A nonlinear extended state observer control method based on multi-channel filter compensation

Abstract

The application discloses a nonlinear extended state observer control method based on multi-channel filtering compensation, constructs a traditional nonlinear extended state observer, and accurately decomposes disturbance estimation error into a second derivative term, a first derivative term and a nonlinear error feedback term of output estimation error, constructs three parallel filtering compensation channels respectively, sets a first filtering compensation channel for the nonlinear error feedback term, sets a second filtering compensation channel with low-frequency differential approximation and high-frequency attenuation characteristics for the first derivative term, and sets a third filtering compensation channel with similar frequency characteristics for the second derivative term; the outputs of the three compensation channels are added to a disturbance estimation value of the traditional observer to form an enhanced disturbance estimation quantity, and finally, global uniform ultimate boundedness of a closed-loop system is proved through a cascade Lyapunov method. The application compensates disturbance estimation error components pertinently on the premise of reserving an internal structure of the traditional observer, and considers compensation accuracy and noise robustness.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, and in particular relates to a nonlinear extended state observer control method based on multi-channel filter compensation. Background Technology

[0002] In precision control scenarios such as electromechanical systems, motion control systems, UAV attitude control systems, and power electronic systems, the tracking accuracy and dynamic performance of the controlled object are often severely degraded due to the coupling of various disturbance factors. Active disturbance rejection control methods treat these factors as a unified total disturbance and use an extended state observer to estimate and feedforward the disturbance in real time, thereby effectively combating uncertainties both inside and outside the system. Among them, the nonlinear extended state observer, by introducing a nonlinear error feedback mechanism, improves to some extent the gain-bandwidth trade-off faced by the linear extended state observer, and can obtain better robustness and transient response. However, when the controlled object is subjected to high-frequency disturbances, complex multi-band disturbances, or non-negligible sensor noise in the feedback channel, the nonlinear extended state observer still suffers from large disturbance estimation errors. If the observer bandwidth is directly increased to improve the disturbance suppression capability, high-frequency measurement noise will be significantly amplified and enter the control channel, deteriorating the control quality; conversely, if a simple post-filter is used to process the disturbance estimate, although noise can be suppressed, phase lag is inevitably introduced, weakening the timeliness and effectiveness of disturbance compensation. Therefore, how to compensate for the key components of the perturbation estimation error in a targeted manner while keeping the original internal structure of the nonlinear extended state observer unchanged, and taking into account both the compensation accuracy and noise robustness, has become a core technical problem that urgently needs to be solved in this field.

[0003] To address the aforementioned technical problems, various improvement methods have been proposed in the existing technology. One type of approach focuses on the online adjustment of observer parameters, such as adaptive gain methods and variable bandwidth design methods. These methods dynamically adjust the observer gain or bandwidth according to the real-time operating status of the system, aiming to achieve a better balance between disturbance estimation capability and noise suppression capability in different frequency bands. Another type of approach focuses on the expansion of the observer structure, such as cascaded observers and internal model introduction methods. The former estimates disturbances with different frequency characteristics by cascading multiple observers to successively estimate disturbances with different frequency characteristics, while the latter embeds the corresponding internal model into the observer for disturbances with specific frequencies or structures to achieve asymptotically accurate estimation. In addition, there are frequency domain phase compensation methods and post-filtering methods. The former compensates for phase lag by performing phase lead processing on the disturbance estimation signal, while the latter directly applies a filter to the disturbance estimation value output by the extended state observer to attenuate high-frequency noise components. Although these methods can partially alleviate the problems of insufficient disturbance estimation accuracy or noise amplification under their respective applicable conditions, they generally treat the disturbance estimation error as a whole black box signal and fail to make in-depth use of the structural information of the internal error dynamics of the nonlinear extended state observer.

[0004] The drawbacks of the existing techniques mentioned above are the lack of precise decomposition of the internal disturbance estimation error structure of the nonlinear extended state observer, making it impossible to distinguish different sources of error and their dynamic characteristics, thus hindering targeted compensation. Simple post-filtering introduces additional phase lag, causing delays in disturbance compensation and reducing the system's ability to suppress rapidly changing disturbances. Directly increasing the observer bandwidth amplifies measurement noise, contaminating the controller output with noise components, and in severe cases, even causing high-frequency jitter in the actuator or wear of components. Cascading observers and the introduction of internal models significantly increase the observer order and implementation complexity, and the internal model method is highly sensitive to the accuracy of disturbance frequency, limiting its robustness. Therefore, a nonlinear extended state observer control method based on multi-channel filter compensation is needed to address these problems. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a nonlinear extended state observer control method based on multi-channel filter compensation. It aims to overcome the shortcomings of traditional nonlinear extended state observer disturbance estimation error compensation methods, which introduce phase lag or noise amplification due to black-box processing and lack error structure decomposition. It has the characteristics of constructing multi-channel filter compensation from the error component level to maintain the original structure of the observer while taking into account the disturbance suppression accuracy and noise robustness.

[0006] To achieve the above technical solution, the technical solution adopted by the present invention is as follows: A nonlinear extended state observer control method based on multi-channel filter compensation includes the following steps: S1. For a second-order integral cascaded controlled object containing total disturbance, establish a controlled object model and treat the total disturbance as an extended state to establish an extended system model. S2, based on the output estimation error, construct a traditional nonlinear extended state observer; S3. Based on the dynamics of the observation error and the derivative of the output estimation error of the traditional nonlinear extended state observer, the perturbation estimation error is derived, and the perturbation estimation error is decomposed into the second derivative term of the output estimation error, the first derivative term of the output estimation error, and the nonlinear error feedback term. S4. For the nonlinear error feedback term, a first filter compensation channel is constructed to obtain the first filter compensation amount, which is used to attenuate high-frequency noise while retaining the low-frequency compensation effect. S5. For the first derivative term of the output estimation error, a second filter compensation channel is constructed to obtain the second filter compensation amount, which makes it approximate the first derivative in the low frequency range and has attenuation characteristics in the high frequency range. S6. For the second derivative term of the output estimation error, a third filter compensation channel is constructed to obtain the third filter compensation amount, so that it approximates the second derivative in the low frequency range and avoids the high frequency noise amplification caused by direct numerical differentiation. S7 adds the disturbance estimate output by the traditional nonlinear extended state observer to the first filter compensation amount, the second filter compensation amount, and the third filter compensation amount to form the enhanced disturbance estimate. The enhanced disturbance estimate is only used for the control law and is not fed back into the dynamics of the traditional nonlinear extended state observer. S8. Based on the tracking error and its derivative, design an active disturbance suppression control law, which includes an enhanced disturbance estimate. S9 establishes a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem. The Lyapunov method is used to prove that the observer error subsystem and the filter subsystem are bounded. Under the condition that the tracking error subsystem is stabilized by controlling the gain, it is proved that the overall closed-loop system is globally consistent and eventually bounded.

[0007] Preferably, in step S1, the controlled object model is: , , ,in The total disturbance consists of unmodeled dynamics, parameter uncertainties, and external disturbances; extended system model. The expansion state is .

[0008] Preferably, in step S2, based on the output estimation error Construct a nonlinear extended state observer: ; ; ; in , , For observer gain, , This is a nonlinear error feedback function.

[0009] Preferably, in step S3, the observation error is dynamically... and The perturbation estimation error is derived. Therefore, the perturbation estimation error of the traditional nonlinear extended state observer is decomposed into three components: the second derivative of the output estimation error, the first derivative of the output estimation error, and the nonlinear error feedback term.

[0010] Preferably, in step S4, the nonlinear error feedback term is addressed. Construct a first-order low-pass filter The first filter compensation amount is obtained. It is used to attenuate high-frequency noise while retaining the effect of low-frequency compensation.

[0011] Preferably, in step S5, for the first derivative term... Construct a second-order filter differentiator whose transfer function satisfies The second filter compensation amount is obtained. This allows it to approach the first derivative in the low-frequency range and exhibit attenuation characteristics in the high-frequency range.

[0012] Preferably, in step S6, the second derivative term is... Construct a third-order filter differentiator whose transfer function satisfies The third filter compensation amount is obtained. This allows it to approximate the second-order derivative in the low-frequency range and avoids the amplification of high-frequency noise caused by direct numerical differentiation.

[0013] Preferably, in step S7, the disturbance estimate output by the conventional nonlinear extended state observer is... The enhanced disturbance estimate is formed by adding the three parallel filter compensation quantities. This enhanced perturbation estimator is used only in the control law and is not fed back into the observer dynamics, thus maintaining the structure and convergence properties of the original nonlinear extended state observer.

[0014] Preferably, in step S8, based on the tracking error and its derivative ,structure The control law, in which and To control the gain.

[0015] Preferably, in step S9, a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem is established; the boundedness of the observer error subsystem and the filter subsystem is proven using the Lyapunov method, and... , Prove that the overall closed-loop system is globally consistent and eventually bounded, provided that the tracking error subsystem is stable. Observer bandwidth. Used to adjust the error convergence speed and filter bandwidth. , , It is used to balance compensation accuracy and noise suppression capability.

[0016] The beneficial effects of this invention are as follows: 1. This invention derives the precise decomposition relationship of the disturbance estimation error of a nonlinear extended state observer, clearly identifying the error sources as the second derivative term, first derivative term, and nonlinear error feedback term of the output estimation error. Three parallel filtering compensation channels are then constructed for targeted approximation, achieving an improvement in the observer's disturbance estimation performance from the perspective of error structure. Traditional methods often treat the disturbance estimation error as a whole signal for post-filtering, making it difficult to consider different frequency components. This invention, however, processes each error component individually, making the compensation logic transparent and highly adjustable. It overcomes the shortcomings of existing technologies, such as vague understanding of the error structure and generalized compensation methods, significantly enhancing the disturbance suppression accuracy and transient response quality of the control system under complex multi-frequency disturbance conditions.

[0017] 2. This invention adds the compensation values ​​output from the three filter compensation channels to the disturbance estimate output from the traditional nonlinear extended state observer, forming an enhanced disturbance estimate which is used only in the control law without being fed back into the observer's own state update dynamics. This achieves improved disturbance suppression capability while preserving the original internal structure and convergence characteristics of the nonlinear extended state observer. This design solidifies the mature engineering implementation method of traditional observers, avoids the difficulties in stability analysis and parameter tuning caused by changes in the observer structure, and solves the defects of existing cascaded observers or variable structure methods that destroy the original observer dynamics and increase the complexity of system debugging. It is conducive to achieving a smooth technical upgrade within the existing active disturbance rejection control framework.

[0018] 3. This invention constructs second-order and third-order filter differentiators to approximate the first and second derivative terms of the output estimation error, respectively. Utilizing their low-frequency approximation differentiation and high-frequency attenuation characteristics, it effectively suppresses high-frequency measurement noise amplification while compensating for the differential components of the error. Compared to the conventional approach of directly performing numerical differentiation on the error signal, which introduces severe noise interference, the filter differentiating channel of this invention naturally attenuates high-frequency noise components while ensuring the accuracy of low-frequency compensation, eliminating the need for additional noise filters. Furthermore, the observer bandwidth and the bandwidth parameters of each filter channel are independently adjustable, allowing for separate design of the convergence speed of the basic observer and the accuracy-noise tradeoff of the compensation channel. This resolves the contradiction of traditional single-bandwidth parameters needing to simultaneously handle multiple control objectives, enhancing the system's robustness and parameter tuning flexibility in complex noise environments. Attached Figure Description

[0019] Figure 1 This is a block diagram of a control system based on a multi-channel filter-compensated nonlinear extended state observer. Figure 2 The amplitude-frequency characteristics of a first-order filter differentiator and an ideal differentiator; Figure 3 The amplitude-frequency characteristics of a second-order filter differentiator and an ideal differentiator; Figure 4 A comparison of the tracking responses of NESO and MCFNESO in a second-order system simulation; Figure 5 A comparison of the perturbation errors of NESO and MCFNESO in a second-order system simulation; Figure 6 This is a schematic diagram of a quadcopter unmanned aerial vehicle (UAV) experimental platform. Figure 7 The attitude tracking response diagrams of NESO and MCFNESO in the roll and pitch channels are shown. Figure 8 The torque control command response diagrams for NESO and MCFNESO are shown in the roll and pitch channels. Detailed Implementation

[0020] Example 1: like Figure 1 As shown, a nonlinear extended state observer control method based on multi-channel filter compensation includes the following steps: S1. For a second-order integral cascaded controlled object containing total disturbance, establish a controlled object model and treat the total disturbance as an extended state to establish an extended system model. S2, based on the output estimation error, construct a traditional nonlinear extended state observer; S3. Based on the dynamics of the observation error and the derivative of the output estimation error of the traditional nonlinear extended state observer, the perturbation estimation error is derived, and the perturbation estimation error is decomposed into the second derivative term of the output estimation error, the first derivative term of the output estimation error, and the nonlinear error feedback term. S4. For the nonlinear error feedback term, a first filter compensation channel is constructed to obtain the first filter compensation amount, which is used to attenuate high-frequency noise while retaining the low-frequency compensation effect. S5. For the first derivative term of the output estimation error, a second filter compensation channel is constructed to obtain the second filter compensation amount, which makes it approximate the first derivative in the low frequency range and has attenuation characteristics in the high frequency range. S6. For the second derivative term of the output estimation error, a third filter compensation channel is constructed to obtain the third filter compensation amount, so that it approximates the second derivative in the low frequency range and avoids the high frequency noise amplification caused by direct numerical differentiation. S7 adds the disturbance estimate output by the traditional nonlinear extended state observer to the first filter compensation amount, the second filter compensation amount, and the third filter compensation amount to form the enhanced disturbance estimate. The enhanced disturbance estimate is only used for the control law and is not fed back into the dynamics of the traditional nonlinear extended state observer. S8. Based on the tracking error and its derivative, design an active disturbance suppression control law, which includes an enhanced disturbance estimate. S9 establishes a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem. The Lyapunov method is used to prove that the observer error subsystem and the filter subsystem are bounded. Under the condition that the tracking error subsystem is stabilized by controlling the gain, it is proved that the overall closed-loop system is globally consistent and eventually bounded.

[0021] Preferably, in step S1, the controlled object model is: , , ,in The total disturbance consists of unmodeled dynamics, parameter uncertainties, and external disturbances; extended system model. The expansion state is .

[0022] Preferably, in step S2, based on the output estimation error Construct a nonlinear extended state observer: ; ; ; in , , For observer gain, , This is a nonlinear error feedback function.

[0023] Preferably, in step S3, the observation error is dynamically... and The perturbation estimation error is derived. Therefore, the perturbation estimation error of the traditional nonlinear extended state observer is decomposed into three components: the second derivative of the output estimation error, the first derivative of the output estimation error, and the nonlinear error feedback term.

[0024] like Figure 2 As shown, preferably, in step S4, for the nonlinear error feedback term Construct a first-order low-pass filter The first filter compensation amount is obtained. It is used to attenuate high-frequency noise while retaining the effect of low-frequency compensation.

[0025] like Figure 3 As shown, preferably, in step S5, for the first derivative term... Construct a second-order filter differentiator whose transfer function satisfies The second filter compensation amount is obtained. This allows it to approach the first derivative in the low-frequency range and exhibit attenuation characteristics in the high-frequency range.

[0026] Preferably, in step S6, the second derivative term is... Construct a third-order filter differentiator whose transfer function satisfies The third filter compensation amount is obtained. This allows it to approximate the second-order derivative in the low-frequency range and avoids the amplification of high-frequency noise caused by direct numerical differentiation.

[0027] Preferably, in step S7, the disturbance estimate output by the conventional nonlinear extended state observer is... The enhanced disturbance estimate is formed by adding the three parallel filter compensation quantities. This enhanced perturbation estimator is used only in the control law and is not fed back into the observer dynamics, thus maintaining the structure and convergence properties of the original nonlinear extended state observer.

[0028] Preferably, in step S8, based on the tracking error and its derivative ,structure The control law, in which and To control the gain.

[0029] Preferably, in step S9, a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem is established; the boundedness of the observer error subsystem and the filter subsystem is proven using the Lyapunov method, and... , Prove that the overall closed-loop system is globally consistent and eventually bounded, provided that the tracking error subsystem is stable. Observer bandwidth. Used to adjust the error convergence speed and filter bandwidth. , , It is used to balance compensation accuracy and noise suppression capability.

[0030] Example 2: This embodiment uses a second-order integral cascaded system as the implementation object, treating the total disturbance as an extended state and constructing a traditional nonlinear extended state observer. The observer gain is then set. , , And the fal function was selected as the nonlinear error feedback function.

[0031] Based on the observer error dynamics, the output estimation error is calculated. ,use The perturbation estimation error is decomposed into three components. For Set a first-order low-pass filter for... Set up a second-order filter differentiator, for... Configure a third-order filter differentiator. The outputs of the three channels are denoted as follows: , and .

[0032] The outputs of the three parallel filter compensation channels are added to the original NESO disturbance estimate to obtain the enhanced disturbance estimate. The enhanced disturbance estimate is substituted into the PD active disturbance suppression control law to counteract the impact of the total disturbance on the tracking performance of the controlled object.

[0033] like Figure 4 and Figure 5 As shown, in the simulation embodiment, NESO and MCFNESO are compared using the same observer bandwidth. The results show that MCFNESO can reduce peak-to-peak tracking error by 52.85% and root mean square tracking error by 55.48%. In the quadcopter UAV experimental embodiment, the peak-to-peak tracking error in the roll channel is reduced by 58.91%, and the peak-to-peak tracking error in the pitch channel is reduced by 59.32%, verifying the effectiveness of the invention.

[0034] In the experimental embodiment of the quadcopter UAV, the schematic diagram of the experimental platform is as follows: Figure 6 As shown, the platform comprises core components such as a quadcopter UAV airframe, flight controller, attitude sensor, motor, and propeller, and is used to verify the attitude control performance of the proposed method under actual flight conditions.

[0035] Figure 7 The attitude tracking response curves for the roll and pitch channels are presented under two conditions: using a traditional nonlinear extended state observer and using the multi-channel filtered compensation nonlinear extended state observer of this method. As can be seen from the figures, even with the simultaneous presence of external disturbances and sensor noise, this method achieves smaller attitude tracking deviations in both the roll and pitch channels. The deviation between the tracking curve and the reference command is significantly reduced, resulting in more stable attitude maintenance.

[0036] Figure 8 The torque control command response curves for the roll and pitch channels under the two methods are presented. The comparison shows that the torque control command waveform corresponding to this method is smoother, and the high-frequency jitter amplitude is significantly reduced. This indicates that the enhanced disturbance estimate effectively compensates for disturbances without introducing additional noise interference components, thereby reducing the high-frequency load on the actuator.

[0037] Experimental results show that in the above-mentioned quadcopter UAV attitude control embodiment, the peak-to-peak tracking error of the roll channel is reduced by 58.91%, and the peak-to-peak tracking error of the pitch channel is reduced by 59.32%, verifying the effectiveness of the method under actual complex working conditions.

Claims

1. A nonlinear extended state observer control method based on multi-channel filter compensation, characterized in that, Includes the following steps: S1. For a second-order integral cascaded controlled object containing total disturbance, establish a controlled object model and treat the total disturbance as an extended state to establish an extended system model. S2, based on the output estimation error, construct a traditional nonlinear extended state observer; S3. Based on the dynamics of the observation error and the derivative of the output estimation error of the traditional nonlinear extended state observer, the perturbation estimation error is derived, and the perturbation estimation error is decomposed into the second derivative term of the output estimation error, the first derivative term of the output estimation error, and the nonlinear error feedback term. S4. For the nonlinear error feedback term, a first filter compensation channel is constructed to obtain the first filter compensation amount, which is used to attenuate high-frequency noise while retaining the low-frequency compensation effect. S5. For the first derivative term of the output estimation error, a second filter compensation channel is constructed to obtain the second filter compensation amount, which makes it approximate the first derivative in the low frequency range and has attenuation characteristics in the high frequency range. S6. For the second derivative term of the output estimation error, a third filter compensation channel is constructed to obtain the third filter compensation amount, so that it approximates the second derivative in the low frequency range and avoids the high frequency noise amplification caused by direct numerical differentiation. S7 adds the disturbance estimate output by the traditional nonlinear extended state observer to the first filter compensation amount, the second filter compensation amount, and the third filter compensation amount to form the enhanced disturbance estimate. The enhanced disturbance estimate is only used for the control law and is not fed back into the dynamics of the traditional nonlinear extended state observer. S8. Based on the tracking error and its derivative, design an active disturbance suppression control law, which includes an enhanced disturbance estimate. S9 establishes a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem. The Lyapunov method is used to prove that the observer error subsystem and the filter subsystem are bounded. Under the condition that the tracking error subsystem is stabilized by controlling the gain, it is proved that the overall closed-loop system is globally consistent and eventually bounded.

2. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S1, the controlled object model is as follows: , , ,in The total disturbance consists of unmodeled dynamics, parameter uncertainties, and external disturbances; Extended system model The expansion state is .

3. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S2, based on the output estimation error Construct a nonlinear extended state observer: ； ； ； in , , For observer gain, , This is a nonlinear error feedback function.

4. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S3, the observation error is dynamically... and The perturbation estimation error is derived. Therefore, the perturbation estimation error of the traditional nonlinear extended state observer is decomposed into three components: the second derivative of the output estimation error, the first derivative of the output estimation error, and the nonlinear error feedback term.

5. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S4, for the nonlinear error feedback term Construct a first-order low-pass filter The first filter compensation amount is obtained. It is used to attenuate high-frequency noise while retaining the effect of low-frequency compensation.

6. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S5, for the first derivative term Construct a second-order filter differentiator whose transfer function satisfies The second filter compensation amount is obtained. This allows it to approach the first derivative in the low-frequency range and exhibit attenuation characteristics in the high-frequency range.

7. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S6, for the second derivative term Construct a third-order filter differentiator whose transfer function satisfies The third filter compensation amount is obtained. This allows it to approximate the second-order derivative in the low-frequency range and avoids the amplification of high-frequency noise caused by direct numerical differentiation.

8. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S7, the disturbance estimate output by the traditional nonlinear extended state observer is... The enhanced disturbance estimate is formed by adding the three parallel filter compensation quantities. This enhanced perturbation estimator is used only in the control law and is not fed back into the observer dynamics, thus maintaining the structure and convergence properties of the original nonlinear extended state observer.

9. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S8, based on the tracking error and its derivative ,structure The control law, in which and To control the gain.

10. The nonlinear extended state observer control method based on multi-channel filter compensation according to claim 1, characterized in that, In step S9, a cascaded closed-loop model consisting of an observer error subsystem, a filter state subsystem, and a tracking error subsystem is established; the boundedness of the observer error subsystem and the filter subsystem is proven using the Lyapunov method, and... , Prove that the overall closed-loop system is globally consistent and eventually bounded, provided that the tracking error subsystem is stable. Observer bandwidth. Used to adjust the error convergence speed and filter bandwidth. , , It is used to balance compensation accuracy and noise suppression capability.

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