CN116227153A - Data-driven extended state observer - Google Patents

Data-driven extended state observer Download PDF

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CN116227153A
CN116227153A CN202310020911.XA CN202310020911A CN116227153A CN 116227153 A CN116227153 A CN 116227153A CN 202310020911 A CN202310020911 A CN 202310020911A CN 116227153 A CN116227153 A CN 116227153A
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extended state
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彭周华
吕旻高
李一鹤
王丹
古楠
刘陆
王浩亮
王安青
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Dalian Maritime University
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Abstract

The present invention provides a data-driven extended state observer comprising: the system comprises an active disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data driving learning law module and a first-order filter; the working principle of the data driving extended state observer is as follows: 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 external disturbance act on an unmanned ship system at the same time, unmanned ship state information, output response and data in a stack after passing through a first-order filter are stored in a data stack module, and an extended state observer obtains system state estimation and aggregate disturbance estimation by utilizing the data in the stack updated by a data driving learning rule module. The technical scheme of the invention solves the disturbance estimation problem of the first-order nonlinear system with unknown internal uncertainty, external disturbance and unknown input gain, and realizes simultaneous estimation of the total disturbance of the system and the control input gain.

Description

Data-driven extended state observer
Technical Field
The invention relates to the technical field of design of an extended state observer, in particular to a data-driven extended state observer.
Background
Disturbances and uncertainties are common in control systems, and controlling a system containing uncertainties and disturbances is a difficult problem. The prior invention has proposed methods such as robust control, self-adaptive control, disturbance observer-based control, active disturbance rejection control, etc. The active disturbance rejection control method is widely applied to various fields of aircrafts, mobile robots, autonomous water surfaces, underwater aircrafts and the like. The extended state observer is a core unit of the active disturbance rejection control technology, and uniformly estimates the internal uncertainty and external disturbance of the system as the total disturbance of the system.
However, existing methods based on extended state observers generally assume that the system control input gain is known a priori. In order to recognize the system control input gain, a large number of test experiments are required in practice. And even if the input gain is obtained through experiments, the actual value may be changed due to a load difference, a change in control efficiency, or a malfunction of the actuator. It is therefore worthwhile to estimate the unknown input gain and the total disturbance of the system simultaneously. Existing methods of processing unknown input gains include knowledgeable functions and adaptive parameter estimation.
A knowledgeable function is often used to address control issues with unknown magnitude and direction of control input gain. The adaptive parameter estimation method is to estimate the input gain by adopting an adaptive parameter projection method with a given boundary, but the input gain estimation cannot guarantee convergence to a true value. Neither of these methods can accurately estimate the control input gain, especially in cases where the internal dynamics and external disturbances are unknown. The prior invention method deduces a data-driven second-order extended state observer based on pseudo-jacobian matrix estimation, and is used for estimating model approximation errors. However, no history data is used in the estimation process, and the use of history data contributes to improvement of estimation performance. In summary, the prior art has the following disadvantages:
(1) The existing extended state observer is established by requiring the input gain of the system to be known a priori, however, the model parameter identification process is complex, which is not beneficial to engineering implementation.
(2) The existing self-adaptive estimation method can only utilize current data, and can not ensure convergence to a true value, and the convergence time is long.
(3) The existing active disturbance rejection control law needs actual or nominal control input gain, cannot completely get rid of dependence on model parameters, control performance depends on the accuracy of the model, and when the input gain changes greatly, the control performance is reduced.
Disclosure of Invention
According to the disturbance estimation problem of the first-order nonlinear system with unknown internal uncertainty, external disturbance and unknown input gain, the invention provides a data-driven extended state observer, which realizes simultaneous estimation of the total disturbance and the control input gain of the system.
The invention adopts the following technical means:
a data-driven extended state observer, comprising: the system comprises an active disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data driving learning law module and a first-order filter; wherein:
the input end of the active disturbance rejection controller is connected with a given speed reference signal, an extended state observer and a data driving learning law module, and the output end of the active disturbance rejection controller is connected with a first-order nonlinear system;
the input end of the first-order nonlinear system is connected with the active disturbance rejection controller, and the output end of the first-order nonlinear system is connected with the first-order filter;
the input end of the first-order filter is connected with the first-order nonlinear system, the extended state observer and the active disturbance rejection observer, and the output end of the first-order filter is connected with the data stack module;
the input end of the data stack module is connected with the first-order filter, and the output end of the data stack module is connected with the data driving learning law module;
the input end of the data driving learning law module is connected with the data stack module, and the output end of the data driving learning law module is connected with the extended state observer and the active disturbance rejection observer;
the input end of the extended state observer is connected with the data driving learning law module, the first-order filter module and the first-order nonlinear system, and the output end of the extended state observer is connected with the active disturbance rejection controller.
Further, the design process of the active disturbance rejection controller is as follows:
definition of tracking error
Figure BDA0004042053080000031
The active disturbance rejection controller based on the data driving extended state observer is designed as follows:
Figure BDA0004042053080000032
wherein ,kc Gain for the controller;
Figure BDA0004042053080000033
further, the first-order nonlinear system is specifically expressed as:
Figure BDA0004042053080000034
wherein ,
Figure BDA0004042053080000035
representing a system state; />
Figure BDA0004042053080000036
Representing an unknown nonlinear function; />
Figure BDA0004042053080000037
Is an unknown external disturbance; />
Figure BDA0004042053080000038
Is unknown input gain and is determined by the system characteristics; />
Figure BDA0004042053080000039
Is a control input.
Further, the first order filter is designed as follows:
Figure BDA00040420530800000310
where a is the filter time constant.
Further, the data stack module is configured to store t k Time-instant filtered data u f (k) And g (k), k=1,..n.
Further, 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:
Figure BDA00040420530800000311
wherein Proj [. Cndot.,)]Representing a projection operator;
Figure BDA00040420530800000312
is the learning gain.
Further, the extended state observer is specifically expressed as:
Figure BDA00040420530800000313
/>
wherein σ=f (x) +w (t) is the total system disturbance;
the extended state observer comprises a reduced order data driven extended state observer and a full order data driven extended state observer, wherein:
the reduced order data driven extended state observer is designed as follows:
Figure BDA0004042053080000041
wherein ,
Figure BDA0004042053080000042
estimating the system state; />
Figure BDA0004042053080000043
Estimating for lumped disturbance; />
Figure BDA0004042053080000044
Estimating for an input gain; kappa is the observed gain;
the full-order data driving extended state observer is designed as follows:
Figure BDA0004042053080000045
compared with the prior art, the invention has the following advantages:
1. compared with the disturbance observer and the extended state observer, which need to be known a priori, the data-driven extended state observer provided by the invention does not require the system input gain to be known, and does not need to carry out complex experiments for identifying model parameters.
2. Compared with the existing self-adaptive estimation method which only uses current data to learn, the data-driven extended state observer provided by the invention uses historical data and current data simultaneously, and improves the parameter convergence speed and the estimation effect.
3. Compared with the existing active disturbance rejection controller based on nominal or actual system parameters, the model-free control law of the data-driven extended state observer provided by the invention does not depend on any model prior parameter, and can adapt to larger input gain change.
For the reasons, the invention can be widely popularized in the fields of the design of the extended state observer and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a schematic diagram of a data driven extended state observer according to the present invention.
Fig. 2 is a schematic structural diagram of a hardware-in-the-loop simulation platform according to an embodiment of the present invention.
Fig. 3 is an output response graph of the unmanned ship according to an embodiment of the present invention.
Fig. 4 is a graph of system lumped disturbance estimation according to an embodiment of the present invention.
Fig. 5 is a system control input graph provided in an embodiment of the present invention.
Fig. 6 is a graph of input gain estimation according to an embodiment of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The invention will be described in detail below with reference to the drawings in connection with embodiments.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of 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, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise. Meanwhile, it should be clear that the dimensions of the respective parts shown in the drawings are not drawn in actual scale for convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail, but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, 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 figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
In the description of the present invention, it should be understood that the azimuth or positional relationships indicated by the azimuth terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal", and "top, bottom", etc., are generally based on the azimuth or positional relationships shown in the drawings, merely to facilitate description of the present invention and simplify the description, and these azimuth terms do not indicate and imply that the apparatus or elements referred to must have a specific azimuth or be constructed and operated in a specific azimuth, and thus should not be construed as limiting the scope of protection of the present invention: the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition, the terms "first", "second", etc. are used to define the components, and are only for convenience of distinguishing the corresponding components, and the terms have no special meaning unless otherwise stated, and therefore should not be construed as limiting the scope of the present invention.
As shown in fig. 1, the present invention provides a data-driven extended state observer including: the system comprises an active disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data driving learning law module and a first-order filter; wherein:
the input end of the active disturbance rejection controller is connected with a given speed reference signal, an extended state observer and a data driving learning law module, and the output end of the active disturbance rejection controller is connected with a first-order nonlinear system;
the input end of the first-order nonlinear system is connected with the active disturbance rejection controller, and the output end of the first-order nonlinear system is connected with the first-order filter;
the input end of the first-order filter is connected with the first-order nonlinear system, the extended state observer and the active disturbance rejection observer, and the output end of the first-order filter is connected with the data stack module;
the input end of the data stack module is connected with the first-order filter, and the output end of the data stack module is connected with the data driving learning law module;
the input end of the data driving learning law module is connected with the data stack module, and the output end of the data driving learning law module is connected with the extended state observer and the active disturbance rejection observer;
the input end of the extended state observer is connected with the data driving learning law module, the first-order filter module and the first-order nonlinear system, and the output end of the extended state observer is connected with the active disturbance rejection controller.
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 external disturbance act on the unmanned ship system at the same time, the unmanned ship state information, the output response and the data which pass through the first order filter are stored in the data stack module, and the extended state observer obtains the system state estimation and the aggregate disturbance estimation by using the data in the stack updated by the data driving learning rule module.
In specific implementation, as a preferred embodiment of the present invention, the design process of the active disturbance rejection controller is as follows:
definition of tracking error
Figure BDA0004042053080000071
The active disturbance rejection controller based on the data driving extended state observer is designed as follows:
Figure BDA0004042053080000072
wherein ,kc Gain for the controller;
Figure BDA0004042053080000073
in specific implementation, as a preferred embodiment of the present invention, the first-order nonlinear system is specifically expressed as:
Figure BDA0004042053080000074
wherein ,
Figure BDA0004042053080000075
representing a system state; />
Figure BDA0004042053080000076
Representing an unknown nonlinear function; />
Figure BDA0004042053080000077
Is an unknown external disturbance; />
Figure BDA0004042053080000078
Is unknown input gain and is determined by the system characteristics; />
Figure BDA0004042053080000079
Is a control input.
In specific implementation, as a preferred embodiment of the present invention, the first order filter is designed as follows:
Figure BDA0004042053080000081
where a is the filter time constant.
In the specific embodiment, the present invention is preferably embodied asIn this way, the data stack module is configured to store t k Time-instant filtered data u f (k) And g (k), k=1,..n.
In specific implementation, as a preferred embodiment 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:
Figure BDA0004042053080000082
wherein Proj [. Cndot.,)]Representing a projection operator;
Figure BDA0004042053080000083
is the learning gain. />
In specific implementation, as a preferred embodiment of the present invention, the extended state observer is specifically expressed as:
Figure BDA0004042053080000084
wherein σ=f (x) +w (t) is the total system disturbance;
the extended state observer comprises a reduced order data driven extended state observer and a full order data driven extended state observer, wherein:
the reduced order data driven extended state observer is designed as follows:
Figure BDA0004042053080000085
wherein ,
Figure BDA0004042053080000086
estimating the system state; />
Figure BDA0004042053080000087
Estimating for lumped disturbance; />
Figure BDA0004042053080000088
Estimating for an input gain; kappa is the observed gain;
the full-order data driving extended state observer is designed as follows:
Figure BDA0004042053080000089
examples
In order to verify the control performance of the proposed data-driven extended state observer, the method is applied to unmanned ship speed tracking and hardware-in-the-loop simulation is performed. The experimental platform comprises a remote control station and an embedded controller arranged in the unmanned ship. The remote control station is communicated with the unmanned ship through a Zigbee network, and the singlechip is connected with the inertial measurement unit and the global navigation satellite system (GPS) to acquire position information, speed information and attitude information. The remote control station can realize that the status information, in particular the track information, of the unmanned ship is displayed on the map. The unmanned ship system model is as follows:
Figure BDA0004042053080000091
wherein ,
Figure BDA0004042053080000092
is the surge speed; />
Figure BDA0004042053080000093
Is the control force; />
Figure BDA0004042053080000094
To control input coefficients; x is X 1 u+X 2 u|u| is the unknown internal dynamics related to hydrodynamic damping forces; />
Figure BDA0004042053080000095
and />
Figure BDA0004042053080000096
Is a hydrodynamic parameter; />
Figure BDA0004042053080000097
For an inertia term related to the mass of the unmanned ship, < ->
Figure BDA0004042053080000098
Is an external disturbance. />
Figure BDA0004042053080000099
b 0 =b/m represents the unknown input gain; sigma (u) =b 0 X 1 u+b 0 X 2 u|u|+b 0 w represents the lumped disturbance. Control input gain b 0 Can be determined by system mass, propeller drive efficiency and drive motor parameters. In the present embodiment, b 0 May vary due to load variations or reduced thrust efficiency.
In this embodiment, specific parameters of the model designed by the present invention are as follows:
when hardware is in ring simulation, model parameters in the unmanned ship are as follows: m is m 11 =12.5 kg, X 1 ＝-0.8327，X 2 ＝-1.513，b＝1，ω＝0.1sin(t)cos(t 2 ) The controller parameter is selected to be k c =1.5, κ=8, a=100. To test the learning ability of the data-driven extended state observer provided by the invention to control the input gain variation, the parameter is changed to m at 60 seconds 11 ＝14。
The simulation results are shown in fig. 3-5. Fig. 3 shows the output response of the unmanned ship, and it can be seen that the anti-interference control law provided by the invention can track a given signal under the conditions of uncertain model, external interference and unknown control input gain. Fig. 4 is a system lumped disturbance estimation, and fig. 5 is a system control input, it can be seen that the lumped disturbance can be accurately estimated in the case that the control input gain is unknown. Fig. 6 shows the estimated input gain of the data driven extended state observer, the solid line is the unknown input gain, the broken line is the unknown input gain, and it can be seen that the unknown input gain changes at 60 seconds, but the data driven extended state observer provided by the invention can adapt to the change by recording new data, and the output performance is not affected in the control process, and the control input gain can be estimated by the data driven extended state observer.
The simulation result graph shows that the data-driven extended state observer has the remarkable characteristics of synchronously estimating the unknown input gain and the aggregate disturbance and ensuring the convergence of the estimation.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.

Claims (7)

1. A data-driven extended state observer, comprising: the system comprises an active disturbance rejection controller, a first-order nonlinear system, an extended state observer, a data stack module, a data driving learning law module and a first-order filter; wherein:
the input end of the active disturbance rejection controller is connected with a given speed reference signal, an extended state observer and a data driving learning law module, and the output end of the active disturbance rejection controller is connected with a first-order nonlinear system;
the input end of the first-order nonlinear system is connected with the active disturbance rejection controller, and the output end of the first-order nonlinear system is connected with the first-order filter;
the input end of the first-order filter is connected with the first-order nonlinear system, the extended state observer and the active disturbance rejection observer, and the output end of the first-order filter is connected with the data stack module;
the input end of the data stack module is connected with the first-order filter, and the output end of the data stack module is connected with the data driving learning law module;
the input end of the data driving learning law module is connected with the data stack module, and the output end of the data driving learning law module is connected with the extended state observer and the active disturbance rejection observer;
the input end of the extended state observer is connected with the data driving learning law module, the first-order filter module and the first-order nonlinear system, and the output end of the extended state observer is connected with 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:
definition of tracking error
Figure FDA0004042053070000011
The active disturbance rejection controller based on the data driving extended state observer is designed as follows:
Figure FDA0004042053070000012
wherein ,kc Gain for the controller;
Figure FDA0004042053070000013
3. the data driven extended state observer according to claim 1, wherein the first order nonlinear system is specifically represented as:
Figure FDA0004042053070000014
wherein ,
Figure FDA0004042053070000015
representing a system state; />
Figure FDA0004042053070000016
Representing an unknown nonlinear function; />
Figure FDA0004042053070000017
Is an unknown external disturbance;
Figure FDA0004042053070000018
is unknown input gain and is determined by the system characteristics; />
Figure FDA0004042053070000019
Is a control input.
4. The data driven extended state observer according to claim 1, wherein the first order filter is designed as follows:
Figure FDA0004042053070000021
where a is the filter time constant.
5. The data driven extended state observer according to claim 1, wherein the data stack module is configured to store t k Time-instant filtered data u f (k) And g (k), k=1,..n.
6. The data driven extended state observer of claim 1, wherein the design of the data driven learning law module is based on data recorded in a data stack, the data driven learning law design being as follows:
Figure FDA0004042053070000022
wherein Proj [. Cndot.,)]Representing a projection operator;
Figure FDA0004042053070000023
is the learning gain.
7. The data driven extended state observer according to claim 1, wherein the extended state observer is specifically represented as:
Figure FDA0004042053070000024
wherein σ=f (x) +w (t) is the total system disturbance;
the extended state observer comprises a reduced order data driven extended state observer and a full order data driven extended state observer, wherein:
the reduced order data driven extended state observer is designed as follows:
Figure FDA0004042053070000025
wherein ,
Figure FDA0004042053070000026
estimating the system state; />
Figure FDA0004042053070000027
Estimating for lumped disturbance; />
Figure FDA0004042053070000028
Estimating for an input gain; kappa is the observed gain;
the full-order data driving extended state observer is designed as follows:
Figure FDA0004042053070000029
/>
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