CN112711190B - Self-adaptive fault-tolerant controller, control equipment and control system - Google Patents
Self-adaptive fault-tolerant controller, control equipment and control system Download PDFInfo
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Abstract
The application provides a self-adaptive fault-tolerant controller, a control device and a control system. The adaptive fault-tolerant controller comprises: the preset distributed comprehensive observer is used for acquiring tracking trigger information of the sub-mechanical system; estimating fault interference information of the sub-mechanical system based on the tracking trigger information; and the preset sliding mode surface is used for determining compensation information of the sub-mechanical system based on the fault interference information and compensating the sub-mechanical system based on the compensation information. By the method, the fault interference information can be estimated based on the trigger information received by the sub-mechanical system, so that the interference compensation is carried out on the sub-mechanical system, and the controller is ensured to stably and effectively track the sub-mechanical system.
Description
Technical Field
The application relates to the technical field of nonlinear systems, in particular to a self-adaptive fault-tolerant controller, control equipment and a control system.
Background
With the continuous improvement of the industrial automation degree, modern industrial systems comprise more and more nonlinear subunits, and in order to complete complex industrial control targets, a plurality of interconnected sub-mechanical systems are often required to be integrated. The system belongs to a typical nonlinear large system, and connection with multi-state multi-physical coupling characteristics is involved in the connection process. However, since the characteristics of each subsystem are different, the connection mechanism is complex, which also brings many challenges to the control of the system. On one hand, as the number of mechanical systems of the interconnected sub-machines is large, the number of channels for interference to enter the system is increased, so that the system is easily influenced by external interference; on the other hand, actuators in the system are prone to failure, and the working performance of the system is also affected.
Disclosure of Invention
An object of the embodiment of the present application is to provide a self-adaptive fault-tolerant controller, a control device, and a control system, so as to improve the problem that "the working performance of the entire interconnection system is affected due to the fact that there are many interconnected sub-mechanical systems, the sub-mechanical systems are easily interfered by the outside, and the actuator itself fails.
The invention is realized by the following steps:
in a first aspect, an embodiment of the present application provides an adaptive fault-tolerant controller, which is applied to a sub-mechanical system in an interconnected nonlinear mechanical system, where the adaptive fault-tolerant controller includes: the preset distributed comprehensive observer is used for acquiring tracking trigger information of the sub-mechanical system; estimating fault interference information of the sub-mechanical system based on the tracking trigger information; and the preset sliding mode surface is used for determining compensation information of the sub-mechanical system based on the fault interference information and compensating the sub-mechanical system based on the compensation information.
In an embodiment of the present application, an adaptive fault tolerant controller includes: a preset distributed comprehensive observer and a preset sliding mode surface. The preset distributed integrated observer acquires tracking trigger information of the sub-mechanical system and estimates fault interference information of the sub-mechanical system based on the tracking trigger information; and the preset sliding mode surface determines compensation information of the system based on the fault interference information, and compensates the sub-mechanical system based on the compensation information. Namely, the fault interference information can be estimated based on the trigger information received by the sub-mechanical system through the mode, so that the interference compensation is carried out on the sub-mechanical system, and the stable and effective tracking of the controller on the sub-mechanical system is ensured.
With reference to the technical solution provided by the first aspect, in some possible implementations, the controller is constructed based on a preset distributed integrated observer and a preset sliding mode surface; the preset distributed comprehensive observer is used for estimating fault interference information of the sub-mechanical system based on the tracking trigger information, and the preset sliding mode surface is used for determining compensation information of the system based on the fault interference information and compensating the sub-mechanical system based on the compensation information.
With reference to the technical solution provided by the first aspect, in some possible implementation manners, the preset distributed comprehensive observer includes a state observer, a failure factor observer, and a total disturbance observer; the state observer is used for estimating the state of the sub-mechanical system and is constructed based on a pre-constructed state model of the sub-mechanical system and a trigger value of an output channel; wherein, the output channel is a channel between a controller and a sensor of the sub-mechanical system;
the mathematical expression of the state model of the sub-mechanical system is as follows:
wherein x isi(t)＝[xi1,xi2,...,xin]T∈RnRepresenting the state of the ith sub-mechanical system, including the speed and acceleration of the ith sub-mechanical system, Δ fi(x,t,χ)＝[Δfi1(x,t,χ),...,Δfin(x,t,χ)]T，Fi(x)＝[Fi1(x),...,Fin(x)]TRespectively representing smooth non-linear functions related to the mass of the ith sub-mechanical system; χ represents a constant related to the friction of the ith sub-mechanical system, di(t)＝[di1(t),...,din(t)]TRepresenting external interference from the ith sub-mechanical system, including wind resistance and external load fluctuation; u. ofi(t)＝[ui1(t),...,uim(t)]TAnd yi(t)＝[yi1(t),...,yip(t)]TRespectively representing the electric signal input of the actuator of the ith sub-mechanical system itself and the speeds and angular velocities of the ith sub-mechanical system, giRepresents the motor torque control gain, C, of the ith sub-mechanical systemiRepresenting the i-th sub-mechanical system output matrix, ΠijAn interconnection matrix representing the ith and jth sub-mechanical systems; x is the number ofj(t) represents a state quantity of the jth sub-mechanical system; lambda [ alpha ]i＝diag(λi1,...,λim) Denotes the ith sub-mechanical system failure factor, λik∈[λ1,λ2](k＝1,...,m)，λ1An upper bound representing a failure factor; lambda [ alpha ]2A lower bound representing a failure factor; sigmai＝diag(σi1,...,σim) Denotes an indicator factor, where σik∈{0,1}(k＝1,...,m)；εi＝diag(εi1,...,εim)，εik∈{0,1}(k＝1,...,m)，usi(t) represents an actuator deflection fault of the ith sub-mechanical system;
wherein the predetermined interference is bounded, then
Wherein the content of the first and second substances,
represents the equivalent interference, theta, of the ith systemsiIs an unknown gain, ξi(t) represents a variable related to the ith sub-mechanical system disturbance;
correspondingly, the mathematical expression of the state observer is as follows:
the above-mentioned
Respectively represent xi(t)，Fi(t)，λi(t)，Δfi(x,t,χ)，yi(t) estimation, yi(tk) A trigger value, L, representing the output channelqiRepresenting the gain, δ, of the state observerqi(t) a compensation term representing the state observer;
the fault failure factor observer is used for estimating a system fault failure factor of the ith sub-mechanical system;
wherein, the mathematical expression of the fault failure factor observer is as follows:
wherein h ism＝-σiudi(t)Tgi TPiesi，
Indicating the state estimation error, PiIs a positive definite symmetric matrix;
the total disturbance observer is used for estimating actuator fault disturbance and external disturbance on the ith sub-mechanical system through the state difference value of the ith sub-mechanical system.
The preset distributed comprehensive observer provided by the embodiment of the application comprises a state observer, a failure factor observer and a total disturbance observer, so that multi-dimensional estimation and estimation are realized.
With reference to the technical solution provided by the first aspect, in some possible implementations, a mathematical expression of the compensation term of the state observer is:
wherein the content of the first and second substances,
is expressed in the pair thetasiEstimate of, LqiRepresenting observer gain, ηm＝2(λ2-λ1)(λn+λ2-λ1) Wherein, in the step (A),
to represent
Euler norm of, λn>0，ξi(t) is a new variable to be defined, km>0 and τm>0 is respectively two scalars, kmExpressed as a constant, τ, preventing the introduction of fluctuations in the interference estimatemA constant relating to the acceleration of the ith sub-mechanical system, g (y) is a known function relating to the centripetal force of the ith sub-mechanical system,
ey＝yi(tk)-yi(t)，Pirepresenting a positive definite symmetric matrix;
g (y, t) and Fi(y) representing two known functions, respectively; wherein, Fi(y) represents a known function related to the mass of the ith sub-mechanical system, and G (y, t) represents a measurable non-linear member function of the interconnection portion of the ith sub-mechanical system.
In the embodiment of the application, the compensation item for compensating the system error is introduced into the state observer, so that the observation flexibility of the observer is improved.
With reference to the technical solution provided by the first aspect, in some possible implementation manners, the preset mathematical expression of the sliding mode surface is as follows:
wherein e ismi＝yi(t)-yid(t) represents the difference between the ith sub-mechanical system speed and the desired speed; y isid(t) represents the ith sub-mechanical system desired speed; u. ofdi(t) represents the control input of the ith sub-mechanical system at time t,
α>0，β>0; two adaptive parameters are respectively expressed as
mi>0，ai>0，ci>0，pi>0，bi>0，zi>0, Q matrix is a selection matrix such that QC is a nonsingular matrix, emi (n-1)(t) represents emi(n-1) derivative of (t), li(I ═ 2, 3., n) corresponds to the gain factor, which is a positive number, and I denotes an identity matrix.
In the embodiment of the application, the influence of the total interference signal and the tracking error on the control precision is respectively considered by the self-adaptive parameters in the sliding mode surface, so that the robustness of the system is enhanced and the trembling property in the approaching process is reduced through the design of the self-adaptive parameters.
With reference to the technical solution provided by the first aspect, in some possible implementations, the controller performs tracking by using two channels;
wherein, the first channel is a channel between a controller and a sensor of the sub-mechanical system; the second channel is the channel between the controller and the actuator of the sub-mechanical system itself.
With reference to the technical solution provided by the first aspect, in some possible implementation manners, the triggering condition of the first channel is:
wherein psimA matrix of weights is represented by a matrix of weights,
ey＝yi(tk)-yi(t)，yi(t) denotes the ith sub-mechanical system current output, y (t)k)(k＝0,1,...,t00) indicates that the ith sub-mechanical system has last triggered the transmission value.
In the embodiment of the application, the condition trigger value is set in the first channel, and by the mode, the information transmission quantity required by the observer for stabilization can be reduced under the condition that the observer is stable, namely, effective variable observation is realized by using relatively less output quantity.
With reference to the technical solution provided by the first aspect, in some possible implementation manners, the triggering condition of the second channel is:
wherein the content of the first and second substances,
to represent
In that
The value of the time of day is,
kci>0,kdi>0,ksi>0,δmi>0,δni>0,δsi>0,δhi>0,tpiin order to trigger the time series,
is an adaptive parameter, whereinaiAnd τbiAre two optionally positive numbers.
In the embodiment of the application, the condition trigger value is set in the second channel, and by the mode, the information transmission quantity required by the observer for stabilization can be reduced under the condition that the observer is stable, namely, effective variable observation is realized by using relatively less output quantity.
In a second aspect, an embodiment of the present application provides an adaptive fault-tolerant control method, which is applied to the adaptive fault-tolerant controller provided in the foregoing first aspect, where the method includes: acquiring tracking trigger information of the sub-mechanical system; estimating fault interference information of the sub-mechanical system based on the tracking trigger information; determining compensation information for the sub-mechanical system based on the fault interference information, and compensating the sub-mechanical system based on the compensation information.
In a third aspect, an embodiment of the present application provides a control apparatus, including: a controller and a memory, the controller and the memory being connected; the memory is used for storing programs; the controller is configured to call a program stored in the memory to perform the method as provided in the embodiment of the second aspect.
In a fourth aspect, an embodiment of the present application provides a control system, including: the controller is respectively connected with the sensor and the actuator; the controller is configured to perform the method as provided in the embodiment of the second aspect.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
Fig. 1 is a block diagram of an interconnected nonlinear mechanical system according to an embodiment of the present disclosure.
Fig. 2 is a control block diagram of an adaptive fault-tolerant control method according to an embodiment of the present disclosure.
Fig. 3 is a flowchart illustrating steps of an adaptive fault-tolerant control method according to an embodiment of the present disclosure.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.
In view of the problems that the existing interconnected sub-mechanical systems are more and are easily interfered by the outside world and the actuators have faults, so that the working performance of the whole interconnected system is affected, the inventor of the present application has conducted research and proposes the following embodiments to solve the problems.
Referring to fig. 1, an interconnected nonlinear mechanical system is provided in an embodiment of the present application, which includes a plurality of sub-mechanical systems, each coupled to one or more other sub-mechanical systems. Each sub-mechanical system comprises a controller, a sensor and an actuator. The controller is respectively connected with the sensor and the actuator.
It should be noted that the actuator is an essential component of the mechanical system. It is used to receive the control signal from the controller and change the size of the controlled medium to maintain the controlled variable in the required value or range.
The sensor is a detection device which can sense the measured information and convert the sensed information into an electric signal or other information in a required form according to a certain rule to output so as to meet the requirements of information transmission, processing, storage, display, recording, control and the like.
The sub-machine system may be a metallurgical machine system, a mining machine system, an engineering transport machine system, or a metal cutting machine system, but the present application is not limited thereto.
The following explains the configuration of the controller. In the embodiment of the application, the controller is constructed based on a preset distributed comprehensive observer and a preset sliding mode surface. The preset distributed comprehensive observer is used for estimating fault interference information of the sub-mechanical system based on the tracking trigger information, and the preset sliding mode surface is used for determining compensation information of the system based on the fault interference information and compensating the sub-mechanical system based on the compensation information.
Optionally, the preset decentralized integrated observer includes a state observer, a failure factor observer, and a total disturbance observer.
The state observer is used for estimating the state of the sub-mechanical system and is constructed based on a pre-constructed state model of the sub-mechanical system and a trigger value of an output channel; wherein the output channel is a channel between a controller and a sensor of the sub-mechanical system itself. That is, the tracking trigger information of the sub-mechanical system can be obtained from the output channel.
The mathematical expression of the state model of the sub-mechanical system is as follows:
the sub-mechanical system state model in the formula (1) is constructed by an initial sub-mechanical system state model and a pre-constructed fault model of the actuator of the interconnected mechanical system.
The expression of the initial sub-mechanical system state model is as follows:
in the formula (2), xi(t)＝[xi1,xi2,...,xin]T∈RnRepresenting the state of the ith sub-mechanical system, including the speed and acceleration of the ith sub-mechanical system, Δ fi(x,t,χ)＝[Δfi1(x,t,χ),...,Δfin(x,t,χ)]T，Fi(x)＝[Fi1(x),...,Fin(x)]TRespectively representing smooth non-linear functions related to the mass of the ith sub-mechanical system; χ represents a constant related to the friction of the ith sub-mechanical system, di(t)＝[di1(t),...,din(t)]TRepresenting external interference from the ith sub-mechanical system, including wind resistance and external load fluctuation; u. ofi(t)＝[ui1(t),...,uim(t)]TAnd yi(t)＝[yi1(t),...,yip(t)]TRespectively represent the ith sub-machineElectrical signal input to the actuator of the system itself and the ith sub-mechanical system speed and angular speed output, giRepresents the motor torque control gain, C, of the ith sub-mechanical systemiRepresenting the ith sub-mechanical system output matrix, CiGenerally, the vector is a row vector, which indicates that the ith sub-mechanical system state quantity is selected as an output quantity (for example, the angular velocity is selected as an output quantity), ΠijAn interconnection matrix representing the ith and jth sub-mechanical systems, i.e., an intercoupling matrix between the two systems. x is the number ofj(t) represents the state quantities of the jth sub-mechanical system, including speed and acceleration.
It should be noted that in a differential equation, there are cases where a derivative with respect to time and a derivative with respect to a certain dimension occur, and the top circle point represents the derivative with respect to time, that is, the dots in the above formula and on the parameter top in the following text represent the derivative.
The expression of the fault model of the interconnected mechanical system actuator is as follows:
λi＝diag(λi1,...,λim) Denotes the ith sub-mechanical system failure factor, λik∈[λ1,λ2](k＝1,...,m)，λ1An upper bound representing a failure factor; lambda [ alpha ]2Representing a lower bound for a failure factor. Sigmai＝diag(σi1,...,σim) Denotes an indicator factor, where σik∈{0,1}(k＝1,...,m)；εi＝diag(εi1,...,εim)，εik∈{0,1}(k＝1,...,m)，usi(t) represents an actuator deflection fault of the ith sub-mechanical system. Suppose that
Wherein the content of the first and second substances,
to represent
Euler norm of (a), where λn>0。
That is, the sub-mechanical system state model of the formula (1) can be obtained by substituting the formula (3) into the formula (2).
Because the external fluctuation of the load of each sub-mechanical system is always bounded, and the corresponding upper bound is not easy to determine, the interference is preset to be bounded, and then
Wherein the content of the first and second substances,
represents the equivalent interference, theta, of the ith systemsiIs an unknown gain, ξi(t) represents a variable related to the ith sub-mechanical system disturbance.
In the embodiment of the application, when the state model of the sub-mechanical system is constructed, the upper bound condition of the equivalent interference is preset, so that the subsequent state observer, the fault failure factor observer and the total interference observer do not need to set specific upper bound values in the interference observation process.
Correspondingly, the mathematical expression of the state observer constructed based on the state model of the sub-mechanical system is as follows:
the above-mentioned
Respectively represent xi(t)，Fi(t)，λi(t)，Δfi(x,t,χ)，yi(t) estimation, yi(tk) A trigger value, L, representing the output channelqiRepresenting the gain, δ, of the state observerqi(t) represents a compensation term for the state observer.
Wherein, the mathematical expression of the compensation term of the state observer is as follows:
in the formula (5), the first and second groups,
is expressed in the pair thetasiEstimate of, LqiRepresenting observer gain, ηm＝2(λ2-λ1)(λn+λ2-λ1),ξi(t) is a new variable to be defined, km>0 and τm>0 is respectively two scalars, kmExpressed as a constant, τ, preventing the introduction of fluctuations in the interference estimatemA constant relating to the acceleration of the ith sub-mechanical system, g (y) is a known function relating to the centripetal force of the ith sub-mechanical system,
ey＝yi(tk)-yi(t)，Pirepresenting a positive definite symmetric matrix;
g (y, t) and Fi(y) representing two known functions, respectively; fi(y) represents a known function related to the mass of the ith sub-mechanical system, and G (y, t) represents a measurable non-linear member function of the interconnection portion of the ith sub-mechanical system.
In the embodiment of the application, the compensation item for compensating the system error is introduced into the state observer, so that the observation flexibility of the observer is improved.
The fault failure factor observer is used for estimating a system fault failure factor of the ith sub-mechanical system.
The mathematical expression of the fault failure factor observer is as follows:
wherein h ism＝-σiudi(t)Tgi TPiesi，
Indicating the state estimation error, PiIs a positive definite symmetric matrix.
It should be noted that, in the embodiment of the present application, the fault failure factor observer is used for detecting the fault failure factor λi(t) observed thati(t) is a function of variable time variation, namely the fault signal can more widely represent the fault in the actual system, and the lambda is further realized by the state error driving of the state observeri(t) accurate observation.
And the total disturbance observer is used for estimating actuator fault disturbance and external disturbance on the ith sub-mechanical system through the state difference value of the ith sub-mechanical system.
The derivation of equation (7) is described below to estimate the mechanical system interference signal
The following variables are defined:
wherein, ω isi(t) is an intermediate variable, which is updated according to the formula (9):
wherein the content of the first and second substances,
αi(t) is defined as formula (10):
wherein the content of the first and second substances,
is thetasiIs determined by the estimated value of (c),
the updating method is as shown in the formula (11)
That is, the interference signal for estimating the mechanical system can be obtained by equations (8) to (11) in combination with equations (4) to (6)
The total disturbance observer of (1).
It should be noted that a compensation term for compensating system errors is also introduced into the total disturbance observer, by which the observer observation flexibility is also increased, where δqiThe mathematical expression of (t) can refer to the aforementioned formula (5).
Of course, in other embodiments, the total disturbance observer and the state observer may not introduce a compensation term, and the application is not limited thereto.
In summary, the preset distributed comprehensive observer provided in the embodiment of the present application includes a state observer, a failure factor observer, and a total disturbance observer, so as to achieve estimation and estimation in multiple dimensions, that is, the failure disturbance information includes information estimated by the state observer, the failure factor observer, and the total disturbance observer.
Of course, in other embodiments, the preset decentralized integrated observer may also include only one or two of the observers, which is not limited in this application.
In the embodiment of the present application, the preset mathematical expression of the sliding mode surface is as follows:
wherein e ismi＝yi(t)-yid(t) represents the difference between the ith sub-mechanical system speed and the desired speed; y isid(t) represents the ith sub-mechanical system desired speed; u. ofdi(t) represents the control input of the ith sub-mechanical system at time t,
α>0，β>0; two adaptive parameters are respectively expressed as
mi>0，ai>0，ci>0，pi>0，bi>0，zi>0, Q matrix is a selection matrix such that QC is a nonsingular matrix, emi (n-1)(t) represents emi(n-1) derivative of (t), li(I ═ 2, 3., n) corresponds to the gain factor, which is a positive number, and I denotes an identity matrix.
In the embodiment of the application, the influence of the total interference signal and the tracking error on the control precision is respectively considered by the self-adaptive parameters in the sliding mode surface, so that the robustness of the system is enhanced and the trembling property in the approaching process is reduced through the design of the self-adaptive parameters.
Optionally, in this embodiment, the controller performs tracking using two channels.
The first channel is a channel between the controller and the sensor of the sub-mechanical system itself, i.e. the output channel mentioned in the previous embodiment. The second channel is a channel between the controller and the actuator of the sub-mechanical system, and is corresponding to the input channel of the sub-mechanical system.
Of course, in other embodiments, the tracking may be performed only through any one of the channels, and the present application is not limited thereto.
Optionally, when the first channel is used for tracking, the triggering condition of the first channel is:
wherein psimThe weight matrix is expressed, and can be selected as a diagonal matrix according to the ith sub-mechanical system in practical application,
ey＝yi(tk)-yi(t)，yi(t) denotes the ith sub-mechanical system current output, y (t)k)(k＝0,1,...,t00) indicates that the ith sub-mechanical system has last triggered the transmission value.
Optionally, when the first channel is used for tracking, the triggering condition of the second channel is:
wherein the content of the first and second substances,
to represent
In that
The value of the time of day is,
kci>0,kdi>0,ksi>0,δmi>0,δni>0,δsi>0,δhi>0,
in order to trigger the time series,
is an adaptive parameter, whereinaiAnd τbiAre two optionally positive numbers.
In the embodiment of the application, the condition trigger values are set in the first channel and the second channel, and by this way, the information transmission quantity required by the observer for stabilization can be reduced under the condition that the observer is stable, that is, effective variable observation is realized by using relatively less output quantity.
Finally, the mathematical expression of the controller can be obtained through the above formula (4), formula (6), formula (7), formula (12) and formula (14).
The mathematical expression of the controller is:
wherein the content of the first and second substances,
in an update manner of
It should be noted that parameters not defined in the present application all belong to intermediate quantities in the calculation process.
The specific meaning of the formula (15) can be understood with reference to the control process shown in fig. 2. I.e. u acquired by two channels respectivelydi(t) and yi(tk) And after observation is carried out by a distributed comprehensive observer of the ith sub-mechanical system, state estimation, failure factor estimation and total interference estimation are output, and finally, compensation is carried out through a sliding mode surface to realize stable control tracking.
The tracking performance is mainly analyzed to be the limited time accessibility of the sliding mode surface, and in the method, parameter self-adaptive updating is introduced to ensure the limited time to reach. The demonstration can be expressed as: the design choice of the Lyapunov function is:
certifying that
The following analysis was performed for the ith mechanical subsystem trigger condition:
for the
It is possible to obtain:
further inferences can be made based on equation (16):
wherein the content of the first and second substances,
the two adjacent triggers have lower bounds, and the situation of infinite triggering cannot occur.
It should be noted that, for parameters in the following formulas, reference may be made to explanations in the embodiments of the foregoing formulas, for example, for parameters in formulas (6) to (17), reference may be made to explanations of the parameters in formulas (1) to (5), and repeated descriptions are not repeated to avoid redundancy.
In summary, the embodiment of the application designs a new adaptive fault-tolerant controller based on an event trigger mechanism, which effectively reduces the information transmission amount of the system while ensuring the output trajectory tracking capability of the interconnected nonlinear mechanical system, and proves the trajectory tracking performance of the designed controller. The method and the device can effectively solve the problem that the system effectively tracks and controls the interconnected nonlinear mechanical system under the conditions of actuator faults and external disturbance.
Referring to fig. 3, based on the same inventive concept, an embodiment of the present application provides an adaptive fault-tolerant control method applied to the above interconnected nonlinear mechanical systems, where each sub-mechanical system executes the control method based on a controller, where the control method includes: step S101-step S103.
Step S101: and acquiring tracking trigger information of the sub-mechanical system.
Step S102: fault interference information for the sub-mechanical system is estimated based on the tracking trigger information.
Step S103: determining compensation information for the sub-mechanical system based on the fault interference information, and compensating the sub-mechanical system based on the compensation information.
In the embodiment of the present application, the tracking control of each sub-mechanical system is performed according to the controller. Specifically, tracking trigger information of the sub-mechanical system is obtained; estimating fault interference information of the sub-mechanical system based on the tracking trigger information; and finally, determining compensation information of the system based on the fault interference information, and compensating the sub-mechanical system based on the compensation information. Namely, the fault interference information can be estimated based on the trigger information received by the sub-mechanical system through the mode, so that the interference compensation is carried out on the sub-mechanical system, and the stable and effective tracking of the controller on the sub-mechanical system is ensured.
Based on the same inventive concept, the embodiment of the application also provides a control device. The control device comprises a controller and a memory, wherein the controller is connected with the memory. The controller is electrically connected, directly or indirectly, with the memory to effect the transfer or interaction of data.
The Memory may be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), and electrically Erasable Programmable Read-Only Memory (EEPROM). The memory is used for storing a program, and the controller executes the program after receiving the execution instruction. For example, after receiving the execution, the controller executes to acquire tracking trigger information of the sub-mechanical system; estimating fault interference information of the sub-mechanical system based on the tracking trigger information; determining compensation information for the system based on the fault interference information, and compensating the sub-mechanical system based on the compensation information.
It should be noted that, as those skilled in the art can clearly understand, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
Based on the same inventive concept, the present application further provides a storage medium, on which a computer program is stored, and when the computer program is executed, the computer program performs the method provided in the foregoing embodiments.
The storage medium may be any available medium that can be accessed by a computer or a data storage device including one or more integrated servers, data centers, and the like. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (8)
1. An adaptive fault-tolerant controller for a sub-mechanical system in an interconnected non-linear mechanical system, the adaptive fault-tolerant controller comprising:
the preset distributed comprehensive observer is used for acquiring tracking trigger information of the sub-mechanical system; estimating fault interference information of the sub-mechanical system based on the tracking trigger information;
the preset sliding mode surface is used for determining compensation information of the sub-mechanical system based on the fault interference information and compensating the sub-mechanical system based on the compensation information;
the preset distributed comprehensive observer comprises a state observer, a fault failure factor observer and a total disturbance observer;
the state observer is used for estimating the state of the sub-mechanical system and is constructed on the basis of a pre-constructed state model of the sub-mechanical system and a trigger value of an output channel; wherein, the output channel is a channel between a controller and a sensor of the sub-mechanical system;
the mathematical expression of the state model of the sub-mechanical system is as follows:
wherein x isi(t)＝[xi1,xi2,...,xin]T∈RnRepresenting the state of the ith sub-mechanical system, including the speed and acceleration of the ith sub-mechanical system, Δ fi(x,t,χ)＝[Δfi1(x,t,χ),...,Δfin(x,t,χ)]T，Fi(x)＝[Fi1(x),...,Fin(x)]TRespectively represent smooth non-linear functions related to the mass of the ith sub-mechanical system and
representing an unknown function associated with the mechanical system; fi(y) represents a known function; χ represents a constant related to the friction of the ith sub-mechanical system, di(t)＝[di1(t),...,din(t)]TRepresenting external interference from the ith sub-mechanical system, including wind resistance and external load fluctuation; u. ofdi(t)＝[udi1(t),...,udim(t)]TAnd yi(t)＝[yi1(t),...,yip(t)]TRespectively representing the electric signal input of the actuator of the ith sub-mechanical system itself and the speeds and angular velocities of the ith sub-mechanical system, giRepresents the motor torque control gain, C, of the ith sub-mechanical systemiRepresenting the i-th sub-mechanical system output matrix, ΠijAn interconnection matrix representing the ith and jth sub-mechanical systems; x is the number ofj(t) represents a state quantity of the jth sub-mechanical system; lambda [ alpha ]i＝diag(λi1,...,λim) Denotes the ith sub-mechanical system failure factor, λik∈[λ1,λ2](k＝1,...,m)，λ1A lower bound representing a failure factor; lambda [ alpha ]2An upper bound representing a failure factor; sigmai＝diag(σi1,...,σim) Denotes an indicator factor, where σik∈{0,1}(k＝1,...,m)；εi＝diag(εi1,...,εim)，εik∈{0,1}(k＝1,...,m)，usi(t) represents an actuator deflection fault of the ith sub-mechanical system; u. ofdi(t) represents a control input to an actuator of the ith sub-mechanical system;
wherein the predetermined interference is bounded, then
Wherein the content of the first and second substances,
represents the equivalent interference, theta, of the ith systemsiIs an unknown gain, ξi(t) represents a variable related to the ith sub-mechanical system disturbance;
correspondingly, the mathematical expression of the state observer is as follows:
the above-mentioned
Respectively represent xi(t)，Fi(t)，λi(t)，Δfi(x,t,χ)，yi(t) estimation, yi(tk) A trigger value, L, representing the output channelqiRepresenting the gain, δ, of the state observerqi(t) a compensation term representing the state observer;
the fault failure factor observer is used for estimating a system fault failure factor of the ith sub-mechanical system;
wherein, the mathematical expression of the fault failure factor observer is as follows:
wherein h ism＝-σiudi(t)Tgi TPiesi，
Indicating the state estimation error, PiIs a positive definite symmetric matrix;
the total disturbance observer is used for estimating actuator fault disturbance and external disturbance on the ith sub-mechanical system through the state difference value of the ith sub-mechanical system;
wherein, the mathematical expression of the preset slip form surface is as follows:
wherein e ismi＝yi(t)-yid(t) represents the difference between the ith sub-mechanical system speed and the desired speed; y isid(t) represents the ith sub-mechanical system desired speed; u. ofdi(t) represents the control input of the ith sub-mechanical system at time t,
alpha is more than 0, beta is more than 0; two adaptive parameters are respectively expressed as
mi＞0，ai＞0，ci＞0，pi＞0，bi＞0，zi> 0, Q matrix is a selection matrix, so that QC is a nonsingular matrix, emi (n-1)(t) represents emi(n-1) derivative of (t), li(I ═ 2, 3., n) corresponds to the gain factor, which is a positive number, and I denotes an identity matrix.
2. The adaptive fault-tolerant controller according to claim 1, characterized in that the mathematical expression of the compensation term of the state observer is:
wherein the content of the first and second substances,
is expressed in the pair thetasiEstimate of, LqiRepresenting observer gain, ηm＝2(λ2-λ1)(λn+λ2-λ1) Wherein, in the step (A),
to represent
Euler norm of, λn＞0，ξi(t) is a new variable to be defined, km> 0 and τm> 0 are two scalars, κ, respectivelymExpressed as a constant, τ, preventing the introduction of fluctuations in the interference estimatemA constant relating to the acceleration of the ith sub-mechanical system, g (y) is a known function relating to the centripetal force of the ith sub-mechanical system,
ey＝yi(tk)-yi(t)，Pirepresenting a positive definite symmetric matrix;
g (y, t) and Fi(y) representing two known functions, respectively;
presentation pair
(ii) an estimate of (d); wherein, Fi(y) represents a known function related to the mass of the ith sub-mechanical system, and G (y, t) represents a measurable non-linear member function of the interconnection portion of the ith sub-mechanical system.
3. The adaptive fault-tolerant controller of claim 1, wherein the controller tracks using two channels;
wherein, the first channel is a channel between a controller and a sensor of the sub-mechanical system; the second channel is the channel between the controller and the actuator of the sub-mechanical system itself.
4. The adaptive fault-tolerant controller according to claim 3, wherein the triggering condition of the first channel is:
wherein psimA matrix of weights is represented by a matrix of weights,
ey＝yi(tk)-yi(t)，yi(t) denotes the ith sub-mechanical system current output, y (t)k)(k＝0,1,...,t00) indicates that the ith sub-mechanical system has last triggered the transmission value.
5. The adaptive fault-tolerant controller according to claim 3, wherein the triggering condition of the second channel is:
wherein the content of the first and second substances,
to represent
At tpiThe value of the time of day is,
kci＞0,kdi＞0,ksi＞0,δmi＞0,δni＞0,δsi＞0,δhi＞0,tpiin order to trigger the time series,
is an adaptive parameter, whereinaiAnd τbiAre two optionally positive numbers.
6. An adaptive fault-tolerant control method applied to an adaptive fault-tolerant controller according to any one of claims 1 to 5, the method comprising:
acquiring tracking trigger information of the sub-mechanical system;
estimating fault interference information of the sub-mechanical system based on the tracking trigger information;
determining compensation information for the sub-mechanical system based on the fault interference information, and compensating the sub-mechanical system based on the compensation information;
the preset distributed comprehensive observer comprises a state observer, a fault failure factor observer and a total disturbance observer;
the state observer is used for estimating the state of the sub-mechanical system and is constructed on the basis of a pre-constructed state model of the sub-mechanical system and a trigger value of an output channel; wherein, the output channel is a channel between a controller and a sensor of the sub-mechanical system;
the mathematical expression of the state model of the sub-mechanical system is as follows:
wherein x isi(t)＝[xi1,xi2,...,xin]T∈RnRepresenting the state of the ith sub-mechanical system, including the speed and acceleration of the ith sub-mechanical system, Δ fi(x,t,χ)＝[Δfi1(x,t,χ),...,Δfin(x,t,χ)]T，Fi(x)＝[Fi1(x),...,Fin(x)]TRespectively represent smooth non-linear functions related to the mass of the ith sub-mechanical system and
representing an unknown function associated with the mechanical system; fi(y) represents a known function; χ represents a constant related to the friction of the ith sub-mechanical system, di(t)＝[di1(t),...,din(t)]TRepresenting external interference from the ith sub-mechanical system, including wind resistance and external load fluctuation; u. ofdi(t)＝[udi1(t),...,udim(t)]TAnd yi(t)＝[yi1(t),...,yip(t)]TRespectively representing the electric signal input of the actuator of the ith sub-mechanical system itself and the speeds and angular velocities of the ith sub-mechanical system, giRepresents the motor torque control gain, C, of the ith sub-mechanical systemiRepresenting the i-th sub-mechanical system output matrix, ΠijAn interconnection matrix representing the ith and jth sub-mechanical systems; x is the number ofj(t) represents a state quantity of the jth sub-mechanical system; lambda [ alpha ]i＝diag(λi1,...,λim) Denotes the ith sub-mechanical system failure factor, λik∈[λ1,λ2](k＝1,...,m)，λ1A lower bound representing a failure factor; lambda [ alpha ]2An upper bound representing a failure factor; sigmai＝diag(σi1,...,σim) Denotes an indicator factor, where σik∈{0,1}(k＝1,...,m)；εi＝diag(εi1,...,εim)，εik∈{0,1}(k＝1,...,m)，usi(t) represents an actuator deflection fault of the ith sub-mechanical system; u. ofdi(t) represents a control input to an actuator of the ith sub-mechanical system;
wherein the predetermined interference is bounded, then
Wherein the content of the first and second substances,
represents the equivalent interference, theta, of the ith systemsiIs an unknown gain, ξi(t) represents a variable related to the ith sub-mechanical system disturbance;
correspondingly, the mathematical expression of the state observer is as follows:
the above-mentioned
Respectively represent xi(t)，Fi(t)，λi(t)，Δfi(x,t,χ)，yi(t) estimation, yi(tk) A trigger value, L, representing the output channelqiRepresenting the gain, δ, of the state observerqi(t) a compensation term representing the state observer;
the fault failure factor observer is used for estimating a system fault failure factor of the ith sub-mechanical system;
wherein, the mathematical expression of the fault failure factor observer is as follows:
wherein h ism＝-σiudi(t)Tgi TPiesi，
Indicating the state estimation error, PiIs a positive definite symmetric matrix;
the total disturbance observer is used for estimating actuator fault disturbance and external disturbance on the ith sub-mechanical system through the state difference value of the ith sub-mechanical system;
wherein, the mathematical expression of the preset slip form surface is as follows:
wherein e ismi＝yi(t)-yid(t) represents the difference between the ith sub-mechanical system speed and the desired speed; y isid(t) represents the ith sub-mechanical system desired speed; u. ofdi(t) represents the control input of the ith sub-mechanical system at time t,
alpha is more than 0, beta is more than 0; two adaptive parameters are respectively expressed as
mi＞0，ai＞0，ci＞0，pi＞0，bi＞0，zi> 0, Q matrix is a selection matrix, so that QC is a nonsingular matrix, emi (n-1)(t) represents emi(n-1) derivative of (t), li(I ═ 2, 3., n) corresponds to the gain factor, which is a positive number, and I denotes an identity matrix.
7. A control apparatus, characterized by comprising: a controller and a memory, the controller and the memory being connected;
the memory is used for storing programs;
the controller is configured to execute a program stored in the memory to perform the method of claim 6.
8. A control system, comprising: the controller is respectively connected with the sensor and the actuator;
the controller is configured to perform the method of claim 6.
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