CN106970611B - Network control system sampling period optimal control method - Google Patents
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Abstract
The present invention provides a kind of network control system sampling period optimal control method, including to controlled device measurement output variable, sampled by tune output variable, and construct discrete system model；Establish sampling period TsWith the relationship between network delay τ；Dynamic Output Feedback robust controller is designed, and constructs closed-loop system model；Detect whether obtained closed-loop system model meets robust asymptotic stability requirement；Establish sampling period TsWith the relationship between optimal robustness performance γ；Sampling step length h is set, and sets a sampling period Ts'=Ts+ h is repeated the above process, and is stopped sampling when closed-loop system loses robust asymptotic stability, is defined next sampling period T corresponding to the smallest optimal robustness performance γs' it is the optional sampling period, and it is denoted as Tγ.The problem of present invention mainly solves sampling period optimal controls devises a kind of state output feedback robust controller, ensure that system in the case where extraneous disturbance, still with good stability, dynamic and robustness.
Description
Technical field
The present invention relates to network control system automatic control technology fields, are a kind of sampling weeks of network control system
Phase optimal control method.
Background technique
With automative control theory, the increasingly developed and Cross slot interference of computer technology, network communication technology, control system
The structure of system becomes increasingly complex, and spatial distribution is more and more wider, network control system (Networked Control System,
It NCS) is the closed-loop feedback control system being made up of real-time network.In network control system, network is situated between as transmission
Matter realizes the data transmission between sensor, controller, actuator and other network nodes, to realize resource-sharing, remote
Journey detects and controls.Network control system is at low cost with its, connection flexibly, the advantages that being easily installed extension, is convenient for safeguarding from
The limitation for fundamentally breaching traditional " point-to-point " formula signal control, is the objective demand of tele-control system, extensively
Applied to fields such as space flight and aviation, smart grid, remote fault diagnosis, robot controls.Fig. 2 is the allusion quotation of network control system
Type structure, the characteristics of due to network to communication media time-sharing multiplex, when multiple nodes are carried out data transmission by network, usually
There is phenomena such as information occlusion, disconnecting, multiframe transmission, thus inevitably the delay of information occurs, therefore time lag is asked
Topic is one of the main problem that network control system faces, it often leads to the major reason of system deterioration.On the other hand,
With the continuous expansion of modern control system scale, complexity is continuously increased, external environment unpredictability, and external disturbance is random
Property etc., so that people is hardly resulted in the description that system determines, therefore consider the external disturbance of system, planned network networked control systems
Robust stabili, to be still able to maintain preferable performance right and wrong when guaranteeing that the dynamic characteristic of system changes in certain range of disturbance
It is often important and necessary.
In actual NCS, due to the limitation of environmental factor or economic condition, there is only network delays in system, and
And be difficult to detect whole states of controlled device, for this purpose, the research of network control system problem has become one of hot spot.Such as
Zhu Qixin, Lu Kaihong, Zhu Yonghong, et al. in document " robust state feedback control of the multi tate without networked control systems with time-delay
[J] " (Suzhou Institute of Science and Technology journal (natural science edition), 2017,34 (1)) middle finger egress sample frequency it is more than one
Network control system is known as multi tate network control system, and this article utilizes robust control and linear inequality method, devises more
Robust State Feedback Controllerss of the rate without networked control systems with time-delay, designed controller can make corresponding closed-loop system
Asymptotically stability.The method has the following disadvantages:
1) it proposes sliding-model control to be carried out with the different sampling periods, to every to sensor node, controller node in text
The sampling period of a node is still to provide in advance, the robust controller that the method obtains, only under the sampling period
Optimum control belongs to local optimum, does not ensure that the global optimum of system, i.e., under the optimal sampling period, system reaches
Optimal robust control；
2) work of author is not consider ideally carrying out for network delay, and in actual industrial system
In, network delay certainly exists；
3) controller designed in text is state feedback robust controller, and in actual engineer application, the shape of system
State often is difficult to measure acquisition, this just limits application of this method in engineering.
Summary of the invention
The technical problem to be solved in the present invention is for all with fixed sampling present in existing network control technology
Phase obtains the problem of robust controller does not ensure that system robustness energy global optimum, and network latency problems, external disturbance is asked
Topic, provides a kind of sampling period optimal control method of network control system.
To achieve the above object, the invention adopts the following technical scheme.
A kind of network control system sampling period optimal control method, including controlled device is measured and is exported
Variable and by the sampling of tune output variable, key step is as follows:
Step 1 samples to the measurement output variable of controlled device, by tune output variable, and constructs discrete system mould
Type；
Wherein,
State variable when x (k) is controlled device current time k；
X (k+1) is the state variable at control (k+1) moment in period under controlled device；
Control input quantity when u (k) is controlled device current time k；
Control input quantity when u (k-1) is previous control period (k-1)；
Measurement output variable when y (k) is current time k；
Z (k) be current time k when by tune output variable；
External disturbance when w (k) is current time k；
A is the coefficient of controlled device continuous time state variable x (t) and is a constant, and t is consecutive hours
Between variable, TsFor the sampling period；
B1Input quantity u is controlled for controlled device continuous time
(t) coefficient and be a constant, τ is network delay；
B2For external disturbance coefficient 1 and be a constant；
C1For state variable x (k) coefficient 1 and be a constant；
C2For state variable x (k) coefficient 2 and be a constant；
D1For external disturbance coefficient 2 and be a constant；
D2For external disturbance coefficient 3 and be a constant；
Step 2 establishes sampling period TsWith the relationship between network delay τ；
Wherein, TsendFor sending cycle, and Ts≥Tsend, m is the length of queue, and n is of contained data packet in queue
Number；
Step 3, design Dynamic Output Feedback robust controller, and construct closed-loop system model；
The expression formula of the closed-loop system model is as follows:
Wherein,
X (k-1) is the state variable at controlled device previous control (k-1) moment in period；
xc(k) be controller current time k when state variable；
xcIt (k+1) is the state variable at control (k+1) moment in period under controller；
xcIt (k-1) is the state variable at controller previous control (k-1) moment in period；
W (k-1) is the external disturbance at previous control (k-1) moment in period；
AcFor controller state variable xc(k) coefficient 1 and be a constant；
BcThe coefficient 1 of y (k) is exported for measurement and is a constant；
CcFor controller state variable xc(k) coefficient 2 and be a constant；
DcThe coefficient 2 of y (k) is exported for measurement and is a constant；
Whether whether step 4, the obtained closed-loop system model of detecting step 3 meet robust asymptotic stability requirement, i.e., full
Sufficient inequality (4), if meeting inequality (4), closed-loop system model meets robust asymptotic stability requirement, enters step 5, otherwise
Return step 1；
Wherein,
W51=Ad+B10DcC2,W51 TFor W51Transposition；
W52=B10Cc,W52 TFor W52Transposition；
W53=B11DcC2,W53 TFor W53Transposition；
W54=B11Cc,W54 TFor W54Transposition；
W61=BCC2,W61 TFor W61Transposition；
For AcTransposition；
P is the coefficient 1 of liapunov function and is a constant, P-1For the inverse of P；
S is the coefficient 2 of liapunov function and is a constant, S-1For the inverse of S；
R is the coefficient 3 of liapunov function and is a constant；
Z is the coefficient 4 of liapunov function and is a constant；
Step 5 establishes sampling period TsWith the relationship between optimal robustness performance γ；
Wherein, W75=B10DcC2+B2,W75 TFor W75Transposition；For BcTransposition；γ is optimal robustness performance；ε is mark
Amount；For unit matrix；
Step 6, setting sampling step length h, and set a sampling period Ts'=Ts+ h repeats steps 1 and 2,3,4,5, works as closed loop
System stops sampling when losing robust asymptotic stability, defines next sampling period corresponding to the smallest optimal robustness performance γ
Ts' it is the optional sampling period, and it is denoted as Tγ。
Preferably, sampling period T is established described in step 2sThe process of relationship between network delay τ includes following step
It is rapid:
Step 2.1 determines queuing model；
Wherein, P0For the probability for containing 0 data packet in queue；
P1For the probability for containing 1 data packet in queue；
Pn-1For the probability containing n-1 data packet in queue；
PnFor the probability containing n data packet in queue；
Pn+1For the probability containing n+1 data packet in queue；
λ is the rate into queue；
μ is the rate of dequeue；
Step 2.2 is 1 by the sum of state probability in queue, supplements equation；
Pn>=0 n=0,1,2 ... m (7)
Step 2.3 can obtain the probability of stability by formula (6) and (7):
Pn=(λ/μ)n(1-λ/μ),λ≤μ (8)
If into the rate of queueThe rate of dequeueThen formula (8) can transform to:
Pn=(Tsend/Ts)n(1-Tsend/Ts),Ts≥Tsend (9)
Thus sampling period T is establishedsWith the relationship between network delay τ:
Preferably, Dynamic Output Feedback robust controller described in step 3 are as follows:
The beneficial effects of the present invention are:
1, the characteristics of being directed to network delay in network control system, using queuing model, establishes sampling period and net
Relationship between network delay；
2, the optional sampling period has been determined, ensure that the global optimum of system, i.e., under the optimal sampling period, system reaches
To optimal robustness characteristic；
3, Dynamic Output Feedback H∞The design of robust controller is convenient for practical engineering application, ensure that system is disturbed in the external world
In the case where dynamic interference, still with good stability, dynamic and robustness.
Detailed description of the invention
Fig. 1 is the flow chart of control method of the present invention.
Fig. 2 is the structure chart of network control system.
Fig. 3 is the relational graph in control method of the present invention between sampling period and network delay.
Fig. 4 is the relational graph adopted in control method of the present invention between sample period and robust performance.
Specific embodiment
Clear, complete description is carried out to technical solution of the present invention below in conjunction with attached drawing.Obviously described to implement
Example is only a part of the embodiment of the present invention, and based on the embodiment of the present invention, those skilled in the art is not making creation
Property labour under the premise of the other embodiments that obtain, all belong to the protection scope of this patent.
The embodiment provides a kind of sampling period optimal control methods of network control system, including to quilt
Control object measurement output variable and by the sampling of tune output variable.
According to the flow chart of control method shown in FIG. 1, embodiment step of the present invention is as follows:
Step 1 samples to the measurement output variable of controlled device, by tune output variable, and constructs discrete system mould
Type；
Wherein, state variable when x (k) is controlled device current time k；
X (k+1) is the state variable at control (k+1) moment in period under controlled device；
Control input quantity when u (k) is controlled device current time k；
Control input quantity when u (k-1) is previous control period (k-1)；
Measurement output variable when y (k) is current time k；
Z (k) be current time k when by tune output variable；
External disturbance when w (k) is current time k；
For the coefficient of controlled device continuous time state variable x (t), t is continuous time
Variable, Ts=10ms is the sampling period；
For the control of controlled device continuous time
The coefficient of input quantity u (t), τ are network delay；
For the coefficient 1 of external disturbance；
C1=[1 0] are the coefficient matrix 1 of state variable x (k)；
C2=[1 1] are the coefficient 2 of state variable x (k)；
D1=[0 0] are the coefficient 2 of external disturbance；
D2=[- 1-2] are the coefficient 3 of external disturbance.
Step 2 establishes sampling period TsWith the relationship between network delay τ；
Wherein, Tsend=10ms is sending cycle, and Ts≥Tsend, m=10 is the length of queue, and n is contained number in queue
According to the number of packet.
Specifically, the derivation process of (2) formula, i.e., described to establish sampling period TsThe mistake of relationship between network delay τ
Journey the following steps are included:
1) queuing model is determined；
Wherein, P0For the probability for containing 0 data packet in queue；
P1For the probability for containing 1 data packet in queue；
Pn-1For the probability containing n-1 data packet in queue；
PnFor the probability containing n data packet in queue；
Pn+1For the probability containing n+1 data packet in queue；
λ is the rate into queue；
μ is the rate of dequeue；
2) it is 1 by the sum of state probability in queue, supplements equation；
Pn>=0 n=0,1,2 ... m (7)
3) probability of stability can be obtained by formula (6) and (7):
Pn=(λ/μ)n(1-λ/μ),λ≤μ (8)
If into the rate of queueThe rate of dequeueThen formula (8) can transform to:
Pn=(Tsend/Ts)n(1-Tsend/Ts),Ts≥Tsend (9)
Thus sampling period T is establishedsWith the relationship between network delay τ:
Step 3, design Dynamic Output Feedback robust controller, and construct closed-loop system model；
The expression formula of the closed-loop system model is as follows:
Wherein, x (k-1) is the state variable at controlled device previous control (k-1) moment in period；
xc(k) be controller current time k when state variable；
xcIt (k+1) is the state variable at control (k+1) moment in period under controller；
xcIt (k-1) is the state variable at controller previous control (k-1) moment in period；
W (k-1) is the external disturbance at previous control (k-1) moment in period；
For controller state variable xc(k) coefficient 1；
For the coefficient 1 of measurement output y (k)；
For controller state variable xc(k) coefficient 2；
For the coefficient 2 of measurement output y (k).
During constructing closed-loop system model, the Dynamic Output Feedback robust controller of design are as follows:
Whether whether step 4, the obtained closed-loop system model of detecting step 3 meet robust asymptotic stability requirement, i.e., full
Sufficient inequality (4), if meeting inequality (4), closed-loop system model meets robust asymptotic stability requirement, enters step 5, otherwise
Return step 1；
Wherein, W51=Ad+B10DcC2,W51 TFor W51Transposition；
W52=B10Cc,W52 TFor W52Transposition；
W53=B11DcC2,W53 TFor W53Transposition；
W54=B11Cc,W54 TFor W54Transposition；
W61=BCC2,W61 TFor W61Transposition；
For AcTransposition；
For the coefficient 1, P of liapunov function-1For the inverse of P；
For liapunov function matrix 2, S-1For the inverse of S；
For liapunov function matrix 3；
For liapunov function matrix 4.
Step 5 establishes sampling period TsWith the relationship between optimal robustness performance γ；
Wherein, W75=B10DcC2+B2,W75 TFor W75Transposition；For BcTransposition；γ=3.1531 are optimal robustness
Energy；ε=5.1217 × 10-7For scalar；For unit matrix.
Step 6, setting sampling step length h=1ms, and set a sampling period Ts'=Ts+ h repeats steps 1 and 2,3,4,5,
Stop sampling when closed-loop system loses robust asymptotic stability, defines next sampling corresponding to the smallest optimal robustness performance γ
Cycle Ts' it is the optional sampling period, and it is denoted as Tγ。
By above-mentioned steps, next sampling period T can be obtaineds' and network delay τ between relationship as shown in figure 3, next sampling
Cycle Ts' and optimal robustness performance γ between relationship it is as shown in Figure 4.Then the smallest optimal robustness performance γ=1.1822 institute is right
The next sampling period T answereds' it is optional sampling period, i.e. Tγ=24ms.
At this point, Dynamic Output Feedback optimal robust controller are as follows:
Wherein, Ac=-0.0069, Bc=-0.0055,
Claims (2)
1. a kind of network control system sampling period optimal control method, including output variable is measured to controlled device and is adjusted
The sampling of output variable, which is characterized in that key step is as follows:
Step 1 samples to the measurement output variable of controlled device, by tune output variable, and constructs discrete system model；
Wherein,
State variable when x (k) is controlled device current time k；
X (k+1) is the state variable at control (k+1) moment in period under controlled device；
Control input quantity when u (k) is controlled device current time k；
Control input quantity when u (k-1) is previous control period (k-1)；
Measurement output variable when y (k) is current time k；
Z (k) be current time k when by tune output variable；
External disturbance when w (k) is current time k；
A is the coefficient of controlled device continuous time state variable x (t) and is a constant, and t is continuous time change
Amount, TsFor the sampling period；
B1Input quantity u (t) is controlled for controlled device continuous time
Coefficient and be a constant, τ is network delay；
B2For external disturbance coefficient 1 and be a constant；
C1For state variable x (k) coefficient 1 and be a constant；
C2For state variable x (k) coefficient 2 and be a constant；
D1For external disturbance coefficient 2 and be a constant；
D2For external disturbance coefficient 3 and be a constant；
Step 2 establishes sampling period TsWith the relationship between network delay τ；
Wherein, TsendFor sending cycle, and Ts≥Tsend, m is the length of queue, and n is the number of contained data packet in queue；
Step 3, design Dynamic Output Feedback robust controller, and construct closed-loop system model；
The expression formula of the Dynamic Output Feedback robust controller is as follows:
The expression formula of the closed-loop system model is as follows:
Wherein,
X (k-1) is the state variable at controlled device previous control (k-1) moment in period；
xc(k) be controller current time k when state variable；
xcIt (k+1) is the state variable at control (k+1) moment in period under controller；
xcIt (k-1) is the state variable at controller previous control (k-1) moment in period；
W (k-1) is the external disturbance at previous control (k-1) moment in period；
AcFor controller state variable xc(k) coefficient 1 and be a constant；
BcThe coefficient 1 of y (k) is exported for measurement and is a constant；
CcFor controller state variable xc(k) coefficient 2 and be a constant；
DcThe coefficient 2 of y (k) is exported for measurement and is a constant；
Whether whether step 4, the obtained closed-loop system model of detecting step 3 meet robust asymptotic stability requirement, i.e., meet not
Equation (4), if meeting inequality (4), closed-loop system model meets robust asymptotic stability requirement, enters step 5, otherwise returns
Step 1；
Wherein,
W51=Ad+B10DcC2,W51 TFor W51Transposition；
W52=B10Cc,W52 TFor W52Transposition；
W53=B11DcC2,W53 TFor W53Transposition；
W54=B11Cc,W54 TFor W54Transposition；
W61=BCC2,W61 TFor W61Transposition；
For AcTransposition；
P is the coefficient 1 of liapunov function and is a constant, P-1For the inverse of P；
S is the coefficient 2 of liapunov function and is a constant, S-1For the inverse of S；
R is the coefficient 3 of liapunov function and is a constant；
Z is the coefficient 4 of liapunov function and is a constant；
Step 5 establishes sampling period TsWith the relationship between optimal robustness performance γ；
Wherein, W75=B10DcC2+B2,W75 TFor W75Transposition；For BcTransposition；γ is optimal robustness performance；ε is scalar；For unit matrix；
Step 6, setting sampling step length h, and set a sampling period Ts'=Ts+ h repeats steps 1 and 2,3,4,5, works as closed-loop system
Stop sampling when losing robust asymptotic stability, defines next sampling period T corresponding to the smallest optimal robustness performance γs' be
The optional sampling period, and it is denoted as Tγ。
2. a kind of network control system sampling period optimal control method according to claim 1, which is characterized in that step
Rapid 2 described establish sampling period TsThe process of relationship between network delay τ the following steps are included:
Step 2.1 determines queuing model；
Wherein, P0For the probability for containing 0 data packet in queue；
P1For the probability for containing 1 data packet in queue；
Pn-1For the probability containing n-1 data packet in queue；
PnFor the probability containing n data packet in queue；
Pn+1For the probability containing n+1 data packet in queue；
λ is the rate into queue；
μ is the rate of dequeue；
Step 2.2 is 1 by the sum of state probability in queue, supplements equation；
Step 2.3 can obtain the probability of stability by formula (6) and (7):
Pn=(λ/μ)n(1-λ/μ),λ≤μ (8)
If into the rate of queueThe rate of dequeueThen formula (8) can transform to:
Pn=(Tsend/Ts)n(1-Tsend/Ts),Ts≥Tsend (9)
Thus sampling period T is establishedsWith the relationship between network delay τ:
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