CN114253133A - Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism - Google Patents

Abstract

The invention discloses a sliding mode fault-tolerant control method and device based on a dynamic event trigger mechanism, and relates to the technical field of sliding mode control. The method comprises the following steps: establishing a dynamic model of a discrete networked control system; designing a state sliding mode observer of a discrete networked control system based on the condition that the system has sensor faults; designing a sliding mode surface based on an observer estimation result; designing a dynamic event trigger mechanism; and designing a sliding mode fault-tolerant controller based on an observer method. The invention provides a sliding mode fault-tolerant control scheme considering sensor faults under a dynamic event trigger mechanism aiming at a networked control system.

Description

Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism

technical field

The invention relates to the technical field of sliding mode control, in particular to a sliding mode fault-tolerant control method and device based on a dynamic event trigger mechanism.

Background technique

As an effective robust control strategy, sliding mode control has received extensive attention in engineering applications. It mainly drives the state trajectory from the initial state to a preset sliding mode surface through a special control method. up and remain stable. Compared with traditional control methods, sliding mode control technology has the advantages of strong robustness, system order reduction and fast response, so it has attracted people's attention and research.

In the network environment, the limited bandwidth is not enough to guarantee the complete transmission of data. It is necessary to propose an event-triggered scheme to determine whether the sampled signal can be transmitted, thereby reducing the frequency of data transmission and reducing the occurrence of network-induced phenomena. In practical systems, sensors are prone to failure, and if handled improperly, the system will become unstable and even lead to catastrophic accidents. The emergence of fault-tolerant control can not only ensure the stability of the closed-loop system, but also keep the function of the faulty system within an acceptable range, thereby improving the safety and reliability of the system. Combining sliding mode control and fault-tolerant control to design a controller can effectively make the state trajectory reach the sliding mode surface and maintain a stable state. Due to the strong robustness and anti-interference of sliding mode control method, it is of great practical significance to use sliding mode fault-tolerant control method to deal with networked systems with event-triggered and sensor faults.

The existing researches on the sliding mode fault-tolerant control problem mainly focus on the actuator failure, but in the actual engineering system, the sensor failure is also inevitable. In addition, in the network environment, data transmission is often affected by network bandwidth. Compared with time triggering, the use of dynamic event triggering mechanism to reduce the amount of data transmission can better relieve the pressure of network bandwidth and reduce the amount of calculation. In this regard, there is currently no sliding-mode fault-tolerant control scheme that considers both dynamic event triggering and sensor faults for networked control systems.

SUMMARY OF THE INVENTION

Aiming at the problem that the networked control system has no sliding mode fault-tolerant control scheme considering sensor faults under the dynamic event trigger mechanism, the present invention proposes the present invention.

In order to solve the above-mentioned technical problems, the present invention provides the following technical solutions:

In one aspect, the present invention provides a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, the method is implemented by an electronic device, and the method includes:

S1. Establish a dynamic model of the discrete networked control system.

S2. Design the state sliding mode observer of the discrete networked control system based on the sensor failure in the system.

S3. Design a sliding mode surface based on the estimated information of the observer.

S4. Design a dynamic event triggering mechanism.

S5. Design a sliding mode fault-tolerant controller based on the observer method.

Optionally, the method further includes: substituting an equivalent control law into the observer to obtain a closed-loop system, and based on the Lyapunov function theory and the linear matrix inequality method, obtaining a closed-loop system that satisfies the asymptotic stability and H _∞ performance index. sufficient evidence.

Optionally, the state space form of the dynamic model of the discrete networked control system in S1 is shown in the following formula (1):

为系统的n维状态向量；

表示实数集；

为系统的m维控制输入；

为系统的p维测量输出；

为系统的q维被控输出；A₁为系统矩阵；B为系统的输入矩阵；C为系统的测量矩阵；D₁和D₂为系统的外部扰动矩阵，A₂为系统的输出矩阵；A₁,A₂,B,C,D₁和D₂为具有适当维数的已知矩阵；

和

分别为w维和v维属于l₂[0，∞)的外部扰动,其中l₂[0，∞)为Hilbert空间的平方可积函数；ΔA代表参数不确定性，满足ΔA＝MFN，其中F是一个未知矩阵，满足F^TF≤I，M和N为具有适当维数的已知矩阵；g(x_k)是非线性扰动，满足‖g(x_k)‖≤r‖x_k‖，其中，‖g(x_k)‖为g(x_k)的范数，‖x_k‖为x_k的范数，r＞0代表一个已知常数。in,

is the n-dimensional state vector of the system;

represents the set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is the q-dimensional controlled output of the system; A ₁ is the system matrix; B is the input matrix of the system; C is the measurement matrix of the system; D ₁ and D ₂ are the external disturbance matrices of the system, and A ₂ is the output matrix of the system; A ₁ , A ₂ , B, C, D ₁ and D ₂ are known matrices with appropriate dimensions;

and

are external disturbances belonging to l ₂ [0, ∞) in w dimension and v dimension, respectively, where l ₂ [0, ∞) is the square integrable function of Hilbert space; ΔA represents parameter uncertainty, satisfying ΔA=MFN, where F is An unknown matrix satisfying F ^T F≤I, M and N are known matrices with appropriate dimensions; g(x _k ) is a nonlinear perturbation satisfying ‖g(x _k )‖≤r‖x _k ‖, where, ‖g(x _k )‖ is the norm of g(x _k ), ‖x _k ‖ is the norm of x _k , and r>0 represents a known constant.

Optionally, the sensor failure model in S2 is shown in the following formula (2):

in,

i＝1,2,…,q，f_i 为f_i的下界，

为f_i的上界，满足

Wherein, F _s =diag{f ₁ ,f ₂ ,...,f _q }, and diag is a diagonal matrix;

i=1,2,...,q, f _i is the lower bound of f _i ,

is the upper bound of f _i , satisfying

When f _i =1, i=1,2,...,q, the sensor is in normal operation.

When f _i = 0, i = 1, 2, . . . , q, the sensor does not work at all.

When f _i ∈ (0,1), i=1,2,...,q, the sensor fails.

Denote the measurement output with sensor failure as y _F =F _s y _k .

Optionally, the sliding mode observer in S2 is represented by the following equation (3):

表示观测器状态，

表示被控输出z_k的估计值，L表示观测器增益矩阵。in,

represents the observer state,

represents the estimated value of the controlled output z _k , and L represents the observer gain matrix.

Optionally, the sliding mode surface function in S3 is represented by the following formula (4):

是待设计的滑模面参数矩阵，G＝B^TP₁，P₁＞0是待求解的正定矩阵。Among them, _Sk represents the sliding mode function at time k,

is the sliding mode surface parameter matrix to be designed, G=B ^T P ₁ , and P ₁ >0 is the positive definite matrix to be solved.

Optionally, the dynamic event trigger mechanism model in S4 is shown in the following formula (5):

表示正整数集合；{l₀,l₁,…}为从观测器到控制器当前状态所处的时间序列；定义l₀＝0；σ、θ为给定的正标量；

其中

为k时刻的状态估计，

为最新释放的状态；η_k表示内部动态变量，满足

其中，T为矩阵的转置，λ∈(0,1)为给定的常数，η₀≥0为给定的初始条件。in,

represents a set of positive integers; {l ₀ , l ₁ ,...} is the time series from the observer to the current state of the controller; define l ₀ =0; σ, θ are given positive scalars;

in

is the state estimate at time k,

is the latest released state; η _k represents the internal dynamic variable, satisfying

Among them, T is the transpose of the matrix, λ∈(0,1) is a given constant, and η ₀ ≥0 is a given initial condition.

Optionally, the design of the observer-based sliding mode fault-tolerant controller in S5 includes:

According to _Sk+1 = _Sk = 0, the equivalent control law is expressed by the following equation (6):

where ^-1 is the inverse matrix.

Based on the dynamic event triggering mechanism, the equivalent control law is rewritten as the following equation (7):

When the difference of the sliding mode surface function satisfies the following equations (8) and (9),

ΔS _k ≤ -ωe ^-μk sgn(S _k )-κS _k if S _k > 0 (8)

ΔS _k ≥ -ωe ^-μk sgn(S _k )-κS _k if S _k <0 (9)

Among them, 0<κ<1, ω>0, and μ≥0.

Design a sliding mode fault-tolerant controller, as shown in the following formula (10):

in,

On the other hand, the present invention provides a sliding mode fault-tolerant control device based on a dynamic event trigger mechanism, the device is applied to realize a sliding mode fault-tolerant control method based on the dynamic event trigger mechanism, and the device includes:

The dynamic model establishment module is used to establish the dynamic model of the discrete networked control system.

The observer design module is used to design the state sliding mode observer of the discrete networked control system based on the situation of sensor failure in the system.

The sliding surface design module is used to design sliding surfaces based on the estimated information of the observer.

The dynamic event trigger mechanism design module is used to design the dynamic event trigger mechanism.

The sliding mode fault tolerant controller design module is used to design a sliding mode fault tolerant controller based on the observer method.

Optionally, the method further includes: substituting an equivalent control law into the observer to obtain a closed-loop system, and based on the Lyapunov function theory and the linear matrix inequality method, obtaining a closed-loop system that satisfies the asymptotic stability and H _∞ performance index. sufficient evidence.

Optionally, the state space form of the dynamic model of the discrete networked control system is shown in the following formula (1):

为系统的n维状态向量；

表示实数集；

为系统的m维控制输入；

为系统的p维测量输出；

为系统的q维被控输出；A₁为系统矩阵；B为系统的输入矩阵；C为系统的测量矩阵；D₁和D₂为系统的外部扰动矩阵，A₂为系统的输出矩阵；A₁,A₂,B,C,D₁和D₂为具有适当维数的已知矩阵；

和

分别为w维和v维属于l₂[0，∞)的外部扰动,其中l₂[0，∞)为Hilbert空间的平方可积函数；ΔA代表参数不确定性，满足ΔA＝MFN，其中F是一个未知矩阵，满足F^TF≤I，M和N为具有适当维数的已知矩阵；g(x_k)是非线性扰动，满足‖g(x_k)‖≤r‖x_k‖，其中，‖g(x_k)‖为g(x_k)的范数，‖x_k‖为x_k的范数，r＞0代表一个已知常数。in,

is the n-dimensional state vector of the system;

represents the set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is the q-dimensional controlled output of the system; A ₁ is the system matrix; B is the input matrix of the system; C is the measurement matrix of the system; D ₁ and D ₂ are the external disturbance matrices of the system, and A ₂ is the output matrix of the system; A ₁ , A ₂ , B, C, D ₁ and D ₂ are known matrices with appropriate dimensions;

and

are external disturbances belonging to l ₂ [0, ∞) in w dimension and v dimension, respectively, where l ₂ [0, ∞) is the square integrable function of Hilbert space; ΔA represents parameter uncertainty, satisfying ΔA=MFN, where F is An unknown matrix satisfying F ^T F≤I, M and N are known matrices with appropriate dimensions; g(x _k ) is a nonlinear perturbation satisfying ‖g(x _k )‖≤r‖x _k ‖, where, ‖g(x _k )‖ is the norm of g(x _k ), ‖x _k ‖ is the norm of x _k , and r>0 represents a known constant.

Optionally, the sensor failure model is shown in the following formula (2):

in,

i＝1,2,…,q，f_i 为f_i的下界，

为f_i的上界，满足

Wherein, F _s =diag{f ₁ ,f ₂ ,...,f _q }, and diag is a diagonal matrix;

i=1,2,...,q, f _i is the lower bound of f _i ,

is the upper bound of f _i , satisfying

When f _i =1, i=1,2,...,q, the sensor is in normal operation.

When f _i = 0, i = 1, 2, . . . , q, the sensor does not work at all.

When f _i ∈ (0,1), i=1,2,...,q, the sensor fails.

Denote the measurement output with sensor failure as y _F =F _s y _k .

Optionally, the sliding mode observer is represented by the following equation (3):

表示观测器状态，

表示被控输出z_k的估计值，L表示观测器增益矩阵。in,

represents the observer state,

represents the estimated value of the controlled output z _k , and L represents the observer gain matrix.

Optionally, the sliding mode surface function is represented by the following formula (4):

是待设计的滑模面参数矩阵，G＝B^TP₁，P₁＞0是待求解的正定矩阵。Among them, _Sk represents the sliding mode function at time k,

is the sliding mode surface parameter matrix to be designed, G=B ^T P ₁ , and P ₁ >0 is the positive definite matrix to be solved.

Optionally, the dynamic event triggering mechanism model is shown in the following formula (5):

表示正整数集合；{l₀,l₁,…}为从观测器到控制器当前状态所处的时间序列；定义l₀＝0；σ、θ为给定的正标量；

其中

为k时刻的状态估计，

为最新释放的状态；η_k表示内部动态变量，满足

其中，^T为矩阵的转置，λ∈(0,1)为给定的常数，η₀≥0为给定的初始条件。in,

represents a set of positive integers; {l ₀ , l ₁ ,...} is the time series from the observer to the current state of the controller; define l ₀ =0; σ, θ are given positive scalars;

in

is the state estimate at time k,

is the latest released state; η _k represents the internal dynamic variable, satisfying

Among them, ^T is the transpose of the matrix, λ∈(0,1) is a given constant, and η ₀ ≥0 is a given initial condition.

Optionally, the sliding mode fault tolerant controller design module is further used to:

According to _Sk+1 = _Sk = 0, the equivalent control law is expressed by the following equation (6):

where ^-1 is the inverse matrix.

Based on the dynamic event triggering mechanism, the equivalent control law is rewritten as the following equation (7):

When the difference of the sliding mode surface function satisfies the following equations (8) and (9),

ΔS _k ≤ -ωe ^-μk sgn(S _k )-κS _k if S _k > 0 (8)

ΔS _k ≥ -ωe ^-μk sgn(S _k )-κS _k if S _k <0 (9)

Among them, 0<κ<1, ω>0, and μ≥0.

Design a sliding mode fault-tolerant controller, as shown in the following formula (10):

in,

In one aspect, an electronic device is provided, the electronic device includes a processor and a memory, the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned dynamic event-based triggering A sliding-mode fault-tolerant control method for the mechanism.

In one aspect, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned sliding mode fault-tolerant control method based on a dynamic event triggering mechanism.

The beneficial effects brought by the technical solutions provided by the embodiments of the present invention include at least:

In the above scheme, the error generated by the event-triggered mechanism is processed, and under the premise of sensor failure, the sliding-mode fault-tolerant control problem of a networked control system with a dynamic event-triggered mechanism based on the observer method is studied. For the first time in the sliding mode fault-tolerant control problem, the error generated by the event-triggered mechanism is regarded as a disturbance, and the bounded H _∞ norm is used for attenuation. Through the method of Lyapunov function, the sufficient criterion to ensure the asymptotic stability of the closed-loop system and satisfy the H _∞ performance index is given. Furthermore, a suitable sliding mode fault-tolerant controller is designed so that the state trajectory of the closed-loop system can reach the preset sliding mode surface and remain stable within a limited time.

Description of drawings

In order to illustrate the technical solutions in the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort.

1 is a schematic flowchart of a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism of the present invention;

2 is a schematic flowchart of a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism of the present invention;

3 is a schematic diagram of a sliding mode fault-tolerant control system based on a dynamic event trigger mechanism of the present invention;

4 is a block diagram of a sliding mode fault-tolerant control device based on a dynamic event trigger mechanism of the present invention;

FIG. 5 is a schematic structural diagram of an electronic device of the present invention.

Detailed ways

In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

As shown in FIG. 1 , an embodiment of the present invention provides a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, and the method is implemented by an electronic device. As shown in Figure 1, the flow chart of the sliding mode fault-tolerant control method based on the dynamic event trigger mechanism, the processing flow of the method may include the following steps:

S11, establish a dynamic model of the discrete networked control system.

S12. Design a state sliding mode observer of the discrete networked control system based on the sensor failure in the system.

S13 , designing a sliding mode surface based on the estimated information of the observer.

S14. Design a dynamic event triggering mechanism.

S15. Design a sliding mode fault-tolerant controller based on the observer method.

Optionally, the method further includes: substituting an equivalent control law into the observer to obtain a closed-loop system, and based on the Lyapunov function theory and the linear matrix inequality method, obtaining asymptotic stability of the closed-loop system and sufficient H _∞ performance index. Criterion.

Optionally, the state space form of the dynamic model of the discrete networked control system in S11 is shown in the following formula (1):

为系统的n维状态向量；

表示实数集；

为系统的m维控制输入；

为系统的p维测量输出；

为系统的q维被控输出；A₁为系统矩阵；B为系统的输入矩阵；C为系统的测量矩阵；D₁和D₂为系统的外部扰动矩阵，A₂为系统的输出矩阵；A₁,A₂,B,C,D₁和D₂为具有适当维数的已知矩阵；

和

分别为w维和v维属于l₂[0，∞)的外部扰动,其中l₂[0，∞)为Hilbert空间的平方可积函数；ΔA代表参数不确定性，满足ΔA＝MFN，其中F是一个未知矩阵，满足F^TF≤I，M和N为具有适当维数的已知矩阵；g(x_k)是非线性扰动，满足‖g(x_k)‖≤r‖x_k‖，其中，‖g(x_k)‖为g(x_k)的范数，‖x_k‖为x_k的范数，r＞0代表一个已知常数。in,

is the n-dimensional state vector of the system;

represents the set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is the q-dimensional controlled output of the system; A ₁ is the system matrix; B is the input matrix of the system; C is the measurement matrix of the system; D ₁ and D ₂ are the external disturbance matrices of the system, and A ₂ is the output matrix of the system; A ₁ , A ₂ , B, C, D ₁ and D ₂ are known matrices with appropriate dimensions;

and

are external disturbances belonging to l ₂ [0, ∞) in w dimension and v dimension, respectively, where l ₂ [0, ∞) is the square integrable function of Hilbert space; ΔA represents parameter uncertainty, satisfying ΔA=MFN, where F is An unknown matrix satisfying F ^T F≤I, M and N are known matrices with appropriate dimensions; g(x _k ) is a nonlinear perturbation satisfying ‖g(x _k )‖≤r‖x _k ‖, where, ‖g(x _k )‖ is the norm of g(x _k ), ‖x _k ‖ is the norm of x _k , and r>0 represents a known constant.

Optionally, the sensor failure model in S12 is shown in the following formula (2):

in,

i＝1,2,…,q，f_i 为f_i的下界，

为f_i的上界，满足

Wherein, F _s =diag{f ₁ ,f ₂ ,...,f _q }, and diag is a diagonal matrix;

i=1,2,...,q, f _i is the lower bound of f _i ,

is the upper bound of f _i , satisfying

When f _i =1, i=1,2,...,q, the sensor is in normal operation.

When f _i = 0, i = 1, 2, . . . , q, the sensor does not work at all.

When f _i ∈ (0,1), i=1,2,...,q, the sensor fails.

Denote the measurement output with sensor failure as y _F =F _s y _k .

Optionally, the sliding mode observer in S12 is represented by the following equation (3):

表示观测器状态，

表示被控输出z_k的估计值，L表示观测器增益矩阵。in,

represents the observer state,

represents the estimated value of the controlled output z _k , and L represents the observer gain matrix.

Optionally, the sliding mode surface function in S13 is represented by the following formula (4):

是待设计的滑模面参数矩阵，G＝B^TP₁，P₁＞0是待求解的正定矩阵。Among them, _Sk represents the sliding mode function at time k,

is the sliding mode surface parameter matrix to be designed, G=B ^T P ₁ , and P ₁ >0 is the positive definite matrix to be solved.

Optionally, the dynamic event trigger mechanism model in S14 is shown in the following formula (5):

表示正整数集合；{l₀,l₁,…}为从观测器到控制器当前状态所处的时间序列；定义l₀＝0；σ、θ为给定的正标量；

其中

为k时刻的状态估计，

为最新释放的状态；η_k表示内部动态变量，满足

其中，T为矩阵的转置，λ∈(0,1)为给定的常数，η₀≥0为给定的初始条件。in,

represents a set of positive integers; {l ₀ , l ₁ ,...} is the time series from the observer to the current state of the controller; define l ₀ =0; σ, θ are given positive scalars;

in

is the state estimate at time k,

is the latest released state; η _k represents the internal dynamic variable, satisfying

Among them, T is the transpose of the matrix, λ∈(0,1) is a given constant, and η ₀ ≥0 is a given initial condition.

Optionally, designing a sliding mode fault-tolerant controller based on the observer method in S15 includes:

According to _Sk+1 = _Sk = 0, the equivalent control law is expressed by the following equation (6):

where ^-1 is the inverse matrix.

Based on the dynamic event triggering mechanism, the equivalent control law is rewritten as the following equation (7):

When the difference of the sliding mode surface function satisfies the following equations (8) and (9),

ΔS _k ≤ -ωe ^-μk sgn(S _k )-κS _k if S _k > 0 (8)

ΔS _k ≥ -ωe ^-μk sgn(S _k )-κS _k if S _k <0 (9)

Among them, 0<κ<1, ω>0, and μ≥0.

Design a sliding mode fault-tolerant controller, as shown in the following formula (10):

in,

In the embodiment of the present invention, the error generated by the event trigger mechanism is processed, and under the premise of sensor failure, the sliding mode fault-tolerant control problem of a networked control system with a dynamic event trigger mechanism based on the observer method is studied. For the first time in the sliding mode fault-tolerant control problem, the error generated by the event-triggered mechanism is regarded as a disturbance, and the bounded H _∞ norm is used for attenuation. Through the method of Lyapunov function, the sufficient criterion to ensure the asymptotic stability of the closed-loop system and satisfy the H _∞ performance index is given. Furthermore, a suitable sliding mode fault-tolerant controller is designed so that the state trajectory of the closed-loop system can reach the preset sliding mode surface and remain stable within a limited time.

As shown in FIG. 2 , an embodiment of the present invention provides a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, and the method is implemented by an electronic device. As shown in Figure 2, the flow chart of the sliding mode fault-tolerant control method based on the dynamic event trigger mechanism, the processing flow of the method may include the following steps:

S21, establish a dynamic model of the discrete networked control system, and its state space form is shown in the following formula (1):

为系统的n维状态向量；

表示实数集；

为系统的m维控制输入；

为系统的p维测量输出；

为系统的q维被控输出；A₁为系统矩阵；B为系统的输入矩阵；C为系统的测量矩阵；D₁和D₂为系统的外部扰动矩阵，A₂为系统的输出矩阵；A₁,A₂,B,C,D₁和D₂为具有适当维数的已知矩阵；

和

分别为w维和v维属于l₂[0,∞)的外部扰动,其中l₂[0,∞)为Hilbert空间的平方可积函数；ΔA代表参数不确定性，满足ΔA＝MFN，其中F是一个未知矩阵，满足F^TF≤I，M和N为具有适当维数的已知矩阵；g(x_k)是非线性扰动，满足‖g(x_k)‖≤r‖x_k‖，其中，‖g(x_k)‖为g(x_k)的范数，‖x_k‖为x_k的范数，r＞0代表一个已知常数。in,

is the n-dimensional state vector of the system;

represents the set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is the q-dimensional controlled output of the system; A ₁ is the system matrix; B is the input matrix of the system; C is the measurement matrix of the system; D ₁ and D ₂ are the external disturbance matrices of the system, and A ₂ is the output matrix of the system; A ₁ , A ₂ , B, C, D ₁ and D ₂ are known matrices with appropriate dimensions;

and

are the external perturbations of the w-dimension and v-dimension belonging to l ₂ [0, ∞), respectively, where l ₂ [0, ∞) is the square integrable function of the Hilbert space; ΔA represents the parameter uncertainty, satisfying ΔA=MFN, where F is An unknown matrix satisfying F ^T F≤I, M and N are known matrices with appropriate dimensions; g(x _k ) is a nonlinear perturbation satisfying ‖g(x _k )‖≤r‖x _k ‖, where, ‖g(x _k )‖ is the norm of g(x _k ), ‖x _k ‖ is the norm of x _k , and r>0 represents a known constant.

Among them, the dynamic model of the discrete networked control system can be the dynamic model of the networked control system with uncertainty and external disturbance;

S22, establish a sensor fault model, as shown in the following formula (2):

in,

i＝1,2,…,q，f_i 为f_i的下界，

为f_i的上界，满足

Wherein, F _s =diag{f ₁ ,f ₂ ,...,f _q }, and diag is a diagonal matrix;

i=1,2,...,q, f _i is the lower bound of f _i ,

is the upper bound of f _i , satisfying

where the relationship between the sensor failure and the matrix F _s can be:

When f _i =1, i=1,2,...,q, the sensor is in normal operation.

When f _i = 0, i = 1, 2, . . . , q, the sensor does not work at all.

When f _i ∈ (0,1), i=1,2,...,q, the sensor fails.

Therefore, the measurement output with sensor failure can be expressed as y _F =F _s y _k .

S23, establish a dynamic event trigger mechanism model, as shown in the following formula (3):

表示正整数集合；定义{l₀,l₁,…}为从观测器到控制器当前状态所处的时间序列；定义l₀＝0；σ、θ为给定的正数；Among them, in order to save computer resources, define

Represents a set of positive integers; defines {l ₀ , l ₁ ,...} as the time series from the observer to the current state of the controller; defines l ₀ =0; σ, θ are given positive numbers;

其中

为k时刻的状态估计，

为最新释放的状态；η_k表示内部动态变量，满足

其中，T为矩阵的转置，λ∈(0,1)为给定的常数，η₀≥0为给定的初始条件。

in

is the state estimate at time k,

is the latest released state; η _k represents the internal dynamic variable, satisfying

Among them, T is the transpose of the matrix, λ∈(0,1) is a given constant, and η ₀ ≥0 is a given initial condition.

S24. Design a sliding mode observer, which is represented by the following formula (4):

表示观测器状态，

表示被控输出z_k的估计值，L表示观测器增益矩阵。in,

represents the observer state,

represents the estimated value of the controlled output z _k , and L represents the observer gain matrix.

In a feasible implementation, the sliding mode observer is designed by using the measurement information of the sensor failure; the measurement information of the sensor failure can be obtained based on the sensor failure model of formula (2), and the sliding mode of formula (4) can be obtained according to the measurement information. Mode observer.

S25. Design the sliding mode surface function, which is represented by the following formula (5):

是待设计的滑模面参数矩阵，G＝B^TP₁，P₁＞0是待求解的正定矩阵。Among them, _Sk represents the sliding mode function at time k,

is the sliding mode surface parameter matrix to be designed, G=B ^T P ₁ , and P ₁ >0 is the positive definite matrix to be solved.

In a feasible implementation, the sliding mode surface function can be designed by using the observation information obtained by the sliding mode observer; the sliding mode surface function can be obtained by the sliding mode observer based on formula (4), and the sliding mode surface function of formula (5) can be obtained according to the observation information. Die-face function.

S26. Design a sliding mode fault-tolerant controller based on the observer method.

According to _Sk+1 = _Sk = 0, the equivalent control law is expressed by the following equation (6):

where -1 is the inverse matrix.

Based on the dynamic event triggering mechanism, the equivalent control law is rewritten as the following equation (7):

When the difference of the sliding mode surface function satisfies the following equations (8) and (9),

ΔS _k ≤ -ωe ^-μk sgn(S _k )-κS _k if S _k > 0 (8)

ΔS _k ≥ -ωe ^-μk sgn(S _k )-κS _k if S _k <0 (9)

Among them, 0<κ<1, ω>0, and μ≥0.

Design a sliding mode fault-tolerant controller, as shown in the following formula (10):

in,

In a feasible implementation, as shown in Figure 3, the sliding mode fault-tolerant control system based on the dynamic event-triggering mechanism, considers the sensor fault under the dynamic event-triggering mechanism, and designs the sliding-mode fault-tolerant controller based on the observer method to ensure discrete The accessibility of the die surface in the event of a failure, and to ensure the normal operation of the system in the event of a failure. The trajectory of this closed-loop system can converge to the sliding mode surface within a finite time and remain stable.

In the embodiment of the present invention, the error generated by the event trigger mechanism is processed, and the sliding mode fault-tolerant control problem of a networked control system with a dynamic event trigger mechanism based on the observer method is studied under the premise of sensor failure. For the first time in the sliding mode fault-tolerant control problem, the error generated by the event-triggered mechanism is regarded as a disturbance, and the bounded H _∞ norm is used for attenuation. Through the method of Lyapunov function, the sufficient criterion to ensure the asymptotic stability of the closed-loop system and satisfy the H _∞ performance index is given. Furthermore, a suitable sliding mode fault-tolerant controller is designed so that the state trajectory of the closed-loop system can reach the preset sliding mode surface and remain stable within a limited time.

As shown in FIG. 4 , an embodiment of the present invention provides a sliding mode fault-tolerant control device 400 based on a dynamic event trigger mechanism. The device 400 is applied to implement a sliding mode fault-tolerant control method based on the dynamic event trigger mechanism. The device 400 includes:

The dynamic model establishment module 410 is used for establishing the dynamic model of the discrete networked control system.

The observer design module 420 is used for designing a state sliding mode observer of the discrete networked control system based on the situation of sensor failure in the system.

The sliding mode surface design module 430 is used to design the sliding mode surface based on the estimated information of the observer.

The dynamic event trigger mechanism design module 440 is used to design a dynamic event trigger mechanism.

The sliding mode fault tolerant controller design module 450 is used to design a sliding mode fault tolerant controller based on the observer method.

Optionally, the method further includes: substituting an equivalent control law into the observer to obtain a closed-loop system, and based on the Lyapunov function theory and the linear matrix inequality method, obtaining a closed-loop system that satisfies the asymptotic stability and H _∞ performance index. sufficient evidence.

Optionally, the state space form of the dynamic model of the discrete networked control system is shown in the following formula (1):

为系统的n维状态向量；

表示实数集；

为系统的m维控制输入；

为系统的p维测量输出；

为系统的q维被控输出；A₁为系统矩阵；B为系统的输入矩阵；C为系统的测量矩阵；D₁和D₂为系统的外部扰动矩阵，A₂为系统的输出矩阵；A₁,A₂,B,C,D₁和D₂为具有适当维数的已知矩阵；

和

分别为w维和v维属于l₂[0,∞)的外部扰动,其中l₂[0,∞)为Hilbert空间的平方可积函数；ΔA代表参数不确定性，满足ΔA＝MFN，其中F是一个未知矩阵，满足F^TF≤I，M和N为具有适当维数的已知矩阵；g(x_k)是非线性扰动，满足‖g(x_k)‖≤r‖x_k‖，其中，‖g(x_k)‖为g(x_k)的范数，‖x_k‖为x_k的范数，r＞0代表一个已知常数。in,

is the n-dimensional state vector of the system;

represents the set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is the q-dimensional controlled output of the system; A ₁ is the system matrix; B is the input matrix of the system; C is the measurement matrix of the system; D ₁ and D ₂ are the external disturbance matrices of the system, and A ₂ is the output matrix of the system; A ₁ , A ₂ , B, C, D ₁ and D ₂ are known matrices with appropriate dimensions;

and

are the external disturbances belonging to l ₂ [0, ∞) in w dimension and v dimension, respectively, where l ₂ [0, ∞) is the square integrable function of Hilbert space; ΔA represents parameter uncertainty, satisfying ΔA=MFN, where F is An unknown matrix satisfying F ^T F≤I, M and N are known matrices with appropriate dimensions; g(x _k ) is a nonlinear perturbation satisfying ‖g(x _k )‖≤r‖x _k ‖, where, ‖g(x _k )‖ is the norm of g(x _k ), ‖x _k ‖ is the norm of x _k , and r>0 represents a known constant.

Optionally, the sensor failure model is shown in the following formula (2):

in,

i＝1,2,…,q，f_i 为f_i的下界，

为f_i的上界，满足

Wherein, F _s =diag{f ₁ ,f ₂ ,...,f _q }, and diag is a diagonal matrix;

i=1,2,...,q, f _i is the lower bound of f _i ,

is the upper bound of f _i , satisfying

When f _i =1, i=1,2,...,q, the sensor is in normal operation.

When f _i = 0, i = 1, 2, . . . , q, the sensor does not work at all.

When f _i ∈ (0,1), i=1,2,...,q, the sensor fails.

Denote the measurement output with sensor failure as y _F =F _s y _k .

Optionally, the sliding mode observer is represented by the following equation (3):

表示观测器状态，

表示被控输出z_k的估计值，L表示观测器增益矩阵。in,

represents the observer state,

represents the estimated value of the controlled output z _k , and L represents the observer gain matrix.

Optionally, the sliding mode surface function is represented by the following formula (4):

是待设计的滑模面参数矩阵，G＝B^TP₁，P₁＞0是待求解的正定矩阵。Among them, _Sk represents the sliding mode function at time k,

is the sliding mode surface parameter matrix to be designed, G=B ^T P ₁ , and P ₁ >0 is the positive definite matrix to be solved.

Optionally, the event triggering mechanism model is shown in the following formula (5):

表示正整数集合；{l₀,l₁,…}为从观测器到控制器当前状态所处的时间序列；定义l₀＝0；σ、θ为给定的正标量；

其中

为k时刻的状态估计，

为最新释放的状态；η_k表示内部动态变量，满足

其中，T为矩阵的转置，λ∈(0,1)为给定的常数，η₀≥0为给定的初始条件。in,

represents a set of positive integers; {l ₀ , l ₁ ,...} is the time series from the observer to the current state of the controller; define l ₀ =0; σ, θ are given positive scalars;

in

is the state estimate at time k,

is the latest released state; η _k represents the internal dynamic variable, satisfying

Among them, T is the transpose of the matrix, λ∈(0,1) is a given constant, and η ₀ ≥0 is a given initial condition.

Optionally, the sliding mode fault-tolerant controller design module 450 is further configured to:

According to _Sk+1 = _Sk = 0, the equivalent control law is expressed by the following equation (6):

where ^-1 is the inverse matrix.

Based on the dynamic event triggering mechanism, the equivalent control law is rewritten as the following equation (7):

When the difference of the sliding mode surface function satisfies the following equations (8) and (9),

ΔS _k ≤ -ωe ^-μk sgn(S _k )-κS _k if S _k > 0 (8)

ΔS _k ≥ -ωe ^-μk sgn(S _k )-κS _k if S _k <0 (9)

Among them, 0<κ<1, ω>0, and μ≥0.

Design a sliding mode fault-tolerant controller, as shown in the following formula (10):

in,

In the embodiment of the present invention, the error generated by the event trigger mechanism is processed, and the sliding mode fault-tolerant control problem of a networked control system with a dynamic event trigger mechanism based on the observer method is studied under the premise of sensor failure. For the first time in the sliding mode fault-tolerant control problem, the error generated by the event-triggered mechanism is regarded as a disturbance, and the bounded H _∞ norm is used for attenuation. Through the method of Lyapunov function, the sufficient criterion to ensure the asymptotic stability of the closed-loop system and satisfy the H _∞ performance index is given. Furthermore, a suitable sliding mode fault-tolerant controller is designed so that the state trajectory of the closed-loop system can reach the preset sliding mode surface and remain stable within a limited time.

5 is a schematic structural diagram of an electronic device 500 according to an embodiment of the present invention. The electronic device 500 may vary greatly due to different configurations or performances, and may include one or more processors (central processing units, CPU) 501 and one or more than one memory 502, wherein, at least one instruction is stored in the memory 502, and at least one instruction is loaded and executed by the processor 501 to realize the following sliding mode fault-tolerant control method based on the dynamic event mechanism:

S1. Establish a dynamic model of the discrete networked control system.

S2. Design the state sliding mode observer of the discrete networked control system based on the sensor failure in the system.

S3. Design a sliding mode surface based on the estimated information of the observer.

S4. Design a dynamic event triggering mechanism.

S5. Design a sliding mode fault-tolerant controller based on the observer method.

In an exemplary embodiment, a computer-readable storage medium, such as a memory including instructions, is also provided, and the instructions can be executed by a processor in the terminal to implement the above sliding mode fault-tolerant control method based on the dynamic event triggering mechanism. For example, the computer-readable storage medium may be ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, optical data storage device, and the like.

Those of ordinary skill in the art can understand that all or part of the steps of implementing the above embodiments can be completed by hardware, or can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. The storage medium mentioned may be a read-only memory, a magnetic disk or an optical disk, etc.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection of the present invention. within the range.

Claims (10)

1. A sliding mode fault-tolerant control method based on a dynamic event trigger mechanism is characterized by comprising the following steps:

s1, establishing a dynamic model of the discrete networked control system;

s2, designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults;

s3, designing a sliding mode surface based on observer estimation information;

s4, designing a dynamic event trigger mechanism;

and S5, designing a sliding-mode fault-tolerant controller based on an observer method.

2. The method of claim 1, further comprising: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method_∞And (4) sufficient criterion of performance index.

3. The method according to claim 1, wherein the state space form of the dynamic model of the discrete networked control system in S1 is represented by the following formula (1):

wherein,

is an n-dimensional state vector of the system;

representing a set of real numbers;

is the m-dimensional control input of the system;

is the p-dimensional measurement output of the system;

is q-dimension controlled output of the system; a. the₁Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d₁And D₂Is an external disturbance matrix of the system, A₂Is the output matrix of the system; a. the₁,A₂,B,C,D₁And D₂A known matrix with appropriate dimensions;

and

respectively w and v dimensions belong to

Wherein the external disturbance is

Is a square integrable function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying F^TF ≦ I, M and N being known matrices with appropriate dimensions; g (x)_k) Nonlinear disturbance, satisfies | | g (x)_k)||≤r||x_kI, where g (x)_k) I is g (x)_k) Norm of | x_kII is x_kR > 0 represents a known constant.

4. The method according to claim 3, wherein the sensor fault model in S2 is as shown in the following equation (2):

wherein,

wherein, F_s＝diag{f₁,f₂,…,f_qPreag, diag is a diagonal matrix;

_ifis f_iThe lower bound of (a) is,

is f_iUpper bound of, satisfy

When f is_iWhen 1, i is 1,2, …, q, the sensor is in normal operation;

when f is_iWhen 0, i is 1,2, …, q, the sensor is completely inoperable;

when f is_iE (0,1), i is 1,2, …, q, the sensor fails.

The measurement output with sensor failure is denoted as y_F＝F_sy_k。

5. The method according to claim 4, wherein the sliding mode observer in S2 is represented by the following formula (3):

wherein,

which represents the state of the observer,

representing the controlled output z_kL represents the observer gain matrix.

6. The method according to claim 5, wherein the sliding mode surface function in S3 is represented by the following equation (4):

wherein S is_kA sliding mode function representing the time k,

is a parameter matrix of a sliding mode surface to be designed, G is B^TP₁，P₁> 0 is the positive definite matrix to be solved.

7. The method according to claim 6, wherein the dynamic event trigger mechanism model in S4 is shown as the following formula (5):

wherein,

represents a set of positive integers; { l₀,l₁… is the time sequence from the observer to the current state of the controller; definition of l₀＝0；σ、θGiven a positive scalar quantity;

wherein

For the state estimation at the time instant k,

is the latest released state; eta_kRepresents internal dynamic variables, satisfies

Wherein,^Tfor the transpose of the matrix, λ ∈ (0,1) is given constant, η₀The initial conditions are given as ≧ 0.

8. The method according to claim 7, wherein designing the sliding-mode fault-tolerant controller based on the observer method in S5 comprises:

according to S_k+1＝S_kThe equivalent control law is represented by the following formula (6) when 0:

wherein,^-1is an inverse matrix;

based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):

when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),

ΔS_k≤-ωe^-μksgn(S_k)-κS_kif S is_k＞0 (8)

ΔS_k≥-ωe^-μksgn(S_k)-κS_kIf S is_k＜0 (9)

Wherein, kappa is more than 0 and less than 1, omega is more than 0, mu is more than or equal to 0;

designing a sliding-mode fault-tolerant controller as shown in the following formula (10):

wherein,

9. a sliding-mode fault-tolerant control apparatus based on a dynamic event trigger mechanism, the apparatus comprising:

the dynamic model establishing module is used for establishing a dynamic model of the discrete networked control system;

the observer design module is used for designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults;

the sliding mode surface design module is used for designing a sliding mode surface based on observer estimation information;

the dynamic event trigger mechanism design module is used for designing a dynamic event trigger mechanism;

and the sliding mode fault-tolerant controller design module is used for designing the sliding mode fault-tolerant controller based on the observer method.

10. The apparatus of claim 9, further comprising: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method_∞And (4) sufficient criterion of performance index.

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