CN111880416A - Networked system fault-tolerant control method based on dynamic event trigger mechanism - Google Patents
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Abstract
The invention discloses a networked system fault-tolerant control method based on a dynamic event trigger mechanism. The invention relates to a networked system fault-tolerant control method based on a dynamic event trigger mechanism, which comprises the following steps: the method comprises the steps of firstly, modeling an inverted pendulum networked control problem into a state space model with uncertain parameters by considering network delay; secondly, based on the Lyapunov stability theory and the linear matrix inequality technology, obtaining sufficient conditions that the system is asymptotically stable and meets the fault-tolerant performance index; and thirdly, providing a design method of a state feedback controller under a dynamic event trigger mechanism, and providing a networked system fault-tolerant control method based on the dynamic event trigger mechanism, which can reduce the network data transmission times and enhance the system fault-tolerant performance.
Description
Technical Field
The invention belongs to the field of networked control, and designs a method which is applied to networked control, reduces network load and energy consumption, reduces the times of data transmission, stabilizes a system and can enhance the fault-tolerant performance of the system.
Background
Nowadays, with the rapid development and wide application of network technology, the trend of the control system towards networking, distribution, intellectualization and synthesis is increasingly shown. In a networked control system, the various elements of the system are connected by a common network, and signals are transmitted and exchanged over a communications network. The communication mode of information interaction through the network also provides new opportunities and challenges for analysis and design of the networked control system, such as problems of network delay, bandwidth limitation, signal quantization, disturbance, packet loss rate, and the like, wherein the most prominent problems are network delay and limited bandwidth of a communication channel. Depending on the type of network, this delay may be constant, time-varying or random, but the presence of any delay may degrade the performance of the system or even cause the system to be unstable, making it difficult to apply the conventional control theory and method directly to the research of the network control system.
In the last 90 s of the century, event-based ideas were first applied to engine control. Many articles have set forth the advantages of event-based control. It is noted that early event-triggered control is so-called continuous event-triggering, requiring special hardware for continuous monitoring of the current state. To overcome this problem, Heemels proposes periodic event triggering. An important issue to be noticed in event triggering is that a minimum time interval between any two event execution time points needs to be ensured, i.e. the minimum event interval time is strictly greater than zero. To address this problem, Yue proposes event triggering based on sampled data. Both periodic event triggering and event triggering based on sampled data belong to discrete event triggering, and some documents have been studied on stability analysis and controller design methods of discrete event triggering. With the increasing degree of system informatization, the control system scale is continuously enlarged, and in order to reduce the communication pressure between systems, distributed event-triggered control and distributed event-triggered control of large-scale systems attract more and more attention of scholars. Girard proposes a dynamic event triggering mechanism that can increase the minimum event interval time, even close to the allowable maximum transmission interval, compared to static event triggering.
However, the existing dynamic time mechanism cannot be applied to a system with uncertain parameters, and cannot solve the problem of network delay at the same time. In view of the limitation of the existing results, a dynamic event trigger mechanism suitable for a networked control system with uncertain parameters and network delay is provided, so that the system can be stabilized and the network data transmission times can be reduced.
Disclosure of Invention
In order to overcome the defects that the conventional networked control method cannot be applied to a system with uncertain parameters and has poor fault tolerance performance, the invention introduces a dynamic event trigger mechanism, provides a networked system fault tolerance control method of the parameter uncertain dynamic event trigger mechanism, and provides a state feedback controller design method under the dynamic event trigger mechanism based on the Lyapunov stability theory and the linear matrix inequality technology, wherein the method reduces the network data transmission times and can also enhance the fault tolerance performance of the system.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a networked system fault-tolerant control method based on a dynamic event trigger mechanism comprises the following steps:
firstly, establishing a dynamic mathematical model of an inverted pendulum system:
the inverted pendulum system comprises a trolley, a pendulum rod connected to the top of the trolley and resistance for the trolley; in the formula, M is the mass of the trolley, M is the mass of the oscillating bar, l is the length from the rotating axis of the oscillating bar to the mass center, x represents the displacement of the trolley, theta is the included angle between the oscillating bar and the vertical downward direction, F is the external force received by the trolley, and b is the friction coefficient of the trolley;
establishing a state space model: selecting four quantities of a trolley position x, a trolley speed swing rod angle theta and a swing rod angular speed as state quantities, and obtaining a state space equation as follows:
secondly, constructing the inverted pendulum fault-tolerant controller with uncertain parameters and network delay, and comprising the following processes:
2.1) dynamic event triggering mechanism as follows: η (t) ═ x (kh) + x (k + j) h (3)
Wherein: η (t) is the event-triggered dynamic variable and is a positive definite matrix, j is 1,2,3, x (kh) is the trigger time vector, and x (k + j) h is the state vector.
2.2) considering that the parameters of the inverted pendulum system are uncertain, considering that the inverted pendulum system under network control has time delay, establishing the following system model by using the inverted pendulum model:
x(t)＝Ax(t)+Bu(t)
y(t)＝Cw(t)+Bw (4)
wherein: x (t) E Rn is the system state vector, u (t) E Rm is the system input vector, w (t) E Rp is the perturbation input to the system, y (t) E Rr is the system output vector, a, B, C, Bw are the parameter matrices of the corresponding dimensions, Δ a, Δ B are the norm-bounded parameter matrices, and [ Δ a, Δ B ] ═ hf (t) [ E1, E2] (5) where: h, E1, E2, are matrices of appropriate dimensions, f (t) is an unknown matrix;
2.3) define a delay function:
ek(t)＝τK+x(t-tK) (6)
defining an error signal ek (t) based on the dynamic event triggering conditions:
ek(t)-ek(t-1)＝τKx(t)+u(t) (7)
wherein i is 1,2,3 … d-1; τ K is the system delay τ M ═ max { τ K }, and is the maximum value of the time delay;
2.4) converting the initial dynamic event trigger condition into a dynamic event trigger form with delay:
u(t-τ(t))＝u(tk-1)，tk≤t≤tk+1(8)
the system model is converted into a system model with delay:
the third step: designing a constraint condition matrix of the controller with fault-tolerant stability performance by adopting a Lyapunov stability analysis method according to the delay model:
the following theorem is given:
for matrices R > 0 and XT ═ X, there are-XR-1X ≦ 2R-2X, where is an arbitrary constant; researching dynamic event triggering problem with fault tolerance, and designing by giving disturbance attenuation coefficient gammaSuch that a system (9) that satisfies the dynamic event trigger mechanism (8) satisfies the following two requirements:
(k)＝argi∈{1，...，N}maxσi(k)/hi
4.1) the closed-loop system (10) under w (t) is fault-tolerant and stable;
4.2) under zero initial conditions, for any non-zero w (t) e L2[0, ∞), the controller output z (t) all satisfies | | Z (t) |2 ≦ γ | | | W (t) | 2; the lyapunov generalized method is established, and the following conclusion is obtained. For given parameters γ, υ, and μ > 0, the system (7) is fault tolerant stable under the triggering mechanism (9) and the feedback gain K ∞ YX-1 under the H ∞ norm bound γ, if appropriate dimensions of the matrix exist such that the following inequality holds:
Θ51＝[CX,DY,0,DY]
selecting upsilon, gamma, mu and tau M, and solving through an LMI tool box to obtain a feedback matrix K and trigger condition parameters
Further, in 2.2), the uncertain reasons of the parameters comprise neglecting nonlinear dynamics, mass and rod length measurement inaccuracy and pendulum rod flexibility.
The technical conception of the invention is as follows: firstly, considering the influence of time delay and network bandwidth, a traditional time period triggering mechanism is changed into a dynamic event triggering mechanism method; then, modeling the closed-loop system into a time-lag model of the parameter uncertain system, wherein the model is based on the Lyapunov stability theory and the linear matrix inequality technology and describes the mutual constraint relation between a dynamic event trigger mechanism, the communication network performance and the system stability; finally, a design method of the state feedback controller under the dynamic event trigger mechanism is provided.
The invention has the following beneficial effects: the dynamic event-triggered approach will reduce the number of "unnecessary" sampled signals sent over the network, which will result in high bandwidth usage of the communication. (1) The dynamic event-triggered control scheme may reduce computing resource, battery device energy and communication resource usage, reduce sensor release time and network communication burden. (2) A dynamic event triggering mechanism is introduced, so that the triggering conditions are more diversified and the operability is stronger, and the number of events is reduced better than that of event triggering. (3) Considering the uncertainty of the parameters of the system increases the fault tolerance of the system. (4) The network delay problem is considered, and the method is more suitable for practical application.
Drawings
FIG. 1 is a schematic view of a first order inverted pendulum;
FIG. 2 is a networked system fault-tolerant control system model of a dynamic event-triggered mechanism;
FIG. 3 is a network system triggering scenario under an event triggering mechanism;
FIG. 4 is a network system triggering scenario under a dynamic event triggering mechanism;
FIG. 5 is the inverted pendulum motion state under an event-triggered mechanism;
FIG. 6 shows the motion state of the inverted pendulum under the dynamic event trigger mechanism;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 and 2, a flow chart of networked system fault-tolerant control of an inverted pendulum model and representative values of various parameters and a dynamic event triggering mechanism is respectively described.
A networked system fault-tolerant control method based on a dynamic event trigger mechanism comprises the following steps:
step 1: measuring the mass M of the trolley to be 1.096kg, the mass M of the small ball to be 0.196kg and the length L of the swing rod to be 0.25M to obtain a state space model of the inverted pendulum and obtain a corresponding parameter matrix C and BW; make and combine
Step 2: considering network time delay, transforming an inverted pendulum general model into a time delay model with uncertain parameters, transforming a dynamic event triggering condition into a dynamic event triggering condition with delay, and enabling τ M to be 0.0014;
and step 3: designing a constraint condition matrix of networked system fault-tolerant control with a dynamic event trigger mechanism by adopting a Lyapunov stability analysis method according to a delay model;
and 4, step 4: solving through an LMI tool box to obtain a feedback matrix K and a triggering condition parameter, wherein the feedback matrix K and the triggering condition parameter are 0.53, gamma is 200, upsilon is 20, and mu is 0.1:
K＝[9.778614.0975-76.3929-13.6949]
and 5: the inverted pendulum system is simulated by the feedback matrix K and the triggering condition parameters through the steps by using a networked system fault-tolerant control method of a dynamic event triggering mechanism, and meanwhile, the networked inverted pendulum control condition under the event triggering mechanism is compared. As can be seen from the comparison of fig. 3 to fig. 6, the dynamic event trigger has a great advantage in the number of triggers without affecting the stability of the system.
Claims (2)
1. A networked system fault-tolerant control method based on a dynamic event trigger mechanism is characterized by comprising the following steps:
firstly, establishing a dynamic mathematical model of an inverted pendulum system:
the inverted pendulum system comprises a trolley, a pendulum rod connected to the top of the trolley and resistance for the trolley; in the formula, M is the mass of the trolley, M is the mass of the oscillating bar, l is the length from the rotating axis of the oscillating bar to the mass center, x represents the displacement of the trolley, theta is the included angle between the oscillating bar and the vertical downward direction, F is the external force received by the trolley, and b is the friction coefficient of the trolley;
establishing a state space model: selecting four quantities of a trolley position x, a trolley speed swing rod angle theta and a swing rod angular speed as state quantities, and obtaining a state space equation as follows:
secondly, constructing the inverted pendulum fault-tolerant controller with uncertain parameters and network delay, and comprising the following processes:
2.1) dynamic event triggering mechanism as follows:
wherein: eta (t) is a dynamic variable triggered by an event, eta (t) is more than 0 and less than or equal to 1, and upsilon is more than 0. Is a positive definite matrix, j 1,2,3, x (kh) is the trigger time vector, x (k + j) h is the state vector;
2.2) considering that the parameters of the inverted pendulum system are uncertain, considering that the inverted pendulum system under network control has time delay, establishing the following system model by using the inverted pendulum model:
x(t)＝Ax(t)+Bu(t)
y(t)＝Cw(t)+Bw
wherein: x (t) E Rn is the system state vector, u (t) E Rm is the system input vector, w (t) E Rp is the perturbation input to the system, y (t) E Rr is the system output vector, a, B, C, Bw are the parameter matrices of the corresponding dimensions, Δ a, Δ B are the norm-bounded parameter matrices, and [ Δ a, Δ B ] ═ hf (t) [ E1, E2] (5) where: h, E1, E2, are matrices of appropriate dimensions, f (t) is an unknown matrix;
2.3) define a delay function: ek (t) ═ K + x (t-tK)
Defining an error signal ek (t) based on the dynamic event triggering conditions: ek (t) -ek (t-1) ═ τ kx (t) + u (t) where i ═ 1,2,3 … d-1; τ K is the system delay τ M ═ max { τ K }, and is the maximum value of the time delay;
2.4) converting the initial dynamic event trigger condition into a dynamic event trigger form with delay: u (t- τ (t)) ═ u (t)k-1)，tk≤t≤tk+1
ek(t)＝X(tkh)-X(t-τ(t)) (8)
The system model is converted into a system model with delay:
the third step: designing a constraint condition matrix of the controller with fault-tolerant stability performance by adopting a Lyapunov stability analysis method according to the delay model:
the following theorem is given:
for matrices R > 0 and XT ═ X, there are-XR-1X ≦ 2R-2X, where is an arbitrary constant;
studying the event triggering problem with fault tolerance H ∞, given a disturbance attenuation coefficient γ, a state feedback controller is designed such that a system (10) that satisfies a dynamic event triggering mechanism (9) satisfies the following two requirements:
4.1) the closed-loop system (10) under w (t) is fault-tolerant and stable;
4.2) under zero initial conditions, for any non-zero w (t) e L2[0, ∞), the controller output z (t) all satisfies | | Z (t) |2 ≦ γ | | | W (t) | 2;
the method for establishing the Lyapunov general function obtains the following conclusion:
for given parameters γ, υ, and μ > 0, the system (7) is fault tolerant stable under the triggering mechanism (9) and the feedback gain K ∞ YX-1 under the H ∞ norm bound γ, if there is a suitable dimensionality of the matrix X > 0, Y, such that the following inequality holds:
2. The method as claimed in claim 1, wherein in 2.2), the uncertain parameter reasons include ignoring nonlinear dynamics, mass and rod length measurement inaccuracies and pendulum rod compliance.
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| CN113050493A (en) * | 2021-03-19 | 2021-06-29 | 大连理工大学 | Output feedback control method for inverted pendulum system of trolley in networked environment |
| CN113191021A (en) * | 2021-05-26 | 2021-07-30 | 深圳大学 | Trigger control method and device based on multiplicative measurement uncertainty and related equipment |
| CN113190056A (en) * | 2021-04-07 | 2021-07-30 | 扬州工业职业技术学院 | Temperature control method based on slowest link |
| CN114137879A (en) * | 2021-11-29 | 2022-03-04 | 南京林业大学 | Water surface unmanned ship event trigger control method based on Lyapunov function difference |
| CN114253133A (en) * | 2021-12-07 | 2022-03-29 | 北京科技大学 | Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism |
| CN114415634A (en) * | 2022-01-19 | 2022-04-29 | 大连理工大学 | Fault estimation method for integral type aircraft engine actuating mechanism |
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Cited By (9)
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| CN113050493A (en) * | 2021-03-19 | 2021-06-29 | 大连理工大学 | Output feedback control method for inverted pendulum system of trolley in networked environment |
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| CN114137879A (en) * | 2021-11-29 | 2022-03-04 | 南京林业大学 | Water surface unmanned ship event trigger control method based on Lyapunov function difference |
| CN114137879B (en) * | 2021-11-29 | 2024-03-19 | 南京林业大学 | Event triggering control method of unmanned surface vehicle based on Liapunov function difference |
| CN114253133A (en) * | 2021-12-07 | 2022-03-29 | 北京科技大学 | Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism |
| CN114253133B (en) * | 2021-12-07 | 2023-09-01 | 北京科技大学 | Sliding mode fault tolerance control method and device based on dynamic event trigger mechanism |
| CN114415634A (en) * | 2022-01-19 | 2022-04-29 | 大连理工大学 | Fault estimation method for integral type aircraft engine actuating mechanism |
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