Improved extended state observer method based on frequency domain disturbance compression

Abstract

The invention discloses a method for improving an extended state observer based on frequency domain disturbance compression, and the method comprises the steps: carrying out the reconstruction of an extended state observer designed for a photoelectric tracking system from a frequency domain angle, carrying out the algorithm based on frequency domain disturbance compression, and obtaining a disturbance compression extended state observer; converting the disturbance compression expansion state observer into a frequency domain form in combination with a linear feedback controller; analyzing the stability of the disturbance compression expansion state observer and the stability of the closed-loop system to obtain a stability constraint condition; setting a parameter setting method of the disturbance compression expansion state observer; and on the basis of satisfying the stability constraint condition, analyzing the influence of the disturbance compression expansion state observer on disturbance suppression and noise sensitivity. According to the method, the disturbance characteristic sensed by the observer is changed, so that the disturbance and the upper bound of the derivative of the disturbance are effectively reduced, the estimation precision of the state and the disturbance is remarkably improved, and the anti-interference capability and the noise insensitivity of the system are improved.

Description

Technical Field

[0001] The invention belongs to the field of signal tracking and processing, and specifically provides an improved extended state observer method based on frequency domain disturbance compression. Background Art

[0002] Disturbance and uncertainty are ubiquitous in control applications and have a negative impact on the controlled systems. Disturbance suppression has always been a key area of ​​interest in both industry and research. The extended state observer (ESO) conceptualizes disturbances and uncertainties as lumped disturbances and minimizes the reliance on prior system knowledge, thus serving as a partial model-based observer.

[0003] Under constant disturbance conditions, the estimation error of the ESO is guaranteed to converge uniformly asymptotically. However, when faced with time-varying disturbances, the limitations of the ESO become increasingly apparent. It has been shown that if the rate of change of the time-varying disturbance is bounded, then the estimation error of the ESO will follow the uniformly ultimately bounded (UUB) criterion within a finite period. In theory, increasing the observation gain of the ESO, or equivalently, increasing the bandwidth of the observer, can potentially minimize the estimation error. Nevertheless, an increase in gain leads to an enhancement of the differential response from the observer. This can cause a large amount of high-frequency noise to be transferred from the observed output to the control signal, significantly impairing the control quality. Therefore, it is difficult for the ESO to resolve the contradiction between the need for high-gain observation accuracy and its sensitivity to noise.

[0004] Have a study Those A disturbance compression-based quadratic extended state observer (TESO) method is proposed. This innovative method actively compresses unknown disturbances, thereby reducing the upper bound of the lumped disturbance encountered by the observer and its derivatives. Compared with the traditional ESO, TESO can significantly reduce the observation error at the same observation gain. Nevertheless, TESO has so far only been analyzed from the state space perspective, which is lacking in the frequency domain perspective and potential enhancement; in addition, TESO still lacks analysis of noise sensitivity. The frequency domain is a basic analysis method in control applications and is also a traditional method favored by engineering professionals. However, the existing ESO is complex to express in the frequency domain, and the analysis perspective is limited to the inherent properties of the ESO. These limitations have hindered engineers from adopting ESO more widely in industrial applications and have also brought challenges to improving ESO from a frequency domain perspective. Summary of the invention

[0005] To solve the above technical problems, the present invention provides an improved extended state observer method (DC-ESO) based on frequency domain disturbance compression. By reconstructing the extended state observer in the frequency domain, a new perspective is provided to understand its limitations and contradictions. By changing the disturbance characteristics perceived by the observer, the upper bound of the disturbance and its derivative is effectively reduced, the estimation accuracy of the state and disturbance is significantly improved, and the contradiction between high-gain observation and noise sensitivity is effectively alleviated, thereby improving the system's anti-interference ability and noise insensitivity.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] An improved extended state observer method based on frequency domain disturbance compression comprises the following steps:

[0008] Step (1): The extended state observer designed for the optoelectronic tracking system is reconstructed from the frequency domain perspective, and the obtained extended state observer disturbance estimation transfer function is expressed as:

[0009] ,

[0010] in, represents the lumped disturbance caused by external disturbances and modeling uncertainties, is the observation bandwidth or observation gain, is the coefficient, is the Laplace operator, To model uncertainty, For external interference, is the control input in the Laplace domain.

[0011] Step (2): Based on the reconstructed frequency domain expression of the extended state observer, a frequency domain disturbance compression algorithm is implemented to obtain a disturbance compression extended state observer, which changes the disturbance characteristics perceived by the observer, effectively reduces the upper bound of the disturbance and its derivative, and significantly improves the estimation accuracy of the state and disturbance. The mathematical expression of the disturbance compression extended state observer algorithm is:

[0012] ,

[0013] The expansion state is estimated as is a parameter and u is the driving voltage.

[0014] Step (3): Introduce a linear feedback controller based on the disturbance compression expansion state observer , and after converting the disturbance compression expansion state observer into frequency domain form, the transfer function of the closed-loop system is obtained as follows:

[0015]

[0016] in, , , is the characteristic polynomial, is the input reference trajectory, For output, For noise, Indicates the object being charged.

[0017] Step (4): Analyze the stability of the disturbance compression expansion state observer and the stability of the closed-loop system to obtain the stability constraint. The stability constraint is:

[0018] If satisfied:

[0019] and ,

[0020] This indicates that the disturbance compression expansion state observer and the closed-loop system are stable.

[0021] Step (5): The parameter tuning method of the disturbance compression expansion state observer is given as , ,in is a constant coefficient, requiring the parameters to satisfy the stability constraints described in step (4). In addition, it is necessary to fine-tune and verify the control settings applied in the experiment.

[0022] Step (6): On the basis of satisfying the stability constraint, analyze the influence of the disturbance compression expansion state observer on disturbance suppression and noise sensitivity. If the stability constraint is satisfied, the disturbance compression expansion state observer satisfies

[0023]

[0024] in, and denote the disturbance estimation transfer functions of the residual and initial lumped disturbance, respectively.

[0025] Redefining the extended state observer from the perspective of frequency domain provides a new perspective and reveals its inherent limitations and internal contradictions. The initial lumped perturbation is , through the lumped disturbance compression technique, the residual lumped disturbance is obtained as , the relationship between the two is . Therefore, compared with the traditional expanded state observer, the proposed disturbance compression expansion state observer changes the observer's perception of disturbance characteristics, effectively reduces the upper bound of the disturbance and its derivative, and can obtain higher observation accuracy under the same observation gain. The trade-off between the high gain observation and noise sensitivity inherent in the disturbance compression expansion state observer is solved through the lumped disturbance compression technology. The step disturbance suppression error of the disturbance compression expansion state observer method is , and the suppression error of the ramp disturbance is ,in is the amplitude constant of step disturbance and ramp disturbance. Therefore, the disturbance compression expansion state observer method can effectively suppress step disturbance and ramp disturbance, thereby significantly improving the accuracy of state and disturbance estimation.

[0026] Step (7): Analyze whether steps (4)-(6) all meet the preset conditions. If not, re-execute steps (1)-(6). If they do, end the design.

[0027] The beneficial effects of the present invention are:

[0028] (1) This paper reconstructs the extended state observer from the frequency domain perspective, providing a new perspective for understanding its limitations and clarifying the contradiction between the high gain observation and noise sensitivity of the extended state observer in the frequency domain.

[0029] (2) A disturbance compression and expansion state observer is proposed from the frequency domain perspective. This innovation changes the disturbance characteristics perceived by the observer, effectively reduces the upper bound of the disturbance and its derivative, and significantly improves the estimation accuracy of the state and disturbance.

[0030] (3) By using disturbance compression technology, this paper explains from a frequency domain perspective how the disturbance compression expansion state observer can alleviate the contradiction between high-gain observation and noise sensitivity, which helps engineers understand and use it.

[0031] (4) The parameter tuning method of the disturbance compression expansion state observer is simple and easy to use, making it more suitable for practical engineering applications.

[0032] (5) Compared with the extended state observer which can only suppress step disturbances, the disturbance compression extended state observer method can effectively suppress step disturbances and ramp disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is the principle block diagram of the extended state observer in the frequency domain;

[0034] Figure 2 This is a principle block diagram of the disturbance compression expansion state observer proposed by the present invention;

[0035] Figure 3This is the principle block diagram of the disturbance compression and expansion state observer in the frequency domain;

[0036] Figure 4 The simulation suppression results of different extended state observers under slope disturbance with varying slopes, where (a) is the slope disturbance curve with varying slope, (b) is the feedback error curve, (c) is the disturbance estimation error curve, and (d) is the driving voltage curve;

[0037] Figure 5 The suppression results of different ESOs under 0.5Hz sinusoidal interference conducted on the experimental platform, where (a) is the reference trajectory and system output curve, (b) is the feedback error curve, (c) is the violin plot curve of the feedback error, and (d) is the driving voltage curve. DETAILED DESCRIPTION

[0038] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0039] The present invention discloses an improved extended state observer method based on frequency domain disturbance compression, which aims to solve the problem that the traditional extended state observer inevitably amplifies the observation noise when increasing the observation gain to reduce the estimation error. By reconstructing the extended state observer in the frequency domain, a new perspective is provided to understand its limitations and contradictions. The disturbance compression extended state observer (DC-ESO) effectively reduces the upper bound of the disturbance and its derivative by changing the disturbance characteristics perceived by the observer, significantly improves the estimation accuracy of the state and disturbance, and effectively alleviates the contradiction between high-gain observation and noise sensitivity, thereby improving the system's anti-interference ability and noise insensitivity.

[0040] Set a second-order optoelectronic tracking system as:

[0041] ,

[0042] in, Defined as the lumped disturbance, and is the coefficient, is the angular position of the optoelectronic tracking system, represents the angular velocity and angular acceleration of the optoelectronic tracking system, is the driving voltage.

[0043] By defining the state , the expanded state object of the second-order optoelectronic tracking system is expressed as:

[0044] ,

[0045] in:

[0046] ,definition .

[0047] Based on the above formula, the standard extended state observer can be expressed as:

[0048] ,

[0049] in, is the state vector The estimate, It is a parameter, and the adjustment rule follows ,in is the identity matrix, is the Laplace operator, It is called observation bandwidth or observation gain.

[0050] By definition , the disturbance estimation result of the extended state observer is obtained as:

[0051]

[0052] in, is the observation bandwidth or observation gain.

[0053] According to the above formula, the frequency domain extended state observer is Figure 1 As shown, is the output of the feedback controller, To measure noise, is an equivalent filter. Definition , where ∆(s) represents the modeling uncertainty. Consider , the disturbance estimation transfer function of the extended state observer is expressed as:

[0054]

[0055] in, represents the lumped disturbance caused by external disturbances and modeling uncertainties, is the observation bandwidth or observation gain, is the coefficient, is the Laplace operator, To model uncertainty, For external interference, is the control input form in the Laplace domain.

[0056] Inspired by the frequency domain expression of ESO, an algorithm based on the concept of frequency domain perturbation compression ESO is proposed. First, the state is defined as Secondly, a disturbance compression channel is proposed in the disturbance compression expansion state observer, such as Figure 2 As shown. On this basis, the disturbance is divided into initial lumped disturbance and residual lumped disturbance, and defined respectively and In this control scheme, yes The characteristics of the residual lumped disturbance are determined by the disturbance compression channel. Based on the above definition, the following is proposed: Figure 2 The disturbance compression expansion state observer is shown in Figure 1. Its mathematical expression is as follows:

[0057] ,

[0058] The expansion state is estimated as is a parameter and u is the driving voltage.

[0059] Based on the disturbance compression and expansion state observer, the classic linear feedback controller is introduced Then, the disturbance compression expansion state observer is transformed into the frequency domain form, as Figure 3 As shown, is the reference trajectory.

[0060] according to Figure 3 , the transfer function of the closed-loop system is obtained as:

[0061] ,

[0062] ,

[0063] ,

[0064] Among them, is the characteristic polynomial, is the input reference trajectory, For output, For noise, Indicates the object being charged.

[0065] Mathematical Expression and Feedback Controller of Compression-Expansion State Observer Considering Disturbance , the following conditions exist:

[0066] (1)

[0067] (2)

[0068] When (1) is satisfied, the disturbance compression expansion state observer is stable; when (1) and (2) are satisfied at the same time, it indicates that the disturbance compression expansion state observer closed-loop system is stable.

[0069] When stability is met, anti-interference and noise insensitivity are considered next.

[0070] Considering the mathematical expression of the disturbance compression expansion state observer, if condition (1) is met, the disturbance compression expansion state observer satisfies:

[0071] ,

[0072] ,

[0073] in, and Denote the disturbance estimation transfer functions of the residual and initial lumped disturbance respectively. Compared with the extended state observer, the disturbance compression extended state observer has an additional disturbance observation and compensation channel, namely . And the disturbance and noise transfer functions of the disturbance compression expansion state observer satisfy:

[0074] ,

[0075] .

[0076] The parameter tuning method of the disturbance compression expansion state observer is given as , ,in is a constant coefficient, requiring the parameters to satisfy stability constraints. In addition, it is necessary to fine-tune and verify the control settings applied in the experiments.

[0077] After disturbance compression, the disturbance suppression effect of the disturbance compression expansion state observer is and The linear superposition of , that is, the disturbance compression channel first suppresses the initial lumped disturbance, which can be expressed as , and then the disturbance compression expansion state observer suppresses the residual lumped disturbance again, which can be expressed as , the relationship between the two is . Therefore, compared with the traditional expanded state observer, the proposed disturbance compression expansion state observer changes the observer's perception of disturbance characteristics, effectively reduces the upper bound of the disturbance and its derivative, and can obtain higher observation accuracy under the same observation gain. Although the disturbance compression expansion state observer enhances its disturbance suppression capability, it does not lead to a significant increase in noise sensitivity. In other words, the disturbance compression expansion state observer exhibits a high degree of noise insensitivity, which provides a new means to alleviate the inherent contradiction between high-gain observation and noise sensitivity.

[0078] When there are step disturbances and ramp disturbances, the step disturbance suppression error of the disturbance compression expansion state observer method is , and the suppression error of the ramp disturbance is ,in is the amplitude constant of step disturbance and ramp disturbance. Therefore, the disturbance compression expansion state observer method can effectively suppress step disturbance and ramp disturbance, thereby significantly improving the accuracy of state and disturbance estimation.

[0079] Next, we will give the relevant simulation verification, the suppression test under the slope interference with slope changes, the simulation results are as follows Figure 4 As shown in (a), the number after the method name represents the observer bandwidth , the larger the number, the higher the observer bandwidth. Figure 4 From the results in (b), it can be seen that for ESO 10Hz, ESO 20Hz and DC-ESO 10Hz, the estimation error of the step disturbance is approximately zero. However, for the ramp disturbance with a slope of 0.5° / s, the estimation errors of ESO 20Hz and ESO 10Hz are 0.003° and 0.009° respectively. In addition, for the ramp disturbance with a slope of 1.5° / s, their estimation errors are 0.01° and 0.026° respectively. Figure 4 As shown in (c), the estimated output of the ESO 20Hz method shows obvious noise amplification, where the noise in the driving voltage is Figure 4 This is obvious in (d). In contrast, the estimation error of DC-ESO for ramp disturbances with slopes of 0.5° / s and 1.5° / s is close to zero. Therefore, the proposed DC-ESO method can effectively estimate ramp disturbances without causing significant noise amplification.

[0080] Next, we will give the relevant experimental verification. The results of the ESO suppression test under 0.5Hz sinusoidal interference are as follows: Figure 5 The results show that the feedback error of DC-ESO 10Hz is reduced by 89.77% and 76.19% compared with ESO 10Hz and ESO 20Hz, respectively. Figure 5 As can be seen in (c), most of the errors of DC-ESO are concentrated between -0.02° and 0.02°. Compared with ESO, the error distribution is more concentrated. Figure 5 Middle (d) shows that ESO 20Hz significantly amplifies the driving noise compared to ESO 10Hz and DC-ESO 10Hz, indicating a serious noise sensitivity problem.

[0081] Based on the above simulation and experimental results, compared with ESO, DC-ESO significantly reduces disturbance estimation error and feedback error without amplifying driving noise. This confirms that DC-ESO can alleviate the contradiction between high-gain observation and noise sensitivity. In other words, DC-ESO has better noise tolerance. In applications with obvious noise, DC-ESO can play a more effective role in disturbance suppression.

[0082] 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. An improved extended state observer method based on frequency domain disturbance compression, characterized in that: The steps include: Step (1): Reconstruct the extended state observer designed for the optoelectronic tracking system from the frequency domain perspective; Step (2): Based on the reconstructed frequency domain expression of the extended state observer, implement a frequency domain disturbance compression algorithm to obtain a disturbance compression extended state observer; Step (3): Combined with Linear Feedback Controller Convert the disturbance compression expansion state observer into frequency domain form; Step (4): Analyze the stability of the disturbance compression expansion state observer and the stability of the closed-loop system to obtain the stability constraint conditions; Step (5): setting a parameter tuning method for a disturbance compression expansion state observer; Step (6): On the basis of satisfying the stability constraint conditions, analyze the influence of the disturbance compression expansion state observer on disturbance suppression and noise sensitivity; Step (7): Analyze whether steps (4)-(6) all meet the preset conditions. If not, re-execute steps (1)-(6). If they do, end the design.

2. The improved extended state observer method based on frequency domain disturbance compression according to claim 1 is characterized in that: The extended state observer disturbance estimation transfer function obtained by reconstructing from the frequency domain in step (1) is expressed as: ， in, represents the lumped disturbance caused by external disturbances and modeling uncertainties, is the observation gain, is the coefficient, is the Laplace operator, To model uncertainty, For external interference, is the control input form in the Laplace domain.

3. The improved extended state observer method based on frequency domain disturbance compression according to claim 2 is characterized in that: The extended state observer designed for the optoelectronic tracking system is a standard extended state observer, which can be expressed as: ， in, is the state vector The estimate, It is an intermediate parameter, and the adjustment rule follows ,in is the identity matrix, and each intermediate matrix .

4. The improved extended state observer method based on frequency domain disturbance compression according to claim 1 is characterized in that: The mathematical expression of the frequency domain disturbance compression algorithm in step (2) is: ， in: The expansion state is estimated to be is the intermediate parameter and u is the driving voltage.

5. The improved extended state observer method based on frequency domain disturbance compression according to claim 4 is characterized in that: The linear feedback controller is introduced in step (3) , and after converting the disturbance compression expansion state observer into frequency domain form, the transfer function of the closed-loop system is obtained as follows: in: , , is the characteristic polynomial, is the input reference trajectory, For output, For noise, Indicates the object being charged.

6. The improved extended state observer method based on frequency domain disturbance compression according to claim 5 is characterized in that: The stability constraint in step (4) is that if it satisfies: and This indicates that the disturbance compression expansion state observer and the closed-loop system are stable.

7. The improved extended state observer method based on frequency domain disturbance compression according to claim 5 is characterized in that: The parameter setting method in step (5) is: , ,in is a constant coefficient, requiring the parameters to satisfy the stability constraints.

8. The improved extended state observer method based on frequency domain disturbance compression according to claim 7 is characterized in that: In step (6), if the stability constraint is satisfied, the disturbance compression expansion state observer satisfies: in, and denote the disturbance estimation transfer functions of the residual and initial lumped disturbance, respectively.

9. The improved extended state observer method based on frequency domain disturbance compression according to claim 7, characterized in that: In step (6), the disturbance suppression effect of the disturbance compression expansion state observer is and The linear superposition of , that is, the disturbance compression channel first suppresses the initial lumped disturbance, which can be expressed as , and then the disturbance compression expansion state observer suppresses the residual lumped disturbance again, which is expressed as , the relationship between the initial lumped disturbance and the residual lumped disturbance is .

10. The improved extended state observer method based on frequency domain disturbance compression according to claim 7, characterized in that: In step (6), when there are step disturbances and ramp disturbances, the step disturbance suppression error of the disturbance compression expansion state observer method is , and the suppression error of the ramp disturbance is ,in is the amplitude constant of step disturbance and ramp disturbance.

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