CN110198236A - A kind of networked system robust control method based on dynamic event trigger mechanism - Google Patents

A kind of networked system robust control method based on dynamic event trigger mechanism Download PDF

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CN110198236A
CN110198236A CN201910437083.3A CN201910437083A CN110198236A CN 110198236 A CN110198236 A CN 110198236A CN 201910437083 A CN201910437083 A CN 201910437083A CN 110198236 A CN110198236 A CN 110198236A
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dynamic event
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CN110198236B (en
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俞立
田栩帆
张丹
周京
陈鹏程
赵磊
廖义辉
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Zhejiang University of Technology ZJUT
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Abstract

A kind of networked system robust control method based on dynamic event trigger mechanism, comprising the following steps: the first step considers network delay, and inverted pendulum network control problem is modeled as a kind of state-space model with Parameter uncertainties；Second step is based on Lyapunov Theory of Stability and linear matrix inequality technology, has obtained system Asymptotic Stability and has met the adequate condition of robust performance index；Third step gives the design method of state feedback controller under dynamic event trigger mechanism.The present invention provides one kind can be reduced network data transmission number, the networked system robust control method based on dynamic event trigger mechanism of strengthen the system robust performance.

Description

A kind of networked system robust control method based on dynamic event trigger mechanism
Technical field
The invention belongs to control based on network fields, design one kind and are applied in control based on network, reduce network load and energy Amount consumption, reduce data transmission number, make system settle out and can strengthen the system robust performance method.
Background technique
Nowadays, with the fast development of network technology and extensive use, control system is to networking, distribution, intelligence Increasingly show with the trend of synthesization development.In network control system, system each unit is connected by public network It connects, signal is transmitted and exchanged by communication network.Networking control is also given by the communication mode that network carries out information exchange The analysis of system processed and design propose new opportunities and challenges, for example, the limitation of network delay, bandwidth, signal quantization, disturbance, The problems such as packet loss, wherein most distinct issues be network delay and communication channel bandwidth it is limited.Not according to network type Together, this delay may be constant, time-varying or random, but no matter the presence of which kind of delay can all reduce the property of system It can even result in that system is unstable, so that traditional control theory is difficult to be applied directly to grinding for network control system with method In studying carefully.
It is taken the lead in being applied in engine control based on the thought of event the nineties in last century.Many articles all elaborate The advantages of based on event control.It may be noted that the event triggering control of early stage is so-called continuous events triggering, it is special to need Hardware current state is continuously monitored.To overcome the problems, such as that this Heemels proposes periodic event triggering.In event It should be noted that an important problem in triggering, that is, between the minimum time for needing to guarantee any two event execution moment Every that is, minimum event-spaced time is strictly larger than zero.In order to solve this problem, Yue proposes the event based on sampled data Triggering.Periodic event triggers and the event triggering based on sampled data belongs to discrete event triggering, triggers about discrete event Stability analysis and controller design method have some documents and studied.With System information degree day increasingly It is deep, the continuous expansion of control system scale, in order to mitigate the communication pressure between system, for the distributing thing of large scale system Part triggering control and distributed event triggering control cause the concern of more and more scholars.Girard proposes dynamic event Trigger mechanism, compared with inactive event triggering, it can increase minimum event-spaced time, it might even be possible to close to allow most Big transmission intercal.
But existing dynamic time mechanism can not be applied to that there are the systems of Parameter uncertainties, while can not also solve Network latency problems.In view of now resultful limitation, propose a kind of suitable for there are Parameter uncertainties and network delays The dynamic event trigger mechanism of network control system can be such that system stablizes while reduce network data transmission number.
Summary of the invention
In order to overcome existing network control method can not be applied to there are the systems of Parameter uncertainties, robust performance Poor deficiency, present invention introduces dynamic event trigger mechanisms, propose the network of Parameter uncertainties dynamic event trigger mechanism Change system robust control method is based on Lyapunov Theory of Stability and linear matrix inequality technology, gives dynamic event State feedback controller design method under trigger mechanism, this method reduce network data transmission numbers can also reinforce simultaneously The robust performance of system.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of networked system robust control method based on dynamic event trigger mechanism, comprising the following steps:
The first step establishes the dynamic mathematical models of reversible pendulum system:
The reversible pendulum system includes trolley, the swing rod on connection car top and the resistance to trolley；M is in above formula The quality of trolley, m are the quality of swing rod, and l is length of the swing rod center of rotation to mass center, and x represents the displacement of trolley, and θ is swing rod With the angle of vertically downward direction, F is the external force that trolley receives, and b is trolley coefficient of friction；
State-space model is established: choosing small truck position x, small vehicle speedSwing rod angle, θ, swing rod angular speedFour Amount is quantity of state, and it is as follows to obtain state space equation:
Second step, construction have Parameter uncertainties, and the inverted pendulum robust controller with network delay, and process is such as Under:
2.1) dynamic event trigger mechanism is as follows:
Wherein: η (t) is the dynamic variable of event triggering, and For a positive definite matrix, J=1,2,3..., x (kh) are triggering moment vectors, and x (k+j) h is state vector.
2.2) consider reversible pendulum system Parameter uncertainties, it is contemplated that the reversible pendulum system under network-control is that having time is prolonged It is existing late, inverted pendulum model is established into following system model:
Wherein: x (t) ∈ RnFor system mode vector, u (t) ∈ RmFor system input vector, w (t) ∈ RpFor disturbing for system Dynamic input, y (t) ∈ RrFor system output vector, A, B, C, BwIt is the parameter matrix of corresponding dimension, Δ A, Δ B are norm-boundeds Parameter matrix, and
[Δ A Δ B]=HF (t) [E1 E2] (5)
Wherein: H, E1, E2, it is the matrix of dimension appropriate, F (t) is unknown matrix；
2.3) delay function is defined:
Based on dynamic event triggering situation, error signal e is definedk(t)。
Wherein, i=1,2,3 ... d-1；τkFor system delay τM=max { τk, it is the maximum value of time delay；
2.4) dynamic event with delay is converted by initial dynamic event trigger condition trigger form:
ek(t)=x (tkh)-x(t-τ(t)) (8)
System model is converted into the system model with delay:
Step 3: there is robust stability using the design of Liapunov stability analysis method according to delay model Controller constraint matrix:
Provide following theorem:
Lemma: for matrix R > 0 and XT=X, there is-XR-1X≤ε2R-2 ε X, wherein ε is arbitrary constant；
The dynamic event Trigger Problems with robust H ∞ are studied, disturbance attenuation coefficient γ, the state feedback of design are given Controller, so that the system (10) for meeting dynamic event trigger mechanism (9) meets following two requirements:
4.1) w (t) ≡ 0 lower closed-loop system (10) is Robust Exponential Stability；
4.2) under zero initial condition, for any non-zero w (t) ∈ L2[0, ∞), controller output z (t) all meets ||z(t)||2≤γ||w(t)||2；
Lyapunov functional counting method is established, is obtained as drawn a conclusion.
For given parameter γ, υ,With parameter μ > 0, system (7) is under trigger mechanism (9) and feedback oscillator K= YX-1It is Robust Exponential Stability at H ∞ norm circle γ, if there is matrix Appropriate dimension so that being set up with lower inequality:
Θ51=[0 DY of CX DY]
Select υ, γ, ε,μ and τM, then solved to obtain feedback matrix K and trigger condition by the tool box LMI Parameter
Further, it is described 2.2) in, Parameter uncertainties reason includes ignoring nonlinear kinetics, the long measurement of quality and bar Inaccuracy and swing rod flexibility.
Technical concept of the invention are as follows: firstly, the influence of time delay and network bandwidth is considered, by Conventional temporal week Phase triggering method mechanism evolves into dynamic event trigger mechanism method；It then, is uncertain parameters systems by closed-loop system modeling Time-Delay model, the model be based on Lyapunov stability theory and linear matrix inequality technology, portray dynamic event touching The mutual restricting relation of hair mechanism, COMMUNICATION NETWORK PERFORMANCES and system stability；Finally, providing shape under dynamic event trigger mechanism The design method of state feedback controller.
Beneficial effects of the present invention are mainly manifested in: dynamic event triggering method will reduce and send many " no by network It is necessary " sampled signal, this will lead to the high utilization rate of bandwidth of communication.(1) dynamic event triggering control program can reduce meter It calculates resource, the cell apparatus energy and the communication resource to use, reduces the release time of sensor and the burden of network communication.(2) draw Enter dynamic event trigger mechanism, keep trigger condition more diversified stronger with operability, and reduces thing better than event triggering The quantity of part.(3) consider that the Parameter uncertainties of system increase the robustness of system.(4) consider network latency problems, more Accord with actual application.
Detailed description of the invention
Fig. 1 is Single Inverted Pendulum schematic diagram.
Fig. 2 is the networked system robust control system model of dynamic event trigger mechanism.
Fig. 3 is event trigger mechanism lower network system trigger situation.
Fig. 4 is dynamic event trigger mechanism lower network system trigger situation.
Fig. 5 is the inverted pendulum motion state under event trigger mechanism.
Fig. 6 is inverted pendulum motion state under dynamic event trigger mechanism.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to Figures 1 and 2, the typical value of inverted pendulum model and parameters, dynamic event trigger mechanism are described respectively Networked system robust control flow chart.
A kind of networked system robust control method based on dynamic event trigger mechanism, comprising the following steps:
Step 1: measurement trolley mass M=1.096kg, pellet quality m=0.196kg, oscillating bar length L=0.25m are obtained The state-space model of inverted pendulum obtains corresponding parameter matrixC, BW；It enablesAnd In conjunction with [Δ A Δ B]=HF (t) [E1 E2]；
Step 2: consider network delay, inverted pendulum universal model is evolved into the Time-Delay model of Parameter uncertainties, it will dynamic Trigger conditions are converted into the dynamic event trigger condition with delay, enable τM=0.0014；
Step 3: using the design of Liapunov stability analysis method there is dynamic event to trigger machine according to delay model The constraint matrix of the networked system robust control of system；
Step 4: being solved to obtain feedback matrix K and trigger condition parameters by the tool box LMIIt enables, ε=0.53, γ=200, υ=20,μ=0.1 solves:
K=[9.7786 14.0975-76.3929-13.6949]
Step 5: by above step to obtained feedback matrix K and trigger condition parametersMachine is triggered with dynamic event The networked system robust control method of system carries out the Realization of Simulation to reversible pendulum system, while under comparison and event trigger mechanism Networking inverted pendulum control situation.By the comparison diagram of Fig. 3-Fig. 6 it can be found that dynamic event triggers in triggering times Also without the stability of influence system while occupying absolutely great advantage.

Claims (2)

1. a kind of networked system robust control method based on dynamic event trigger mechanism, which is characterized in that the method packet Include following steps:
The first step establishes the dynamic mathematical models of reversible pendulum system:
The reversible pendulum system includes trolley, the swing rod on connection car top and the resistance to trolley；M is trolley in above formula Quality, m are the quality of swing rod, and l is length of the swing rod center of rotation to mass center, and x represents the displacement of trolley, and θ is for swing rod and vertically Angle in downward direction, F are the external force that trolley receives, and b is trolley coefficient of friction；
State-space model is established: choosing small truck position x, small vehicle speedSwing rod angle, θ, swing rod angular speedFour amounts are shape State amount, it is as follows to obtain state space equation:
Second step, construction are as follows with Parameter uncertainties, and the inverted pendulum robust controller with network delay, process:
2.1) dynamic event trigger mechanism is as follows:
Wherein: the dynamic variable that η (t) triggers for event, and 0 < η (t)≤1,υ > 0.For a positive definite matrix, j= 1,2,3..., x (kh) are triggering moment vectors, and x (k+j) h is state vector；
2.2) consider reversible pendulum system Parameter uncertainties, it is contemplated that the reversible pendulum system under network-control is that having time delay exists , inverted pendulum model is established into following system model:
Wherein: x (t) ∈ RnFor system mode vector, u (t) ∈ RmFor system input vector, w (t) ∈ RpIt is defeated for the disturbance of system Enter, y (t) ∈ RrFor system output vector, A, B, C, BwIt is the parameter matrix of corresponding dimension, Δ A, Δ B are the parameters of norm-bounded Matrix, and
[Δ A Δ B]=HF (t) [E1 E2] (5)
Wherein: H, E1, E2, it is the matrix of dimension appropriate, F (t) is unknown matrix；
2.3) delay function is defined:
Based on dynamic event triggering situation, error signal e is definedk(t):
Wherein, i=1,2,3 ... d-1；τkFor system delay τM=max { τk, it is the maximum value of time delay；
2.4) dynamic event with delay is converted by initial dynamic event trigger condition trigger form:
ek(t)=x (tkh)-x(t-τ(t)) (8)
System model is converted into the system model with delay:
Step 3: having the control of robust stability using the design of Liapunov stability analysis method according to delay model The constraint matrix of device:
Provide following theorem:
Lemma: for matrix R > 0 and XT=X, there is-XR-1X≤ε2R-2 ε X, wherein ε is arbitrary constant；
The event Trigger Problems with robust H ∞ are studied, disturbance attenuation coefficient γ is given, the state feedback controller of design makes The system (10) that dynamic event trigger mechanism (9) must be met meets following two requirements:
4.1) w (t) ≡ 0 lower closed-loop system (10) is Robust Exponential Stability；
4.2) under zero initial condition, for any non-zero w (t) ∈ L2[0, ∞), controller exports z (t) and all meets | | z (t) ||2≤γ||w(t)||2；
Lyapunov functional counting method is established, is obtained as drawn a conclusion:
For given parameter γ, υ,With parameter μ > 0, system (7) is under trigger mechanism (9) and feedback oscillator K=YX-1? It is Robust Exponential Stability under H ∞ norm circle γ, if there is matrix X > 0,The appropriate dimension of Y Number, so that being set up with lower inequality:
Θ51=[0 DY of CX DY]
Select υ, γ, ε,μ and τM, then solved to obtain feedback matrix K and trigger condition parameters by the tool box LMI
2. a kind of networked system robust control method based on dynamic event trigger mechanism as described in claim 1, special Sign is, it is described 2.2) in, Parameter uncertainties reason includes ignoring the long measurement inaccuracy of nonlinear kinetics, quality and bar and pendulum Bar flexibility.
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CN111146778A (en) * 2019-12-24 2020-05-12 浙江工业大学 Multi-region power grid system design method based on adaptive event triggering dynamic output feedback control
CN111538244A (en) * 2020-05-15 2020-08-14 闽江学院 Net cage lifting control method based on distributed event triggering strategy
CN111880416A (en) * 2020-09-18 2020-11-03 哈尔滨理工大学 Networked system fault-tolerant control method based on dynamic event trigger mechanism
CN112286051A (en) * 2020-09-20 2021-01-29 国网江苏省电力有限公司信息通信分公司 Neural network quantitative control method based on adaptive event trigger mechanism under complex network attack
CN112537340A (en) * 2020-12-18 2021-03-23 北京交通大学 Multi-train scattered event trigger control method based on discrete communication data
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Publication number Priority date Publication date Assignee Title
CN110673474A (en) * 2019-09-17 2020-01-10 浙江工业大学 Intrusion-tolerant control method of networked motion control system based on event triggering
CN113031431A (en) * 2019-12-09 2021-06-25 南京理工大学 Event-triggered networked T-S fuzzy H-infinity control method under generalized system
CN111146778A (en) * 2019-12-24 2020-05-12 浙江工业大学 Multi-region power grid system design method based on adaptive event triggering dynamic output feedback control
CN111146778B (en) * 2019-12-24 2021-10-15 浙江工业大学 Multi-region power grid system design method based on adaptive event triggering dynamic output feedback control
CN111538244A (en) * 2020-05-15 2020-08-14 闽江学院 Net cage lifting control method based on distributed event triggering strategy
CN111538244B (en) * 2020-05-15 2022-12-09 闽江学院 Net cage lifting control method based on distributed event trigger strategy
CN111880416A (en) * 2020-09-18 2020-11-03 哈尔滨理工大学 Networked system fault-tolerant control method based on dynamic event trigger mechanism
CN112286051A (en) * 2020-09-20 2021-01-29 国网江苏省电力有限公司信息通信分公司 Neural network quantitative control method based on adaptive event trigger mechanism under complex network attack
CN112537340B (en) * 2020-12-18 2022-03-25 北京交通大学 Multi-train scattered event trigger control method based on discrete communication data
CN112537340A (en) * 2020-12-18 2021-03-23 北京交通大学 Multi-train scattered event trigger control method based on discrete communication data
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
CN113050493B (en) * 2021-03-19 2022-03-04 大连理工大学 Output feedback control method for inverted pendulum system of trolley in networked environment
CN113471955A (en) * 2021-09-02 2021-10-01 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Island direct current micro-grid distributed dynamic event trigger control method
CN113471955B (en) * 2021-09-02 2021-12-14 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Island direct current micro-grid distributed dynamic event trigger control method
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

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