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,

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).

here,

,

,

,

,

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

Represents a delayed state variable,

0.0 > a < / RTI > unknown,

and

. here,

,

,

Represents an unknown positive constant.

Represents the initial condition of the state variable.

and

Known

Represents a non-linear function,

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

Represents a nonlinear function.

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.

Dead-zone actuator of the i-th sub-system that contains an unknown fault (

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

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).

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).

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).

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.

Assumption 1: Output of dead-zone actuator (

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

Assumption 2: Dead-zone parameters

,

,

,

Is an unknown positive number,

,

There is an unknown constant. here,

ego,

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

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.

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.

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.

Nonlinear function

) Is approximated by Equation (6).

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 >

.

Assumption 4: The reconstruction error and the optimal weight vector are

and

Respectively. here,

Wow

Is a positive constant,

Represents the Euclidian.

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.

For learning of all weights of large nonlinear systems

On by

(Taylor series) of equation

here,

,

And

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

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.

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).

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.

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).

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).

here,

,

ego,

Represents a positive design constant. if

If so,

Due to

to be.

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.

Proof:

After that,

About

to be.

Lt; RTI ID = 0.0 >

Set performance of

To prove that

Can be obtained.

Performance-based error surface (

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

) Is defined as Equation (13).

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.

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

The difference between

Respectively.

here,

.

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

First Virtual Control Law (

) Of the nominal control part (

) Is designed as shown in Equation (14).

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).

Here,

Is used. Also,

Is a variable,

Is a positive constant.

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).

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.

The kth virtual control (

) Of the nominal control law (

) ≪ / RTI >

here,

,

and

Are design parameters, respectively,

,

to be.

Lyapunov Candidate Function (

), The following equations (21) and

,

,

If you use,

≪ EMI ID = 22.0 >

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).

here,

Is a time constant.

Step ni: Considering the ni th equation of the subsystem of Equation (1)

Is the ni-th error surface.

Using Equations (1) and (5)

Can be expressed as follows.

here,

,

to be.

Consequently, as a result,

) ≪ / RTI >

) ≪ / RTI >

here,

Is a design parameter.

Lyapunov Candidate Function (

)

As a result,

≪ / RTI > here,

Is an unknown constant.

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.

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.

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.

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).

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

.

,

,

,

,

to be. here,

.

and

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

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.

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.

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).

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)

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

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

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.

set

The

. here,

,

to be.

end

Because it is a compact set within,

Lt; / RTI >

in

to be. here,

The

.

≪ / RTI >

and

Can be summarized as follows.

here,

to be.

top

Therefore, the inequality

. here,

The

Lt; / RTI >

,

,

to be.

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).

If you use,

Is satisfied.

Thus, as time increases, the modified error surface exponentially becomes a compact set

. ≪ / RTI >

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.

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.

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.

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.

Images