CN110687800B - Data-driven self-adaptive anti-interference controller and estimation method thereof - Google Patents
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Abstract
The invention discloses a data-driven self-adaptive anti-interference controller and an estimation method thereof. The input controller of the invention only needs to control the parameters output by the gain estimation module
And the gain parameter b is not required to be controlled, and when the control gain of the second-order nonlinear system is unknown, the simultaneous online estimation of the uncertainty and the control gain of the second-order nonlinear system is realized. The invention realizes the on-line estimation of the control gain of the second-order nonlinear system in a limited time by establishing the control gain estimation module. The invention tracks errors by introducing a state tracking error signal xeThe method and the device realize effective tracking of the expected state, make the control state converge to the expected state, effectively ensure the parameter estimation accuracy and realize accurate control of a second-order nonlinear system.
Description
Technical Field
The invention relates to the field of self-adaptive control, in particular to a data-driven self-adaptive anti-interference controller and an estimation method thereof.
Background
The control is to control the controlled object with an appropriate control force, the purpose of which is to make its movement vary in a desired manner, i.e. according to a given target trajectory or set value, also under the effect of various disturbances. For a controlled object, an error exists between the expected behavior and the actual behavior, and how to eliminate the error is a core problem of the research of the control theory. In the past, controller errors have often been eliminated using PID (proportional, integral, derivative) controllers based on error control, which is a weighted sum of "past, present state and future trend of change" of the error. The PID controller is popular in the industrial field due to the advantages of simple structure, wide application range, strong robustness and the like. However, the PID controller also has the disadvantages of frequent gain change in the closed-loop system, contradiction between rapidity and overshoot, difficulty in obtaining differential signals, and insignificant suppression of time-varying disturbance of integral feedback, which limits the control capability of the PID controller.
In recent years, with the development of modern control theory, the disturbance action affecting the controlled input is expanded into a new state variable, and the expanded state is observed by establishing a special feedback mechanism, and the method is called an expanded state observer. The control method based on the extended state observer does not depend on a specific mathematical model for generating the disturbance, does not need to directly measure the action of the disturbance, and is a universal and practical disturbance observer in a certain sense. However, the following problems still exist in the existing control method based on the extended state observer:
firstly, in the existing method of the adaptive anti-interference controller based on the extended state observer, control gain is needed when a control signal is designed, and when the control gain of the nonlinear system is unknown and the control gain is not easy to obtain, an effective control signal cannot be output, and the design of control input of the controller cannot be completed.
Secondly, in the existing method of the adaptive anti-interference controller based on the extended state observer, the system only depends on external control input, the effective tracking of the expected state cannot be realized, and the convergence of the actual state to the expected state cannot be ensured. Meanwhile, the method cannot adapt to the change of the state parameters within a limited time, and cannot effectively ensure the real-time performance of the nonlinear system.
Third, in existing methods for adaptive immunity controllers based on extended state observers, only the uncertainty of the system can be estimated, and the control input gain of the system cannot be estimated at the same time. The important parameters reflecting the size of the control input of the system are reflected when the gain is controlled, and the uncertainty and the control gain of the nonlinear system are simultaneously estimated, so that the parameters required by the whole system are fewer, and the method can adapt to more complex working conditions.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to design a data-driven adaptive anti-interference controller structure and an estimation method thereof, wherein the data-driven adaptive anti-interference controller structure can control an unknown second-order nonlinear system and can carry out online estimation on uncertainty and control gain of the unknown second-order nonlinear system.
In order to achieve the purpose, the technical scheme of the invention is as follows: a data-driven self-adaptive anti-interference controller comprises an input controller, an extended state observer, a control gain estimation module and a second-order nonlinear system, wherein the second-order nonlinear system is a second-order nonlinear system with unknown control gain, and the input end of the input controller is respectively connected with the output end of the second-order nonlinear system, the output end of the control gain estimation module and an external expected parameter; the input end of the extended state observer is respectively connected with the output end of the input controller and the output end of the second-order nonlinear system; the input end of the control gain estimation module is respectively connected with the output end of the input controller, the output end of the second-order nonlinear system and the output end of the extended state observer; and the input end of the second-order nonlinear system is connected with the output end of the input controller.
A method for estimating a data-driven adaptive anti-interference controller comprises the following steps:
A. establishing a second-order nonlinear system with unknown control gain
The second order nonlinear system is described by:
in the formula, x1Representing the first-order state, x, of a second-order nonlinear system2Representing a second order state of a second order nonlinear system;
respectively representing the first and second stages of a second-order nonlinear systemState x1、x2U represents the control input of the second-order nonlinear system, b represents the control gain to be measured of the second-order nonlinear system, f (x)1,x2And t) represents the uncertainty of the second order nonlinear system, wherein t represents the time of change of the second order nonlinear system.
B. Establishing an input controller
Introducing a state tracking error signal:
xe＝x1-x1d (2)
wherein x1dFirst order state x representing a second order nonlinear system1Expected state of (a), xeIndicating a state tracking error.
The output signals of the input controller are:
wherein
An observed value representing the control gain to be measured,
represents the expected state x of the system1dFirst derivative of (k)1Scalar gain, k, representing the rate of convergence of the tracking error of the regulation state2A scalar gain representing the rate of convergence of the adjustment error,
and an observed value representing the output signal after the extended state of the extended state observer is established.
C. Establishing extended state observer
The extended state observer expands the disturbance action influencing the controlled output into a new state variable, and a feedback mechanism is used for establishing the state capable of observing the expansion, so that the influence of disturbance is eliminated.
The dilated state observer is described by equation (4):
wherein the content of the first and second substances,
first order state x representing a second order nonlinear system1Is detected by the measured values of (a) and (b),
second order state x representing a second order nonlinear system2Of the observed value of alpha1Indicating accommodation of the expanded state
Gain parameter of alpha2Indicating accommodation of the expanded state
Gain parameter of alpha3Representing a gain parameter for adjusting the dilated state output signal epsilon.
D. Establishing control gain estimation module
First, the second order nonlinearity is systemized as the following differential equation:
wherein the content of the first and second substances,
second order state x representing a second order nonlinear system2The first derivative of (a).
To represent
Initial state of (1), x2(0) Denotes x2The initial state of (1).
Then, the above equations are input to the filter 1 and the filter 2, respectively, to obtain:
G＝bM (6)
where G denotes the state derivatives of filter 1 and filter 2 and M denotes the filtered regression matrix.
Establishing a storage stack
Wherein G (k) and M (k) respectively represent G and M at tkThe data stored in the stack is timed, and N is a positive integer representing the length of the stack.
Using the data stored by stack S, equation (6) is transformed into the following matrix form:
(G (1), G (2), … G (k)), (b × [ M (1), M (2), … M (k)) ] (7) and finally, an online estimation equation of the control gain parameter b to be measured of the second-order nonlinear system is established:
wherein, gamma is1＞0,Γ2> 0 are two scalar gains used to adjust convergence speed.
Compared with the prior art, the invention has the following beneficial effects:
first, compared with the existing method of adaptive anti-interference controller based on extended state observer, the input controller of the invention only needs to control the parameters output by the gain estimation module
And the gain parameter b does not need to be controlled, and when the control gain of the second-order nonlinear system is unknown, the simultaneous online estimation of the uncertainty and the control gain of the second-order nonlinear system is realized.
Secondly, compared with the existing method of the self-adaptive anti-interference controller based on the extended state observer, the method provided by the invention can realize online estimation of the control gain of the second-order nonlinear system within a limited time by establishing the control gain estimation module.
Thirdly, compared with the existing method of the adaptive anti-interference controller based on the extended state observer, the method introduces a state tracking error signal xeThe method and the device realize effective tracking of the expected state, make the control state converge to the expected state, effectively ensure the parameter estimation accuracy and realize accurate control of a second-order nonlinear system.
Fourthly, compared with the existing method of the self-adaptive anti-interference controller based on the extended state observer, the method disclosed by the invention is used for carrying out online estimation on unknown parameters only based on the expected state information of a second-order nonlinear system, adopts a parallel learning method, and utilizes the stored data to realize online estimation on the parameters b.
Drawings
The invention is shown in the attached figure 5, wherein:
FIG. 1 is a schematic diagram of a data-driven adaptive immunity controller and method.
FIG. 2 is a first stage state x of a second order nonlinear system1And its expected state x1dAnd (5) observing an effect graph.
FIG. 3 is a second-order state x of a second-order nonlinear system2And (5) observing an effect graph.
Fig. 4 is a diagram showing the observation effect of the output signal epsilon after the second-order nonlinear system expansion state.
Fig. 5 is a graph of the observed effect of the control gain b of the second-order nonlinear system.
Detailed Description
The invention will be further described with reference to the accompanying drawings. The design of the data-driven adaptive anti-interference controller and the method related by the invention is shown in figure 1. The input controller tracks the first stage state x of the second order nonlinear system1And the expected state x1dError x ofeTo converge and output a control signal u to the second-order nonlinear system. Establishing an extended state observer to convert the first and second states x of a second-order nonlinear system into a first and second-order states x1、x2Output is as
And observed value of output signal after expansion state
And establishing a stack S for storing data, storing the state derivative after passing through the filter and the data of the regression matrix in the stack S, and outputting the estimated control gain b through the control gain estimation module. The aim of the invention is to enable a second-order nonlinear system to complete the control of the second-order nonlinear system and the accurate estimation of its uncertainty f (-) and control gain b while satisfying equations (2) - (8).
The simulation results are shown in fig. 2-5. FIG. 2 shows the first stage state x of a second order nonlinear system1And its expected state x1dObservation of the effects, FIG. 3 shows the second-order state x of a second-order nonlinear system2And (3) observing the effect, wherein fig. 4 shows the observation effect of the output signal epsilon after the second-order nonlinear system is in the expansion state, and fig. 5 shows the observation effect of the control gain b of the second-order nonlinear system. As can be seen from the simulation result diagram, the observed parameters are converged with the actual parameters, that is, the first-stage state x traced by the invention1And the expected state x1dError x ofeThe method realizes the accurate control of the second-order nonlinear system, and the uncertainty f (x) of the second-order nonlinear system1,x2T) and control gain b enable simultaneous estimation.
The present invention is not limited to the embodiment, and any equivalent idea or change within the technical scope of the present invention is to be regarded as the protection scope of the present invention.
Claims (2)
1. A data-driven adaptive anti-interference controller is characterized in that: the system comprises an input controller, an extended state observer, a control gain estimation module and a second-order nonlinear system, wherein the second-order nonlinear system is a second-order nonlinear system with unknown control gain, and the input end of the input controller is respectively connected with the output end of the second-order nonlinear system, the output end of the control gain estimation module and an external expected parameter; the input end of the extended state observer is respectively connected with the output end of the input controller and the output end of the second-order nonlinear system; the input end of the control gain estimation module is respectively connected with the output end of the input controller, the output end of the second-order nonlinear system and the output end of the extended state observer; the input end of the second-order nonlinear system is connected with the output end of the input controller;
the second order nonlinear system is expressed as the following formula:
wherein x is1Representing the first-order state, x, of a second-order nonlinear system2Representing a second order state of a second order nonlinear system;
respectively representing the first and second-order states x of a second-order nonlinear system1、x2U represents the control input of the second-order nonlinear system, b represents the control gain to be measured of the second-order nonlinear system, f (x)1,x2T) represents the uncertainty of the second order nonlinear system, where t represents the time of change of the second order nonlinear system;
the input controller is expressed as the following formula:
wherein the content of the first and second substances,
an observed value representing the control gain to be measured,
represents the expected state x of the system1dToDerivative of order, k1Scalar gain, k, representing the rate of convergence of the tracking error of the regulation state2A scalar gain representing the rate of convergence of the adjustment error,
an observed value representing the output signal after the established extended state observer is extended in state;
the extended state observer is represented by the following formula:
wherein the content of the first and second substances,
first order state x representing a second order nonlinear system1Is measured in a time-domain manner by a time-domain,
second order state x representing a second order nonlinear system2Of the observed value of alpha1Indicating accommodation of the expanded state
Gain parameter of alpha2Indicating accommodation of the expanded state
Gain parameter of alpha3A gain parameter indicative of an adjustment of the dilated state output signal epsilon;
the control gain estimation module is represented in the form:
wherein, gamma is1＞0,Γ2> 0 are two scalar gains for adjusting convergence speed; g meterThe state derivatives of filter 1 and filter 2 are shown, and M represents the filtered regression matrix; n represents the length of the stack and takes a positive integer; k is 1,2, …, and N is a data recording time node; g (k) and M (k) denote G and M at t, respectivelykThe data stored in the stack at the time.
2. An estimation method of a data-driven adaptive anti-interference controller is characterized by comprising the following steps: the method comprises the following steps:
A. establishing a second-order nonlinear system with unknown control gain
The second order nonlinear system is described by:
in the formula, x1Representing the first-order state, x, of a second-order nonlinear system2Representing a second order state of a second order nonlinear system;
respectively representing the first and second states x of a second-order nonlinear system1、x2U represents the control input of the second-order nonlinear system, b represents the control gain to be measured of the second-order nonlinear system, f (x)1,x2T) represents the uncertainty of the second order nonlinear system, where t represents the time of change of the second order nonlinear system;
B. establishing an input controller
Introducing a state tracking error signal:
xe＝x1-x1d (2)
wherein x1dFirst order state x representing a second order nonlinear system1Expected state of (a), xeIndicating a state tracking error;
the output signals of the input controller are:
wherein
An observed value representing the control gain to be measured,
represents the expected state x of the system1dFirst derivative of (k)1Scalar gain, k, representing the rate of convergence of the tracking error of the regulation state2A scalar gain representing the rate of convergence of the adjustment error,
an observed value representing the output signal after the established extended state observer is extended in state;
C. establishing extended state observer
The extended state observer expands the disturbance effect influencing the controlled output into a new state variable, and a feedback mechanism is used for establishing a state capable of observing the expansion, so that the influence of disturbance is eliminated;
the dilated state observer is described by equation (4):
wherein the content of the first and second substances,
first order state x representing a second order nonlinear system1Is detected by the measured values of (a) and (b),
second order state x representing a second order nonlinear system2Of the observed value of alpha1Indicating accommodation of the expanded state
Gain parameter of alpha2Indicating accommodation of the expanded state
Gain parameter of alpha3A gain parameter indicative of an adjustment of the dilated state output signal epsilon;
D. establishing control gain estimation module
First, the second order nonlinearity is systemized as the following differential equation:
wherein the content of the first and second substances,
second order state x representing a second order nonlinear system2The first derivative of (a);
to represent
Initial state of (1), x2(0) Denotes x2The initial state of (a);
then, the above equations are input to the filter 1 and the filter 2, respectively, to obtain:
G＝bM (6)
where G represents the state derivatives of filter 1 and filter 2, and M represents the filtered regression matrix;
establishing a storage stack
Wherein G (k) and M (k) respectively represent G and M at tkThe data stored in the stack at any moment, N is a positive integer and represents the length of the stack;
using the data stored in stack S, equation (6) is transformed into the following matrix form:
[G(1),G(2),…G(k)]＝b×[M(1),M(2),…M(k)] (7)
and finally, establishing an online estimation equation of the to-be-detected control gain parameter b of the second-order nonlinear system:
wherein, gamma is1＞0,Γ2> 0 are two scalar gains used to adjust convergence speed.
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| CN111208734B (en) * | 2020-02-18 | 2022-05-31 | 大连海事大学 | Data drive anti-interference control structure for controlling gain-unknown uncertain system |
| CN111352344B (en) * | 2020-02-28 | 2022-05-31 | 大连海事大学 | Data-driven self-adaptive predictor of dynamic completely unknown system |
| CN111258215B (en) * | 2020-03-13 | 2022-05-31 | 大连海事大学 | Data driving controller of model unknown system |
| CN113467247B (en) * | 2021-07-21 | 2023-06-30 | 中国北方车辆研究所 | Design method of federal expanded state observer |
| CN114383879A (en) * | 2022-01-11 | 2022-04-22 | 安胜（天津）飞行模拟系统有限公司 | Test method of second order differential loop in flight simulator identification test guidance system |
| CN114755917A (en) * | 2022-03-18 | 2022-07-15 | 大连海事大学 | Model-free self-adaptive anti-interference ship speed controller and design method |
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