CN110967975A - Self-adaptive extended state observer structure - Google Patents

Self-adaptive extended state observer structure Download PDF

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CN110967975A
CN110967975A CN201911287504.5A CN201911287504A CN110967975A CN 110967975 A CN110967975 A CN 110967975A CN 201911287504 A CN201911287504 A CN 201911287504A CN 110967975 A CN110967975 A CN 110967975A
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CN110967975B (en
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刘陆
古楠
阮明昊
王丹
李铁山
彭周华
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Dalian Maritime University
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention provides a self-adaptive extended state observer structure, which is applied to a complex uncertain nonlinear system and comprises the following steps: the device comprises a robust adaptive observer module, a filter module, a data storage module, a control input gain calculation module, an adaptive rate module and a time judgment module. The invention combines the self-adaptive method with the extended state observer, has the characteristics of high precision, high benefit and strong environmental adaptability, and can realize accurate estimation of control input gain, effective estimation of unknown uncertainty and convergence of state parameters.

Description

Self-adaptive extended state observer structure
Technical Field
The invention relates to the field of nonlinear system parameter estimation and disturbance observation, in particular to a self-adaptive extended state observer structure.
Background
Various disturbances and uncertainty factors are prevalent in practical non-linear systems and can negatively impact various performance of the control system. Meanwhile, control parameters of the system cannot be easily measured and obtained, and the control precision is influenced by the external complex and changeable environment. Therefore, the observation of non-linear system parameters and uncertainty estimates is an important issue in the field of control theory.
Modern control theories include adaptive control, fuzzy control, robust control, optimal control, and the like. Corresponding research results have been obtained at home and abroad in the aspect of nonlinear system control. W.Y.Wang provides a stable adaptive fuzzy backstepping recursion design technology for the first time aiming at a strict feedback uncertain nonlinear system with single input and single output and constant virtual control gain based on a backstepping recursion design technology in the nonlinear system and in combination with a fuzzy adaptive control method, and solves the problem that uncertainty in a controlled system is necessarily the limit of linear parameters. Simone applies the optimization problem of reducing probability uncertainty set in the optimization theory to the field of system control, adjusts and determines the probability of a concentrated objective function through uncertainty factors, and realizes the control system design with adjustable robustness. Ye provides a global robust self-adaptive control method of an unknown control uncertainty system, and can be expanded to any system. An Active Disturbance Rejection Controller (ADRC) does not need an accurate model of a control system during control, but refers to the internal disturbance and the non-measurable external disturbance action of the model as the total disturbance of the system, estimates and compensates parameters by calculating input and output data of a control object, and has high reliability and convenience. The idea of an Extended State Observer (ESO), which is a core component of ADRC and is one more step than the conventional observer, is to extend the disturbance action that can affect the controlled output into new state variables, where the extended new state variables are used to estimate the uncertainty affecting the system as well as external disturbances.
The control analysis of the nonlinear system has attracted the attention of a plurality of control theory and control engineering researchers in the past, and scholars at home and abroad have obtained a series of research results. However, from the aspects of the convergence of parameters and estimation effect of the nonlinear system, the current technology still has the following problems:
although the existing extended state observer can estimate the unknown uncertainty of the nonlinear system, it needs to assume that the control parameters of the nonlinear system are known, but the control parameters of the complex uncertain nonlinear system are difficult to obtain, so that the method is limited in practical application.
Although the existing adaptive method can realize the estimation of the control input gain, the estimation of unknown uncertainty can not be realized in the face of a large amount of disturbance in a complex uncertain nonlinear system, so that the stability of the system can not be guaranteed.
Although the existing adaptive method can realize the estimation of the control input gain by designing the adaptive rate, the parameter can not be ensured to be converged to the true value. The complicated uncertain nonlinear system can cause poor control effect when lacking accurate control parameters.
Disclosure of Invention
According to the technical problems that control parameters of the existing extended state observer are difficult to obtain and system performance is unstable, the invention provides the structure of the self-adaptive extended state observer, and the self-adaptive extended state observer combines a self-adaptive method with the extended state observer, has the characteristics of high precision, high benefit and strong environmental adaptability, and can realize accurate estimation of control input gain, effective estimation of unknown uncertainty and convergence of state parameters.
The technical means adopted by the invention are as follows:
an adaptive extended state observer structure applied to a complex uncertain nonlinear system, comprising: the system comprises a robust adaptive observer module, a filter module, a data storage module, a control input gain calculation module, an adaptive rate module and a time judgment module; wherein the content of the first and second substances,
accurate estimation of the input and control inputs u, the nonlinear system state x, and the control input gain of the robust adaptive observer module
Figure BDA0002318446330000021
Connected, the output of the robust adaptive observer module and the unknown uncertainty estimate
Figure BDA0002318446330000022
Connecting;
input of the filter module and nonlinear system state x, control input u, unknown uncertainty estimation
Figure BDA0002318446330000023
The output end of the filter module is connected with the filtered regression matrix H and the filtered state derivative f;
the input end of the data storage module is connected with the output end of the filter module, and the output end of the data storage module is connected with the regression quantities M (t) and G (t) after integral filtering;
the input end of the control input gain calculation module is connected with the integral filtered regressions M (t) and G (t), and the output end of the control input gain calculation module is connected with the calculation estimation of the control input gain
Figure BDA0002318446330000031
Connecting;
input and control input gain calculation estimates for the adaptive rate module
Figure BDA0002318446330000032
Integrating the filtered regressions M (t) and G (t), filtering regression matrix H and filter state derivative f, the output end of the adaptive rate module is connected with the control input gain estimation obtained by adaptive rate
Figure BDA0002318446330000033
Connecting;
calculation estimation of input end and control input gain of the time judgment module
Figure BDA0002318446330000034
Control input gain estimation from adaptation rate
Figure BDA0002318446330000035
And time t, the output end of the time judgment module is connected with the accurate estimation of the control input gain
Figure BDA0002318446330000036
Are connected.
Compared with the prior art, the invention has the following advantages:
first, the control method based on the adaptive extended state observer provided by the invention is directed at a complex uncertain nonlinear system with unknown control parameters, not only realizes estimation of unknown uncertainty, but also can estimate unknown control input gain parameters. The method solves the problem that the unknown uncertainty of the nonlinear system can be estimated only by assuming that the control parameters are known in the existing extended state observer method.
Secondly, the control method based on the self-adaptive extended state observer not only can estimate the control input gain parameter, but also realizes the unknown uncertainty estimation of the nonlinear system. The method solves the problem that the unknown uncertainty of the nonlinear system cannot be estimated although the parameter estimation of the control input gain can be realized by the existing control method based on the parameter self-adaptation.
Thirdly, the adaptive extended state observer provided by the invention can ensure that the estimated value of the control parameter is converged to the true value, and the estimation precision of the control input gain is obviously improved. The method solves the problem that the convergence of the parameters cannot be ensured although the control parameter estimation can be realized by the existing control method based on the parameter self-adaptation.
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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 needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic structural diagram of an adaptive extended state observer system according to the present invention.
FIG. 2 is a diagram illustrating the observation effect of the control state x of the nonlinear system of the present invention.
FIG. 3 is a graph of the observed effect of unknown uncertainty σ for the nonlinear system of the present invention.
FIG. 4 shows the control gain b of the nonlinear system of the present invention0The observation effect map of (1).
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
As shown in FIG. 1, the present invention provides a method for manufacturing a semiconductor device
The invention combines an adaptive method with an extended state observer, provides an adaptive extended state observer structure with high precision, high benefit and strong environmental adaptability and a design method thereof, and realizes accurate estimation of control input gain, effective estimation of unknown uncertainty and convergence of state parameters.
In order to achieve the purpose, the technical scheme of the invention is as follows: the state equation of a complex uncertain nonlinear system is described as:
Figure BDA0002318446330000041
the input end of the complex uncertain nonlinear system is connected with the control input u, and the output end of the complex uncertain nonlinear system is connected with the nonlinear system state x. F (x, t) in the equation of state represents the unknown uncertainty function, and is the control input b0The gain of (c).
An architecture of an adaptive extended state observer includes the following modules: the device comprises a robust adaptive observer module, a filter module, a data storage module, a control input gain calculation module, an adaptive rate module and a time judgment module.
Accurate estimation of the input and control inputs u, the nonlinear system state x, and the control input gain of the robust adaptive observer module
Figure BDA0002318446330000042
Connected, said robust adaptationOutput of response observer module and unknown uncertainty estimation
Figure BDA0002318446330000043
Are connected. Input of the filter module and nonlinear system state x, control input u, unknown uncertainty estimation
Figure BDA0002318446330000044
And the output end of the filter module is connected with the filtered regression matrix H and the filtered state derivative f. The input end of the data storage module is connected with the output end of the filter module, and the output end of the data storage module is connected with the regression quantities M (t) and G (t) after integral filtering. The input end of the control input gain calculation module is connected with the integral filtered regressions M (t) and G (t), and the output end of the control input gain calculation module is connected with the calculation estimation of the control input gain
Figure BDA0002318446330000051
Are connected. Input and control input gain calculation estimates for the adaptive rate module
Figure BDA0002318446330000052
Integrating the filtered regressions M (t) and G (t), filtering regression matrix H and filter state derivative f, the output end of the adaptive rate module is connected with the control input gain estimation obtained by adaptive rate
Figure BDA0002318446330000053
Are connected. Calculation estimation of input end and control input gain of the time judgment module
Figure BDA0002318446330000054
Control input gain estimation from adaptation rate
Figure BDA0002318446330000055
And time t, the output end of the time judgment module is connected with the accurate estimation of the control input gain
Figure BDA0002318446330000056
Are connected.
The specific functions and structures of the modules are described below
Robust adaptive observer module building
Input end of robust adaptive observer module, control input u and control input gain accurate estimation
Figure BDA0002318446330000057
And the nonlinear system state x is connected, and the robust adaptive observer is designed as follows:
Figure BDA0002318446330000058
unknown uncertainty estimation output by robust adaptive observer module through calculation
Figure BDA0002318446330000059
Connected to the filter module input.
Wherein
Figure BDA00023184463300000510
Represents the estimation of the unknown function f (x, t), i.e. the model internal unknown and external perturbations,
Figure BDA00023184463300000511
which represents the non-linear system state estimate,
Figure BDA00023184463300000512
represents the derivative of the non-linear system state estimate,
Figure BDA00023184463300000513
derivative, k, representing an estimate of unknown uncertainty1∈R3×3And k2∈R3×3And (3) stably introducing parameters for a control system.
Filter module establishment
Input end of filter module and nonlinear system state x, unknown uncertaintySexual estimation
Figure BDA00023184463300000514
And a control input u.
The nonlinear system state x outputs the filter state derivative through a filter module:
Figure BDA00023184463300000515
estimation of unknown uncertainty
Figure BDA00023184463300000516
Outputting the filter state derivative through a low pass filter:
Figure BDA00023184463300000517
the control input u outputs a filtering regression matrix through a low-pass filter:
Figure BDA0002318446330000061
derivative of the filter state f1And f2Obtaining f by a subtracter:
f＝f1-f2(6)
the filter state derivative f and the filter regression matrix H output by the filter module are connected with the input of the data storage module.
Data storage module establishment
The input end of the data storage module is connected with the filtering state derivative f and the regression matrix H after filtering, and the calculation is carried out as follows:
Figure BDA0002318446330000062
the data storage module is connected with the input of the control input gain calculation module and the input of the adaptive rate module through the calculated and output integral filtering regression quantities M (t) and G (t).
H and HTBy multiplication moduleBlock action, and then an integral module is carried out to obtain a regression quantity M (t) after integral filtering,
Figure BDA0002318446330000063
HTf, the regression quantity G (t) is obtained through the action of a multiplication module and an integration module,
Figure BDA0002318446330000064
control input gain calculation Module setup
The input end of the control input gain calculation module is connected with the regression quantities M (t) and G (t) after integral filtering, and the control input gain calculation estimation output by the control input gain calculation module
Figure BDA0002318446330000065
Connected with the input of the self-adaptive rate module and the input of the time judgment module. Said parameters
Figure BDA0002318446330000066
The calculation estimate incorporates the following differential equation:
Figure BDA0002318446330000067
wherein
Figure BDA0002318446330000068
Is an unknown calculation estimation of the control input gain, which is done by referencing the data M (t) and G (t) registered in the data memory
Figure BDA0002318446330000069
And (4) calculating.
Adaptive rate module establishment
Calculating and estimating the input of the adaptive rate module, the regression variables M (t) and G (t) after integral filtering, the derivative f of the filtering state and the control input gain
Figure BDA00023184463300000610
The filtered regression matrix H is connected, and the control input gain estimation obtained by the adaptive rate is output by the adaptive rate module
Figure BDA00023184463300000611
And is connected with the input of the time judgment module.
Introducing an adaptation rate to the control input gain estimate:
Figure BDA0002318446330000071
wherein
Figure BDA0002318446330000072
Is an estimate of the unknown control input gain by the adaptation rate, where k is1∈R3×3And k2∈R3×3Is a design parameter;
time judgment module establishment
Input end and control input gain calculation estimation of time judgment module
Figure BDA0002318446330000073
Control input gain estimation from adaptation rate
Figure BDA0002318446330000074
And time t, the accurate control input gain estimation output by the time judgment module
Figure BDA0002318446330000075
Connected to the robust adaptive observer module input.
To realize the parameter b0Accurate estimation of. Set-up time determination for parameter b0Carrying out online estimation:
Figure BDA0002318446330000076
wherein
Figure BDA0002318446330000077
Is to control the input gain b0Accurate estimation of (c), assuming tupdateFor updating the time, at switch b0T.t.tupdateThe control input gain is updated at times by the adaptation rate, at t > tupdateWhen the temperature of the water is higher than the set temperature,
Figure BDA0002318446330000078
can be obtained by controlling the input gain calculation module.
Examples
An adaptive extended state observer system architecture is shown in FIG. 1. Equation of state for complex uncertain nonlinear systems:
Figure BDA0002318446330000079
the robust adaptive state observer is designed as follows:
Figure BDA00023184463300000710
the control parameters of the robust adaptive state observer are selected as follows: k is a radical of1＝60；k2＝900；
The adaptive rate is designed as follows:
Figure BDA00023184463300000711
the specific parameters of the self-adaptive rate are selected as follows: k is a radical of1＝10；k2＝100；
The design goal of the invention is to make the nonlinear system realize effective estimation of the unknown uncertainty f (-) of the nonlinear system under the condition of satisfying the formulas (1) to (10), and control the input gain b0Accurate estimation of and convergence of control parameters.
Fig. 2 is a diagram of the observed effect of a control state x of a nonlinear system, where x represents the control system state and hatx represents the control system state estimate.
FIG. 3 is a graph of observed effects of an unknown uncertainty σ of a nonlinear system, where sigma represents the unknown uncertainty and hatsigma represents the unknown uncertainty estimate.
FIG. 4 shows the control input gain b of a nonlinear system0B in the figure0Indicating the control input gain, hatb0Representing the control input gain estimate.
Two curves are actually provided in the simulation diagram, and in the local detail diagram in the large diagram, it can be seen that the results of the nonlinear system control state estimation, the unknown uncertainty estimation and the control input gain estimation are relatively good and are generally consistent with the actual value trajectory. As can be seen from the simulation result diagram, the observed parameters and the actual parameters are converged.
Within limited time, the self-adaptive extended state observer designed by the invention can ensure the convergence of the control state of a nonlinear system, the effective estimation of unknown uncertainty, the accurate estimation of control input gain, and the satisfaction of design targets.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. An adaptive extended state observer structure for use in complex uncertain nonlinear systems, comprising: the system comprises a robust adaptive observer module, a filter module, a data storage module, a control input gain calculation module, an adaptive rate module and a time judgment module; wherein the content of the first and second substances,
accurate estimation of the input and control inputs u, the nonlinear system state x, and the control input gain of the robust adaptive observer module
Figure FDA0002318446320000011
Connected, the output of the robust adaptive observer module and the unknown uncertainty estimate
Figure FDA0002318446320000012
Connecting;
input of the filter module and nonlinear system state x, control input u, unknown uncertainty estimation
Figure FDA0002318446320000013
The output end of the filter module is connected with the filtered regression matrix H and the filtered state derivative f;
the input end of the data storage module is connected with the output end of the filter module, and the output end of the data storage module is connected with the regression quantities M (t) and G (t) after integral filtering;
the input end of the control input gain calculation module is connected with the integral filtered regressions M (t) and G (t), and the output end of the control input gain calculation module is connected with the calculation estimation of the control input gain
Figure FDA0002318446320000014
Connecting;
input and control input gain calculation estimates for the adaptive rate module
Figure FDA0002318446320000015
Integrating the filtered regressions M (t) and G (t), filtering regression matrix H and filter state derivative f, the output end of the adaptive rate module is connected with the control input gain estimation obtained by adaptive rate
Figure FDA0002318446320000016
Connecting;
calculation estimation of input end and control input gain of the time judgment module
Figure FDA0002318446320000017
By adaptive rateDerived control input gain estimation
Figure FDA0002318446320000018
And time t, the output end of the time judgment module is connected with the accurate estimation of the control input gain
Figure FDA0002318446320000019
Are connected.
2. The adaptive extended state observer structure of claim 1, wherein the state equation of the complex uncertain nonlinear system is described as:
Figure FDA00023184463200000110
where f (x, t) represents the unknown uncertainty function, b0Is the gain of the control input.
3. The adaptive extended state observer structure of claim 1, wherein the robust adaptive observer module is configured to output an unknown uncertainty estimate from the following calculation
Figure FDA00023184463200000111
Figure FDA00023184463200000112
Wherein
Figure FDA0002318446320000021
Representing the estimation of the unknown function f (x, t),
Figure FDA0002318446320000022
which represents the non-linear system state estimate,
Figure FDA0002318446320000023
represents the derivative of the non-linear system state estimate,
Figure FDA0002318446320000024
derivative, k, representing an estimate of unknown uncertainty1∈R3×3、k2∈R3×3And (3) stably introducing parameters for a control system.
4. The adaptive extended state observer structure of claim 1, wherein the filter module is arranged to compute the output filtered state derivative f and the filtered regression matrix H according to:
the nonlinear system state x outputs the filter state derivative through a filter module:
Figure FDA0002318446320000025
estimation of unknown uncertainty
Figure FDA0002318446320000026
Outputting the filter state derivative through a low pass filter:
Figure FDA0002318446320000027
the control input u outputs a filtering regression matrix through a low-pass filter:
Figure FDA0002318446320000028
derivative of the filter state f1And f2Obtaining f by a subtracter:
f＝f1-f2(6)。
5. the adaptive extended state observer structure of claim 4, wherein the data storage module is arranged to output the integral filtered regressions M (t) and G (t) according to the following calculations:
Figure FDA0002318446320000029
6. the adaptive extended state observer structure of claim 5, wherein the control input gain calculation module is configured to output a control input gain calculation estimate based on calculating
Figure FDA00023184463200000210
Figure FDA00023184463200000211
Wherein
Figure FDA00023184463200000212
Is a calculated estimate of the unknown control input gain.
7. The adaptive extended state observer structure of claim 5, wherein the adaptation rate module is configured to output a control input gain estimate derived from an adaptation rate according to a calculation that outputs a control input gain estimate derived from an adaptation rate
Figure FDA0002318446320000031
Figure FDA0002318446320000032
Wherein
Figure FDA0002318446320000033
Is an estimate of the unknown control input gain by the adaptation rate, where k is1∈R3×3And k2∈R3 ×3Are design parameters.
8. The adaptive extended state observer structure of claim 7, wherein the time determination module is configured to output a fine control input gain estimate based on the following calculation
Figure FDA0002318446320000034
Figure FDA0002318446320000035
Wherein
Figure FDA0002318446320000036
Is to control the input gain b0Accurate estimation of, tupdateWhen t is less than or equal to t for updating timeupdateThe control input gain is updated by the adaptive rate when t > tupdateThe time is obtained by controlling the input gain calculation module.
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