KR101564888B1 - Decentralized fault compensation method and apparatus of large-scale nonlinear systems - Google Patents

Abstract

A distributed fault control method and apparatus for large-scale nonlinear systems are disclosed. Each sub-system included in a large-scale non-linear system includes: a controller for controlling the sub-system according to a control input; And a compensation unit for compensating the control error without a failure diagnosis such that a control error based on a measurable state variable value of the subsystem according to the control input is included within a predetermined performance inheritance range.

Description

[0002] Decentralized fault compensation methods and apparatuses for large-scale nonlinear systems [

The present invention relates to a distributed fault control method and apparatus for a large scale nonlinear system including a physical interconnect structure and a failure in a dead-zone actuator.

Distributed control of large systems involving nonlinear interconnection structures between subsystems has been studied steadily over the past few years. The main advantage of this distributed control is that if a new sub-system is added, there is no need to redesign the control system again, and the controller type of each sub-system can be designed simply.

However, conventional distributed control research has a disadvantage in that it can not compensate for an unknown time delayed failure in a nonlinear interconnect structure due to communication delay between subsystems.

In addition, the conventional distributed control research has a disadvantage in that it can not adaptively compensate for the failure phenomenon even though the dead-zone nonlinearity in the actuator frequently occurs.

SUMMARY OF THE INVENTION The present invention is directed to a distributed fault control method and apparatus that can compensate for faults without fault / anomaly diagnosis in a large scale nonlinear system that includes physical interconnect structures and faults in dead-zone actuators.

According to an aspect of the present invention, there is provided an apparatus for distributed fault control capable of compensating faults without fault / anomaly diagnosis in a large-scale nonlinear system including physical interconnect structures and faults in dead-zone actuators.

According to the first embodiment, in each sub-system included in a large-scale non-linear system, a controller for controlling the sub-system according to a control input; And a compensation unit for compensating the control error without a failure diagnosis so that a control error based on the measurable state variable value of the subsystem according to the control input is included within a predetermined performance inheritance range.

The failure includes a failure in a dead-zone actuator failure and a connection structure between the subsystems.

The compensation unit may compensate the failure without diagnosing the failure based on a function approximation model and error conversion to compensate for the dynamic change due to the failure so that the control error is included within the predetermined performance range.

Wherein the control error is limited to within the range of the performance metric according to the equation,

는 제어 에러를 나타내고,

는 설계 상수를 나타내고,

는 유계된 성능 함수이며, t는 시간을 나타낸다.here,

Lt; / RTI > represents a control error,

Represents a design constant,

Is the relatived performance function and t is the time.

The controller includes a nominal controller and an adaptive fault distribution controller. Even if a failure occurs, the control error is present within the predetermined performance range, so that control performance can be ensured even after a failure occurs.

The controller passes the virtual control input to the first order filter to avoid repeated derivative calculations.

The large-scale non-linear system has a plurality of subsystems physically interconnected.

According to another aspect of the present invention, there is provided a distributed fault control method capable of compensating faults without fault / anomaly diagnosis in a large-scale nonlinear system including a fault in a physical interconnect structure and a dead-zone actuator.

According to a first embodiment, there is provided a method of compensating for the failure of each subsystem included in a large-scale non-linear system, the method comprising the steps of: Obtaining a measurable state variable value according to a control input of each subsystem including a fault; And compensating the control error without a failure diagnosis such that a control error based on the state variable value is included within a predetermined performance range even if a failure occurs.

Performing nominal control on the large scale nonlinear system such that the control error does not deviate from the performance metric range irrespective of failure occurrence;

And performing the performance-based adaptive compensation control on the large-scale nonlinear system when a failure occurs.

Performing the adaptive compensation control comprises: modeling a function approximation model and an error transform to compensate for a dynamic change due to the failure, and modeling the function approximation model; And compensating for the control error based on the modeling to be included within the predetermined performance metric range.

It is an object of the present invention to provide a performance guarantee type distributed fault control method and apparatus for a large scale nonlinear system according to an embodiment of the present invention to provide a faultless and trouble- Can be compensated.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a view schematically showing a configuration of each sub system included in a large scale nonlinear system according to the first embodiment; Fig.
2 is a flowchart showing a method for compensating for a failure of a large-scale nonlinear system according to the first embodiment;

BRIEF DESCRIPTION OF THE DRAWINGS The present invention is capable of various modifications and various embodiments, and specific embodiments are illustrated in the drawings and described in detail in the detailed description. It is to be understood, however, that the invention is not to be limited to the specific embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

The terms first, second, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another.

The terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

The present invention relates to distributed fault control capable of compensating for faults with guaranteed control performance without fault diagnosis (i.e., fault detection) for faults in large scale nonlinear systems consisting of N subsystems. In an embodiment of the present invention, it is assumed that a failure occurs in the interconnect structure between the actuator and the subsystem of the N subsystems. Also, a large-scale nonlinear system according to an embodiment of the present invention is assumed to have a failure including a dead-zone period in the actuator. Here, the dead zone refers to a section until the actual control input is input, but the output of the actuator is accordingly output.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

As already mentioned above, a large-scale non-linear system according to an embodiment of the present invention includes N subsystems. It is assumed that a large nonlinear system is an interconnected structure with an unknown time delay between subsystems and that each subsystem includes dead-zone actuator failures.

FIG. 1 is a view schematically showing a configuration of each subsystem included in a large-scale nonlinear system according to the first embodiment.

Referring to FIG. 1, each subsystem included in a large-scale nonlinear system includes a controller 110 and a compensation unit 115.

The controller 110 is a means for controlling the subsystem according to the control input.

As will be described in greater detail below, the controller 110 is a means for controlling the subsystem to follow the desired signal at the output of each subsystem.

For example, the controller 110 may generate a control input such that the control error does not deviate regardless of whether the performance range is faulty. In addition, the controller 110 includes a nominal controller in a state in which no failure has occurred, and a failure compensation controller that performs adaptive control by compensating the failure after occurrence of a failure. This will be more clearly understood from the following description.

The compensation unit 115 compensates for the control error based on the measurable state variable value of the subsystem according to the control input without any failure diagnosis so that the control error is always included within the predetermined performance inheritance range.

As already mentioned above, a large-scale nonlinear system according to an embodiment of the present invention includes interconnected structures with unknown time delays between each of the subsystems and failures in the dead-zone actuators of each subsystem. Generally, systems that are physically interconnected operate have dead-zone nonlinearities in the actuator and an unknown delayed interconnect structure. Thus, the unknown interconnect structure between each subsystem and the failure in the dead-zone actuator must be compensated locally without delay.

Therefore, the large-scale nonlinear system according to an embodiment of the present invention can be configured to have a physically interconnected structure having an unknown time delay between each of the subsystems, and a control error set in advance without diagnosing faults / faults in the dead- Failures can be compensated without leaving the range. This will be more clearly understood by the following.

2 is a flowchart illustrating a method of compensating for a failure of a large-scale nonlinear system according to the first embodiment.

In step 210, each sub-system obtains a measurable state variable value according to the control input.

Each subsystem in step 215 compensates for the control error without anomaly / failure diagnosis so that the control error based on the state variable value is always included within the predetermined performance metric range.

Here, each subsystem can perform nominal control such that the control error is included within the range of the performance tolerance regardless of whether a failure has occurred or not. In addition, each subsystem can perform adaptive compensation control for the large nonlinear system when a failure occurs.

For example, each subsystem uses a function approximation model to compensate for dynamic changes due to failure, modeling it as a function approximator, and then compensating the control error to be included within a predetermined performance range based on the result, can do.

This will be more clearly understood from the following description.

Modeling a large nonlinear system that includes physically interconnected structures between the N subsystems and failures in the dead-zone actuators of each subsystem is shown in Equation (1).

,

,

,

,

는 i번째 부시스템의 상태 변수와 제어 변수를 각각 나타낸다. here,

,

,

,

,

Represents the state variable and the control variable of the i-th subsystem, respectively.

는 지연된 상태 변수를 나타내고,

는 미지의 유계된 시변 지연으로,

Represents a delayed state variable,

0.0 > a < / RTI > unknown,

과

을 만족한다. 여기서,

,

,

는 미지의 양의 상수를 나타낸다.

는 상태 변수의 초기 조건을 나타낸다.

and

. here,

,

,

Represents an unknown positive constant.

Represents the initial condition of the state variable.

과

는 알려진

비선형 함수를 나타내고,

는 부 시스템들간의 시간 지연된 상호 연결을 나타내는 미지의

비선형 함수를 나타낸다.

and

Known

Represents a non-linear function,

Lt; RTI ID = 0.0 > time-delayed < / RTI >

Represents a nonlinear function.

비선형 항

은 고장으로 인한 i번째 부 시스템에서 시간 지연된 상호 연결 효과의 변화를 나타낸다.

은 미지의 시간(

)에서 발생한 고장의 시간 프로파일을 나타낸다.

는 막 시작된 초기 고장 시간과 고장이 검출된 시간 사이의 시간으로 간주될 수 있다. 여기서, 한시적 고장(incipient fault)의 경우,

이면

이고,

이면

는 단조롭게 증가한다. 돌연 고장(abrupt fault)의 경우,

이면

이고,

이면

이다.

과

은 궤환 제어 기술의 제어 안정성을 보장하기 위해

,

각각에 대해 원점으로부터 멀리 유계되며, 양수로 가정한다.Unknown

Nonlinear term

Represents the change in the time delayed interconnect effect in the ith subsystem due to failure.

Unknown time (

) Of the failure.

Can be regarded as the time between the initial failure time just started and the time the failure is detected. Here, in the case of an incipient fault,

If

ego,

If

Lt; / RTI > increases monotonically. In the case of an abrupt fault,

If

ego,

If

to be.

and

To ensure control stability of feedback control technology

,

For each, the distance from the origin is assumed and assumed to be a positive number.

)는 수학식 2와 같이 모델링될 수 있다.Dead-zone actuator of the i-th sub-system that contains an unknown fault (

) Can be modeled as shown in Equation (2).

는 유효한 부분적 손실을 나타내는 미지의 상수를 나타내고,

는 미지의 액츄에이터 바이어스를 나타내는 상수이다.

는 비-대칭 데드-존 비선형성으로, 수학식 3과 같다.here,

Represents an unknown constant representing a valid partial loss,

Is a constant indicating an unknown actuator bias.

Is a non-symmetric dead-zone nonlinearity, as shown in Equation (3).

과

은 데드-존 특유의 왼쪽 오른쪽 기울기를 나타낸다.

과

은 입력 비선형성의 중단점(break-point)를 나타낸다.here,

and

Represents a left-right slope characteristic of a dead-zone.

and

Represents the break-point of input nonlinearity.

Equation (3) can be rewritten as Equation (4).

이다.here,

to be.

From the equations (2) and (4), the dead-zone actuator model of the ith subsystem having an unknown failure can be redefined as shown in equation (5).

이고,

인 수학식 5로 나타낼 수 있다. 여기서, i=1,...,N이다.Remark 1: If there is no failure, the dead-zone actuator model

ego,

Lt; / RTI > Here, i = 1, ..., N.

Remark 2: Equation 1 shows the actual nonlinear time-delay effect of time-delayed interconnections and dead-zone actuator failures, such as interconnected recycling storage tanks, interconnected wind tunnels, interconnected cooling rollers with transmission delay, System. Most interconnected machine-operated systems have unknown delayed interconnections and dead-zone non-linearities in the actuators. Thus, failures in these unknown interconnections and dead-zone nonlinearities must be compensated locally without delay information.

)은 피드백으로 이용 가능하지 않다. 여기서, i는 1,...,N이다.Assumption 1: Output of dead-zone actuator (

) Are not available as feedback. Here, i is 1, ..., N.

,

,

,

은 미지의 양수이고,

,

인 미지의 상수가 존재한다. 여기서,

이고,

이다. 또한, i=1,...,N이다.Assumption 2: Dead-zone parameters

,

,

,

Is an unknown positive number,

,

There is an unknown constant. here,

ego,

to be. Also, i = 1, ..., N.

), 제어 입력(

)의 계수 항(

)은 시변하고 알려지지 않았다. 미지의 고장이 존재하는 이러한 항을 처리하는 것은 매우 어렵다.Remark 3: By assumption 2, unknown constants (

), Control input (

) ≪ / RTI >

) Was not always known. It is very difficult to deal with this term for which there is an unknown failure.

) 및 고장(

)은

과

을 각각 만족한다. 여기서,

이고,

이며,

는 미지의

분류-K 함수이다. Assumption 3: Unknown time delayed interconnection function (

) And failure

)silver

and

Respectively. here,

ego,

Lt;

Unknown

Class-K function.

This assumption is widely used in the field of control of nonlinear time-delay systems.

The purpose of a large-scale nonlinear system according to an embodiment of the present invention is to detect the presence of an unknown time delayed interconnect structure and a dead-zone actuator failure while the transient performance of all error surfaces is preserved within a given set- Delayed independent, distributed fault compensation controller for the system.

Remark 4: In one embodiment of the present invention, a failure in a time-delayed interconnect structure between each sub system of a large-scale nonlinear system and an unknown failure in a dead-zone actuator are detected in a distributed fault control problem Will be described. Also, the time delayed nonlinear interconnect structure is unmatched within the control input.

Remark 5: Distributed fault-compensated control in these large-scale nonlinear systems can be extended to a number of failures occurring within dead-zone actuators and time-delayed interconnect structures in the local subsystem.

However, in order to facilitate understanding and explanation, a single failure in the interconnect structure that will be delayed with the dead-zone actuator will be described below.

The controller 110 according to an exemplary embodiment of the present invention applies a function approximation technique used in a neural network to compensate for an unknown nonlinear function according to a control input.

Hereinafter, the function approximation technique will be briefly described as follows.

는

에서

로의 미지의 스무스 함수(unknown smooth fuction)이다. 함수 근사자는 꽉찬 집합(compact set)(

)상의 충분한 정확도를 가지도록 임의의 미지의 비선형 함수(

)를 근사화할 수 있다.

The

in

Lt; RTI ID = 0.0 > unknown < / RTI > smooth function. The function approximator is a compact set (

Lt; RTI ID = 0.0 > (e. G., ≪ / RTI &

) Can be approximated.

)의 근사화 과정을 수학식으로 정리하면 수학식 6과 같다.Nonlinear function

) Is approximated by Equation (6).

는 함수 근사자의 입력을 나타내고,

는 함수 근사자의 출력을 나타낸다. 또한,

는 복원 에러를 나타내고,

는 최적 가중치 벡터(

)의 예측치이며,

과 같이 정의된다.here,

Represents the input of a function approximator,

Represents the output of the function approximator. Also,

Indicates a restoration error,

Is an optimal weight vector

), ≪ / RTI >

.

과

로 유계된다. 여기서,

와

는 양의 상수이고,

는 유클리드 놈을 나타낸다.Assumption 4: The reconstruction error and the optimal weight vector are

and

Respectively. here,

Wow

Is a positive constant,

Represents the Euclidian.

)은 본 발명의 일 실시예에 따른 대규모 비선형 시스템에서의 고장 보상 제어를 위해 요구되지 않으며, 이는 단지 시스템의 안정성 분석을 위해 사용된다.Stated value (

) Is not required for failure compensation control in a large scale nonlinear system according to an embodiment of the present invention, which is only used for stability analysis of the system.

에 의한

의 테일러 급수(Taylor series)를 전개하면 수학식 7과 같다For learning of all weights of large nonlinear systems

On by

(Taylor series) of equation

,

및

은 고차항이다. 수학식 7을 수학식 6에 대입하면, 수학식 8과 같다.here,

,

And

Is a high-order term. Substituting Equation (7) into Equation (6), Equation (8) is obtained.

는 잔여 근사 에러를 나타내고,

는 예측될 수 있는 미지의 값이다.here,

Represents a residual approximation error,

Is an unknown value that can be predicted.

Remark 6: Neural networks, wavelet neural networks, and fuzzy systems can be used as function analyzers.

As described above, a large-scale nonlinear system according to an embodiment of the present invention can compensate for failures in a time-delayed interconnect structure that is unmatched with an unknown dead-zone actuator failure within a predetermined performance metric range without any diagnosis have.

The large-scale nonlinear system according to an embodiment of the present invention can compensate the transient performance of the error surface based on the performance curve through the preset performance-based distributed dynamic surface design.

The performance-based error surface is used to compensate for distributed dynamic surface failures.

This is explained as follows.

과 같이 정의될 수 있다. 여기서,

,

,

,

는 i번째 부시스템의 k번째 필터링된 가상 제어 입력을 나타낸다. 에러 표면의 미리 설정된 성능은 각각의 에러(

)가 수학식 10과 같이 미리 설정된 유계내에서 발생되도록 함으로써 수행될 수 있다.The error surface vector of the ith subsystem is

Can be defined as follows. here,

,

,

,

Represents the kth filtered virtual control input of the ith sub-system. The preset performance of the error surface depends on each error (

) Is generated in a predetermined flow system as shown in Equation (10).

,

는 설계 상수를 나타내고,

는 성능 함수로 유계되며, 양의 감소하는 스무스 함수

이다.

는 상수이다. 성능 함수는

과 같은 지수 함수 형태로 사용된다. 여기서,

,

및

는 양의 상수이고,

이며,

는

조건이 만족되면 선택된다.here,

,

Represents a design constant,

Lt; RTI ID = 0.0 > smoothed < / RTI > function

to be.

Is a constant. The performance function

And so on. here,

,

And

Is a positive constant,

Lt;

The

It is selected when the condition is satisfied.

)는 인위적으로 작은 값으로 조절할 수 있는 정상상태 상태에서

의 허용 가능한 최대 사이즈를 나타낸다. 감소 율(

)은

의 수렴 속도의 하한 유계를 나타낸다.

의 최대 오버슛은

보다 작게 설정된다. 그러므로, 성능 함수(

)와 상수(

,

)는 에러 표면(

)의 성능 유계내에서 적정하게 결정될 수 있다.In addition,

) Is in a steady-state condition that can be artificially adjusted to a small value

≪ / RTI > Reduction rate (

)silver

The lower limit of convergence speed.

The maximum overshoot of

. Therefore, the performance function (

) And constant (

,

) Is the error surface (

) Can be appropriately determined within the performance curve.

For compensation of the compensation unit 115, the performance-based-based error surface of Equation (10) can be modified as shown in Equation (11).

,

,

는 변형된 에러를 나타내고,

는 전단 사상(

)을 포함하는 증가하는 스무스 함수를 나타낸다. 전단 사상에 의해

이 성립한다.here,

,

,

Lt; / RTI > represents a modified error,

Is the shear mapping (

) ≪ / RTI > By shearing thought

.

The candidate distortion function can be selected as shown in Equation (12).

,

이고,

는 양의 설계 상수를 나타낸다. 만일

이면,

에 기인하여

이다.here,

,

ego,

Represents a positive design constant. if

If so,

Due to

to be.

)과 변형 에러(

)을 고려하자. 여기서,

이고,

이다. 만일

가 유계되면, 에러 표면의 설정된 성능은

을 위해 만족된다. 즉, 수학식 10이 만족된다.Lemma 1: Error surface (

) And deformation error (

). here,

ego,

to be. if

, The set performance of the error surface is

Lt; / RTI > In other words, equation (10) is satisfied.

이 유계된 후,

에 대해

이다.

로부터 수학식 10의

의 설정된 성능이

을 만족하는 것을 증명하는

이 획득될 수 있다.Proof:

After that,

About

to be.

Lt; RTI ID = 0.0 >

Set performance of

To prove that

Can be obtained.

)은 수학식 11과 같고, 경계층 에러(

)가 수학식 13과 같이 정의하자.Performance-based error surface (

) Is expressed by Equation (11), and the boundary layer error

) Is defined as Equation (13).

,

,

는 가상 제어를 나타내고,

는 필터링된 가상 제어를 나타낸다. 이에 따라, i번째 부시스템의 k번째 가상 제어 법칙(

)은

과 같이 재작성될 수 있다. 여기서,

는 nominal 제어 파트이고,

는 미지의 함수와 고장을 보상하기 위한 근사화-기반 적응적 제어 파트를 나타낸다.here,

,

,

Represents a virtual control,

Represents the filtered virtual control. Thus, the kth virtual control law of the ith subsystem (

)silver

Can be rewritten as shown in FIG. here,

Is a nominal control part,

Shows an approximation-based adaptive control part for compensating for unknown functions and faults.

의 차이는

과 같다. Step 1: Consider the first error surface based on the performance metric. In Equations (1), (11), (12) and

The difference between

Respectively.

를 포함한다.here,

.

항은 0이 아니고, 수학식 10의 조건에 따라 잘 정의된다.

The term is not zero and is well defined according to the condition of equation (10).

)의 nominal 제어 파트(

)는 수학식 14와 같이 설계된다.First Virtual Control Law (

) Of the nominal control part (

) Is designed as shown in Equation (14).

이고,

과

는 설계 파라미터이고,

,

이다. Lyapunov 후보 함수(

)를

로 선택하는 경우, 수학식 14의

의 시간 미분(time derivative)은 수학식 15와 같다. here,

ego,

and

Is a design parameter,

,

to be. Lyapunov Candidate Function (

)

, The following equation

Is the time derivative of equation (15).

Equations 16 through 18 can be derived using Assumption 3.

Substituting Equations (16) to (18) into Equation (15) yields Equation (19).

이 사용된다. 또한,

는 변수이고,

는 양의 상수이다. Here,

Is used. Also,

Is a variable,

Is a positive constant.

)를 획득하기 위해, 가상 제어 입력(

)을 저역 통과 1차 필터를 통과시킨다. 여기서,

는 시간 상수이다. 이를 수식으로 나타내면, 수학식 20과 같다.Filtered virtual control (

), The virtual control input (

Pass a low-pass first-order filter. here,

Is a time constant. This can be expressed by the following equation (20).

): 수학식 1의 i번째 부 시스템의 k번째 등식을 고려하면, 수학식 1, 12, 및 13에서 k번째 에러 표면(

)의 미분은

이다. 여기서,

이다.Step k (k = 2, ...,

): Considering the kth equation of the i < th > subsystem of equation (1), the kth error surface in equations (1),

)

to be. here,

to be.

)의 nominal의 제어 법칙(

)은 수학식 21과 같다.The kth virtual control (

) Of the nominal control law (

) ≪ / RTI >

,

과

는 각각 설계 파라미터이며,

,

이다. here,

,

and

Are design parameters, respectively,

,

to be.

)를 고려하면, 수학식 21과

,

,

를 사용하면,

의 시간 미분은 수학식 22와 같다.Lyapunov Candidate Function (

), The following equations (21) and

,

,

If you use,

≪ EMI ID = 22.0 >

를 k번째 저역 통과 1차 필터를 통과시켜 i번째 부시스템의 k번째 필터링된 가상 제어 벡터(

)가 획득되며, 이를 수학식으로 나타내면 수학식 23과 같다.

Pass through the k-th low-pass first-order filter to generate a k-th filtered virtual control vector (

) Is obtained, which can be expressed by the following equation (23).

는 시간 상수이다.
here,

Is a time constant.

는 ni번째 에러 표면이다. Step ni: Considering the ni th equation of the subsystem of Equation (1)

Is the ni-th error surface.

의 시간 미분은 다음과 같이 나타낼 수 있다.Using Equations (1) and (5)

Can be expressed as follows.

,

이다.here,

,

to be.

)의 nominal 제어 항(

)은 수학식 24와 같다.Consequently, as a result,

) ≪ / RTI >

) ≪ / RTI >

는 설계 파라미터이다.here,

Is a design parameter.

)를

로 선택함으로서,

의 시간 미분은 수학식 25와 같다. 여기서,

는 미지의 상수이다.Lyapunov Candidate Function (

)

As a result,

≪ / RTI > here,

Is an unknown constant.

이다. here,

to be.

Using the inequality, Equation (26) and Equation (27) are obtained.

Applying this to Equation (25), Equation (28) is obtained.

Remark 7: Fault-compensated control can be extended using Beck stepping design for nonlinear feedback systems where actuator failure is considered. In addition, a predetermined performance metric can be used for the initial error definition of the backstepping design process.

However, a large-scale nonlinear system according to an embodiment of the present invention relates to failure compensation including failures in a structure in which N subsystems are physically interconnected and failures in a dead-zone actuator.

은 에러 동역학 내에서

를 다루기 위해 설계된다.
Thus, the predetermined performance metric is used for the definition of the error surface in the dynamic surface design process, such as Equation 11, and in the virtual control law of Equation 21

Lt; RTI ID = 0.0 >

. ≪ / RTI >

The controller 110 according to one embodiment of the present invention performs a function approximation model and adaptive control to compensate for changes in the dynamic due to time delayed interconnections and dead-zone actuator failures.

Hereinafter, this will be described.

여기서, i=1, ..., N이고,

이다. 가정 3과 감소하는 함수(

)의 유계에 의해,

과

이 쉽게 획득될 수 있다. 여기서,

과

은 필터링된 가상 제어(

),

과

에 제시된 미지의

분류-K 함수이다. Remark 8: The performance-based error surface of Equation 11 can be summarized as follows.

Here, i = 1, ..., N,

to be. Assumption 3 and decreasing function (

),

and

Can be easily obtained. here,

and

Is a filtered virtual control (

),

and

Unknown

Class-K function.

과

이 존재한다.Also,

and

Lt; / RTI >

The functional approximation-based distributed virtual controller and the real controller to compensate for the failure are defined as shown in equations (29) and (32).

,

,

와

는 튜닝 파라미터이고,

과

는

-조정을 위한 양의 상수이고,

,

과

는

과

의 예측치이다. 또한,

는 비선형 함수인

의 예측치이며,

는 비선형 함수인

의 예측치이다.here,

,

,

Wow

Is a tuning parameter,

and

The

- a positive constant for adjustment,

,

and

The

and

. Also,

Is a nonlinear function

, ≪ / RTI >

Is a nonlinear function

.

,

,

,

,

이다. 여기서,

를 포함한다.

과

은 이론 1의 증명내에서 설명된 안정성 분석 과정에서 제시되어 있다.

,

,

,

,

to be. here,

.

and

Is presented in the stability analysis process described in the proof of theory 1.

)을 포함하는 전체 Lyapunov 함수 후보 V를 고려하면, 수학식 36과 같다.For adaptive control through stability analysis and function approximation based fault compensation, the Lyapunov-Krasovskii function term (

), The following equation (36) is obtained.

,

, here,

,

,

.

.

Theorem 1: Large-scale system with fault and dead-zone actuator failures in unknown time-varying delayed interconnect structures, distributed nominal control of equations 14, 21 and 24, decentralized control based on functionally approximated models of equations 29-34 Consider a closed loop fault compensation control consisting of an adaptive controller.

을 만족하는 초기 조건을 위해, 폐루프 시스템의 모든 신호는 균일하게 유계되고, 에러 표면(

)은 조절 가능하게 원점 근처로 수렴된다. Under Home 1-4,

, All signals of the closed-loop system are uniformly distributed, and the error surface (< RTI ID = 0.0 >

) Converge to near the origin adjustably.

에 대해 미리 설정된 성능 유계 내에서 보증된다.In addition, the transient performance of all system states, despite failure in the unknown time delayed nonlinear interconnect structure and dead-zone actuator failure,

Within a predetermined performance metric.

Proof: Assume that the dynamics of the boundary error surface are as shown in equations (37) to (38).

,

,

과

는 가상 제어기의 도함수를 의미하는 연속 함수이다.here,

,

,

and

Is a continuous function representing the derivative of the virtual controller.

The time variations of V can be expressed by Equation (39) by Equations (19), (22), (28), (37)

과 Remark 8을 사용하여 수학식 39는 수학식 40과 같이 정리될 수 있다.

And Remark 8, Equation (39) can be summarized as Equation (40).

Using Equations (29), (32) and (40), Equation (41) can be obtained.

는 수학식 34 및 35로부터 파생되며,

이 사용된다.here,

Is derived from Equations (34) and (35)

Is used.

From equations (8), (9), (30), (31), and (33), this inequality can be summarized as follows.

는

로 정의된다. 여기서,

,

이다.

가

내에서 컴팩트 집합이므로,

이 존재하며,

에서

이다. 여기서,

는

의 차원을 나타낸다.set

The

. here,

,

to be.

end

Because it is a compact set within,

Lt; / RTI >

in

to be. here,

The

.

을 선택하고,

과

을 사용하여, 다음과 같이 정리될 수 있다.

≪ / RTI >

and

Can be summarized as follows.

이다.here,

to be.

상의

이므로, 부등식은

이 된다. 여기서,

는

로 선택되며,

,

,

이다.

top

Therefore, the inequality

. here,

The

Lt; / RTI >

,

,

to be.

이면,

에서

은 것을 의미한다. 따라서,

는 불변 집합이다. 예를 들어,

이면,

에 대해

이다. 시간에 대해 부등식을 적분하면, 수학식 42를 획득할 수 있다.The inequality above

If so,

in

. therefore,

Is an invariant set. E.g,

If so,

About

to be. Integrating the inequality for time can yield equation (42).

를 사용하면,

이 만족된다.

If you use,

Is satisfied.

로 유계될 수 있다.Thus, as time increases, the modified error surface exponentially becomes a compact set

. ≪ / RTI >

)는

를 조정하는 것에 의해 임의적으로 작게 만들 수 있다. Lemma 1으로부터

는 유계되고, 시스템의 모든 상태의 미리 설정된 성능이 보증된다. 따라서, 일시적인 성능이 수학식 10에 미리 설정된 성능 유계 내에서 보증된다. 또한,

는

로 인해, 임의적으로 작게 줄일 수 있다.
Compact set (

)

To be arbitrarily small. From Lemma 1

And the predetermined performance of all states of the system is guaranteed. Thus, the temporary performance is guaranteed within the performance metric preset in Equation (10). Also,

The

, It can be arbitrarily reduced to a small size.

)를 위한

파라미터는 일시적이고 안정적인 상태 성능 유계를 조정하기 위해 적정하게 선택될 수 있다.

과

는 과도 응답 성능 유계를 결정하고

는 정상 상태 성능의 유계를 나타낸다. 수학식 42로부터

의 과도/정상 상태 성능에 대한 만족은 초기 에러와

을 위한 명확한 설계 파라미터와 관련이 있다. 그러므로, 초기 에러를 작게 설정하고, 큰 감쇄 율(

)을 얻기 위해

,

,

을 적절하게 선택한다. 더욱이

을 작게 만들기 위해,

과

은 고정할 수 있다. Remark 9: From the proof of theory 1, the design parameters can be chosen to ensure a preset performance. Performance function (

)for

The parameters can be appropriately selected to adjust the transient and stable state performance curve.

and

Determines the transient response performance curve

Represents the steady-state performance curve. From equation (42)

The satisfaction of the transient / steady-state performance of

Which is related to the clear design parameters for Therefore, the initial error is set small and the large attenuation rate (

) To obtain

,

,

Is appropriately selected. Furthermore

In order to make small,

and

Can be fixed.

는 미리 설정된 성능 유계 내에 있는 동안 임의적으로 작게 만들 수 있다.In conclusion, from Lemma 1,

May be made arbitrarily small while in the preset performance metric.

Remark 10: Distributed adaptive beck stepping control technique is proposed for large nonlinear time delay systems with dead-zone nonlinearity. Since the delayed outputs between subsystems are interacted, the dead - zone inverse model is required for controller design, and the derivative functions and unknown nonlinearities for delayed interactions are known.

However, a large nonlinear system according to an embodiment of the present invention considers interconnection between subsystems associated with all delayed state variables, and knowledge of the dead-zone inverse model and the derivative functions is not required for controller design Do not.

In addition, the time-delayed interconnect structure and the dead-zone actuator dispersion fault compensation method of a large-scale nonlinear system according to an embodiment of the present invention is characterized in that the transient / steady-state performance having a predetermined performance- And is simpler than the back stepping controller since it does not require repeated derivatives of the virtual controller.

) 처리를 위해 설계된다.
The distributed fault compensation control of equations (29) and (32) can be used to compensate for dead-zone nonlinearity and to compensate for the failure of the time delayed interconnect structure, despite the unmatched time delayed interconnections associated with the state variables of the subsystem , A function approximator with one or three inputs. In particular, the absolute value of the function approximator of Equation (32) and the condition of Equation (35) for the adaptation law of Equation (34) are the unknown control term caused by the dead-zone nonlinearity of Remark 3

) Processing.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention as defined in the appended claims. It will be understood that the invention may be varied and varied without departing from the scope of the invention.

110:
115:

Claims (11)

For each subsystem included in a large nonlinear system,
A controller for controlling the sub-system according to a control input; And
And a compensation unit for compensating the control error without a failure diagnosis such that a control error based on a measurable state variable value of the subsystem according to the control input is included within a predetermined performance inheritance range,
Wherein the compensation unit comprises:
Compensating the control error to be included within a predetermined performance range based on a function approximation model and error distortion to compensate for the dynamic change due to the failure,
The controller comprising a nominal controller and an adaptive fault distribution controller,
Wherein the nominal controller performs nominal control on the large scale nonlinear system such that the control error is included within the performance range regardless of whether a failure has occurred and the adaptive failure distribution controller is configured to control the large non- And performs adaptive compensation control on the sub-system.
The method according to claim 1,
Wherein the failure includes a failure in a dead-zone actuator failure and a time delayed connection between subsystems.
delete The method according to claim 1,
Wherein the control error is limited within a range of performance ratios according to the following equation.

here,

Lt; / RTI > represents a control error,

Represents a design constant,

Is the relatived performance function, and t is the time.
delete The method according to claim 1,
Wherein the controller passes the control input through a first filter.
The method according to claim 1,
Wherein the large nonlinear system is a plurality of subsystems physically interconnected.
A method of compensating for a failure in each subsystem included in a large nonlinear system, the subsystem including a failure in a time delayed connection structure between a dead-zone actuator failure and subsystems,
Obtaining a measurable state variable value according to a control input of each sub system;
Compensating the control error without a fault diagnosis such that a control error based on the state variable value is included within a predetermined performance range;
Performing nominal control on the large-scale nonlinear system such that the control error is included within the range of the performance metric, irrespective of the occurrence of a fault; And
Performing adaptive compensation control on the large nonlinear system when a failure occurs,
Wherein performing the adaptive compensation control comprises:
Modeling a function approximation model by applying a function approximation model to compensate for the dynamic change due to the failure; And
And compensating for the control error to be included within the predetermined performance range based on the modeling.
delete delete A computer-readable recording medium having recorded thereon a program code for performing the method according to claim 8.

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