is only a specific embodiment of the present invention and is 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 virtual composite axis disturbance suppression backstepping control design method based on error, characterized in that: The steps include: Step (1): Design a virtual composite axis structure for the tracking system where the target position, velocity and acceleration are unknown and cannot be directly measured, which makes it impossible to use the composite axis structure; Step (2): using the improved backstepping control method to estimate and eliminate the total disturbance existing in the virtual composite shaft structure; Step (3): Analyze the stability of the physical axis and the virtual axis of the virtual composite axis structure to obtain a first constraint condition, and confirm whether the tracking system satisfies the first constraint condition; Step (4): Analyze the stability of the improved backstepping control method, obtain the second constraint condition, and confirm whether the tracking system satisfies the second constraint condition; Step (5): When the tracking system satisfies both the first constraint and the second constraint, the tracking error characteristics and disturbance suppression characteristics of the virtual composite axis structure are calculated to determine whether the tracking error transfer function and the total disturbance of the tracking system are satisfied. If not, re-execute steps (1) to (4). If satisfied, end the design. The controlled object model of the virtual composite shaft structure in step (1) satisfies: ， in, Represents the controlled object of the virtual axis structure, Indicates the physical axis controlled object, , The uncertainty difference between the controlled object of the virtual axis structure and the controlled object of the physical axis; The total disturbance existing in the virtual composite shaft structure in step (2) includes external disturbance outside the tracking system and internal uncertainty existing in the modeling; The first constraint in step (3) is: ， When the virtual axis controller in the virtual composite axis system When the above formula is satisfied, the tracking system is determined to be stable, where represents the Laplace operator, Represents the system tracking transfer function The extreme point, Represents the controlled object of the virtual axis structure, Is plural The real part of , which represents the position on the complex plane; The second constraint in step (4) is: Construct the state vector Scalar Lyapunov function with continuous first-order partial derivatives , , and an attraction region Ω around the origin of the state space, so that all non-zero state vectors The following conditions must be met: ， ， For any non-zero state vector ; And the derivative of the total disturbance The estimated value satisfies , The third derivative of satisfies: Then the state vector that makes the original system balanced is It is asymptotically stable in the Ω domain; Among them, the parameters , It represents the tracking error required in the backstepping design process. is the disturbance estimation error, represents the time derivative of the Lyapunov function along the trajectory of the system, is an adjustable parameter, For non-zero states In the attraction area In the Lyapunov function, the derivative is not always equal to zero, that is, the system state will not remain stationary in a non-zero state; In step (5), when the system is a single-axis drive, its tracking error transfer function is: , Tracking error characteristics of virtual composite axis structure It is expressed as: ， In the formula, Indicates the physical axis controlled object, Represents the physical axis controller, Represents the controlled object of the virtual axis structure, Represents the virtual axis controller, represents the system tracking transfer function; The disturbance suppression characteristic in step (5) is expressed as: the total disturbance derivative The estimated value satisfies .

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