CN109765942A - Water level of open channel control method based on input and output feedback and generalized predictive control - Google Patents
Water level of open channel control method based on input and output feedback and generalized predictive control Download PDFInfo
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Abstract
The open channel systematic water level control method based on input and output feedback transformation and generalized predictive control that the invention discloses a kind of, the method comprising the steps of: S1, the kinetic model that open channel system is described based on Saint-venant Equations；S2, spatial discretization is carried out to the Saint-venant Equations, and further obtains the Time Continuous spatial spreading difference model of the Saint-venant Equations；S3, regard the difference model as Affine Systems, using based on input and output feedback transformation and generalized predictive control be directly controlled the i.e. gatage of input, realize that the accurate water level of open channel system controls.The present invention to mention high control precision, can only need the water level of two points of on-line measurement, generalized predictive control can further increase control precision with on-line identification model parameter to avoid the direct linearization to nonlinear terms using input and output feedback transformation.
Description
Technical field
It is specifically a kind of based on input and output feedback transformation and wide the invention belongs to open channel systematic water level control field
The open channel systematic water level control method of adopted PREDICTIVE CONTROL.
Background technique
Open channel system is a kind of big system of typical distributed complex, and the water flow dynamic characteristic in channel shows as strong non-thread
Property and delay time long feature.The hydraulics dynamic model Saint-venant Equations of open channel system are one group nonlinear partially micro-
Divide equation group, it is difficult to directly as the Controlling model of open channel system.At present using it is more be by Saint-venant Equations space or
Ordinary differential system is obtained after person's time discretization, and then is used after linearizing use using nonlinear control method or to it
Lineary system theory processing.There are also a kind of method be for there is the canal ponds of certain specific hydraulic characteristics, by identification or other
Mathematical method establishes corresponding linear state space model or transfer function model.The above method, which more or less all exists, to be calculated
Amount is big, and on-line measurement data point is more and the disadvantages of being not easy measurement or complicated control law.
Summary of the invention
For above-mentioned technical problem in the related technology, the invention proposes a kind of based on input and output feedback transformation and wide
The open channel systematic water level control method of adopted PREDICTIVE CONTROL, can be to avoid to the straight of nonlinear terms using input and output feedback transformation
Linearisation is connect, to mention high control precision, only needs the water level of two points of on-line measurement, generalized predictive control can be with on-line identification mould
Shape parameter further increases control precision.
To realize the above-mentioned technical purpose, the technical scheme of the present invention is realized as follows:
A kind of open channel systematic water level control method based on input and output feedback transformation and generalized predictive control, including it is following
Step:
S1, the kinetic model that open channel system is described based on Saint-venant Equations；
S2, to the Saint-venant Equations carry out spatial discretization, and further obtain the Saint-venant Equations when
Between continuous space discrete differential model；
S3, regard the difference model as Affine Systems, using based on input and output feedback transformation and Generalized Prediction control
System is directly controlled input i.e. gatage, realizes the accurate water level control of open channel system.
Preferably, the kinetic model of the open channel system is described by Saint-venant Equations:
Wherein in the Saint-venant Equations, a upper equation is continuity equation, and next equation is the equation of momentum,
In, H is open channel system liquid level height, and Q is water flow, if B is open channel system bottom width, A is discharge area, and Z is channel
Slope coefficient, S0 are channel gradient, and Sf is hydraulic slope.
Preferably, in the step S2, spatial discretization is carried out to Saint-venant Equations and is specifically included: free flow channel is pressed
Space is divided into n-1 sections, obtains n sampled point, and sets Gate1 as upstream door, and Gate2 is aft-gate, HuFor on upper gate
Swim end level value, it is assumed that the upstream end level value is invariable amount, HdFor aft-gate downstream level value, it is assumed that described
Downstream level value is invariable amount, if h1, h2... hnThe liquid level of each sampled point, Δ H respectively in channelu, Δ HdRespectively
Upper gate, the liquid level difference at aft-gate both ends, qi, i=1,2 ..., n are respectively water flow at each sampled point of channel, gate
The flow at place and the relationship of control amount U are as follows:
Wherein L is gate widths, and U is gatage, and C is water flow constant, and Δ H is gate both ends liquid level difference；
Preferably for the continuity equation in the Time Continuous spatial spreading difference model of the Saint-venant Equations, the 1st
Point uses single order forward difference, i.e., the 2nd point obtains the 1st difference:
Single order centered difference is used for the 2nd point, what is utilized is and the 1st point data at the 3rd point:
Single order centered difference is used for the the 3 to the n-th -2 point:
Single order centered difference is used to (n-1)th point, the data of use are the n-th -2 point and nth point data:
Single order backward difference is used to nth point, the data of use are the data of and n-th at (n-1)th point:
Preferably for the equation of momentum in the Time Continuous spatial spreading difference model of the Saint-venant Equations, lock
Flow Q at door1It is determined by gatage, to Q2Do centered difference:
To Q3To Qn-2Centered difference:
To Qn-1Do centered difference:
Enable (H1,...Hn,Q2...Qn-1)=(x1,...xn,xn+1,...x2n-2), then the difference model is considered as imitating
Penetrate system:
Preferably, there are two inputs and two to export for the Affine Systems, and the output can be according to the water of control open channel
Position needs to choose, and select the water level for two points that output is channel at upper gate and at aft-gate, defeated by input
Feedback transformation out can make intermediate control amount v respectively1、v2Respectively with output water level y1、y2And its derivative constitutes linear ordinary differential
Equation for intermediate variable and exports the water level that control method used in the linear system constituted is two points of online acquisition,
Generalized forecast control method is respectively adopted and obtains v1And v2, then input is directly controlled by input and output feedback transformation respectively
That is gatage u1And u2。
The present invention can be to avoid to the straight of nonlinear terms using the feedback transformation based on input and output than prior art ratio
Linearisation is connect, high control precision can be effectively mentioned, only needs the water level of two points of on-line measurement；In combination with generalized predictive control
Control precision can be further increased with on-line identification model parameter.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is single channel open channel system construction drawing of the invention；
Fig. 2 is the simulation effect picture using control method of the invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art's every other embodiment obtained belong to what the present invention protected
Range.
Illustrate by taking the water level control of column list channel as an example, it is intended that illustrate the principle of the present invention and method, rather than limit this
The range of invention.If taking output is x1And xn, Affine Systems can indicate are as follows:
y1=x1
y2=xn
The then Relative order vector of system are as follows:
R=(r1,r2)
Wherein r1=1, r2=1.
Because of r1+r2< 2n-2 (n >=3), chooses new state variable in the present invention
ξ1 1=x1
ξ1 2=xn
It is apparent from x1And xnLinear independence, so ξ1 1And ξ1 2Linear independence, the selection for remaining 2n-4 state variable
Guarantee
η1(x),…,η2n-4(x)
Then { g1(x),g2(x) } distribution opened must be pairing.
Affine Systems are demonstrated in the present inventionPair of the distribution of vector contained by matrix
Conjunction property:
Similarly,
So
Therefore { g1(x),g2(x) } distribution opened must be pairing.
To which there are a Nonlinear Mapping Φ:
Make x → (ξ, η), become original system:
y1=ξ1 1
y2=ξ1 2
Wherein:
Then it enables:
It must assure thatIt just can guarantee that system is stable.That is:
It is considered as two subsystems:
The control of generalized forecast control method with parameter identification can be respectively adopted for the two subsystems, can be obtained
It arrives:
Obtain the control input of original system.Control effect of the invention is tested using Matlab/SIC associative simulation
Card: one section of rectangular section prism-shaped channel of simulation, length 100m, channel bottom width B are 10m, are highly 10m, upper water
Position Hu=9m, level of tail water Hd=1m, the steady-state flow water level of channel are 4m, and upstream initial flow is 0.34m3/s, target water level
For 6m, simulation time 10min, step-length 1s, effect is as shown in Figure 2.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of open channel systematic water level control method based on input and output feedback transformation and generalized predictive control, feature exist
In, comprising the following steps:
S1, the kinetic model that open channel system is described based on Saint-venant Equations；
S2, spatial discretization is carried out to the Saint-venant Equations, and the time for further obtaining the Saint-venant Equations connects
Continuous spatial spreading difference model；
S3, regard the difference model as Affine Systems, using based on input and output feedback transformation and generalized predictive control obtain
To input i.e. gatage is directly controlled, the accurate water level control of open channel system is realized.
2. a kind of open channel systematic water level based on input and output feedback transformation and generalized predictive control according to claim 1
Control method, which is characterized in that the kinetic model of the open channel system is described by Saint-venant Equations:
Wherein in the Saint-venant Equations, a upper equation is continuity equation, and next equation is the equation of momentum, wherein H is
Open channel system liquid level height, Q are water flow, if B is open channel system bottom width, A is discharge area, and Z is channel side slopes system
Number, S0For channel gradient, SfFor hydraulic slope, g is terrestrial gravitation constant.
3. a kind of open channel system based on input and output feedback transformation and generalized predictive control according to claim 1 or 2
Method for controlling water level, which is characterized in that in the step S2, spatial discretization is carried out to Saint-venant Equations and is specifically included: will
Free flow channel is spatially divided into n-1 sections, obtains n sampled point, and sets Gate1 as upstream door, and Gate2 is aft-gate, HuFor
Upper gate upstream end level value, it is assumed that the upstream end level value is invariable amount, HdFor aft-gate downstream liquid level
Value, it is assumed that the downstream level value is invariable amount, if h1, h2... hnThe liquid level of each sampled point, Δ respectively in channel
Hu, Δ HdRespectively upper gate, the liquid level difference at aft-gate both ends, qi, i=1,2 ..., n is respectively at each sampled point of channel
Water flow, the relationship of flow and control amount U at gate are as follows:
Wherein L is gate widths, and U is gatage, and C is water flow constant, and Δ H is gate both ends liquid level difference, and g is that terrestrial gravitation is normal
Number.
4. a kind of open channel systematic water level based on input and output feedback transformation and generalized predictive control according to claim 3
Control method, which is characterized in that for the continuous side in the Time Continuous spatial spreading difference model of the Saint-venant Equations
Journey, the 1st point uses single order forward difference, i.e., the 2nd point obtains the 1st difference:
Single order centered difference is used for the 2nd point, what is utilized is and the 1st point data at the 3rd point:
Single order centered difference is used for the the 3 to the n-th -2 point:
Single order centered difference is used to (n-1)th point, the data of use are the n-th -2 point and nth point data:
Single order backward difference is used to nth point, the data of use are the data of and n-th at (n-1)th point:
5. a kind of open channel systematic water level based on input and output feedback transformation and generalized predictive control according to claim 3
Control method, which is characterized in that for the momentum side in the Time Continuous spatial spreading difference model of the Saint-venant Equations
Journey, flow Q at gate1It is determined by gatage, to Q2Do centered difference:
To Q3To Qn-2Centered difference:
To Qn-1Do centered difference:
6. a kind of open channel system based on input and output feedback transformation and generalized predictive control according to claim 4 or 5
Method for controlling water level, which is characterized in that enable (H1,...Hn,Q2...Qn-1)=(x1,...xn,xn+1,...x2n-2), then the difference
Sub-model is considered as Affine Systems:
7. a kind of open channel systematic water level based on input and output feedback transformation and generalized predictive control according to claim 6
Control method, which is characterized in that there are two inputs and two to export for the Affine Systems, and the output can be according to control open channel
Water level need to choose, the water level for two points that output is channel at upper gate and at aft-gate is selected, by defeated
Enter to export feedback transformation, intermediate control amount v can be made respectively1、v2Respectively with output water level y1、y2And its derivative composition is linear normal
The differential equation for intermediate variable and exports the water that control method used in the linear system constituted is two points of online acquisition
Position, is respectively adopted generalized forecast control method and obtains v1And v2, then be directly controlled respectively by input and output feedback transformation defeated
Enter i.e. gatage u1And u2。
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| WO2024192931A1 (en) * | 2023-03-17 | 2024-09-26 | 中国长江三峡集团有限公司 | Water supply network system and control method and apparatus therefor, and storage medium |
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