CN104749965B - Nonlinear multi-cabin series-parallel Euler fixed-step-length simulation method - Google Patents
Nonlinear multi-cabin series-parallel Euler fixed-step-length simulation method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000004088 simulation Methods 0.000 title abstract description 15
- 230000010354 integration Effects 0.000 claims description 10
- 230000002969 morbid Effects 0.000 claims description 5
- 230000014509 gene expression Effects 0.000 claims description 3
- 239000011800 void material Substances 0.000 claims description 2
- 230000010355 oscillation Effects 0.000 abstract description 6
- 230000001575 pathological effect Effects 0.000 abstract 2
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- 238000013459 approach Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
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Abstract
The invention provides a modeling method for multi-cabin series-parallel Euler fixed-step-size simulation. It is characterized by comprising: removing a pathologic algebraic ring of the linear system, namely adding virtual integrals to convert an algebraic equation model with the pathologic algebraic ring into a differential equation model; the rigidity of the system can be reduced by adjusting the virtual integral parameters; and then, the linear system is reduced into a nonlinear system, and a method for solving euler fixed-step-length simulation steady-state oscillation is provided for ensuring the stability of the system.
Description
Technical field
The present invention relates to more cabin series-parallel connections emulation, and the emulation problem is given and is analyzed, devises new emulation mode, is protected
The emulation of more cabin series-parallel connection Euler fixed step sizes and actual conditions are demonstrate,proved close to being of great significance.
Background technology
For the emulation of more cabin series-parallel connections, there are two class emulation modes of fixed step size and variable step.Wherein, variable step simulation run
As a result be usually stable, and compared with actual conditions close to.But variable step emulation cannot be guaranteed the real-time of emulation, and,
When system needs to carry out semi-physical simulation, i.e. real-time simulation, which does not apply to.
Invention content
In view of the above problems, the present inventor's selection emulates more cabin series-parallel connections with fixed step size emulation mode.Wherein
Euler method is emulation mode the simplest, practical.And when the present inventor emulates more cabin series-parallel connections with fixed step size Euler method
When, it finds when closing particular valve, system can be because there are dissipated during algebraic loop.For algebraic loop, it can be divided into benign
Algebraic loop and ill two kinds of algebraic loop, wherein ill algebraic loop can be not normally functioning system, once there is ill algebraic loop to produce
Raw, emulation just dissipates.The present invention further studies the problem, it is determined that the method for the ill algebraic loop of removal, and really
The method for having determined to emulate nonlinear system with Euler's fixed step size emulation mode, and eventually generate stable state for system
The situation of oscillation, it is proposed that improved method, including given threshold, system variable is more than that the threshold value will carry out turning for corresponding model
It changes.Obtained new simulation model can ensure that system is stablized, and operation result is approached with actual conditions.
The present invention provides the method emulated with Euler's fixed step size simulation method to more cabin series-parallel connections, this method：
First, practical nonlinear system is linearized, the relational expression of all flow pressures is analyzed, finds to deposit
In special algebraic relation formula, when closing specific valve, system will appear morbid state, this namely system dissipate the reason of；
Secondly, virtual integration is added, instead of there is the algebraic equation of ill algebraic loop, i.e. the system only exists benign algebraically
Equation group and include empty quasi-integral differential equation group；
Third adjusts virtual integral parameter, so as to reduce the rigidity of system；
4th, linear system is reduced to it is non-linear, i.e., it is identical with actual conditions；But with Euler's fixed step size emulation side
In the case of method, system finally will appear steady oscillation, stablizes for guarantee system, flow threshold has been set in advance in this method,
It when flow system flow value is more than the threshold value, is emulated with nonlinear model, when flow system flow is less than the threshold value, is converted to line
Sexual system, so as to ensure that system is stablized.
Figure of description
Tetra- cabin series-to-parallel models of Fig. 1.
Fig. 2 additions four cabin series-to-parallel models of virtual integration.
Fig. 3 (a) adjusts the situation of change of characteristic value relative position before and after virtual integral parameter to 3 (b).
Steady oscillation situation occurs for flow pressure in Fig. 4 (a) to (b) nonlinear system simulation.
Fig. 5 (a) to (b) is using the flow pressure simulation result under the change over condition of nonlinear and linear model.
The emulation mode implementation process of Fig. 6 present invention.
Specific embodiment
Detailed description below technical solution according to an embodiment of the invention.
By taking four cabin mixed connections as an example, system model according to the system model as shown in Figure 1, establish simulation model, such as Fig. 6
Step (601).
First, the relationship of pressure flow such as (1)
Wherein,
W represents mass of system flow, and unit is kg/m3；
V represents square of mass of system flow, and unit is (kg/m3)2；
G expressions, which rub, to be led, and unit is (kg/s)2/Pa；
Pressure difference between P represents at 2 points, unit is Pa；
Subscript represents different location respectively, as shown in fig. 1.
According to the simulation model that formula (1) is established, there are closing particular valve, system Divergent Phenomenons, such as the step of Fig. 6
(602)。
Pressure flow relationship in analysis equation group (1) obtains two algebraic equations that there is ill algebraic loop, such as formula
(2) shown in.
Wherein,
DP represents the boosting pressure difference of wind turbine, and unit is Pa；
Define 1：For equation Ax=b, as long as A or b have small variation, huge change will occur for solution of equations
Change, such equation is referred to as ill-condition equation.
As can be seen that within the system, G and G42During very little, the coefficient of pressure is infinity in system, then by G and G42Into
The variation of row very little, the solution of the system can also occur very big transformation, that is, meet the definition of ill-condition equation, illustrate that the system exists
Ill-condition equation, the reason of here it is system emulation is caused to dissipate, such as the step of Fig. 6 (603).
In order to which system can be emulated correctly, the morbid state algebraic equation is replaced with virtual integration.System can be expressed as (3)
Form,
Wherein, (3a) is differential equation group, x, xa, t is independent variable, represents situations of change of the x about t, and (3b) is to exist
The algebraic equation of ill algebraic loop.Two virtual integrations are added at the physical model both ends represented by ill-condition equation, i.e., by system
Model is changed into Fig. 2 forms, meanwhile, the ill algebraic equation part in system is replaced with virtual integration, is obtained shaped like (4)
System form,
Wherein, (4a) is that the formed differential equation of virtual integration is added in original differential equation group, they can
Instead of two in (3b) ill algebraic equations, (3b) removes two ill algebraic equations, (4b) is obtained, such as the step of Fig. 6
(604).System shaped like (4) is emulated, transmitting case will not occur, such as the step of Fig. 6 (605).
Due to being added to two virtual integrations to the system, and the quasi-integral parameter of the void does not influence the operation of real system
Situation, it is contemplated that the corresponding parameter of adjustment, making the rigidity of system, that is, rigidity is minimum than minimum.
Define 2：Rigidity ratio is the ratio of system maximum eigenvalue and minimal eigenvalue
System features value can be obtained according to system performance, and rigidity can be obtained and closed than corresponding with virtual integral parameter
System, adjusts the parameter, makes rigidity than minimum, and before and after adjustment, the characteristic value position of system is respectively Fig. 3 (a) and 3 (b), Ke Yifa
Now after the adjustment, in all characteristic values of system, the gap of maximum eigenvalue and minimal eigenvalue reduces, i.e., system rigidity subtracts
It is small, such as the step of Fig. 6 (606).
In order to be approached with actual conditions, linear system is being switched into nonlinear system, is being emulated, such as the step of Fig. 6
(607).It was found that it can cause system that steady oscillation occurs with Euler's fixed step size emulation mode, such as Fig. 4 (a) and 4 (b) difference table
Flow and the emulation oscillatory condition of pressure are showed, such as the step of Fig. 6 (608).According to research before, the generation of the steady oscillation
It is caused by its is non-linear, unavoidably, so good threshold w is set in advance in wemin, i.e., when flow system flow is more than metered flow
2% i.e. wminWhen, Nonlinear Simulation is carried out to the system, once flow system flow is less than wmin, i.e. flow system flow is very small, conversion
For linear system simulation, such as the step of Fig. 6 (609).It both ensure that system can finally reach stable state in this way, and also ensured emulation knot
Fruit approaches with actual conditions, makes emulation significant, such as the step of Fig. 6 (610), simulation result such as Fig. 5 (a) and 5 (b).
Claims (4)
- The series-parallel connection of cabin more than 1. Euler's fixed step size emulation mode, it is characterised in that including：More cabin combined hybrid systems are linearized, analyze its linear character, search emulation is caused to dissipate there are morbid state algebraic loops Algebraic equation,When find emulation is caused to dissipate there are morbid state algebraic loop algebraic equation when, virtual integration is added to system, substituting should There are the algebraic equations of ill algebraic loop, ensure that system emulation will not dissipate,The quasi-integral parameter of void of addition is set, so as to reduce the rigidity of system,Linear system is reduced into nonlinear system, flow threshold is set in advance and is tended towards stability with ensureing to emulate final result, together When system model is adjusted, with ensure when flow value be more than the threshold value when system carry out nonlinear model emulation and flow it is small System carries out linear model emulation when the threshold value.
- 2. the method according to claim 1, it is characterised in that：For the relationship of flow and pressure, such as formula (1)w2=v=GdP (1)Wherein,W represents mass of system flow, and unit is kg/s；V represents square of mass of system flow, and unit is (kg/s)2；G expressions, which rub, to be led, and unit is (kg/s)2/Pa；Pressure difference between dP represents at 2 points, unit is Pa；Nonlinear system is linearized, that is, considers the relationship between v and pressure difference, the pass between all flows and pressure is obtained System, when finding to have the relationship shaped like (2)：Wherein,G1, G2, G3It represents rubbing at position 1,2,3 respectively to lead, unit is (kg/s)2/Pa；dP1,dP2,dP3The pressure difference at position 1,2,3 is represented respectively, and unit is Pa；It can be seen that the G in formula (2) is too small When, when which can show the valve that G representatives are closed in morbid state, that is, real system, system can dissipate.
- 3. method according to claim 2, it is characterised in that：Virtual integration is added to system, instead of the similar algebraic equation shaped like (2), original characterized systematically is as follows：Wherein, (3a) is differential equation group, x, xa, t is independent variable, f (x, xa, t) and represent situations of change of the x about t, (3b) is There are the algebraic equations of ill algebraic loop；Algebraic equation in (3b) is converted into virtual integrated form, system is changed into following form：Wherein, f ' (x, xa, t) and it is f (x, xa, t) and derivative about t,Then ill algebraic loop is not present in the system, and emulation will not dissipate.
- 4. method according to claim 3, it is characterised in that：Due to there is virtual integration in system, carrying out arbitrary adjustment to empty quasi-integral parameter does not influence analogue system and practical feelings The approximate situation of condition so as to by adjusting empty quasi-integral parameter, and ensures system rigidity minimum.
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