A data-driven extended state observer

Abstract

The present invention provides a data-driven extended state observer, comprising: an active disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data-driven learning law module, and a first-order filter; wherein, the working principle of the data-driven extended state observer is as follows: a piecewise continuous speed reference signal is input to the active disturbance rejection controller, and the speed signal generated by the active disturbance rejection controller and the external disturbance act on the unmanned ship system simultaneously. The unmanned ship state information, output response, and the output response after passing through the first-order filter are saved in the data stack module. The extended state observer obtains the system state estimation and lumped disturbance estimation by using the data in the stack updated by the data-driven learning law module. The technical solution of the present invention solves the problem of disturbance estimation for a first-order nonlinear system with unknown internal uncertainties, external disturbances, and unknown input gains, and realizes the simultaneous estimation of the total system disturbance and control input gain.

Description

Technical Field

[0001] The present invention relates to the technical field of the design of extended state observers, and more particularly, to a data-driven extended state observer. Background Art

[0002] Disturbances and uncertainties are ubiquitous in control systems, and it is a difficult problem to control systems with uncertainties and disturbances. Existing inventions have proposed methods such as robust control, adaptive control, disturbance observer-based control, and active disturbance rejection control. Among them, the active disturbance rejection control method has been widely applied in various fields such as aircraft, mobile robots, autonomous surface and underwater vehicles. The extended state observer is the core unit of the active disturbance rejection control technology, which unifies the estimation of internal uncertainties and external disturbances of the system as the total disturbance of the system.

[0003] However, existing methods based on extended state observers usually assume that the system control input gain is known a priori. To identify the system control input gain, a large number of test experiments need to be carried out in practice. Moreover, even if the input gain is obtained through experiments, the actual value may change due to different loads, changes in control efficiency, or actuator failures. Therefore, it is worth studying the simultaneous estimation of unknown input gain and system total disturbance. Existing methods for dealing with unknown input gain include the Nussbaum function and adaptive parameter estimation.

[0004] The Nussbaum function is often used to deal with control problems where the magnitude and direction of the control input gain are unknown. The adaptive parameter estimation method estimates the input gain using an adaptive parameter projection method with a given boundary, but the input gain estimation cannot guarantee convergence to the true value. Neither of these two methods can accurately estimate the control input gain, especially when the internal dynamics and external disturbances are unknown. The existing invention method derived a data-driven second-order extended state observer based on pseudo-Jacobian matrix estimation for estimating model approximation errors. However, historical data is not used in the estimation process, and the use of historical data helps to improve the estimation performance. To sum up, the existing technologies have the following deficiencies:

[0005] (1) The establishment of existing extended state observers requires the system input gain to be known a priori, but the model parameter identification process is complex, which is not conducive to engineering implementation.

[0006] (2) Existing adaptive estimation methods can only utilize current data, and cannot guarantee convergence to the true value, and the convergence time is long.

[0007] (3) Existing active disturbance rejection control laws require actual or nominal control input gains, cannot completely get rid of the dependence on model parameters, the control performance depends on the accuracy of the model, and when the input gain changes greatly, it will lead to a reduction in control performance. Summary of the Invention

[0008] Regarding the problem of disturbance estimation for a first - order non - linear system with unknown internal uncertainties, external disturbances, and unknown input gains proposed above, the present invention provides a data - driven extended state observer, which realizes the simultaneous estimation of the total system disturbance and the control input gain.

[0009] The technical means adopted by the present invention are as follows:

[0010] A data - driven extended state observer, comprising: an active disturbance rejection controller, a first - order non - linear system, an extended state observer, a data stack module, a data - driven learning law module, and a first - order filter; where:

[0011] The input end of the active disturbance rejection controller is connected to the given speed reference signal, the extended state observer, and the data - driven learning law module, and the output end of the active disturbance rejection controller is connected to the first - order non - linear system;

[0012] The input end of the first - order non - linear system is connected to the active disturbance rejection controller, and the output end of the first - order non - linear system is connected to the first - order filter;

[0013] The input end of the first - order filter is connected to the first - order non - linear system, the extended state observer, and the active disturbance rejection observer, and the output end of the first - order filter is connected to the data stack module;

[0014] The input end of the data stack module is connected to the first - order filter, and the output end of the data stack module is connected to the data - driven learning law module;

[0015] The input end of the data - driven learning law module is connected to the data stack module, and the output end of the data - driven learning law module is connected to the extended state observer and the active disturbance rejection observer;

[0016] The input end of the extended state observer is connected to the data - driven learning law module, the first - order filter module, and the first - order non - linear system, and the output end of the extended state observer is connected to the active disturbance rejection controller.

[0017] Furthermore, the design process of the active disturbance rejection controller is as follows:

[0018] Define the tracking error The active disturbance rejection controller based on the data - driven extended state observer is designed as follows:

[0019]

[0020] where, k c is the controller gain;

[0021] Furthermore, the first-order nonlinear system is specifically expressed as:

[0022]

[0023] Wherein, represents the system state; represents an unknown nonlinear function; is an unknown external disturbance; is an unknown input gain, determined by the system characteristics; is the control input.

[0024] Furthermore, the design of the first-order filter is as follows:

[0025]

[0026] Wherein, a is the filter time constant.

[0027] Furthermore, the data stack module is used to store the filtered data u k at time t f (k) and g(k), k = 1,..., N.

[0028] Furthermore, the design of the data-driven learning law module is based on the data recorded in the data stack, and the data-driven learning law is designed as follows:

[0029]

[0030] Wherein, Proj[·,·] represents the projection operator; is the learning gain.

[0031] Furthermore, the extended state observer is specifically expressed as:

[0032]

[0033] Wherein, σ = f(x) + w(t) is the total system disturbance;

[0034] The extended state observer includes a reduced-order data-driven extended state observer and a full-order data-driven extended state observer, wherein:

[0035] The design of the reduced-order data-driven extended state observer is as follows:

[0036]

[0037] Wherein, is the system state estimate; is the lumped disturbance estimate; is the input gain estimate; κ is the observation gain;

[0038] The full-order data-driven extended state observer is designed as follows:

[0039]

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. The data-driven extended state observer provided by the present invention, compared with the existing disturbance observers and extended state observers that require the system input gain to be known a priori, does not require the system input gain to be known and does not need to perform complex experiments for identifying model parameters.

[0042] 2. The data-driven extended state observer provided by the present invention, compared with the existing adaptive estimation methods that only use current data for learning, uses both historical data and current data, improving the parameter convergence speed and estimation effect.

[0043] 3. The data-driven extended state observer provided by the present invention, compared with the existing active disturbance rejection controllers based on nominal or actual system parameters, the model-free control law does not depend on any model prior parameters and can adapt to large input gain changes.

[0044] For the above reasons, the present invention can be widely promoted in the fields such as the design of extended state observers. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0046] Figure 1 It is a schematic structural diagram of the data-driven extended state observer of the present invention.

[0047] Figure 2 It is a schematic structural diagram of the hardware-in-the-loop simulation platform provided by the embodiment of the present invention.

[0048] Figure 3 It is a curve graph of the output response of the unmanned ship provided by the embodiment of the present invention.

[0049] Figure 4 It is a curve graph of the lumped disturbance estimation of the system provided by the embodiment of the present invention.

[0050] Figure 5 It is a curve graph of the system control input provided by the embodiment of the present invention.

[0051] Figure 6 This is the input gain estimation curve graph provided by the embodiments of the present invention. Detailed implementation manners

[0052] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. The description of at least one exemplary embodiment below is actually only illustrative and in no way constitutes a limitation to the present invention and its application or use. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0054] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments of the present invention. As used herein, unless otherwise clearly specified in the context, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0055] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions and values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for the convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationship. Technologies, methods and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods and devices should be regarded as part of the authorization specification. In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0056] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by orientation words such as "front, back, up, down, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom", etc. is usually based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description. Without contrary instructions, these orientation words do not indicate and imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation on the protection scope of the present invention: the orientation words "inside, outside" refer to the inside and outside relative to the contour of each component itself.

[0057] For the sake of convenience of description, spatial relative terms such as "above...", "over...", "on the upper surface of...", "upper" etc. can be used here to describe the spatial positional relationship between a device or feature shown in the drawings and other devices or features. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation described in the drawings for the device. For example, if the device in the drawing is inverted, the device described as "above other devices or structures" or "over other devices or structures" will then be positioned as "below other devices or structures" or "under other devices or structures". Thus, the exemplary term "above..." can include both the orientations of "above..." and "below...". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations should be made for the spatial relative descriptions used here.

[0058] In addition, it should be noted that the use of words such as "first", "second" etc. to limit components is only for the convenience of differentiating the corresponding components. Without additional statements, the above words have no special meanings. Therefore, it should not be construed as a limitation on the protection scope of the present invention.

[0059] As Figure 1 shown, the present invention provides a data-driven extended state observer, including: an auto-disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data-driven learning law module, and a first-order filter; where:

[0060] The input end of the auto-disturbance rejection controller is connected to a given speed reference signal, the extended state observer, and the data-driven learning law module, and the output end of the auto-disturbance rejection controller is connected to the first-order nonlinear system;

[0061] The input end of the first-order nonlinear system is connected to the auto-disturbance rejection controller, and the output end of the first-order nonlinear system is connected to the first-order filter;

[0062] The input end of the first-order filter is connected to a first-order nonlinear system, an extended state observer, and an active disturbance rejection observer, and the output end of the first-order filter is connected to a data stack module;

[0063] The input end of the data stack module is connected to the first-order filter, and the output end of the data stack module is connected to a data-driven learning law module;

[0064] The input end of the data-driven learning law module is connected to the data stack module, and the output end of the data-driven learning law module is connected to the extended state observer and the active disturbance rejection observer;

[0065] The input end of the extended state observer is connected to the data-driven learning law module, a first-order filter module, and a first-order nonlinear system, and the output end of the extended state observer is connected to an active disturbance rejection controller.

[0066] In this embodiment, a piecewise continuous speed reference signal is input to the active disturbance rejection controller. The speed signal generated by the active disturbance rejection controller and the external disturbance act on the unmanned ship system at the same time. The unmanned ship state information and output response are saved in the data stack module after passing through the first-order filter. The extended state observer obtains the system state estimation and lumped disturbance estimation by using the data in the stack updated by the data-driven learning law module.

[0067] Specifically, as a preferred embodiment of the present invention, the design process of the active disturbance rejection controller is as follows:

[0068] Define the tracking error The active disturbance rejection controller based on the data-driven extended state observer is designed as follows:

[0069]

[0070] where k c is the controller gain;

[0071] Specifically, as a preferred embodiment of the present invention, the first-order nonlinear system is specifically expressed as:

[0072]

[0073] where represents the system state; represents an unknown nonlinear function; is an unknown external disturbance; is an unknown input gain, which is determined by the system characteristics; is the control input.

[0074] Specifically, as a preferred embodiment of the present invention, the design of the first-order filter is as follows:

[0075]

[0076] Among them, a is the filter time constant.

[0077] In specific implementation, as a preferred implementation manner of the present invention, the data stack module is used to store the filtered data u k at time t f (k) and g(k), where k = 1,..., N.

[0078] In specific implementation, as a preferred implementation manner of the present invention, the design of the data-driven learning law module is based on the data recorded in the data stack, and the data-driven learning law is designed as follows:

[0079]

[0080] Among them, Proj[·,·] represents the projection operator; is the learning gain.

[0081] In specific implementation, as a preferred implementation manner of the present invention, the extended state observer is specifically expressed as:

[0082]

[0083] Among them, σ = f(x) + w(t) is the total system disturbance;

[0084] The extended state observer includes a reduced-order data-driven extended state observer and a full-order data-driven extended state observer, where:

[0085] The design of the reduced-order data-driven extended state observer is as follows:

[0086]

[0087] Among them, is the system state estimation; is the lumped disturbance estimation; is the input gain estimation; κ is the observation gain;

[0088] The design of the full-order data-driven extended state observer is as follows:

[0089]

[0090] Embodiment

[0091] To verify the control performance of the proposed data-driven extended state observer, it is applied to the speed tracking of an unmanned ship, and hardware-in-the-loop simulation is carried out. The experimental platform consists of a remote control station and an embedded controller installed in the unmanned ship. The remote control station communicates with the unmanned ship through the Zigbee network. The single-chip microcomputer is connected to the inertial measurement unit and the global satellite navigation system GPS to obtain position information, speed information and attitude information. The remote control station can display the state information of the unmanned ship, especially the trajectory information, on the map. The unmanned ship system model is as follows:

[0092]

[0093] where, is the surge speed; is the control force; is the control input coefficient; X1u + X2u|u| is the unknown internal dynamic force related to the hydrodynamic damping force; and are the hydrodynamic parameters; is the inertia term related to the mass of the unmanned ship, is the external disturbance. b0 = b / m represents the unknown input gain; σ(u) = b0X1u + b0X2u|u| + b0w represents the lumped disturbance. The control input gain b0 can be determined by the system mass, propeller drive efficiency and drive motor parameters. In this embodiment, b0 may vary due to load changes or reduced thrust efficiency.

[0094] In this embodiment, the specific parameters of the model designed by the present invention are as follows:

[0095] During hardware-in-the-loop simulation, the model parameters in the unmanned ship are: m 11 = 12.5 kg, X1 = -0.8327, X2 = -1.513, b = 1, ω = 0.1sin(t)cos(t 2 ), the controller parameters are selected as k c = 1.5, κ = 8, a = 100. To test the learning ability of the data-driven extended state observer provided by the present invention for changes in the control input gain, the parameter is changed to m 11 = 14 at 60 seconds.

[0096] The simulation results are as Figures 3 - 5 shown. Figure 3 is the output response of the unmanned ship. It can be seen that under the conditions of model uncertainty, external interference and unknown control input gain, the anti-interference control law proposed by the present invention can track the given signal. Figure 4 is the estimation of the system lumped disturbance, Figure 5 is the system control input. It can be seen that the lumped disturbance can be accurately estimated under the condition of unknown control input gain.Figure 6 To utilize the estimated input gain of the proposed data-driven extended state observer, the solid line represents the unknown input gain and the dashed line represents the estimated unknown input gain. It can be seen that although the unknown input gain changes at 60 seconds, the data-driven extended state observer provided by the present invention can adapt to the change by recording new data and does not affect the output performance during the control process. The control input gain can be estimated through the data-driven extended state observer.

[0097] From the above simulation result diagram, it can be seen that a remarkable feature of the data-driven extended state observer proposed by the present invention is that it can synchronously estimate the unknown input gain and the lumped disturbance while ensuring the convergence of the estimation.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data-driven extended state observer, characterized in that Including: An active disturbance rejection controller, a first-order non-linear system, an extended state observer, a data stack module, a data-driven learning law module, and a first-order filter; where: The input end of the active disturbance rejection controller is connected to a given speed reference signal, an extended state observer, and a data-driven learning law module, and the output end of the active disturbance rejection controller is connected to the first-order non-linear system; The input end of the first-order non-linear system is connected to the active disturbance rejection controller, and the output end of the first-order non-linear system is connected to the first-order filter; The input end of the first-order filter is connected to the first-order non-linear system, the extended state observer, and the active disturbance rejection observer, and the output end of the first-order filter is connected to the data stack module; The input end of the data stack module is connected to the first-order filter, and the output end of the data stack module is connected to the data-driven learning law module; The input end of the data-driven learning law module is connected to the data stack module, and the output end of the data-driven learning law module is connected to the extended state observer and the active disturbance rejection observer; The input end of the extended state observer is connected to the data-driven learning law module, the first-order filter module, and the first-order non-linear system, and the output end of the extended state observer is connected to the active disturbance rejection controller.

2. The data-driven extended state observer according to claim 1, wherein The design process of the active disturbance rejection controller is as follows: Define the tracking error where is the system state estimation. The active disturbance rejection controller based on the data-driven extended state observer is designed as follows: where k c is the controller gain; is the lumped disturbance estimate; is the input gain estimate.

3. The data-driven extended state observer according to claim 1, wherein The first-order non-linear system is specifically expressed as: Among them, represents the system state; represents an unknown nonlinear function; is an unknown external disturbance; is an unknown input gain, which is determined by the system characteristics; is the control input.

4. The data-driven extended state observer according to claim 1, wherein The design of the first-order filter is as follows: Where a is the filter time constant.

5. The data-driven extended state observer according to claim 1, wherein The data stack module is used to store the filtered data u k at time t f (k) and g(k), where k = 1,..., N.

6. The data-driven extended state observer according to claim 5, wherein The design of the data-driven learning law module is based on the data recorded in the data stack, and the data-driven learning law is designed as follows: where Proj[·,·] represents a projection operator; is the learning gain.

7. The data-driven extended state observer according to claim 1, characterized in that, The extended state observer is specifically expressed as: Where σ = f(x) + w(t) is the total system disturbance; The extended state observer includes a reduced-order data-driven extended state observer and a full-order data-driven extended state observer, where: The design of the reduced-order data-driven extended state observer is as follows: wherein, is the system state estimation; is the lumped disturbance estimation; is the input gain estimation; κ is the observation gain; The design of the full-order data-driven extended state observer is as follows:

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