CN109197539A - A kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm - Google Patents
A kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm Download PDFInfo
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Abstract
The present invention proposes a kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm, belongs to and irrigates the automatic control of transmission & distribution water and agricultural water resources management domain.The present invention obtains the design data and service condition data for irrigating multistage channel first, establishes controlling channel model and is converted into state space equation form；Then the output quantity in irrigation canal water distribution system future is predicted, and Model Predictive Control Algorithm objective function, identification constraint condition is established according to service condition；Optimum control amount is obtained finally by Optimization Solution, realizes and the multistage channel of irrigation is safely and effectively automatically controlled.The present invention is based on irrigate multistage channel designing data and service condition designs a model predictive control algorithm, the known water intaking variation and constraint condition irrigated in multistage canal's moving can be successfully managed, it can be used for irrigating the auto-control Design of multistage channel, it can ensure safe and reliable water services, effectively realize the efficient management of Water Resources Irrigation and utilize.
Description
Technical field
The invention belongs to irrigate transmission & distribution water to automatically control and agricultural water resources management domain, and in particular to one kind is based on model
The irrigation multistage canal automatic control method of predictive control algorithm.
Background technique
In current water resource using in structure, agricultural water accounting is maximum, and agricultural water accounts for using water in world wide
The 70% of total amount, however since agricultural irrigation water mode is rough, manage and dispatch is not scientific and control mode backwardness, it causes
A large amount of wastes of water resource, while also leading to not provide the water services of high efficient and reliable for water user, cause Water Resources Allocation
It is inefficient, utilization rate is low, wherein being during irrigation canal water delivery due to management and running there are about 20%~30% water loss
Caused by unreasonable.Irrigation canal transmission & distribution water is automatically controlled through the real-time monitoring and integrated dispatch pipe to channel hydraulic information
Reason, can be such that channel hydraulic pipeline process safety reliably carries out, and supply water on demand, effectively reduce canal system water loss and waste, improve canal system
Operational management and service level, be the inexorable trend of modern agriculture Irrigation Development.
The operational objective of irrigation canal is to realize to supply water to agricultural water family timely and appropriate discovery.The intrinsic time lag of irrigation canal,
Coupling and characteristic is disturbed, so that the artificial method of operation is difficult to meet water user and want to water services reliability and flexibility more
It asks, needs to carry out the automatic control of irrigation water delivery channel.Wherein PID class feedback control algorithm is the most classical, but is based on single input
The PID class algorithm singly exported is not ideal enough in the control effect of multi-cascade canal for water conveyance, needs to develop the excellent of multiple-input and multiple-output
Change control algolithm, Linear-Quadratic Problem (LQR) has more achievement as one of system optimizing control.Optimized using Linear-Quadratic Problem and is controlled
Algorithm processed irrigate multistage canal automatic control and needs using following steps:
1) it establishes and irrigates multistage controlling channel model；Specific step is as follows:
It 1-1) determines channel to be controlled, collects the design data and service condition data of the channel；
Irrigation Project Design multistage canalization includes channel and the control structure by manual adjustment.It is assumed that multistage canal to be controlled
Road is made of f canal pond, and the channel designing data for needing to collect include the length L in each canal pondi, longitudinal slope Sbi, roughness ni, design
Flow QiWith form of fracture data etc., the service condition data for needing to collect include each canal pond water draw rate qi, control point design fortune
Row depth of water hspi, design and operation water level yspi, system export reference value yriAnd operational envelope ± ri(riRepresent i-th of canal
The corresponding control point water level operational process in pond allows the maximum value fluctuated) etc..
1-2) controlling channel model is established using the data that step 1-1) is collected；Expression formula is as follows:
In formula, yiIt is the corresponding downstream control point water level in i-th of canal pond relative to yspiVariable quantity, unit: m；When t is
Between, unit: s；AsiFor the corresponding backwater zone area in i-th of canal pond, unit: m2；qini、qoutiAnd qdiRespectively i-th of canal pond pair
Canal pond inbound traffics, outflow and the water draw rate answered correspond to the variable quantity of original steady-state, unit: m3/s；τiIt is i-th
The corresponding lag time in canal pond, unit: s.
The return water in each canal pond is obtained by theoretical formula method or numerical simulation recognition methods under the conditions of design discharge
Area area AsiWith lag time τiTwo parameters, so that it is determined that the hydraulic characteristic(s) in each canal pond of multistage channel is irrigated, in conjunction with each canal pond
Water draw rate qi, controlling channel modular form (1-1) can be obtained.
2) the controlling channel model conversation for establishing step 1) is state space equation form；
According to the controlling channel modular form (1-1) established in step 1), the separate manufacturing firms equation of multistage channel is constructed,
Assuming that irrigation canal is stational system, shown in discrete form state space equation such as formula (1-2):
X (k+1)=Ax (k)+Bu (k)+Dd (k) (1-2)
In formula, k is the time under discrete form；X is state variable；U is control variable；D is disturbance variable；A is system
Matrix；B is control matrix；D is perturbation matrix.
3) it constructs the objective function of Linear-Quadratic Problem algorithm and solves optimum control amount；
3-1) set the quadratic sum of state variable in formula (1-2) and control variable to the target function type of canal's moving
(1-3).In canal's moving control process, the flow of change control structure is adjusted by appropriateness to realize that control water level is finally steady
It is scheduled on the target of setting value, the objective function expression formula of canal's moving is as follows:
In formula, J is objective function, and Q is n × n dimension state weight matrix (n be state variable dimension), for symmetric positive definite (or
Positive semidefinite) matrix；R is f × f dimension control weighting matrix (f is control variable dimension, equal to the number in canal pond), is symmetric positive definite
Matrix.
First item on the right of target function type (1-3) equation is the function of measurement system dynamic deviation, and Section 2 is used to weigh
Amount control energy consumption.Linear quadratic gaussian control can be understood as keeping lesser output inclined by little control amount
Difference, so that the synthesis for reaching controlled system dynamic deviation and energy consumption is optimal.
3-2) linear quadratic optimal control problem is to find optimum control variable u* (k) under the constraint of formula (1-2),
So that formula (1-3) reaches minimum.By control theory it is found that under state space equation constraint, when performance indicator takes minimum, most
Excellent control variable meets formula (1-4) form:
u*(k)=- Kx (k) (1-4)
In formula, K=(BTPB+R)-1BTPA, referred to as Optimal Feedback matrix；P is that the algebra multitude as shown in formula (1-5) blocks the side of mentioning
The solution of journey:
P=ATPA-ATPB(BTPB+R)-1BTPA+Q (1-5)
Formula (1-5) can be solved by numerical method, wherein callable function dlqr is according to system square in MATLAB
Battle array A, control matrix B, state weight matrix Q and control weighted matrix R solve to obtain K and P.
By Linear quadratic gaussian control amount formula (1-4) it is found that control variable is the linear combination of state variable, by most
Excellent feedback matrix K determines that Linear-Quadratic Problem feedback control algorithm carries out real-time feedback control, thus nothing according to system current state
Method successfully manages inside the plan water intaking and operation constraint condition.
Model Predictive Control Algorithm (MPC) is provided simultaneously with feedback and feed forward function, be the research of current process control field with
The hot spot of application, algorithm are based on Linear Control modelling, are predicted by Linear Control model the output of system future, and
Control is optimized by the finite time-domain objective function of foundation, MPC can successfully manage determining or predictable external disturbance,
Simultaneously it can be considered that the constraint condition that system is subject to.However the Model Predictive Control Algorithm design and solution under constraint condition at present
It is still insufficient, limit the effective application of MPC in practical projects.
Summary of the invention
The purpose of the present invention is the shortcoming to overcome prior art, propose a kind of based on Model Predictive Control Algorithm
Irrigate multistage canal automatic control method.The present invention can successfully manage known water intaking variation and constraint condition in canal's moving,
The Design of Automatic Control System that can be used for multi-stage irrigation channel can be realized safe and reliable water services, effectively realization irrigated area
The efficient management and utilization of water resource.
The present invention proposes that a kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm, feature exist
In, comprising the following steps:
1) it establishes and irrigates multistage controlling channel model, the specific steps are as follows:
It 1-1) determines channel to be controlled, collects the design data and service condition data of the channel；
The irrigation multistage canalization for selecting any irrigated area is channel to be controlled, it is assumed that the canalization is by f canal pond group
At channel designing data include the length L in each canal pond in f canal pondi, longitudinal slope Sbi, roughness ni, design discharge QiAnd form of fracture
Data, service condition data include each canal pond water draw rate qi, control point design and operation depth of water hspi, design and operation water level yspi、
System exports reference quantity yriAnd operational envelope ± rI,, wherein riRepresent the corresponding control point water level operation in i-th of canal pond
Process allows the maximum value fluctuated；
1-2) controlling channel model is established using the data that step 1-1) is collected；Expression formula is as follows:
In formula, yiIt is the corresponding downstream control point water level in i-th of canal pond relative to design and operation water level yspiVariable quantity,
Unit: m；T is time, unit: s；AsiFor the corresponding backwater zone area in i-th of canal pond, unit: m2；qini、qoutiAnd qdiRespectively
The variable quantity of original steady-state is corresponded to for the corresponding canal pond inbound traffics in i-th of canal pond, outflow and water draw rate, unit:
m3/s；τiFor the corresponding lag time in i-th of canal pond, unit: s；
2) the controlling channel model conversation for establishing step 1) is state space equation form；
According to formula (1), shown in the separate manufacturing firms equation such as formula (2) and formula (3) for constructing multistage channel:
X (k+1)=Ax (k)+Bu (k)+Dd (k) (2)
Y (k)=Cx (k) (3)
In formula, k is the time under discrete form；X is state variable；U is control variable；D is disturbance variable；Y is output
Variable；A is sytem matrix；B is control matrix；C is output matrix；D is perturbation matrix；
3) output quantity for irrigating multistage canalization future is predicted, and constructs the target of Model Predictive Control Algorithm
Function；Specific step is as follows:
3-1) control is run according to system to require to determine prediction time domain p and control time domain c, using formula (2) and formula (3), by
Period carries out rolling forecast to system state variables and output variable, obtains system in the output result of prediction time domain end；
In control time domain c, state variable and the output variable predicted value of canalization are respectively as follows:
Predict that the response of remainder in time domain p is free response after controlling time domain；
It is that following matrix form is expressed that system, which exports predicted value and arranges:
Y (k+1 | k)=Sxx(k)+SuU(k)+SdD(k) (19)
The formula (18) and reference quantity y for 3-2) obtaining step 3-1)rDeviation and control variable u carry out quadratic form summation,
Obtain the objective function of Model Predictive Control Algorithm；
In formula,For system prediction output quantity, yrReference quantity is exported for system, u is control variable, QjIt is inclined for j-th of water level
Matrix, R are punished in the weighting of differencejMatrix is punished in the weighting for controlling variable for j-th；
Output reference quantity and weighting matrix are expressed as following matrix form,
Yr(k+1 | k)=[yr(k+1)；yr(k+2)；…；yr(k+p)] (23)
Q=diag (Q1,Q2,...,Qp), R=diag (R1,R2,...,Rc) (24)
Convolution (23) and formula (24) export the matrix form of prediction and control variable, target function type (22) table to system
It is shown as following matrix reduction form:
J=[Q (Y (k+1 | k)-Yr(k+1))]2+[RU(k)]2 (25)
4) based on step 3) as a result, identifying system constraint condition, and optimum control amount is calculated by Optimization Solution；
Specific step is as follows:
4-1) identifying system constraint condition；It is specific as follows:
Control structure flow Filters with Magnitude Constraints；
Qlb≤Q0(t-1)+ΦU(k)≤Qub (26)
In formula, Φ is control variables transformations matrix, Q0For control structure current time flow, QubAnd QlbRespectively control knot
The minimum and maximum inflow-rate of water turbine of structure；
The constraint of control structure flow luffing；The constraint of control structure flow luffing includes the constraint of control variable maximum luffing and control
Structure flow minimum luffing constraint processed；
Control the expression-form of variable maximum luffing constraint are as follows:
Ulb≤U(k)≤Uub (27)
The expression-form of control structure flow minimum luffing constraint are as follows:
|U(k)|≥Udb (28)
In formula, UubAnd UlbThe respectively control structure maximum stream flow variable quantity that allows, U when flow increases and reducesdb
The minimum discharge variable quantity of requirement is adjusted for control structure；
Water level Filters with Magnitude Constraints；
Ylb≤Y(k+1|k)≤Yub (29)
In formula, YubAnd YlbRespectively irrigate control point water level allows to reach in multistage Canal's Moving Process maximum and most
Small value；
Range of stage constraint；
ΔYlb≤RX(k+1|k)≤ΔYub (30)
In formula, R is sparse coefficient matrix, Δ YubWith Δ YlbRespectively control point water level allows in rise and whereabouts
Maximum stage variable quantity；
4-2) according to formula (25), the identification of constraint condition is run to system in conjunction with step 4-1), Model Predictive Control is calculated
The objective function of method is converted into the canonical form of quadratic programming, and when by solving to obtain prediction using quadratic programming optimization algorithm
Optimal control sequence in domain；The specific method is as follows:
Formula (25) is arranged into the canonical form such as formula (31) for quadratic programming problem objective function:
In formula, HuIt is symmetric positive semidefinite matrix for Hessian matrix；GrFor gradient vector；e0For constant term；T is transposition operation
Symbol；
Formula (19) are substituted into formula (25) and arranged and obtain formula (32):
Wherein Hessian matrix, gradient vector and constant term are respectively as shown in formula (33), (34) and (35):
Hu=(QSu)TQSu+RTR (33)
Gr(k+1)=- (QSu)TQ[Yr(k+1)-Sxx(k)-SdD(k)] (34)
e0=0.5 × { Q [Yr(k+1)-Sxx(k)-SdD(k)]}T{Q[Yr(k+1)-Sxx(k)-SdD(k)]} (35)
4-2-1) unconstrained optimization solves；
When the input and output of system unfettered condition influences, there are analytic solutions for quadratic programming problem at this time；By formula
(31) derivation is carried out to control variable U (k), and its derivative 0 is made to obtain the analytical expression (36) of optimal solution:
By solve formula (36) obtain control time domain in without constrained optimum control sequence Uuc(k) analytical expression
(37), which is that formula (25) reaches the smallest optimum control amount U in control time domainuc(k):
4-2-2) constrained optimization solves；
Quadratic programming expression formula containing linear restriction is as follows:
s.t.ΓU(k)≤b (39)
In formula, Γ and b are the matrix and vector for defining linear restriction；
The canonical form that control structure flow Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
The constraint of control structure maximum flow luffing arranges the canonical form for quadratic programming linear restriction are as follows:
In formula, I is the unit matrix of c × c dimension；
The canonical form that water level Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
Range of stage constraint arranges the canonical form for quadratic programming linear restriction are as follows:
In formula, coefficient matrix Sux, Sxx, SdxIt is divided by obtain with output matrix C by formula (21)；
Model Predictive Control Algorithm predicts future output according to the controlling channel model of foundation, and is predicted with exporting
Value and reference quantity yrThe sum of deviation and the quadratic form of control variable u are objective function, under constraint condition, by running to system
The identification of constraint condition solves and obtains the optimum control amount U in control time domain, which is formula (22) table in control time domain
The objective function shown reaches the smallest optimum control amount.
The features of the present invention and beneficial effect are:
The irrigation multistage canal automatic control method based on Model Predictive Control Algorithm that the invention proposes a kind of, utilizes canal
Road design data and service condition construct controlling channel model, predict the output of channel future by state space equation and in mesh
Scalar functions consider constraint condition in canalization operation in solving, and model prediction algorithm is enabled to successfully manage known fetched water
Journey and operation constraint condition, to keep algorithm more practical.Model Predictive Control Algorithm can efficiently solve multi-stage irrigation canal
The sluggishness and coupled characteristic faced in road operation, sluggish and coupled characteristic can not be successfully managed by compensating for single feedback control algorithm
And can not consider the problems of known water intaking process and operation constraint condition, it automatically controls and refines for irrigation canal transmission & distribution water
Agricultural water management provides effective technical solution, has the advantages that strong operability, conveniently obtains practical application and promote.
Detailed description of the invention
Fig. 1 is the overall flow figure of the method for the present invention.
Fig. 2 is the water level change of error process schematic of case study on implementation of the present invention.
Specific embodiment
The present invention proposes a kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm, below with reference to
Attached drawing and specific implementation are further described as follows.
A kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm proposed by the present invention, this method
Overall flow is as shown in Figure 1, comprising the following steps:
1) it establishes and irrigates multistage controlling channel model, the specific steps are as follows:
It 1-1) determines channel to be controlled, collects the design data and service condition data of the channel；
Channel to be controlled is the irrigation multistage canalization in any irrigated area in the present invention, for the ladder being made of f canal pond
For shape section channel, the channel designing data for needing to collect include the length L in each canal pond in f canal pondi, longitudinal slope Sbi, roughness
ni, design discharge Qi(for trapezoidal cross-section, form of fracture data include: the bottom width b in each canal pond with form of fracture datai, side
Slope coefficient S li, design canal depth hi), the service condition data of collection include each canal pond water draw rate qi, control point design and operation water
Deep hspi, design and operation water level yspi, system export reference quantity yriAnd operational envelope ± ri(riRepresent i-th of canal pond pair
The control point water level operational process answered allows the maximum value fluctuated) etc..
One embodiment of the present of invention is two points of trunk canals in the irrigated area northwest China Chang Manan, which includes 4 canals
Pond, each canal pond parameter value scheme are as shown in table 1.
1 channel designing parameter of the embodiment of the present invention of table
1-2) controlling channel model is established using the data that step 1-1) is collected；
The present invention uses integral Time-Delay model shown in formula (1) for controlling channel model, and the model is between adjacent control structure
Canal pond i be control unit, be the obtained linear equation of lumped parameter after Saint-Venant equation linearisation, expression formula is as follows:
In formula, yiIt is the corresponding downstream control point water level in i-th of canal pond relative to design and operation water level yspiVariable quantity,
Unit: m；T is time, unit: s；AsiFor the corresponding backwater zone area in i-th of canal pond, unit: m2；qini、qoutiAnd qdiRespectively
The variable quantity of original steady-state is corresponded to for the corresponding canal pond inbound traffics in i-th of canal pond, outflow and water draw rate, unit:
m3/s；τiFor the corresponding lag time in i-th of canal pond, unit: s.
The return water in each canal pond is obtained by theoretical formula method or numerical simulation recognition methods under the conditions of design discharge
Area area AsiWith lag time τiTwo parameters, so that it is determined that the hydraulic characteristic(s) in each canal pond of multistage channel, fetches water in conjunction with each canal pond
Flow qi, controlling channel modular form (1) can be obtained.
In the present embodiment, integral Time-Delay model parameter calculates theoretical equation: two points of trunk canal channels in the prosperous irrigated area Ma Nan are
Prismatic channel, form of fracture is unified, and theoretical formula can be used and calculated.
Wherein, the method for calculating the corresponding backwater zone area in each canal pond is；
Using integral Time-Delay model backwater zone water surface curve level it is assumed that can determine return water section length by geometrical relationship,
And know that water surface geometry in backwater zone is determined by form of fracture under this assumption, in conjunction with geometric characteristic and the return water head of district
Degree can fast calculate backwater zone area parameters.Assuming that prismatic canal for water conveyance is made of f canal pond, canal pond i is flowed in design
Measure QiUniform flow normal depth of flow under operation is hni, the downstream Qu Chi control point depth of water setting value is hspi(hspi>hni), when channel is disconnected
Face be it is trapezoidal when, the corresponding backwater zone area in i-th of canal pond can approximate calculation obtain, calculation formula are as follows:
In formula, biFor the corresponding trapezoidal section canal bottom width in i-th of canal pond, m；SliIt is corresponding trapezoidal disconnected for i-th of canal pond
Face slope coefficient.SbiFor the corresponding canal grade in i-th of canal pond,
Calculate the corresponding lag time method in each canal pond are as follows:
According to integral Time-Delay model it is assumed that when entire canal pond is in backwater zone, lag time 0；When canal pond part
When in backwater zone, lag time is upstream end perturbation wave in the propagation time of uniform stream part, integrates Time-Delay model developer
Schuurmans et al. (1995) is proposed with movement wave pattern to simulate the water flow communication process of open channel water delivery process.?
It moves in wave pattern, the spread speed of water flow is the function of the depth of water, and water flow movement velocity of wave propagation formula is as follows:
In formula, Q is water delivery flow, unit: m3/s；TiFor the corresponding water surface width in i-th of canal pond, unit: m；H is the depth of water,
Unit: m.
For prismatic channel uniform flow water delivery part, lag time can be according to uniform flow section length and kinematic wave velocity of wave
Calculating acquires, the calculation formula of lag time are as follows:
After linearizing Saint-venant Equations to dQ/dh progress approximations, the calculation formula of lag time are as follows:
In formula, LuiFor the corresponding return water section length in i-th of canal pond, m；P is wetted perimeter, m；AiFor the corresponding mistake in i-th of canal pond
Flow area, m2；TiFor the corresponding water surface width in i-th of canal pond, m；H is the depth of water, m；viFor the corresponding mean flow rate in i-th of canal pond,
m3/s；Subscript 0 indicates parameter value when initial steady state.
Backwater zone area A of each canal pond of the multistage channel being calculated according to step 1-2) under the conditions of design dischargesiWith
Lag time τiParameter determines water draw rate change programme according to channel designing operating flux scheduling scheme as shown in table 2, from
And obtain the controlling channel model as shown in formula (1).
2 case design discharge of canal integral model parameter of table
2) the controlling channel model conversation for establishing step 1) is state space equation form；
There are lag times for controlling channel model, and control system control action occurs at certain time intervals, according to formula
(1), the separate manufacturing firms equation (2) and formula (3) of multistage channel are constructed, it is assumed that irrigation canal is stational system, discrete
Form state space equation can indicate are as follows:
X (k+1)=Ax (k)+Bu (k)+Dd (k) (2)
Y (k)=Cx (k) (3)
In formula, k is the time under discrete form；X is state variable；U is control variable；D is disturbance variable；Y is output
Variable；A is sytem matrix；B is control matrix；C is output matrix；D is perturbation matrix.
By taking the i of canal pond as an example, choosing control time step is Δ t, then integrates the discrete form of Time-Delay model are as follows:
In formula, Δ t is control time step, unit: s；kτiFor the sluggishness under the corresponding discrete time model in i-th of canal pond
Duration is obtained by practical lag time and the ratio of control time step, remaining parameter is consistent with conitnuous forms.
Define the corresponding water level deviation luffing Δ y in i-th of canal pondi(k)=yi(k)-yi(k-1), i-th of canal pond is corresponding
Control flow luffing Δ qi(k)=qi(k)-qi(k-1), and after arranging deformation to formula (4) following formula is obtained:
Choose water level deviation yi(k) and its luffing Δ yi(k) and beforehand control flow luffing Δ qini(k-i) (i=
1...kτ) it is state variable, i.e. x (k)=[yi(k),Δyi(k),Δqini(k-1),…,Δqini(k-kτi)]T, choose current
It is control variable, i.e. u (k)=[Δ q that period, which controls flow luffing,ini(k)], choosing future time period intake changes in flow rate is to disturb
Dynamic variable, i.e. d (k)=[Δ qdi(k)], choosing water level deviation is output variable, i.e. y (k)=[yi(k)], it is hereby achieved that
The state space equation of canal pond i.
When considering the canalization of whole f canal pond compositions, state variable x (k)=[x is taken1(k)；x2(k)；…；xf
(k)] variable u (k)=[u, is controlled1(k)；u2(k)；…；uf(k)], disturbance variable d (k)=[d1(k)；d2(k)；…；df(k)],
Output variable y (k)=[y1(k)；y2(k)；…；yf(k)], the state space equation formula of available multistage channel discrete form
(2) and formula (3), wherein sytem matrix A, controls matrix B, output matrix C and perturbation matrix D are joined by each canal pond controlling channel model
Number determines.
According to above-mentioned calculation method, state variable x, control variable u, disturbance variable d and the output for obtaining case channel become
Y and sytem matrix A is measured, controls matrix B, output matrix C and perturbation matrix D are as follows.
3) output quantity for irrigating multistage canalization future is predicted, and constructs the target of Model Predictive Control Algorithm
Function；Specific step is as follows:
3-1) control is run according to system to require to determine prediction time domain p and control time domain c, using formula (2) and formula (3), by
Period carries out rolling forecast to system state variables and output variable, obtains system in the output result of prediction time domain end.Canal
Predicted value of the state variable and output variable of road system at the k+1 moment can respectively indicate as follows:
Predicted value of the canalization state variable at the k+2 moment are as follows:
It is similar, predicted value of the canalization output variable at the k+2 moment are as follows:
Prediction process is performed until control time domain c, at this time the state variable of canalization and output variable calculating value distribution
Not are as follows:
It is above the prediction in control time domain c to system state variables and output variable, after controlling time domain
The response for predicting remainder in time domain p is free response.
Above system exports the matrix form expression that predicted value can be following by arrangement:
Y (k+1 | k)=Sxx(k)+SuU(k)+SdD(k) (19)
The formula (18) and reference quantity y for 3-2) obtaining step 3-1)rDeviation and control variable u carry out quadratic form summation,
Obtain the objective function of Model Predictive Control Algorithm.
In formula, J is objective function, and p is prediction time domain, and c is control time domain,For system prediction output variable, yrFor system
Reference quantity is exported, u is control variable, QjMatrix, R are punished for the weighting of j-th of water level deviationjThe weighting of variable is controlled for j-th
Punish matrix.
Output reference quantity and weighting matrix are expressed as following matrix form,
Yr(k+1 | k)=[yr(k+1)；yr(k+2)；…；yr(k+p)] (23)
Q=diag (Q1,Q2,...,Qp), R=diag (R1,R2,...,Rc) (24)
And convolution (23) and formula (24) export the matrix form of prediction and control variable, target function type (22) to system
It can be expressed as matrix reduction form:
J=[Q (Y (k+1 | k)-Yr(k+1))]2+[RU(k)]2 (25)
4) using the formula (25) of step 3) building, identifying system constraint condition simultaneously proposes processing scheme, passes through Optimization Solution
Optimum control amount is calculated；Specific step is as follows:
Properties of flow, control point water level operational envelope 4-1) are crossed according to control structure, carry out the knowledge of system constraints
Not and propose processing scheme.Irrigating main constraints in need of consideration in water distribution system operation includes: according to control structure
Conveyance capacity by control structure flow restriction within the allowable range, guarantee the enforceability of control action；By control structure stream
The luffing limitation of amount within limits, consumes to reduce and avoids damage etc.；Water level is maintained to the safe range of setting
Between boundary, to realize safe and efficient transmission & distribution water and prevent canal dike from overflowing；Needs are protected according to channel, SEA LEVEL VARIATION rate is limited
System in a certain range, prevents water level in channel hydraulic pipeline operational process from changing the damage to canal lining rapidly.Above-mentioned constraint item
Part can inductive generalization be control variable and two class of output variable constraint, every class can be divided into again amplitude and permission two kinds of luffing about
Beam.It can classify for the concrete condition constraint for controlling variable and output variable in multi-stage irrigation water distribution system of the invention
Are as follows:
1, control variation amplitude constraint: the minimum and maximum conveyance capacity of control structure (gate)；
2, control variable luffing constraint: the minimum and maximum flow luffing that control structure allows constrains；
3, output variable Filters with Magnitude Constraints: the operational envelope of control point water level；
4, output variable luffing constrains: the safe luffing constraint of control point water level.
Above-mentioned constraint condition can be embodied as following form:
1. control structure flow Filters with Magnitude Constraints；
Control structure flow Filters with Magnitude Constraints in multi-stage irrigation canalization of the invention be control structure maximum and
Minimum conveyance capacity.In control time domain, the expression formula of control structure flow Filters with Magnitude Constraints are as follows:
Qlb≤Q0(t-1)+ΦU(k)≤Qub (26)
In formula, Φ is control variables transformations matrix, Q0For control structure current time flow, QubAnd QlbRespectively control knot
The minimum and maximum inflow-rate of water turbine of structure.
2. control structure flow luffing constrains；
It is the minimum and maximum of control structure permission in irrigation system of the invention that control structure flow luffing, which constrains in,
Changes in flow rate amount.In control time domain, the expression-form of control variable maximum luffing constraint are as follows:
Ulb≤U(k)≤Uub (27)
In control time domain, the expression-form of control structure flow minimum luffing constraint are as follows:
|U(k)|≥Udb (28)
In formula, UubAnd UlbThe respectively control structure maximum stream flow variable quantity that allows, U when flow increases and reducesdb
The minimum discharge variable quantity of requirement is adjusted for control structure.
3. water level Filters with Magnitude Constraints；
In the multi-stage irrigation canalization of water level Filters with Magnitude Constraints in the present invention be operational process in control point water level permit
Permitted the maximum and minimum value reached.In prediction time domain, the expression formula of water level Filters with Magnitude Constraints are as follows:
Ylb≤Y(k+1|k)≤Yub (29)
In formula, YubAnd YlbRespectively in multi-stage irrigation Canal's Moving Process control point water level allow to reach maximum and most
Small value.
4. range of stage constrains；
Similar with control structure flow luffing constraint, water level equally exists luffing constraint, the difference is that water level is only deposited
It is constrained in maximum luffing, in prediction time domain, the expression formula of water level maximum luffing constraint are as follows:
ΔYlb≤RX(k+1|k)≤ΔYub (30)
In formula, R is sparse coefficient matrix, by R effect by total state variables transformations for only containing water level change of error
Vector, Δ YubWith Δ YlbThe respectively maximum stage variable quantity that allows in rise and whereabouts of control point water level.
Type, property and the processing method that difference constrains are as shown in the table.
3 multi-stage irrigation channel model prediction algorithm constrained type of table and processing method
4-2) the formula (25) constructed according to step 3), the identification in conjunction with step 4-1) to system operation constraint condition, can incite somebody to action
The objective function of Model Predictive Control Algorithm is converted into the canonical form of quadratic programming, and by utilizing quadratic programming optimization algorithm
It solves and obtains the optimal control sequence in prediction time domain.The specific method is as follows:
Formula (25) is arranged as quadratic programming problem and is solved using related algorithm.Quadratic programming is that objective function is
Quadratic function, constraint condition are the nonlinear programming problem of linear forms, the canonical form of quadratic programming problem objective function
Such as formula (31):
In formula, HuIt is symmetric positive semidefinite matrix for Hessian matrix；GrFor gradient vector；e0For constant term；T is transposition operation
Symbol.
To arrange objective function for the canonical form of quadratic programming problem objective function, model prediction is exported into result
(19) formula (25) are substituted into and are arranged and obtain formula (32):
Objective function equation (32) is a typical quadratic programming problem, wherein Hessian matrix, gradient vector and often
It is several respectively as shown in formula (33), (34) and (35):
Hu=(QSu)TQSu+RTR (33)
Gr(k+1)=- (QSu)TQ[Yr(k+1)-Sxx(k)-SdD(k)] (34)
e0=0.5 × { Q [Yr(k+1)-Sxx(k)-SdD(k)]}T{Q[Yr(k+1)-Sxx(k)-SdD(k)]} (35)
4-2-1) unconstrained optimization solves
When the input and output of system unfettered condition limits, there are analytic solutions for quadratic programming problem.In order to obtain
Formula (31) is carried out derivation to control variable U (k), and its derivative 0 is made to obtain optimal solution by the Analytical Expression formula of optimal solution
Analytical expression (36):
By solve formula (36) obtain control time domain in without constrained optimum control sequence Uuc(k) analytical expression
(37), which is that formula (25) reaches the smallest optimum control amount in control time domain, in practical applications, without constraint item
Control structure is according to optimum control amount U under partuc(k) control action is executed:
4-2-2) constrained optimization solves
In actual Process Control System, restrict of the system input with output usually by various external conditions,
Therefore it establishes design of the Model Predictive Control Algorithm under constraint condition and solves and be more of practical significance and application value.Model is pre-
The objective function for surveying control algolithm uses finite time-domain form, therefore application can be directly added into the solution of objective function
In the related constraint of controlled system input and output, it can be considered that system restriction and being optimized in the presence of constraint
It is also one of most important advantage of Model Predictive Control Algorithm.
System input and the constrained type of output can be divided into two class of linear and nonlinear.It controls and asks when being constrained to linear
Entitled typical quadratic programming problem can be solved and be analyzed by the related algorithm of quadratic programming；It is non-thread when being constrained to
Property when then need the related derivation algorithm using Non-Linear Programming to be solved.The present invention is directed to the feelings for being constrained to linear restriction
Scape, the quadratic programming containing linear restriction can be as follows with expression formula at this time:
s.t.ΓU(k)≤b (39)
In formula, Γ and b are the matrix and vector for defining linear restriction.
In addition to the constraint of dead zone, corestriction can be expressed as linear restriction form shown in formula (39).
The canonical form that control structure flow Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
The constraint of control structure maximum flow luffing arranges the canonical form for quadratic programming linear restriction are as follows:
In formula, I is the unit matrix of c × c dimension.
The canonical form that water level Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
Range of stage constraint arranges the canonical form for quadratic programming linear restriction are as follows:
In formula: coefficient matrix Sux, Sxx, SdxIt is divided by obtain with output matrix C by formula (21).
Model Predictive Control Algorithm predicts future output according to the controlling channel model of foundation, and is predicted with exporting
Value and reference quantity yrThe sum of deviation and the quadratic form of control variable u are objective function, under constraint condition, by running to system
The identification of constraint condition solves to obtain the optimum control amount U (k) in control time domain using MATLAB active set optimization algorithm, should
Control amount is the optimum control amount for controlling the objective function that formula (31) indicates in time domain and reaching the smallest each control structure, in reality
The control structure irrigated in multistage channel in the application of border executes corresponding control action according to optimum control amount U (k).
Model Predictive Control Algorithm based on above-mentioned foundation is simulated Canal's Moving Process, as a result such as 2 institute of attached drawing
Show, abscissa is simulated time in figure, and ordinate is control point water level deviation, and straight dotted line represents control point SEA LEVEL VARIATION and permits up and down
Perhaps range, curve is control point SEA LEVEL VARIATION process in figure.Before analog result is shown in water intaking variation generation, Model Predictive Control
Algorithm can adjust control in advance, by water intaking disturbance after through control and regulation so that controlling channel point water level operate in it is fair
Perhaps it in range, and is finally restored near water level operation setting value.The above results show that Model Predictive Control Algorithm has reply
The ability of known water intaking disturbance and processing constraint condition, can effectively control two points of the prosperous irrigated area Ma Nan trunk canal, can be applied to
The automatic control of Irrigation Project Design multistage channel.
Claims (1)
1. a kind of irrigation multistage canal automatic control method based on Model Predictive Control Algorithm, which is characterized in that including following
Step:
1) it establishes and irrigates multistage controlling channel model, the specific steps are as follows:
It 1-1) determines channel to be controlled, collects the design data and service condition data of the channel；
The irrigation multistage canalization for selecting any irrigated area is channel to be controlled, it is assumed that the canalization is made of f canal pond, canal
Road design data includes the length L in each canal pond in f canal pondi, longitudinal slope Sbi, roughness ni, design discharge QiWith form of fracture data,
Service condition data include each canal pond water draw rate qi, control point design and operation depth of water hspi, design and operation water level yspi, system it is defeated
Reference quantity y outriAnd operational envelope ± rI,, wherein riThe corresponding control point water level operational process in i-th of canal pond is represented to permit
Perhaps the maximum value fluctuated；
1-2) controlling channel model is established using the data that step 1-1) is collected；Expression formula is as follows:
In formula, yiIt is the corresponding downstream control point water level in i-th of canal pond relative to design and operation water level yspiVariable quantity, unit:
m；T is time, unit: s；AsiFor the corresponding backwater zone area in i-th of canal pond, unit: m2；qini、qoutiAnd qdiRespectively i-th
The corresponding canal pond inbound traffics in a canal pond, outflow and water draw rate correspond to the variable quantity of original steady-state, unit: m3/s；τi
For the corresponding lag time in i-th of canal pond, unit: s；
2) the controlling channel model conversation for establishing step 1) is state space equation form；
According to formula (1), shown in the separate manufacturing firms equation such as formula (2) and formula (3) for constructing multistage channel:
X (k+1)=Ax (k)+Bu (k)+Dd (k) (2)
Y (k)=Cx (k) (3)
In formula, k is the time under discrete form；X is state variable；U is control variable；D is disturbance variable；Y is output variable；
A is sytem matrix；B is control matrix；C is output matrix；D is perturbation matrix；
3) output quantity for irrigating multistage canalization future is predicted, and constructs the target letter of Model Predictive Control Algorithm
Number；Specific step is as follows:
It 3-1) runs control according to system to require to determine prediction time domain p and control time domain c, using formula (2) and formula (3), by the period
Rolling forecast is carried out to system state variables and output variable, obtains system in the output result of prediction time domain end；
In control time domain c, state variable and the output variable predicted value of canalization are respectively as follows:
Predict that the response of remainder in time domain p is free response after controlling time domain；
It is that following matrix form is expressed that system, which exports predicted value and arranges:
Y (k+1 | k)=Sxx(k)+SuU(k)+SdD(k) (19)
The formula (18) and reference quantity y for 3-2) obtaining step 3-1)rDeviation and control variable u carry out quadratic form summation, obtain mould
The objective function of type predictive control algorithm；
In formula,For system prediction output quantity, yrReference quantity is exported for system, u is control variable, QjFor j-th water level deviation
Weighting punishment matrix, RjMatrix is punished in the weighting for controlling variable for j-th；
Output reference quantity and weighting matrix are expressed as following matrix form,
Yr(k+1 | k)=[yr(k+1)；yr(k+2)；…；yr(k+p)] (23)
Q=diag (Q1,Q2,...,Qp), R=diag (R1,R2,...,Rc) (24)
Convolution (23) and formula (24) export the matrix form of prediction and control variable to system, and target function type (22) is expressed as
Following matrix reduction form:
J=[Q (Y (k+1 | k)-Yr(k+1))]2+[RU(k)]2 (25)
4) based on step 3) as a result, identifying system constraint condition, and optimum control amount is calculated by Optimization Solution；Specifically
Steps are as follows:
4-1) identifying system constraint condition；It is specific as follows:
Control structure flow Filters with Magnitude Constraints；
Qlb≤Q0(t-1)+ΦU(k)≤Qub (26)
In formula, Φ is control variables transformations matrix, Q0For control structure current time flow, QubAnd QlbRespectively control structure
Minimum and maximum inflow-rate of water turbine；
The constraint of control structure flow luffing；The constraint of control structure flow luffing includes the constraint of control variable maximum luffing and control knot
The constraint of structure flow minimum luffing；
Control the expression-form of variable maximum luffing constraint are as follows:
Ulb≤U(k)≤Uub (27)
The expression-form of control structure flow minimum luffing constraint are as follows:
|U(k)|≥Udb (28)
In formula, UubAnd UlbThe respectively control structure maximum stream flow variable quantity that allows, U when flow increases and reducesdbFor control
The minimum discharge variable quantity of requirement is adjusted in structure processed；
Water level Filters with Magnitude Constraints；
Ylb≤Y(k+1|k)≤Yub (29)
In formula, YubAnd YlbRespectively irrigate the maximum and minimum value that control point water level allows to reach in multistage Canal's Moving Process；
Range of stage constraint；
ΔYlb≤RX(k+1|k)≤ΔYub (30)
In formula, R is sparse coefficient matrix, Δ YubWith Δ YlbThe respectively most flood that allows in rise and whereabouts of control point water level
Position variable quantity；
4-2) according to formula (25), the identification of constraint condition is run to system in conjunction with step 4-1), by Model Predictive Control Algorithm
Objective function is converted into the canonical form of quadratic programming, and by solving to obtain in prediction time domain using quadratic programming optimization algorithm
Optimal control sequence；The specific method is as follows:
Formula (25) is arranged into the canonical form such as formula (31) for quadratic programming problem objective function:
In formula, HuIt is symmetric positive semidefinite matrix for Hessian matrix；GrFor gradient vector；e0For constant term；T is transposition operator；
Formula (19) are substituted into formula (25) and arranged and obtain formula (32):
Wherein Hessian matrix, gradient vector and constant term are respectively as shown in formula (33), (34) and (35):
Hu=(QSu)TQSu+RTR (33)
Gr(k+1)=- (QSu)TQ[Yr(k+1)-Sxx(k)-SdD(k)] (34)
e0=0.5 × { Q [Yr(k+1)-Sxx(k)-SdD(k)]}T{Q[Yr(k+1)-Sxx(k)-SdD(k)]} (35)
4-2-1) unconstrained optimization solves；
When the input and output of system unfettered condition influences, there are analytic solutions for quadratic programming problem at this time；By formula (31)
Derivation is carried out to control variable U (k), and its derivative 0 is made to obtain the analytical expression (36) of optimal solution:
By solve formula (36) obtain control time domain in without constrained optimum control sequence Uuc(k) analytical expression (37), should
Control amount is that formula (25) reaches the smallest optimum control amount U in control time domainuc(k):
4-2-2) constrained optimization solves；
Quadratic programming expression formula containing linear restriction is as follows:
s.t.ΓU(k)≤b (39)
In formula, Γ and b are the matrix and vector for defining linear restriction；
The canonical form that control structure flow Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
The constraint of control structure maximum flow luffing arranges the canonical form for quadratic programming linear restriction are as follows:
In formula, I is the unit matrix of c × c dimension；
The canonical form that water level Filters with Magnitude Constraints arranges as quadratic programming linear restriction are as follows:
Range of stage constraint arranges the canonical form for quadratic programming linear restriction are as follows:
In formula, coefficient matrix Sux, Sxx, SdxIt is divided by obtain with output matrix C by formula (21)；
Model Predictive Control Algorithm predicts future output according to the controlling channel model of foundation, and with export predicted value with
Reference quantity yrThe sum of deviation and the quadratic form of control variable u are objective function, under constraint condition, are constrained by running to system
The identification of condition solves and obtains the optimum control amount U in control time domain, which is that formula (22) indicates in control time domain
Objective function reaches the smallest optimum control amount.
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| JP2022541568A (en) * | 2020-04-02 | 2022-09-26 | 中国長江三峡集団有限公司 | Water Level Prediction and Control Method for Series Canal Based on Fuzzy Neural Network |
| CN112434424A (en) * | 2020-11-24 | 2021-03-02 | 中国矿业大学 | Method for constructing irrigation mode of yam in sandy land |
| CN112434424B (en) * | 2020-11-24 | 2022-07-05 | 中国矿业大学 | Method for constructing irrigation mode of yam in sandy land |
| CN113093531A (en) * | 2021-03-01 | 2021-07-09 | 武汉大学 | Large pipe-channel combined system emergency dispatching control method based on model predictive control |
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| CN114417631A (en) * | 2022-01-26 | 2022-04-29 | 清华大学 | Irrigation area water transmission and distribution system modeling method based on observation data |
| CN114415520B (en) * | 2022-01-26 | 2023-08-25 | 清华大学 | Full-canal system self-adaptive predictive control method for water networking irrigation areas |
| CN114417631B (en) * | 2022-01-26 | 2023-10-03 | 清华大学 | Modeling method of infusion area water delivery and distribution system based on observation data |
| CN114415520A (en) * | 2022-01-26 | 2022-04-29 | 清华大学 | Full-canal-system self-adaptive prediction control method for water-based network irrigation area |
| CN115456422A (en) * | 2022-09-16 | 2022-12-09 | 中国水利水电科学研究院 | Irrigation district water distribution plan dynamic preview correction method based on computational hydrodynamics |
| CN115456422B (en) * | 2022-09-16 | 2024-02-02 | 中国水利水电科学研究院 | Dynamic previewing correction method for irrigation area water distribution plan based on computational hydrodynamics |
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