CN102880772A - Motor train unit power optimizing prediction and control method based on model - Google Patents

Abstract

The invention provides a motor train unit power optimizing prediction and control method based on a model. The motor train unit power optimizing prediction and control method comprises the following steps of: S1) taking a running speed of a motor train unit compartment and displacement between compartments as state variables, and establishing a motor train unit state equation after a motor train unit is lineated; S2) establishing a constraint condition in a running process of the motor train unit according to an effective tractive force borne during running of the motor train unit and an interaction force between the compartments; S3) according to the model after the motor train unit is lineated, the interaction force between the compartments, a prediction time domain and a control time domain, determining an optimizing control target function; and S4) solving the target function under the constraint condition so as to obtain optimizing control of motor train unit speed variation and power distribution in the running process of the motor train unit. According to the motor train unit power optimizing prediction and control method based on the model disclosed by the invention, motor train unit power distribution model predication and control can be realized, power distribution is optimized according to variation of a motor train unit speed in the running process of the motor train unit, so that energy saving and economy can be kept when the motor train unit runs, and power distribution efficiency is improved.

Description

A kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model

Technical field

The present invention relates to the distributed optimization control method technical field of motor train unit, particularly relate to a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model.

Background technology

Motor train unit has become a national overall national strength, urban economy strength, people's living standard and modern important symbol as quick, convenient, the clean and efficient vehicles of modern city.In recent years, economic strength and the overall national strength of China significantly strengthened, and the railway system of China has also experienced significantly upgrading and expansion.On April 18th, 2007, China railways has been carried out the sixth time speed-raising, and in current speed-raising, China has released EMU CRH1, CRH2 and the CRH5 of CRH series first.The overall trip speed of these motor train unit reaches 250km/h.According to the planning of China railways Long-and Medium-term Development, to the year two thousand twenty, Chinese Railway network planning mould reaches more than 120,000 kilometers, will build up 1.6 ten thousand kilometers " four vertical five horizontal strokes " High-speed Railway Networks, and following motor train unit will be the online main forces of these high-speed railways.At present, by the external advanced technology of import, digestion and absorption, China has grasped the advanced and mature railway locomotive and rolling stock manufacturing technologies in the world.In service in actual motor train unit, because the constraint of the resource factors such as soil, the energy, Road Network Capacity, operation is had higher requirement to motor train unit.But evening is relatively carried out getting in the domestic research that motor train unit operation is optimized, the optimization research platform of therefore setting up motor train unit in the urgent need to.Optimize research platform and can be used for design, test and proofread and correct purpose, and become the multiple traffic experiment under the complicated uncertain environmental baseline when carrying out.

Find through the open source literature retrieval to prior art, document [YANG Ciann-Dong, SUN Yun-Ping, Mixed H2/H cruise controller design for high speed train[J], International Journal of Control, 2001,74 (9), 905-920], although the author independently considers every joint compartment, set up many bodies Longitudinal Dynamic Model, but in this method, suffered dynamic resistance had carried out simplifying processing when the author moved motor train unit, suppose that namely dynamic resistance only acts on the first segment compartment, the actual loading situation of this hypothesis and motor train compartment differs and wins far, can not reflect the operation conditions of motor-car, can't embody power distribution between different compartments and the inner link between the Optimized Operation.

Summary of the invention

The shortcoming of prior art in view of the above, the object of the present invention is to provide a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model, thereby be used for solving the problem that motor train unit operational process motor-car speed exists variation power distribution not to be optimized.

Reach for achieving the above object other relevant purposes, the invention provides a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model, may further comprise the steps:

S1, as state variable, set up the motor train unit state equation after the motor train unit linearization with the travelling speed of motor train unit carriage and the displacement between the compartment: Y=Cx;

Wherein, x=[δ v ₁, δ v ₂..., δ v _n, δ x ₁, δ x ₂..., δ x _N-1] ^TU=[δ u ₁, δ u ₂..., δ u _n] ^TA, B and C are the State Equation Coefficients matrix; X is the displacement between the compartment; Y is the column vector that the speed in every joint compartment forms; U is the effective traction that the compartment is subject to;

First order derivative for the displacement between the compartment; δ v ₁, δ v ₂, δ v _nBe respectively near the side-play amount equilibrium point of travelling speed near the side-play amount equilibrium point of travelling speed in the 1st joint compartment, the 2nd joint compartment, n joint compartment; δ x ₁, δ x ₂, δ x _N-1Be respectively the 1st joint compartment the relative the 2nd and save near the side-play amount of relative shift equilibrium point that compartment, the 2nd saves relative the 3rd joint compartment, compartment, relative n joint compartment, n-1 joint compartment; δ u ₁, δ u ₂, δ u _nBe respectively the tractive force in the 1st joint compartment, the 2nd joint compartment, n joint compartment and near the side-play amount of the equilibrium point of making a concerted effort of damping force; N is the compartment joint number; T is matrix transpose;

S2, the effective traction that is subject to when moving according to motor train unit and the interaction force between the compartment are set up the constraint condition in the motor train unit operational process: u _Min-u ^e≤ u≤u _Max-u ^e,

Wherein, $x\left(k\right)={[\frac{f_1}{k_1},\frac{f_2}{k_2},...\frac{f_{n-1}}{k_{n-1}}]}^T;$ $x_{\min }={[\frac{f_{1\min }}{k_1},\frac{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\min }}{k_2},...,\frac{f_{n-1\min }}{k_{n-1}}]}^T;$ $x_{\max }={[\frac{f_{1\max }}{k_1},\frac{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\mathrm{<figure-callout\; id="2"\; label="max\; k"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">max</figure-callout>}}}{k_{}},...,\frac{f_{n-1\max }}{k_{n-1}}]}^T;$

With

Be the State Equation Coefficients discrete matrix; K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; U is the effective traction that the compartment is subject to; u ^eBe the effective traction that compartment under the equilibrium point state is subject to, e is the equilibrium point state; u _Min, u _MaxBe respectively the tractive force in compartment and the minimum value of making a concerted effort, the maximal value of damping force; x _Min, x _MaxBe respectively minimum value, the maximal value of the displacement between the compartment; f ₁, f ₂, f _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force between the compartment; f _1min, f _2min, f _N-1minBe respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force minimum value between the compartment; f _1max, f _2max, f _N-1maxBe respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force maximal value between the compartment; k ₁, k ₂, k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; N is the compartment joint number; T is matrix transpose;

S3 according to the motor train unit state equation after the motor train unit linearization, interaction force, prediction time domain and control time domain between the compartment, determines the objective function of optimal control: J (k)=u ^THu+2u ^TF;

Wherein, $H={\tilde{B}}^T\tilde{Q}\tilde{B}+\tilde{R},$ $f=\tilde{B}\tilde{Q}\tilde{A}x\left(k\right),$

K is time parameter; J (k) is in the constantly output of objective function of k; X (k) is at k state constantly; U is the effective traction that the compartment is subject to; F is the interaction force between the compartment; H is intermediate transform matrices, and P is the prediction time domain, and M is the control time domain, and Q, R are positive definite matrix,

Be the diagonal matrix that is formed by positive definite matrix Q,

Be the diagonal matrix that is formed by positive definite matrix R,

Be the State Equation Coefficients transformation matrix,

Be the State Equation Coefficients transformation matrix; N is the compartment joint number; T is matrix transpose;

S4 finds the solution described objective function under described constraint condition, the optimal control of motor-car velocity variations and power distribution in the acquisition motor train unit operational process.

Preferably, comprise also in step S1 the power system model set up in vertical operation of motor train unit that so that the variable in the described motor train unit state equation is limited, described power system model comprises:

$m_1{\stackrel{\&CenterDot;}{v}}_1=u_1-w_{01}-f_{{\mathrm{in}}_1}$

$m_i{\stackrel{\&CenterDot;}{v}}_i=u_i-w_{0i}+f_{{\mathrm{in}}_{i-1}}-f_{{\mathrm{in}}_i},$ i=2,…,n-1

$m_n{\stackrel{\&CenterDot;}{v}}_n=u_n-w_{0n}+f_{{\mathrm{in}}_{n-1}}$

${\stackrel{\&CenterDot;}{x}}_i=v_i-v_{i+1},$ i=1,...,n-1

Wherein, m ₁Be the quality in the 1st joint compartment, m _iBe the quality in i joint compartment, m _nQuality for n joint compartment; Be the acceleration in the 1st joint compartment,

Be the acceleration in i joint compartment,

Acceleration for n joint compartment; u ₁Be the 1st joint tractive force in compartment and damping force make a concerted effort u _iBe the tractive force in i joint compartment and damping force make a concerted effort u _nBe the tractive force in n joint compartment and making a concerted effort of damping force; w ₀₁Be the datum drag in the 1st joint compartment, w _0iBe the datum drag in i joint compartment, w _0nIt is the datum drag in n joint compartment; f _In1Be the interaction force in the 1st joint compartment and the 2nd joint compartment,

Be the interaction force in i-2 joint compartment and i-1 joint compartment,

Be the interaction force in i-1 joint compartment and i joint compartment,

It is the interaction force in n-1 joint compartment and n joint compartment; v _iBe the speed in i joint compartment, v _I+1Be the speed in i+1 joint compartment;

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment; N is the compartment joint number.

Preferably, the connector between the two joint compartments and the satisfied constraint condition of the interaction force between the compartment are:

$f_{{\mathrm{in}}_i}=k_i{x}_{{\mathrm{in}}_i}+d_i{\stackrel{\&CenterDot;}{x}}_{{\mathrm{in}}_i},$ i=1,…,n-1, $f_{{\mathrm{in}}_0}=f_{{\mathrm{in}}_n}=0,$

Wherein: k _iThe elasticity coefficient of connector between i joint compartment and the i+1 joint compartment, d _iIt is the ratio of damping of connector between i joint compartment and the i+1 joint compartment;

Be the relative displacement between i joint compartment and the i+1 joint compartment,

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment;

Be the interaction force in i joint compartment and i+1 joint compartment, Be the interaction force in the 0th joint compartment and the 1st joint compartment,

Be the interaction force in n joint compartment and n+1 joint compartment, n is the compartment joint number.

Preferably, in step S1:

The State Equation Coefficients matrix A is:

$A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ Wherein, A ₁₁=-diag (c ₁₁+ c ₂₁v _r..., c _1n+ c _2nv _r), A ₂₂=0 _{(n-1) * (n-1)},

The State Equation Coefficients matrix B is: $B=\left[\begin{array}{c}{B}_{11}\\ 0_{(n-1)\&times;n}\end{array}\right],$ $B_{11}=\mathrm{diag}(\frac{1}{m_1},\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">m</figure-callout>}}_2},...,\frac{1}{m_n});$

The State Equation Coefficients Matrix C is: C=[I _{N * n}0 _{(n-1) * (n-1)}];

v _rReference velocity for the motor train unit operation; m ₁Be the quality in the 1st joint compartment, m ₂Be the quality in the 2nd joint compartment, m _N-1Be the quality in n-1 joint compartment, m _nIt is the quality in n joint compartment; k ₁, k ₂, k _N-2And k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-2 joint compartment saves between the compartment with n-1 and n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; c ₁₁, c ₂₁, c _1nAnd c _2nParameter for the motor train unit datum drag; I is unit matrix; N is the compartment joint number.

Preferably, in step S2:

u _min=[u _1min,u _2min,…,u _nmin] ^T，u _max=[u _1max,u _2max,…,u _nmax] ^T， $u^e={[u_1^e,u_2^e,...,u_n^e]}^T;$

u _1min, u _2min, u _NminBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the minimum value of making a concerted effort of damping force; u _1max, u _2max, u _NmaxBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the maximal value of making a concerted effort of damping force; Be respectively the compartment is subject under the equilibrium point state the effective traction of being in the 1st joint compartment, the 2nd joint compartment, n joint compartment; T is matrix transpose;

The State Equation Coefficients discrete matrix

For:

The State Equation Coefficients discrete matrix For:

Wherein, L=[0 _{(n-1) * n}I _{(n-1) * (n-1)}]; L is matrix of coefficients, and A ' is State Equation Coefficients matrix A discrete state matrix, and B ' is the discrete state matrix of State Equation Coefficients matrix B; M is the control time domain, and I is unit matrix; N is the compartment joint number.

Preferably, in step S3:

The State Equation Coefficients transformation matrix

For: $\tilde{A}=\left[\begin{array}{c}{A}^{\&prime;}\\ A^{\&prime;2}\\ .\\ .\\ .\\ A^{\&prime;P}\end{array}\right],$

The State Equation Coefficients transformation matrix For: $\tilde{B}=\left[\begin{array}{ccccc}{B}^{\&prime;}& 0& 0& ...& 0\\ A^{\&prime;}{B}^{\&prime;}& B^{\&prime;}& 0& ...& 0\\ A^{\&prime;2}{B}^{\&prime;}& A^{\&prime;}{B}^{\&prime;}& B^{\&prime;}& ...& 0\\ .& .& .& & .\\ .& .& .& ...& .\\ .& .& .& & .\\ A^{\&prime;P-1}{B}^{\&prime;}& A^{\&prime;P-2}{B}^{\&prime;}& A^{\&prime;P-3}{B}^{\&prime;}& ...& A^{\&prime;P-M}{B}^{\&prime;}\end{array}\right],$

A ' is the discrete state matrix of State Equation Coefficients matrix A, and B ' is the discrete state matrix of State Equation Coefficients matrix B; P is the prediction time domain, and M is the control time domain.

Preferably, in step S3, before the objective function of determining optimal control, also comprise with T _SFor the sampling period to the motor train unit state equation

Carry out discretize with y=Cx and process, obtain the motor train unit state equation of discretize:

x(k+1)=A′x(k)+B′u(k)

y(k+1)=Cx(k)；

K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; X (k+1) is the function of state in k+1 compartment displacement constantly; Y (k+1) is the column vector that the speed in the k+1 moment every joint compartment forms; The effective traction of u (k) for being subject in k moment compartment; A ' is the discrete state matrix of State Equation Coefficients matrix A; B ' is the discrete state matrix of State Equation Coefficients matrix B.

Preferably, according to motor train unit state equation, prediction time domain and the control time domain of discretize, set up the forecast model that is used for determining objective function:

$J\left(k\right)=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{\left|\right|y(k+i|k)-y_r(k+i)\left|\right|}_{{\mathrm{<figure-callout\; id="2"\; label="Q\; i"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">Q</figure-callout>}}_i}^2+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left|\right|u(k+i-1|k)\left|\right|}_{R_i}^2,$

Wherein, k, i are the time state parameter; J (k) is in the constantly output of objective function of k; Y (k+i|k) predicts the constantly output of objective function of k+i constantly at k; Yr (k+i) is the output reference value of k+i objective function constantly; U (k+i-1|k) predicts the tractive force in k+i-1 compartment constantly and the input quantity of making a concerted effort of damping force constantly at k, and P is the prediction time domain, and M is control time domain, Q _iAnd R _iIt is respectively positive definite matrix.

Preferably, in step S4, described objective function found the solution specifically under described constraint condition comprise:

By finding the solution the optimal control that obtains motor-car velocity variations and power distribution in the motor train unit operational process, wherein, minJ (k) is the minimum value of the output of objective function.

As mentioned above, a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention has following beneficial effect:

Method of the present invention is applicable to have motor train unit and other high-speed train of powered distributed, the motor train unit power distributed model PREDICTIVE CONTROL that the present invention can realize, by thereby motor-car velocity variations in the motor train unit operational process is optimized power distribution, so method of the present invention improves power distribution efficient so that motor train unit keeps energy saving economy when operation.

Description of drawings

Fig. 1 is shown as the process flow diagram of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

Fig. 2 is shown as the process flow diagram of the S1 of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

Fig. 3 is shown as the process flow diagram of the S3 of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

Fig. 4 is shown as a kind of stressed synoptic diagram based on motor train unit in the motor train unit Dynamic Optimum forecast Control Algorithm of model of the present invention.

Fig. 5 is shown as a kind of dynamic analysis figure based on motor train unit in the motor train unit Dynamic Optimum forecast Control Algorithm of model of the present invention.

Fig. 6 is shown as a kind of topology diagram based on single-unit compartment in the motor train unit Dynamic Optimum forecast Control Algorithm of model of the present invention.

Fig. 7 is shown as the whole vehicle model of a kind of motor train unit based on adopting SIMAPCK to set up in the motor train unit Dynamic Optimum forecast Control Algorithm of model of the present invention.

Fig. 8 is shown as of the present invention a kind of based on relative displacement change curve between the compartment in the motor train unit Dynamic Optimum forecast Control Algorithm of model.

Fig. 9 be shown as of the present invention a kind of based in the motor train unit Dynamic Optimum forecast Control Algorithm of model at connector extending and contracting design sketch between each compartment on the SIMPACK platform.

Embodiment

Below by specific instantiation explanation embodiments of the present invention, those skilled in the art can understand other advantages of the present invention and effect easily by the disclosed content of this instructions.The present invention can also be implemented or be used by other different embodiment, and the every details in this instructions also can be based on different viewpoints and application, carries out various modifications or change under the spirit of the present invention not deviating from.

Need to prove, the diagram that provides in the present embodiment only illustrates basic conception of the present invention in a schematic way, satisfy only show in graphic with the present invention in relevant assembly but not component count, shape and size drafting when implementing according to reality, kenel, quantity and the ratio of each assembly can be a kind of random change during its actual enforcement, and its assembly layout kenel also may be more complicated.

The inventive method is applicable to have motor train unit and other high-speed train of powered distributed.In the prior art, suffered dynamic resistance had carried out simplifying processing when motor train unit was moved, suppose that namely dynamic resistance only acts on the first segment compartment, the actual loading situation of this hypothesis and motor train compartment differs and wins far, the operation conditions that can not reflect motor-car can't embody power distribution between different compartments and the inner link between the Optimized Operation.

In view of this, the invention provides a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model, thereby be used for solving the problem that motor train unit operational process motor-car speed exists variation power distribution not to be optimized.Below will elaborate principle and the embodiment of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention, and make those skilled in the art not need creative work can understand a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

See also Fig. 1, be shown as the process flow diagram of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.As shown in Figure 1, the invention provides a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model and specifically comprise step:

S1 as state variable, sets up the motor train unit state equation after the motor train unit linearization according to the travelling speed of motor train unit carriage and the displacement between the compartment.

S2, the effective traction that is subject to when moving according to motor train unit and the interaction force between the compartment are set up the constraint condition in the motor train unit operational process.

S3 according to the model after the motor train unit linearization, interaction force, prediction time domain and control time domain between the compartment, determines the objective function of optimal control.

S4 finds the solution described objective function under described constraint condition, the optimal control of motor-car velocity variations and power distribution in the acquisition motor train unit operational process.

Below in detail foundation and the implementation method of each step described.

[one] S1 as state variable, sets up the motor train unit state equation after the motor train unit linearization according to the travelling speed of motor train unit carriage and the displacement between the compartment.

See also Fig. 2, be shown as the particular flow sheet of the S1 of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

As shown in Figure 2, the process of setting up the motor train unit state equation comprises:

S11 sets up the power system model to vertical operation of motor train unit, and so that the variable in the described motor train unit state equation is limited, described power system model comprises:

$m_1{\stackrel{\&CenterDot;}{v}}_1=u_1-w_{01}-f_{{\mathrm{in}}_1}$

$m_i{\stackrel{\&CenterDot;}{v}}_i=u_i-w_{0i}+f_{{\mathrm{in}}_{i-1}}-f_{{\mathrm{in}}_i},$ i=2,…,n-1

$m_n{\stackrel{\&CenterDot;}{v}}_n=u_n-w_{0n}+f_{{\mathrm{in}}_{n-1}}$

${\stackrel{\&CenterDot;}{x}}_i=v_i-v_{i+1},$ i=1,...,n-1

Wherein, m ₁Be the quality in the 1st joint compartment, m _iBe the quality in i joint compartment, m _nQuality for n joint compartment;

Be the acceleration in the 1st joint compartment,

Be the acceleration in i joint compartment,

Acceleration for n joint compartment; u ₁Be the 1st joint tractive force in compartment and damping force make a concerted effort u _iBe the tractive force in i joint compartment and damping force make a concerted effort u _nBe the tractive force in n joint compartment and making a concerted effort of damping force; w ₀₁Be the datum drag in the 1st joint compartment, w _0iBe the datum drag in i joint compartment, w _0nIt is the datum drag in n joint compartment; f _In1Be the interaction force in the 1st joint compartment and the 2nd joint compartment,

Be the interaction force in i-2 joint compartment and i-1 joint compartment,

Be the interaction force in i-1 joint compartment and i joint compartment,

It is the interaction force in n-1 joint compartment and n joint compartment; v _iBe the speed in i joint compartment, v _I+1Be the speed in i+1 joint compartment;

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment; N is the compartment joint number.

S12, connector and the satisfied constraint condition of the interaction force between the compartment set between the two joint compartments are:

$f_{{\mathrm{in}}_i}=k_i{x}_{{\mathrm{in}}_i}+d_i{\stackrel{\&CenterDot;}{x}}_{{\mathrm{in}}_i},$ i=1,…,n-1, $f_{{\mathrm{in}}_0}=f_{i{n}_n}=0$

Wherein: k _iThe elasticity coefficient of connector between i joint compartment and the i+1 joint compartment, d _iIt is the ratio of damping of connector between i joint compartment and the i+1 joint compartment;

Be the relative displacement between i joint compartment and the i+1 joint compartment,

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment;

Be the interaction force in i joint compartment and i+1 joint compartment,

Be the interaction force in the 0th joint compartment and the 1st joint compartment,

Be the interaction force in n joint compartment and n+1 joint compartment, n is the compartment joint number.

In fact the 0th joint compartment and n+1 joint compartment do not exist, and only are explanation at this:

The interaction force that expression first segment compartment is subject to previously, actual value is 0;

Represent the interaction force that n joint compartment (being the final section compartment) is subject to later, actual value is 0.

S13 sets up the motor train unit state equation after the motor train unit linearization.

Described motor train unit state equation is specially

Y=Cx;

Wherein, x=[δ v ₁, δ v ₂..., δ v _n, δ x ₁, δ x ₂..., δ x _N-1] ^TU=[δ u ₁, δ u ₂..., δ u _n] ^TA, B and C are the State Equation Coefficients matrix; X is the displacement between the compartment; Y is the column vector that the speed in every joint compartment forms; U is the effective traction that the compartment is subject to;

First order derivative for the displacement between the compartment; δ v ₁, δ v ₂, δ v _nBe respectively near the side-play amount equilibrium point of travelling speed near the side-play amount equilibrium point of travelling speed in the 1st joint compartment, the 2nd joint compartment, n joint compartment; δ x ₁, δ x ₂, δ x _N-1Be respectively the 1st joint compartment the relative the 2nd and save near the side-play amount of relative shift equilibrium point that compartment, the 2nd saves relative the 3rd joint compartment, compartment, relative n joint compartment, n-1 joint compartment; δ u ₁, δ u ₂, δ u _nBe respectively the tractive force in the 1st joint compartment, the 2nd joint compartment, n joint compartment and near the side-play amount of the equilibrium point of making a concerted effort of damping force; N is the compartment joint number; T is matrix transpose.

So-called equilibrium point refers to the state point that the train speed of being in operation remains unchanged.Motor-car has Accelerating running, runs slowly in actual motion, but can not accelerate always or run slowly always, and motor-car all is in operation with relatively stable constant speed in the time of most.The opportunity of each side-play amount that we get, namely to be train chose under running status stablizing constant speed.

In the present embodiment, particularly, the State Equation Coefficients matrix A is:

$A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ Wherein, A ₁₁=-diag (c ₁₁+ c ₂₁v _r..., c _1n+ c _2nv _r), A ₂₂=0 _{(n-1) * (n-1)}

The State Equation Coefficients matrix B is: $B=\left[\begin{array}{c}{B}_{11}\\ 0_{(n-1)\&times;n}\end{array}\right],$ $B_{11}=\mathrm{diag}(\frac{1}{m_1},\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">m</figure-callout>}}_2},...,\frac{1}{m_n});$

The State Equation Coefficients Matrix C is: C=[I _{N * n}0 _{(n-1) * (n-1)}];

v _rReference velocity for the motor train unit operation; m ₁Be the quality in the 1st joint compartment, m ₂Be the quality in the 2nd joint compartment, m _N-1Be the quality in n-1 joint compartment, m _nIt is the quality in n joint compartment; k ₁, k ₂, k _N-2And k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-2 joint compartment saves between the compartment with n-1 and n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; c ₁₁, c ₂₁, c _1nAnd c _2nParameter for the motor train unit datum drag; I is unit matrix; N is the compartment joint number.

[two] S2, the effective traction that is subject to when moving according to motor train unit and the interaction force between the compartment are set up the constraint condition in the motor train unit operational process.

u _min-u ^e≤u≤u _max-u ^e，

Wherein, $x\left(k\right)={[\frac{f_1}{k_1},\frac{f_2}{k_2},...\frac{f_{n-1}}{k_{n-1}}]}^T;$ $x_{\min }={[\frac{f_{1\min }}{k_1},\frac{f_{2\min }}{k_2},...,\frac{f_{n-1\min }}{k_{n-1}}]}^T;$ $x_{\max }={[\frac{f_{1\max }}{k_1},\frac{f_{2\max }}{k_2},...,\frac{f_{n-1\max }}{k_{n-1}}]}^T;$

With

Be the State Equation Coefficients discrete matrix; K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; U is the effective traction that the compartment is subject to; u ^eBe the effective traction that compartment under the equilibrium point state is subject to, e is the equilibrium point state; u _Min, u _MaxBe respectively the tractive force in compartment and the minimum value of making a concerted effort, the maximal value of damping force; x _Min, x _MaxBe respectively minimum value, the maximal value of the displacement between the compartment; f ₁, f ₂, f _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force between the compartment; f _1min, f _2min, f _N-1minBe respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force minimum value between the compartment; f _1max, f _2max, f _N-1maxBe respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force maximal value between the compartment; k ₁, k ₂, k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; N is the compartment joint number; T is matrix transpose.

Particularly, u _Min=[u _1min, u _2min..., u _Nmin] ^T, u _Max=[u _1max, u _2max..., u _Nmax] ^T,

u _1min, u _2min, u _NminBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the minimum value of making a concerted effort of damping force; u _1max, u _2max, u _NmaxBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the maximal value of making a concerted effort of damping force; Be respectively the compartment is subject under the equilibrium point state the effective traction of being in the 1st joint compartment, the 2nd joint compartment, n joint compartment; T is matrix transpose;

The State Equation Coefficients discrete matrix

For:

The State Equation Coefficients discrete matrix

For:

Wherein, L=[0 _{(n-1) * n}I _{(n-1) * (n-1)}]; L is matrix of coefficients, and A ' is State Equation Coefficients matrix A discrete state matrix, and B ' is the discrete state matrix of State Equation Coefficients matrix B; M is the control time domain, and I is unit matrix; N is the compartment joint number.

In S2, the detailed process of setting constraint condition is as follows.

Consider the damping force that has that hitch between motor train unit effective tractive force of when operation and compartment bears, its constraint condition can be described as:

u _imin≤u _i≤u _imax,i=1,…,n

$f_{\mathrm{in}\min }\&le;f_{{\mathrm{in}}_i}\&le;f_{\mathrm{in}\max },$ i=1,…,n-1

Tractive force is as the control inputs u of system, and its constraint can be converted to:

u _min-u ^e≤u≤u _max-u ^e

Wherein:

u _min=[u _1min,u _2min,…,u _nmin] ^T，u _max=[u _1max,u _2max,…,u _nmax] ^T， $u^e={[u_1^e,u_2^e,...,u_n^e]}^T;$

u _1min, u _2minAnd u _NminBe respectively the 1st joint compartment, the 2nd joint compartment and the tractive force in n joint compartment and the minimum value of making a concerted effort of damping force; u _1max, u _2maxAnd u _NmaxBe respectively the 1st joint compartment, the 2nd joint compartment and the tractive force in n joint compartment and the maximal value of making a concerted effort of damping force;

With

What be respectively the 1st joint compartment, the 2nd joint compartment and n joint compartment is the effective traction that the compartment is subject under the equilibrium point state; T is matrix transpose.

At ratio of damping d _iIn=0 the situation, the acting force constraint condition between the compartment can be transformed to:

$\frac{f_{\mathrm{in}\min }}{k_i}\&le;x_i\&le;\frac{f_{\mathrm{in}\max }}{k_i},$ I=1 ..., n-1 is x _Min≤ Tx≤x _MaxT=[0 wherein _{(n1) * n}I _{(n1) * (n1)}], $x_{\min }={[\frac{f_{1\min }}{k_1},\frac{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\mathrm{<figure-callout\; id="2"\; label="min\; k"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">min</figure-callout>}}}{k_{}},...,\frac{f_{n-1\min }}{k_{n-1}}]}^T,$ $x_{\max }={[\frac{f_{1\max }}{k_1},\frac{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\mathrm{<figure-callout\; id="2"\; label="max\; k"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">max</figure-callout>}}}{k_{}},...,\frac{f_{n-1\max }}{k_{n-1}}]}^T$ f _IminBe the minimum value of the interaction force in i-1 joint compartment and i joint compartment, f _ImaxIt is the maximal value of the interaction force in i-1 joint compartment and i joint compartment.Bring the state equation of system into

Y=Cx, we can obtain:

Wherein, $x\left(k\right)={[\frac{f_1}{k_1},\frac{f_2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">k</figure-callout>}}_2},...,\frac{f_{n-1}}{k_{n-1}}]}^T,$

The constraint condition of system is write as the form that contains optimized variable and is obtained last constraint condition by conversion:

u _min-u ^e≤u≤u _max-u ^e

[three] S3 according to the model after the motor train unit linearization, interaction force, prediction time domain and control time domain between the compartment, determines the objective function of optimal control.

See also Fig. 3, be shown as the particular flow sheet of the S3 of a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention.

As shown in Figure 3, determine that the detailed process of objective function of optimal control is as follows:

S31 also comprised with T before the objective function of determining optimal control _SFor the sampling period to the motor train unit state equation

Carry out discretize with y=Cx and process, obtain the motor train unit state equation of discretize:

x(k+1)=A′x(k)+B′u(k)

y(k+1)=Cx(k)；

K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; X (k+1) is the function of state in k+1 compartment displacement constantly; Y (k+1) is the column vector that the speed in the k+1 moment every joint compartment forms; The effective traction of u (k) for being subject in k moment compartment; A ' is the discrete state matrix of State Equation Coefficients matrix A; B ' is the discrete state matrix of State Equation Coefficients matrix B.

S32, according to motor train unit state equation, prediction time domain and the control time domain of discretize, set up the forecast model that is used for determining objective function:

$J\left(k\right)=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{\left|\right|y(k+i|k)-y_r(k+i)\left|\right|}_{{\mathrm{<figure-callout\; id="2"\; label="Q\; i"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">Q</figure-callout>}}_i}^2+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left|\right|u(k+i-1|k)\left|\right|}_{{\mathrm{<figure-callout\; id="2"\; label="R\; i"\; filenames="HDA00002342911000041.png"\; state="\{\{state\}\}">R</figure-callout>}}_i}^2,$

Wherein, k, i are the time state parameter; J (k) is in the constantly output of objective function of k; Y (k+i|k) predicts the constantly output of objective function of k+i constantly at k; y _r(k+i) be the output reference value of k+i objective function constantly; U (k+i-1|k) predicts the tractive force in k+i-1 compartment constantly and the input quantity of making a concerted effort of damping force constantly at k, and P is the prediction time domain, and M is control time domain, Q _iAnd R _iIt is respectively positive definite matrix.

S33 can be converted to objective function with performance index by forecast model, and described objective function is specially:

J (k)=u ^THu+2u ^TF; Wherein, $H={\tilde{B}}^T\tilde{Q}\tilde{B}+\tilde{R},$ $f=\tilde{B}\tilde{Q}\tilde{A}x\left(k\right),$

K is time parameter; J (k) is in the constantly output of objective function of k; X (k) is at k state constantly; U is the effective traction that the compartment is subject to; F is the interaction force between the compartment; H is intermediate transform matrices, and P is the prediction time domain, and M is the control time domain, and Q, R are positive definite matrix, Be the diagonal matrix that is formed by positive definite matrix Q,

Be the diagonal matrix that is formed by positive definite matrix R,

Be the State Equation Coefficients transformation matrix,

Be the State Equation Coefficients transformation matrix; N is the compartment joint number; T is matrix transpose.

The State Equation Coefficients transformation matrix

For:

The State Equation Coefficients transformation matrix

For:

A ' is the discrete state matrix of State Equation Coefficients matrix A, and B ' is the discrete state matrix of State Equation Coefficients matrix B; P is the prediction time domain, and M is the control time domain.

[four] S4 finds the solution described objective function under described constraint condition, the optimal control of motor-car velocity variations and power distribution in the acquisition motor train unit operational process.

Particularly, described objective function found the solution specifically under described constraint condition comprise:

By finding the solution the optimal control that obtains motor-car velocity variations and power distribution in the motor train unit operational process, wherein, minJ (k) is the minimum value of the output of objective function.

Further specify realization effect of the present invention in conjunction with instantiation.

In the present embodiment, suppose first segment compartment m ₁Be 42.8t, second section compartment m ₂Be 48t, the 3rd joint compartment m ₃Be 46.5t, the 4th joint compartment m ₄Be 42t, resistance coefficient C ₀0.8806N/KN/kg, C ₁0.007444N/KNm/skg, C ₂0.0001143N/KNm2/s2kg.Optimization Prediction time domain P=4, control time domain M=2, sampling period Ts=20s.Elasticity coefficient k between the compartment _i10488KN/m.

Utilize dynamics software SIMAPCK, as shown in Figure 4 and Figure 5, set up the Dynamics Simulation Model of motor train unit (take the CRH2 type as example).As shown in Figure 6, wherein, wheel is processed as rigid body structures such as, bogie, car bodies, and the connector between single stage suspension, compartment and the compartment, mechanical resistance, air resistance, tractive force etc. are processed as external force, exist degree of freedom, restriction, hinged etc. related between rigid body and the rigid body, the eight joint motor train unit carriage models of setting up afterwards as shown in Figure 7.

In objective function, obtain between numerical simulation compartment as shown in Figure 8 design sketch as shown in Figure 9 in the relative displacement variable quantity and SIMPACK platform after the above parameter of substitution.Each motor train unit is under the allotment of rational tractive force as can see from Figure 8, the variation of the relative shift between the compartment.The stroke of connector between the compartment as can see from Figure 9, secondary indication the reasonable distribution stressing conditions of each compartment under the method is optimized.

In sum, a kind of motor train unit Dynamic Optimum forecast Control Algorithm based on model of the present invention has following beneficial effect:

Method of the present invention is applicable to have motor train unit and other high-speed train of powered distributed, the motor train unit power distributed model PREDICTIVE CONTROL that the present invention can realize, by thereby motor-car velocity variations in the motor train unit operational process is optimized power distribution, so method of the present invention improves power distribution efficient so that motor train unit keeps energy saving economy when operation.

So the present invention has effectively overcome various shortcoming of the prior art and the tool high industrial utilization.

Above-described embodiment is illustrative principle of the present invention and effect thereof only, but not is used for restriction the present invention.Any person skilled in the art scholar all can be under spirit of the present invention and category, and above-described embodiment is modified or changed.Therefore, have in the technical field under such as and know that usually the knowledgeable modifies or changes not breaking away from all equivalences of finishing under disclosed spirit and the technological thought, must be contained by claim of the present invention.

Claims (9)

1. the motor train unit Dynamic Optimum forecast Control Algorithm based on model is characterized in that, may further comprise the steps:

S1, as state variable, set up the motor train unit state equation after the motor train unit linearization with the travelling speed of motor train unit carriage and the displacement between the compartment:

Y=Cx;

Wherein, x=[δ v ₁, δ v ₂..., δ v _n, δ x ₁, δ x ₂..., δ x _N-1] ^TU=[δ u ₁, δ u ₂..., δ u _n] ^TA, B and C are the State Equation Coefficients matrix; X is the displacement between the compartment; Y is the column vector that the speed in every joint compartment forms; U is the effective traction that the compartment is subject to;

First order derivative for the displacement between the compartment; δ v ₁, δ v ₂, δ v _nBe respectively near the side-play amount equilibrium point of travelling speed near the side-play amount equilibrium point of travelling speed in the 1st joint compartment, the 2nd joint compartment, n joint compartment; δ x ₁, δ x ₂, δ x _N-1Be respectively the 1st joint compartment the relative the 2nd and save near the side-play amount of relative shift equilibrium point that compartment, the 2nd saves relative the 3rd joint compartment, compartment, relative n joint compartment, n-1 joint compartment; δ u ₁, δ u ₂, δ u _nBe respectively the tractive force in the 1st joint compartment, the 2nd joint compartment, n joint compartment and near the side-play amount of the equilibrium point of making a concerted effort of damping force; N is the compartment joint number; T is matrix transpose;

S2, the effective traction that is subject to when moving according to motor train unit and the interaction force between the compartment are set up the constraint condition in the motor train unit operational process: u _Min-u ^e≤ u≤u _Max-u ^e,

Wherein, $x\left(k\right)={[\frac{f_1}{k_1},\frac{f_2}{k_2},...\frac{f_{n-1}}{k_{n-1}}]}^T;$ $x_{\min }={[\frac{f_{1\min }}{k_1},\frac{f_{2\min }}{k_2},...,\frac{f_{n-1\min }}{k_{n-1}}]}^T;$ $x_{\max }={[\frac{f_{1\max }}{k_1},\frac{f_{2\max }}{k_2},...,\frac{f_{n-1\max }}{k_{n-1}}]}^T;$

With

Be the State Equation Coefficients discrete matrix; K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; U is the effective traction that the compartment is subject to; u ^eBe the effective traction that compartment under the equilibrium point state is subject to, e is the equilibrium point state; u _Min, u _MaxBe respectively the tractive force in compartment and the minimum value of making a concerted effort, the maximal value of damping force; x _Min, x _MaxBe respectively minimum value, the maximal value of the displacement between the compartment; f ₁, f ₂, f _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force between the compartment; f _1min, f _2min, f _N-1minBe respectively between the 1st joint compartment and the 2nd joint compartment, between the 2nd joint compartment and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force minimum value between the compartment; f _1max, f _2max, f _N-1maxBe respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves compartment and n and saves interaction force maximal value between the compartment; k ₁, k ₂, k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; N is the compartment joint number; T is matrix transpose;

S3 according to the motor train unit state equation after the motor train unit linearization, interaction force, prediction time domain and control time domain between the compartment, determines the objective function of optimal control: J (k)=u ^THu+2u ^TF;

Wherein, $H={\tilde{B}}^T\tilde{Q}\tilde{B}+\tilde{R},$ $f=\tilde{B}\tilde{Q}\tilde{A}x\left(k\right),$

K is time parameter; J (k) is in the constantly output of objective function of k; X (k) is at k state constantly; U is the effective traction that the compartment is subject to; F is the interaction force between the compartment; H is intermediate transform matrices, and P is the prediction time domain, and M is the control time domain, and Q, R are positive definite matrix,

Be the diagonal matrix that is formed by positive definite matrix Q,

Be the diagonal matrix that is formed by positive definite matrix R,

Be the State Equation Coefficients transformation matrix,

Be the State Equation Coefficients transformation matrix; N is the compartment joint

Number; T is matrix transpose;

S4 finds the solution described objective function under described constraint condition, the optimal control of motor-car velocity variations and power distribution in the acquisition motor train unit operational process.

2. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1, it is characterized in that: in step S1, also comprise the power system model is set up in vertical operation of motor train unit, so that the variable in the described motor train unit state equation is limited, described power system model comprises:

$m_1{\stackrel{\&CenterDot;}{v}}_1=u_1-w_{01}-f_{{\mathrm{in}}_1}$

$m_i{\stackrel{\&CenterDot;}{v}}_i=u_i-w_{0i}+f_{{\mathrm{in}}_{i-1}}-f_{{\mathrm{in}}_i},$ i=2,…,n-1

$m_n{\stackrel{\&CenterDot;}{v}}_n=u_n-w_{0n}+f_{{\mathrm{in}}_{n-1}}$

${\stackrel{\&CenterDot;}{x}}_i=v_i-v_{i+1},$ i=1,...,n-1

Wherein, m ₁Be the quality in the 1st joint compartment, m _iBe the quality in i joint compartment, m _nQuality for n joint compartment;

Be the acceleration in the 1st joint compartment,

Be the acceleration in i joint compartment,

Acceleration for n joint compartment; u ₁Be the 1st joint tractive force in compartment and damping force make a concerted effort u _iBe the tractive force in i joint compartment and damping force make a concerted effort u _nBe the tractive force in n joint compartment and making a concerted effort of damping force; w ₀₁Be the datum drag in the 1st joint compartment, w _0iBe the datum drag in i joint compartment, w _0nIt is the datum drag in n joint compartment; f _In1Be the interaction force in the 1st joint compartment and the 2nd joint compartment,

Be the interaction force in i-2 joint compartment and i-1 joint compartment, Be the interaction force in i-1 joint compartment and i joint compartment,

It is the interaction force in n-1 joint compartment and n joint compartment; v _iBe the speed in i joint compartment, v _I+1Be the speed in i+1 joint compartment;

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment; N is the compartment joint number.

3. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 2 is characterized in that: the constraint condition that the connector between the interaction force between the compartment and the two joint compartments satisfies is:

$f_{{\mathrm{in}}_i}=k_i{x}_{{\mathrm{in}}_i}+d_i{\stackrel{\&CenterDot;}{x}}_{{\mathrm{in}}_i},$ i=1,…,n-1, $f_{{\mathrm{in}}_0}=f_{{\mathrm{in}}_n}=0,$

Wherein: k _iThe elasticity coefficient of connector between i joint compartment and the i+1 joint compartment, d _iIt is the ratio of damping of connector between i joint compartment and the i+1 joint compartment; Be the relative displacement between i joint compartment and the i+1 joint compartment,

It is the first order derivative of the relative displacement between i joint compartment and the i+1 joint compartment;

Be the interaction force in i joint compartment and i+1 joint compartment,

Be the interaction force in the 0th joint compartment and the 1st joint compartment,

Be the interaction force in n joint compartment and n+1 joint compartment, n is the compartment joint number.

4. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1 is characterized in that: in step S1:

The State Equation Coefficients matrix A is:

$A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ Wherein, A ₁₁=-diag (c ₁₁+ c ₂₁v _r..., c _1n+ c _2nv _r), A ₂₂=0 _{(n-1) * (n-1)},

The State Equation Coefficients matrix B is: $B=\left[\begin{array}{c}{B}_{11}\\ 0_{(n-1)\&times;n}\end{array}\right],$ $B_{11}=\mathrm{diag}(\frac{1}{m_1},\frac{1}{m_2},...,\frac{1}{m_n});$

The State Equation Coefficients Matrix C is: C=[I _{N * n}0 _{(n-1) * (n-1)}];

v _rReference velocity for the motor train unit operation; m ₁Be the quality in the 1st joint compartment, m ₂Be the quality in the 2nd joint compartment, m _N-1Be the quality in n-1 joint compartment, m _nIt is the quality in n joint compartment; k ₁, k ₂, k _N-2And k _N-1Be respectively between the 1st joint compartment and the 2nd joint compartment, between 2 joint compartments and the 3rd joint compartment, n-2 joint compartment saves between the compartment with n-1 and n-1 saves the elasticity coefficient that compartment and n save the connector between the compartment; c ₁₁, c ₂₁, c _1nAnd c _2nParameter for the motor train unit datum drag; I is unit matrix; N is the compartment joint number.

5. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1 is characterized in that: in step S2:

u _min=[u _1min,u _2min,…,u _nmin] ^T，u _max=[u _1max,u _2max,…,u _nmax] ^T， $u^e={[u_1^e,u_2^e,...,u_n^e]}^T;$

u _1min, u _2min, u _NminBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the minimum value of making a concerted effort of damping force; u _1max, u _2max, u _NmaxBe respectively the 1st joint compartment, the 2nd joint compartment, the tractive force in n joint compartment and the maximal value of making a concerted effort of damping force;

Be respectively the compartment is subject under the equilibrium point state the effective traction of being in the 1st joint compartment, the 2nd joint compartment, n joint compartment; T is matrix transpose;

The State Equation Coefficients discrete matrix

For:

The State Equation Coefficients discrete matrix

For:

Wherein, L=[0 _{(n-1) * n}I _{(n-1) * (n-1)}]; L is matrix of coefficients, and A ' is State Equation Coefficients matrix A discrete state matrix, and B ' is the discrete state matrix of State Equation Coefficients matrix B; M is the control time domain, and I is unit matrix; N is the compartment joint number.

6. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1 is characterized in that: in step S3:

The State Equation Coefficients transformation matrix

For: $\tilde{A}=\left[\begin{array}{c}{A}^{\&prime;}\\ A^{\&prime;2}\\ .\\ .\\ .\\ A^{\&prime;P}\end{array}\right],$

The State Equation Coefficients transformation matrix

For: $\tilde{B}=\left[\begin{array}{ccccc}{B}^{\&prime;}& 0& 0& ...& 0\\ A^{\&prime;}{B}^{\&prime;}& B^{\&prime;}& 0& ...& 0\\ A^{\&prime;2}{B}^{\&prime;}& A^{\&prime;}{B}^{\&prime;}& B^{\&prime;}& ...& 0\\ .& .& .& & .\\ .& .& .& ...& .\\ .& .& .& & .\\ A^{\&prime;P-1}{B}^{\&prime;}& A^{\&prime;P-2}{B}^{\&prime;}& A^{\&prime;P-3}{B}^{\&prime;}& ...& A^{\&prime;P-M}{B}^{\&prime;}\end{array}\right],$

A ' is the discrete state matrix of State Equation Coefficients matrix A, and B ' is the discrete state matrix of State Equation Coefficients matrix B; P is the prediction time domain, and M is the control time domain.

7. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1 is characterized in that: in step

Among the S3, before the objective function of determining optimal control, also comprise take TS as the sampling period the motor train unit state equation Carry out discretize with y=Cx and process, obtain the motor train unit state equation of discretize:

x(k+1)=A′x(k)+B′u(k)

y(k+1)=Cx(k)；

K is the time state parameter; X (k) is the function of state in k compartment displacement constantly; X (k+1) is the function of state in k+1 compartment displacement constantly; Y (k+1) is the column vector that the speed in the k+1 moment every joint compartment forms; The effective traction of u (k) for being subject in k moment compartment; A ' is the discrete state matrix of State Equation Coefficients matrix A; B ' is the discrete state matrix of State Equation Coefficients matrix B.

8. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 7 is characterized in that: according to motor train unit state equation, prediction time domain and the control time domain of discretize, set up the forecast model that is used for determining objective function:

$J\left(k\right)=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{\left|\right|y(k+i|k)-y_r(k+i)\left|\right|}_{Q_i}^2+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left|\right|u(k+i-1|k)\left|\right|}_{R_i}^2,$

Wherein, k, i are the time state parameter; J (k) is in the constantly output of objective function of k; Y (k+i|k) predicts the constantly output of objective function of k+i constantly at k; y _r(k+i) be the output reference value of k+i objective function constantly; U (k+i-1|k) predicts the tractive force in k+i-1 compartment constantly and the input quantity of making a concerted effort of damping force constantly at k, and P is the prediction time domain, and M is control time domain, Q _iAnd R _iAll are positive definite matrixes.

9. the motor train unit Dynamic Optimum forecast Control Algorithm based on model according to claim 1 is characterized in that: in step S4, described objective function found the solution specifically under described constraint condition comprise:

Obtain in the motor train unit operational process motor-car velocity variations and power and divide by finding the solution

The optimal control of joining, wherein, minJ (k) is the minimum value of the output of objective function.

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