CN104570760B - Distributed simulation method for continuous control system in unit operation - Google Patents
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Abstract
The invention discloses a distributed simulation method for a continuous control system in unit operation, and belongs to the technical field of computer simulation. The method comprises the following steps: firstly, dividing sub-models forming an initial system into two types namely straight-through models and non-straight-through models; secondly, splitting the initial system and deploying each split part on a separate simulation node to run to form a distributed simulation structure, wherein the straight-through model is prevented from being deployed on the separate simulation node during the splitting; finally, setting a simulation period in the distributed environment according to a calculated maximum simulation period. According to the method, the initial system is not required to be modified; data delay generated when the continuous control system in unit operation is converted into one in distributed operation due to the characteristics of parallel computation is reduced by the first two steps; the maximum simulation period is determined to enable the converted distributive system to keep the stability characteristic of the initial system; the data exchange frequency among all distributed simulation nodes is reduced to the greatest extent.
Description
Technical field
The invention belongs to computer simulation technique field, and in particular to a kind of continuous control system to unit operation is carried out
The method of distributed emulation.
Background technology
The continuous control system of tradition exploitation is usually unit operation.But, under some specific occasions, need this
A little system operations are in distributed environment.One typical example is the flight model device with distributed frame, its attitude control
Device processed is operated on a simulation node, and controlled device (aircraft) model running is on another simulation node.
In order to describe conveniently, the continuous control system of unit operation is designated as into CS, or starter system；After transformed, run
Control system under distributed environment is referred to as DS, or goal systems.If according to the form of general " controller-controlled device ",
Then CS can be expressed as follows：
The implication of each parameter is：
●xc：The state variable of controller；
●uc：The output of the input of controller, i.e. controlled device；
●yc：The output of controller；
●fc(*)：The state equation of controller；
●gc(*)：The output equation of controller；
●xp：The state variable of controlled device；
●up：The output of the input of controlled device, i.e. controller；
●yp：The output of controlled device；
●fp(*)：The state equation of controlled device；
●gp(*)：The output equation of controlled device.
The system is converted to distributed system (i.e. DS), and its state equation is expressed as：
Wherein,
●(*)q：Discretization function, to represent and carry out discretization to signal * by sampling.When the continuous system of unit operation
It is split into some and is deployed to when running in distributed environment, the output of each several part can be discretized.This is by being distributed
What the characteristic of formula emulation parallel computation caused, unavoidably；
●(t-T)：Represent signalDelay the T moment.
The conversion of CS to DS, can be completed by modes such as multiple programmings, but be required a great deal of time with expense to mould
Type code is modified.But then, if be not added with it is any process directly conversion, such as equation (1a), (1b) and equation (2a),
(2b) shown in, can because introduce discretization and delay factor, so as to cause starter system and goal systems state trajectory it
Between there is error.
The content of the invention
The purpose of the present invention is that the continuous control system to conventional individual operation carries out distributed transformation, is changing very little
In the case of realize the distributed operation of one-of-a-kind system, while ensureing systematic function.In order to reach this purpose, the invention provides
A kind of method that continuous control system to unit operation carries out distributed emulation.
The method that a kind of continuous control system to unit operation of the present invention carries out distributed emulation, including following step
Suddenly：
Step 1, by composition starter system submodel classified, be divided into through-type model with non-through-type model two
Class；
Whether the output for judging submodel is directly determined that if so, the submodel is through-type model, the otherwise son by input
Model is non-through-type model；
Step 2, starter system is split, each section of fractionation is deployed on single simulation node and is run,
Form distributed emulation structure；
Splitting rule is：A non-straight-through model is arbitrarily selected, m is designated asstart, the outfan of the model is disconnected, and edge
Straight-through model of all input paths backtracking of the model before the model, until running into another non-straight-through model, note
For mend；mstartTo mendBetween part as an independent split cells；The each section of fractionation is independent by split cells
Composition combines composition；
Step 3, step-length T for determining distributed emulationf, it is desirable to TfLess than or equal to maximum emulation cycle Tmax。
Maximum emulation cycle T in described step 3maxAcquisition methods be：
Step 3.1：Find a liapunov function V of starter system；
Step 3.2：Calculate following α (*) function：
Wherein：X represents the system variable of the control system that step 2 is obtained；The output produced by distributed operation postpones to lead
The error of cause includes：Error delta x of the controller state variable when unit operation is with distributed operationc, the change of controlled device state
Error delta x of the amount when unit operation is with distributed operationp, the output of controlled device is when unit operation is with distributed operation
Error delta yp；Included by error caused by discretization is forced during distributed operation：Controller output unit operation with it is distributed
Error delta y during operationcq, error delta y of the output of controlled device when unit operation is with distributed operationpq；xpIt is controlled right
The state variable of elephant；xcIt is the state variable of controller；fp(*) be controlled device state equation；fc(*) be controller shape
State equation；gc(*) be controller output equation；gp(*) be controlled device output equation.
Step 3.3：Selection parameter s and s1, meet below equation (2)～(4)：
β (0,0,0,0,0) ＜-s (3)
β(Δxc, Δ xp, Δ yp, Δ ycq, Δ ypq) ＜-s1 (4)
Wherein, function β (*) is defined as：
Step 3.4：According to equation (4), a real number ρ can be found, be met：
||(Δxc, Δ xp, Δ yp, Δ ycq, Δ ypq) | | ＜ ρ (6)
| | * | | represents modulus；According to equation (4) and equation (6), the maximum that ρ may be obtained is assessed.
Step 3.5：Determine system dynamics parameter Mfc, Mfp, Mgc, Mgp, wherein：It is the upper bound of controller state equation；It is the upper bound of controlled device state equation；It is the Lipschitz constant of controller output function；It is controlled device
The Lipschitz constant of output function.
Step 3.6：Maximum emulation cycle T is calculated according to below equationmax：
Relative to prior art, advantages of the present invention and good effect are：
(1) method proposed by the invention is on the premise of any model code is changed, by specific rule and behaviour
Make, realize and starter system CS is converted to into distributed system DS, and ensure that the error between simulation result and starter system has
Boundary, stability features are consistent；
(2) the system fractionation that rule is carried out is split according to proposed by the present invention, makes parallel computation characteristic under distributed environment
The submodel output for causing postpones minimum so that simulated delay problem is alleviated；
(3) the distributed emulation step-length that the inventive method determines, it is ensured that starter system retains original in distributed operation
The stability features come, while making the data exchange frequency between distributed emulation node minimum.
Description of the drawings
Fig. 1 is that the flow process of the method that the continuous control system to unit operation of the present invention carries out distributed emulation is illustrated
Figure；
Fig. 2 is the Control System of Inverted Pendulum schematic diagram of the embodiment of the present invention；
Fig. 3 is the operation result schematic diagram not operated according to the method for the present invention, wherein (a) be truck position with the time
Conversion schematic diagram is (b) pendulum angle with time change schematic diagram；
Fig. 4 is the result schematic diagram split to system shown in Figure 2 according to the fractionation rule of step 2；
Fig. 5 is the operation result schematic diagram operated according to the method for the present invention, wherein (a) is truck position anaplasia at any time
Change schematic diagram, (b) for pendulum angle with time change schematic diagram.
Specific embodiment
The method that a kind of continuous control system to unit operation proposed by the present invention carries out distributed emulation, such as Fig. 1 institutes
Show, including three big steps：Category of model, system split and calculate maximum simulation step length.It is specific real below in conjunction with one
Example and accompanying drawing are described further to the implementation process of the present invention.The example be Control System of Inverted Pendulum, system structure such as Fig. 2 institutes
Show.
Step 1：Category of model.
Contact control system be typically made up of multiple submodels, with band feedback or without feedback submodel series connection or and
It is coupled structure.These submodels can be divided into two categories below according to the relation between its input, output：
● straight-through model：Straight-through model refers to the model with straight-through port.Straight-through port is defined as ＜ input ports, defeated
Exit port ＞ pair, wherein, the value of output port is directly determined by input port.If 3 variables collections of each model：It is defeated
Enter variables collection X, internal state variable set S, and output variable set Y, then lead directly to model and can be described as：
Wherein, function I (*) is input function, and T (*) is state transition function, and O (*) is output function.Xn+1、Sn+1With
Yn+1Input vector, the internal state vector sum output vector at n+1 moment are represented respectively；SnRepresent the n moment internal state to
Amount；H represents model integration step.As can be seen that the output Y at current timen+1With the input X at current timen+1There is direct relation.
S=Φ are a special cases of straight-through model, and wherein Φ is null set, represents that the model does not have internal state, is memoryless.Often
The straight-through model seen includes the models such as gain, algebraic operation (addition subtraction multiplication and division), differential.
● non-straight-through model：Non- straight-through model does not have straight-through port.Non- straight-through model can be described as：
The output Y at current timen+1Only with current internal state Sn+1It is relevant, with current input Xn+1It is unrelated.This means
Non- straight-through model produces newest output without waiting for newest being input to up to by.Common non-straight-through model include integration,
Pure input signal, memory etc..
After classifying to model, the computation sequence of each submodel when can calculate unit operation, principle is as follows：For
Straight-through model, it should calculate the model of those straight-through ports for driving it first；For non-straight-through model, can be according to arbitrarily suitable
Sequence is calculated, as long as before the straight-through model driven positioned at it.Here, the implication of model a driving models b is：The output conduct of a
The input of b.
According to the characteristics of each submodel input, output, the submodel in Fig. 2 Control System of Inverted Pendulum is divided into straight-through
Pattern type 101, and non-through-type model 102, control system includes 9 submodels in Fig. 2, and the classification results of each submodel are such as
Shown in table 1.
The control system neutron category of model of table 1
After classification, it may be determined that the computation sequence of each submodel in starter system.Digital 1-9 in Fig. 2 illustrates this enforcement
Computation sequence in example.If directly the starter system in Fig. 2 is carried out distributed arithmetic, system performance is deteriorated, such as Fig. 3
Shown in (a) and (b)；By caused by distributed arithmetic, submodel output postpones and discretization causes for this change.
Step 2：System splits.It is reasonably to be divided starter system that the system splits, and each section is all by portion
Administration runs on single simulation node, so as to form distributed emulation structure.Simulation node refers to general purpose computer.Present invention side
The system of method splits and will be performed according to the fractionation of setting rule, and main principle is to avoid for through-type model being deployed in individually emulation
On node.
Starter system need split, be converted to can distributed deployment form.It has been proved that starter system is split as
After distributed system, the output of submodel is compared to can produce delay during unit operation.And these delays can change starter system
Characteristic, for example, make original stable system become unstable.The contrast of operation 1h and 2h is shown in Fig. 3, it can be seen that operation
2h is unstable compared with what the system of operation 1h became.The situation of particularly multiple through-type model series connection, can postpone accumulation so as to add
Acute this phenomenon.In order to reduce delay phenomenon, the present invention proposes following fractionation rule：
● a non-straight-through model is arbitrarily selected, m is designated asstart.Its outfan is disconnected, and along its all inputs
The straight-through model before it is recalled in path, until running into another non-straight-through model, is designated as mend。mstartAnd mendBetween portion
Removable branching away is divided individually to be disposed.In the process, if mstart=mend, illustrate that the backtracking path is a ring；Ring will be by
As the internal component for being split part.
The fractionation rule can be used alone, it is also possible to which iteration is used.When iteration is used, to some for splitting out
Merge, merging the part for being formed can be deployed in operation on single simulation node.According to this rule, what is splitted out is each
Individual part has eliminated independent through-type model；Thus the accumulated delay for causing also just is not present.
According to rule is split, starter system is split into some for being suitable to distributed emulation, can be only per part
Vertical deployment.Fig. 4 show according to split rule, the starter system shown in Fig. 2 is split as 4 parts 21～24.According to the present invention
This mode sets up distributed emulation, and simulation result is improved, as shown in Figure 5.(a) and (b) in Fig. 5 sets forth
The situation of operation 5h, 10h, 50h and 100h, it can be seen that using the distributed emulation of the method for the present invention, system stability is strong, leads to
Cross and Fig. 3 contrasts, it is seen that the effectiveness of distributed simulation method of the present invention.
Step 3：Distributed emulation step-length TfIt is determined that, it is desirable to TfLess than or equal to maximum emulation cycle Tmax。
Through the process of step 2, simulated delay problem is alleviated.At this time, it may be necessary to find an operating process, energy
Enough determine the maximum emulation cycle T of distributed emulationmax.It is determined that maximum emulation cycle Tmax, it is to reduce distribution fortune as far as possible
The frequency of the swapping data of each node during row；Meanwhile, during using the cycle, distributed system should keep the base of starter system
This characteristic, such as stability.The operating process of step 3 is as follows：
Step 3.1：Find a liapunov function V of starter system；
Step 3.2：Calculate following α (*) function：
Wherein：X represents the state variable of control system, and control system herein is operating in point Jing after step 2 is divided
Control system DS under cloth environment；xpIt is the state variable of controlled device；xcIt is the state variable of controller；Liapunov
Function V (x)=V (xp, xc)；ΔxcIt is error of the controller state variable when unit operation is with distributed operation, by distributed
The output that operation is produced postpones to cause；ΔxpIt is error of the controlled device state variable when unit operation is with distributed operation,
The output produced by distributed operation postpones to cause；ΔypIt is the output of controlled device when unit operation is with distributed operation
Error, the output produced by distributed operation postpones to cause；ΔycqIt is that controller is exported when unit operation is with distributed operation
Error, by during distributed operation force discretization cause.Discretization is forced to refer to the mistake of the output sampling to each simulation node
Journey, is to be caused by the parallel computation mode of distributed operation, unavoidably.ΔypqIt is the output of controlled device in unit operation
With error during distributed operation, caused by the pressure discretization of distributed operation introducing.fp(*) be controlled device state
Equation；gc(*) be controller output equation；gp(*) be controlled device output equation；fc(*) be controller state side
Journey.
α (*) function be liapunov function V at state x to xp、xcPartial derivative.
Step 3.3：Selection parameter s and s1, meet below equation (4)～(6)：
β (0,0,0,0,0) ＜-s (5)
β(Δxc, Δ xp, Δ yp, Δ ycq, Δ ypq) ＜-s1 (6)
Wherein, function β (*) is defined as：
In formula (4)：
For the derivative of liapunov function；Sup (*) represents the supremum asked in gathering；D3=D1-D2, wherein D1
Represent that what is formed mutually cut in starter system original state position along state trajectory vertical direction with liapunov function curved surface
One closed area, D2By after system state change finite time in new position along state trajectory vertical direction and Liapunov
Function surface mutually cuts the closed area to be formed.For stabilisation systemss, D2Must be in D1Inside, i.e. D2Inside is less than D1。
Step 3.4：According to equation (6), a real number ρ can be found, be met：
||(Δxc, Δ xp, Δ yp, Δ ycq, Δ ypq) | | ＜ ρ (8)
| | * | | represents modulus；According to equation (6) and equation (8), the possible maximums of assessment ρ；
Step 3.5：Determine system dynamics parameter Mfc, Mfp, Mgc, Mgp；Wherein：It is controller state Equation fc(*)
The upper bound；It is the upper bound of controlled device state equation；It is controller output function gc(*) Lipschitz constant；
It is controlled device output function gp(*) Lipschitz constant.This four dynamic parameters can be obtained by various methods, such as,
Directly starter system operation can just be obtained into these dynamic parameter values one time.
Step 3.6：Maximum emulation cycle T is calculated according to below equationmax：
According to 6 step 3.1～3.6 for determining maximum step-length, final available maximum simulation step length T is calculatedmax.Using
The step-length carries out distributed emulation, thus it is ensured that the error of simulation result remains the stability features of starter system by boundary.
Claims (1)
1. a kind of method that continuous control system to unit operation carries out distributed emulation, it is characterised in that including following step
Suddenly：
Step 1, by composition starter system submodel classified, be divided into through-type model with the non-class of through-type model two；
Whether the output for judging submodel is directly determined that if so, the submodel is through-type model, the otherwise submodel by input
For non-through-type model；
Step 2, starter system is split, each section of fractionation is deployed on single simulation node and is run, formed
Distributed emulation structure；
Splitting rule is：A non-straight-through model is arbitrarily selected, m is designated asstart, the outfan of the model is disconnected, and along this
The straight-through model before the model is recalled in all input paths of model, until running into another non-straight-through model, is designated as
mend；mstartTo mendBetween part as an independent split cells；The each section of fractionation is by independent group of split cells
Into or combination composition；
Step 3, determine distributed emulation cycle Tf, it is desirable to TfLess than or equal to maximum emulation cycle Tmax；
Maximum emulation cycle TmaxAcquisition methods be：
Step 3.1：Find a liapunov function V of starter system；
Step 3.2：Calculate following α (*) function：
Wherein：X represents system variable；Error includes caused by the output produced by distributed operation postpones：Controller state becomes
Error delta x of the amount when unit operation is with distributed operationc, controlled device state variable is when unit operation is with distributed operation
Error delta xp, error delta y of the output of controlled device when unit operation is with distributed operationp；Forced by during distributed operation
Error includes caused by discretization：Controller exports error delta y when unit operation is with distributed operationcq, controlled device
Error delta y of the output when unit operation is with distributed operationpq；xpIt is the state variable of controlled device；xcIt is the shape of controller
State variable；fp(*) be controlled device state equation；fc(*) be controller state equation；gc(*) be controller output side
Journey；gp(*) be controlled device output equation；
Step 3.3：Selection parameter s and s1, meet below equation (2)～(4)：
β(0,0,0,0,0)<-s (3)
β(Δxc,Δxp,Δyp,Δycq,Δypq)<-s1 (4)
Wherein, function β (*) is defined as：
Wherein, sup (*) represents the supremum asked in gathering；D3=D1-D2, D1Represent starter system original state position
The closed area to be formed, D are mutually cut along state trajectory vertical direction and liapunov function curved surface2By system state change
The closed area to be formed mutually is cut after finite time with liapunov function curved surface along state trajectory vertical direction in new position；
Step 3.4：According to equation (4), a real number ρ is found, meet formula (6)：
||(Δxc,Δxp,Δyp,Δycq,Δypq)||<ρ(6)
| | * | | represents modulus, according to equation (4) and equation (6), assesses the maximum that ρ can be obtained；
Step 3.5：Determine system dynamics parameter Mfc,Mfp,Mgc,Mgp, wherein：It is the upper bound of controller state equation；It is
The upper bound of controlled device state equation；It is the Lipschitz constant of controller output function；It is controlled device output letter
Several Lipschitz constants；
Step 3.6：Maximum emulation cycle T is calculated according to below equationmax：
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| CN101710361A (en) * | 2009-11-13 | 2010-05-19 | 北京航空航天大学 | Distributed traffic simulating platform based on Service-Oriented Architecture (SOA) and simulating method thereof |
| CN101741642A (en) * | 2009-12-17 | 2010-06-16 | 北京航空航天大学 | Task deployment system for distributed simulation of computer network attack and defense training |
| CN102346442A (en) * | 2011-05-12 | 2012-02-08 | 天津大学 | Method for carrying out parallel transient simulation computing on microgrid suitable for nodal analysis frameworks |
| CN103984240A (en) * | 2014-04-27 | 2014-08-13 | 中国航空工业集团公司沈阳飞机设计研究所 | Distributed real-time simulation method based on reflective memory network |
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| CN101710361A (en) * | 2009-11-13 | 2010-05-19 | 北京航空航天大学 | Distributed traffic simulating platform based on Service-Oriented Architecture (SOA) and simulating method thereof |
| CN101741642A (en) * | 2009-12-17 | 2010-06-16 | 北京航空航天大学 | Task deployment system for distributed simulation of computer network attack and defense training |
| CN102346442A (en) * | 2011-05-12 | 2012-02-08 | 天津大学 | Method for carrying out parallel transient simulation computing on microgrid suitable for nodal analysis frameworks |
| CN103984240A (en) * | 2014-04-27 | 2014-08-13 | 中国航空工业集团公司沈阳飞机设计研究所 | Distributed real-time simulation method based on reflective memory network |
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