CN107966908A - The fuzzy control method of non-linear truck-trailer systems based on event trigger mechanism - Google Patents
The fuzzy control method of non-linear truck-trailer systems based on event trigger mechanism Download PDFInfo
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Abstract
The invention discloses a kind of fuzzy control method of the non-linear truck-trailer systems based on event trigger mechanism, Step 1: establishing the dynamic mathematical models of truck-trailer systems；Step 2: being based on event trigger mechanism, the trigger conditions of truck-trailer systems are set, and construct the fuzzy controller of truck-trailer systems；Step 3: Fuzzy Control Law u (t) instructs control signal sends system actuators to by event trigger device, control purpose is realized.The fuzzy control method of non-linear truck-trailer systems of the invention based on event trigger mechanism, it can obtain ideal dynamic characteristic, have certain robustness to systematic parameter and the change of exterior interference signal so that system is with good stability.Further, since the introducing of event-triggered communication mechanism, effectively inhibits the Time-varying time-delays characteristic of truck-trailer systems, and reduce the transmission data in network, alleviate the burden of network bandwidth occupation rate.
Description
Technical field
The present invention relates to the control method of Control of Nonlinear Systems technical field, more particularly to truck-trailer systems.
Background technology
Truck-trailer systems are a typical multivariables, non-linear, unstable dynamical system.In a practical situation,
In order to successfully be driven to desired position, driver will repeatedly attempt to retreat, and advance, retreat again, again the operation such as advance, most
Zhongdao reaches preferable position, and it is a more difficult job that it, which is controlled,.In addition, the stability right and wrong of Guarantee control system
It is often important, although the method for being currently based on various classical linear control theories and advanced control theory it has been proposed that due to
The inside multimode characteristic of truck-trailer systems, and uncertainty and running environment in system there are model parameter constantly become
The problems such as change, general linear control theory are no longer applicable in.
Fuzzy control is a kind of new control mode to be grown up based on fuzzy mathematics, it is accurately controlled with traditional
Method processed has larger difference, using fuzzy mathematics, the inference method of fuzzy linguistic rules, forms a kind of closed loop with feedback
Automatic control system, it belongs to intelligent control, has the ability of processing fuzzy message.The core of fuzzy control theory research is
How to solve in fuzzy control on stability and robust analysis, the design method of system, the raising of the performance of control system etc.
Problem, this has become several generally acknowledged basic problems in fuzzy control research.Takagi-Sugeno (T-S) fuzzy model is
Fuzzy control system one of very famous mark in history.Numerous control problem, such as stability analysis, robust filtering, most
The problems such as excellent control, self adaptive control, network controls, all employ research object of the T-S fuzzy models as them.The opposing party
Face, if truck-trailer systems are realized by wireless network connection, a problem needed to be considered is exactly in network control system
In whether have enough bandwidth, information is fed back on controller, then control command is sent on actuator and object.Thing
Part trigger mechanism can substantially reduce the transmission data in network, mitigate the burden of network bandwidth occupation rate, save limited communication
Resource, reduces the power consumption of network node.Therefore, the correlative study based on event trigger mechanism has important theory significance
And real value.And the research that the fuzzy control method based on event triggering is applied to truck-trailer systems does not almost have at present
Have.
The content of the invention
In view of this, a kind of Fuzzy Control of the non-linear truck-trailer systems based on event trigger mechanism of the purpose of the present invention
Method processed, effectively to solve the inside multimode characteristic of truck-trailer systems, and there are the uncertain of model parameter in system
Property and running environment the problems such as constantly changing, ideal dynamic characteristic is obtained, to systematic parameter and exterior interference signal
Change has certain robustness so that system is with good stability；And it can effectively suppress the time-varying of truck-trailer systems
Time lag characteristic, reduces the transmission data in network, mitigates the burden of network bandwidth occupation rate.
The fuzzy control method of non-linear truck-trailer systems of the invention based on event trigger mechanism, including following step
Suddenly：
Step 1: establish the dynamic mathematical models of truck-trailer systems：
In formula, L be trailer length, unit m；L be truck length, unit m,It is single for constant speed of moving backward
Position is m/s；For sampling time, unit s；For system initial time, unit s；For acceleration of gravity, unit is
m/s2；
OrderT-S fuzzy controls are designed using fuzzy rule as follows
Device：
Rule 1：
If θ (t) ≈ 0,
So
Z (t)=D1x(t)+E1u(t)+F1w(t)；
Rule 2：
If θ (t) ≈ ± π,
So
Z (t)=D2x(t)+E2u(t)+F2w(t)；
Wherein x (t)=[x1(t) x2(t) x3(t)]T, w (t)=[w1(t) w2(t)]T, x (t) be system state to
Amount, u (t) are the control inputs of system, and w (t) is exogenous disturbances, scope L2[0, ∞), z (t) is measurement output；
So far, the state-space model of truck-trailer systems is obtained；
Step 2: being based on event trigger mechanism, the trigger conditions of truck-trailer systems are set, and construct truck trailer
The fuzzy controller of system；
1) the event triggering form of truck-trailer systems is as follows：
ek T(skT)Λ1ek(skT)≤δxT(t-h(t))Λ2x(t-h(t))
Wherein：ek(skT the error of the sampling instant and newest transmission time of current transmission between the two, i.e. e) are representedk
(skT)=x (skT)-x(tkT)；Λ1,Λ2Represent designed event triggering weighting matrix；δ is given constant scalar, is met
δ∈[0,1)；H (t) represents time delay；X (t-h (t)) represents delay state；
2) event trigger mechanism parameter Λ is designed1, Λ2With constant scalar δ；Wherein event triggering matrix Λ1,Λ2Can profit
Solved to obtain with the solver feasp in Matlab-LMI tool boxes；[0,1) δ meets δ ∈；
3) in fuzzy system control, Fuzzy Control Law is equivalent to Kj=Ωjξ-1Form, KjIt is the gain of fuzzy controller
Matrix, matrix ΩjMeet condition K in stability condition design with given scalar ξjξ=Ωj；
4) Fuzzy Control Law is constructed：
U (t)=Kjx(tkT)
Wherein：KjIt is fuzzy controller gain matrix；x(tkT present sample state) is represented；Whether sampled data is transmitted to
Corresponding fuzzy controller is determined by following trigger conditions：
[x(kT)-x(tkT)]TΛ1[x(kT)-x(tkT)]≤δxT(kT)Λ2x(kT)
Wherein：Λ1,Λ2Represent designed event triggering weighting matrix, x (kT) represents present sample state, x (tkT)
Represent newest transmission state, δ is given constant scalar, meet δ ∈ [0,1)；
Finally, it is as follows that T-S closed loop fuzzy control systems can be obtained：
Z (t)=Dix(t)+EiKjx(t-h(t))-EiKjek(skT)+Fiw(t)；
Step 3: Fuzzy Control Law u (t) instructs control signal sends system actuators to by event trigger device,
Realize control purpose.
Beneficial effects of the present invention：
The fuzzy control method of non-linear truck-trailer systems of the invention based on event trigger mechanism, it makes system near
Like being a series of linear Input output Relationship, using the intelligent control method of fuzzy control, truck trailer system is efficiently solved
The inside multimode characteristic of system, and the problems such as constantly change there are the uncertainty and running environment of model parameter in system,
Ideal dynamic characteristic can be obtained, there is certain robustness to systematic parameter and the change of exterior interference signal so that
System is with good stability.Further, since the introducing of event-triggered communication mechanism, effectively inhibits truck-trailer systems
Time-varying time-delays characteristic, and reduce the transmission data in network, alleviate the burden of network bandwidth occupation rate.
Brief description of the drawings
Fig. 1 is event trigger device figure.As can be seen from the figure the principle of event trigger mechanism is by system current state
It is compared with last state, judges whether to transmit last state, the target for saving the communication resource is reached with this.If newest shape
When state and current state meet certain trigger condition, transmission last state is to controller, conversely, being transmitted without state.It is aobvious
And be clear to, event-triggered communication mechanism is introduced into the transmission data that can be substantially reduced in network, mitigates network bandwidth occupation rate
Burden, reduces the power consumption of network node.
Fig. 2 is the fuzzy control block diagram of event triggering.For obtained mathematical model, its system mode is transmitted by sensor
To event trigger device, judged whether the state of sensor transmission being transmitted to controller by event trigger mechanism.If meet
Corresponding trigger conditions, system mode will by signal by transmission of network to fuzzy controller, then controller again will
Signal, to actuator, realizes control effect by transmission of network.
Fig. 3 is truck-trailer systems rough schematic view.
Fig. 4 is its condition responsive curve x after former truck-trailer systems are subject to external disturbance1(t)。
Fig. 5 is its condition responsive curve x after former truck-trailer systems are subject to external disturbance2(t)。
Fig. 6 is its condition responsive curve x after former truck-trailer systems are subject to external disturbance3(t).It can be seen by Fig. 4-6
Go out former truck trailer open cycle system (not adding fuzzy controller) after external disturbance is subject to, system mode is unstable and in hair
Bulk state.
Fig. 7 is event triggering release moment and the interval schematic diagram of Fuzzy control system.
Fig. 8 is the response curve x of former truck-trailer systems state after adding fuzzy controller1(t)。
Fig. 9 is the response curve x of former truck-trailer systems state after adding fuzzy controller2(t)。
Figure 10 is the response curve x of former truck-trailer systems state after adding fuzzy controller3(t).Comprehensive analysis Fig. 4-
6 and Fig. 8-10, it can be seen that designed fuzzy controller can make the truck trailer after external disturbance is received in embodiment
System mode asymptotically stability simultaneously converges to expectation state, realizes control targe.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples.
The fuzzy control method of non-linear truck-trailer systems based on event trigger mechanism, comprises the following steps：
Step 1: establish the dynamic mathematical models of truck-trailer systems：
In formula, L be trailer length, unit m；L be truck length, unit m,It is single for constant speed of moving backward
Position is m/s；For sampling time, unit s；For system initial time, unit s；For acceleration of gravity, unit is
m/s2。
OrderT-S fuzzy controls are designed using fuzzy rule as follows
Device：
Rule 1：
If θ (t) ≈ 0,
So
Z (t)=D1x(t)+E1u(t)+F1w(t)；
Rule 2：
If θ (t) ≈ ± π,
So
Z (t)=D2x(t)+E2u(t)+F2w(t)；
Wherein x (t)=[x1(t)x2(t)x3(t)]T, w (t)=[w1(t)w2(t)]T, x (t) is the state vector of system, u
(t) be system control input, w (t) is exogenous disturbances, scope L2[0, ∞), z (t) is measurement output.
So far, the state-space model of truck-trailer systems is obtained.
Step 2: being based on event trigger mechanism, the trigger conditions of truck-trailer systems are set, and construct truck trailer
The fuzzy controller of system；
1) the event triggering form of truck-trailer systems is as follows：
ek T(skT)Λ1ek(skT)≤δxT(t-h(t))Λ2x(t-h(t))
Wherein：ek(skT the error of the sampling instant and newest transmission time of current transmission between the two, i.e. e) are representedk
(skT)=x (skT)-x(tkT)；Λ1,Λ2Represent designed event triggering weighting matrix；δ is given constant scalar, is met
δ∈[0,1)；H (t) represents time delay；X (t-h (t)) represents delay state.
2) event trigger mechanism parameter Λ is designed1, Λ2With constant scalar δ；Wherein event triggering matrix Λ1,Λ2Can profit
Solved to obtain with the solver feasp in Matlab-LMI tool boxes；[0,1) δ meets δ ∈.
3) in fuzzy system control, Fuzzy Control Law is equivalent to Kj=Ωjξ-1Form, KjIt is the gain of fuzzy controller
Matrix, matrix ΩjMeet condition K in stability condition design with given scalar ξjξ=Ωj。
4) Fuzzy Control Law is constructed：
U (t)=Kjx(tkT)
Wherein：KjIt is fuzzy controller gain matrix；x(tkT present sample state) is represented；Whether sampled data is transmitted to
Corresponding fuzzy controller is determined by following trigger conditions：
[x(kT)-x(tkT)]TΛ1[x(kT)-x(tkT)]≤δxT(kT)Λ2x(kT)
Wherein：Λ1,Λ2Represent designed event triggering weighting matrix, x (kT) represents present sample state, x (tkT)
Represent newest transmission state, δ is given constant scalar, meet δ ∈ [0,1).
Finally, it is as follows that T-S closed loop fuzzy control systems can be obtained：
Z (t)=Dix(t)+EiKjx(t-h(t))-EiKjek(skT)+Fiw(t)；
Step 3: Fuzzy Control Law u (t) instructs control signal sends truck-trailer systems to by event trigger device
Actuator, realizes control purpose.
Emulated below by using Matlab, to verify, fuzzy control method drags non-linear truck in the present embodiment
The validity of car system control.
Non-linear truck-trailer systems as shown in Figure 3, wherein system parameter setting are as follows：
L=2.8, L=5.5,
In addition, it is assumed that the relevant parameter of truck-trailer systems：H=0.12, τ=0.5, system initial state are：x0
=[0.16-0.1 0.16].Then linear matrix inequality is solved with MATLAB-LMI tool boxes, this implementation can be obtained
Designed fuzzy controller gain matrix K is as follows in example：K1=[1.0519-0.3633 0.0364], K2=[0.5766-
0.1740 0.0321]；
And matrix can be triggered in the hope of event and be：
Finally obtain simulation result as shown in figs. 4 through 10.From analogous diagram as can be seen that designed by the present embodiment based on thing
The fuzzy controller of part triggering can not only ensure the stability of closed-loop system, and (former truck drags for former nonlinear system
Car system) it can also ensure its stabilization.Additionally due to the introducing of event-triggered communication mechanism, reduces making for grid bandwidth
With rate, limited communication computing resource has been saved.
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with
The present invention is described in detail in good embodiment, it will be understood by those of ordinary skill in the art that, can be to the skill of the present invention
Art scheme technical scheme is modified or replaced equivalently, without departing from the objective and scope of technical solution of the present invention, it should all cover at this
Among the right of invention.
Claims (1)
1. the fuzzy control method of the non-linear truck-trailer systems based on event trigger mechanism, it is characterised in that：Including following
Step：
Step 1: establish the dynamic mathematical models of truck-trailer systems：
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In formula, L be trailer length, unit m；L be truck length, unit m,For constant speed of moving backward, unit
For m/s；For sampling time, unit s；For system initial time, unit s；For gravity acceleration, unit is
m/s2；
OrderT-S fuzzy controllers are designed using fuzzy rule as follows：
Rule 1：
If θ (t) ≈ 0,
So
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Z (t)=D1x(t)+E1u(t)+F1w(t)；
Rule 2：
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So
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Z (t)=D2x(t)+E2u(t)+F2w(t)；
Wherein x (t)=[x1(t) x2(t) x3(t)]T, w (t)=[w1(t) w2(t)]T, x (t) is the state vector of system, u
(t) be system control input, w (t) is exogenous disturbances, scope L2[0, ∞), z (t) is measurement output；
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So far, the state-space model of truck-trailer systems is obtained；
Step 2: being based on event trigger mechanism, the trigger conditions of truck-trailer systems are set, and construct truck-trailer systems
Fuzzy controller；
1) the event triggering form of truck-trailer systems is as follows：
ek T(skT)Λ1ek(skT)≤δxT(t-h(t))Λ2x(t-h(t))
Wherein：ek(skT the error of the sampling instant and newest transmission time of current transmission between the two, i.e. e) are representedk(skT)
=x (skT)-x(tkT)；Λ1,Λ2Represent designed event triggering weighting matrix；δ is given constant scalar, meets δ ∈
[0,1)；H (t) represents time delay；X (t-h (t)) represents delay state；
2) event trigger mechanism parameter Λ is designed1, Λ2With constant scalar δ；Wherein event triggering matrix Λ1,Λ2It can utilize
Solver feasp in Matlab-LMI tool boxes is solved to obtain；[0,1) δ meets δ ∈；
3) in fuzzy system control, Fuzzy Control Law is equivalent to Kj=Ωjξ-1Form, KjIt is the gain matrix of fuzzy controller,
Matrix ΩjMeet condition K in stability condition design with given scalar ξjξ=Ωj；
4) Fuzzy Control Law is constructed：
U (t)=Kjx(tkT)
Wherein：KjIt is fuzzy controller gain matrix；x(tkT present sample state) is represented；Whether sampled data is transmitted to accordingly
Fuzzy controller determined by following trigger conditions：
[x(kT)-x(tkT)]TΛ1[x(kT)-x(tkT)]≤δxT(kT)Λ2x(kT)
Wherein：Λ1,Λ2Represent designed event triggering weighting matrix, x (kT) represents present sample state, x (tkT) represent
Newest transmission state, δ are given constant scalars, meet δ ∈ [0,1)；
Finally, it is as follows that T-S closed loop fuzzy control systems can be obtained：
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Z (t)=Dix(t)+EiKjx(t-h(t))-EiKjek(skT)+Fiw(t)；
Step 3: Fuzzy Control Law u (t) instructs control signal sends system actuators to by event trigger device, realize
Control purpose.
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| CN108717264A (en) * | 2018-05-29 | 2018-10-30 | 重庆大学 | A method of the magnetic suspension system fuzzy controller that design is triggered based on event |
| CN111352442A (en) * | 2020-01-08 | 2020-06-30 | 重庆大学 | Towed trailer trajectory tracking method based on robust H-infinity control |
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| CN113031644A (en) * | 2021-02-06 | 2021-06-25 | 中南大学 | Communication time lag oriented aircraft formation control system event triggering method, device and medium |
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| CN108490787A (en) * | 2018-04-29 | 2018-09-04 | 天津大学 | Saturation system Composite nonlinear feedback control device design method based on event triggering |
| CN108717264A (en) * | 2018-05-29 | 2018-10-30 | 重庆大学 | A method of the magnetic suspension system fuzzy controller that design is triggered based on event |
| CN108717264B (en) * | 2018-05-29 | 2021-02-09 | 重庆大学 | Method for designing magnetic suspension system fuzzy controller based on event triggering |
| CN108667673B (en) * | 2018-06-22 | 2022-02-22 | 东北大学 | Nonlinear network control system fault detection method based on event trigger mechanism |
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| CN112882389A (en) * | 2021-01-13 | 2021-06-01 | 吉林大学 | Vehicle stability controller design method based on segmented T-S fuzzy model |
| CN113031644A (en) * | 2021-02-06 | 2021-06-25 | 中南大学 | Communication time lag oriented aircraft formation control system event triggering method, device and medium |
| CN113093537B (en) * | 2021-03-24 | 2022-04-01 | 大连理工大学 | Event-triggered observer design method based on online asynchronous front-part reconstruction |
| CN113093537A (en) * | 2021-03-24 | 2021-07-09 | 大连理工大学 | Event-triggered observer design method based on online asynchronous front-part reconstruction |
| CN114859725A (en) * | 2022-05-09 | 2022-08-05 | 广东工业大学 | Self-adaptive event trigger control method and system for nonlinear system |
| CN114859725B (en) * | 2022-05-09 | 2024-04-05 | 广东工业大学 | Nonlinear system self-adaptive event trigger control method and system |
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