CN101719671A - Method for analyzing structural properties of RLC electric network - Google Patents
Method for analyzing structural properties of RLC electric network Download PDFInfo
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- CN101719671A CN101719671A CN200910244973A CN200910244973A CN101719671A CN 101719671 A CN101719671 A CN 101719671A CN 200910244973 A CN200910244973 A CN 200910244973A CN 200910244973 A CN200910244973 A CN 200910244973A CN 101719671 A CN101719671 A CN 101719671A
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Abstract
The invention relates to a method for analyzing structural properties of an RLC electric network, which has the functions of drawing the graph of an electric network, analyzing a topological structure of the electric network, generating a state equation and an output equation, analyzing the structural properties of the electric network, simulating the electric network and the like. The aim of drawing the graph of the electric network is to draw the graph of the RLC electric network to be analyzed; the function of analyzing the topological structure of the electric network can realize the selection of branches and links, and number the selected branches and links; the state equation and the output equation of the electric network can be obtained after the selection of a state variable; the structural properties (controllability and observability) can be analyzed according to the state equation and the output equation; and the function of simulating the electric network can realize the simulation of a specific electric network. The method has the advantages that: by adopting the symbolic operation of the electric network, the structural performance of the electric network can be directly analyzed, which is universal; and the simulation of the electric network can be implemented when elements of the electric network are endowed with detail parameters.
Description
[technical field]: the invention belongs to electric network and automatic control technology field.The present invention is by to the analysis of electric network topological structure, can obtain the structural property (if can the property controlled and controllability etc.) of electric network.This method provides the generation method of system of selection, state equation and the output equation of the electric network topological structure analytical method of (comprising determining of node, branch, chord), state variable, the analytical method and the electric network method of emulation of electric network structural property.
[background technology]: former people mainly are based on real number field research to the research of electric network character, and promptly the element in the electric network all is that concrete parameter value is arranged.Though character that like this can phase-split network, but owing to the calculation of parameter that directly adopts in the electric network, the conclusion of the just certain electric network that often obtains do not possess generality for the structural property of electric network, thereby the structural property of research electric network needs other finding method.If do not give electric network concrete parameter value, but directly symbolization computing, just it doesn't matter for conclusion that obtains like this and concrete parameter, and only relevant with the structure of electric network.So just can get on to study electric network, be applicable to the structural behaviour of analyzing electric network from structure.Based on this method, can carry out electric network topological structure (comprising determining of node, branch, chord) analysis, state variable selection, state equation and the generation of output equation, the analysis and the electric network emulation of electric network structural property.The design software of circuit aspect mainly contains Protel, Orcad, Viewlogic, Mentor Graphics etc. at present, and they are mainly used in circuit design, can not analyze the structural property of electric network.Pspice can realize electric network graphic plotting and numerical computations, but it can not carry out the structural property analysis of electric network equally.
[summary of the invention]: the present invention seeks to overcome the prior art above shortcomings, a kind of analytical method of RLC electric network structural property is provided, this method is carried out the structural property analysis based on the symbolic operation of electric network element set.Based on this method, can draw the electric network figure, can carry out the electric network topological structure (comprising determining of node, branch, chord) analysis, state equation and the generation of output equation, the analysis and the electric network emulation of electric network structural property.
" electric network " of the present invention is meant interconnecting of electric elements, only studies lumped parameter network in the present invention, do not relate to partial differential equation or difference equation.The electric network system equation that obtains does not contain integration, is the differential equation of first order group.The initial value (except the plenary capacitance device loop) that can setting voltage device voltage and the initial value of inductor current (except the full inductor cut set).From topological structure, a tree voltage is the substrate of all voltages, and we place branch to capacitor as much as possible.For all branch currents, the chord electric current is substrate, and we place chord to inductor as much as possible.All voltage sources are by a tree processing, and all current sources are pressed chord and handled.Occurred plenary capacitance device loop in electric network, then one of them capacitor is set to chord; Occur full inductor cut set in electric network, then one of them inductor is set to set and props up.
The analytical method of RLC electric network structural property provided by the invention by drawing electric network figure and electric network topological analysis, generates the state equation and the output equation of electric network, analyzes and electric network emulation thereby carry out the electric network control performance; This method is by studying the structural property of electric network to the topological structure property analysis of electric network, thereby provides new approach for the research of research electric network structural property; This method specifically comprises:
The first, draw electric network figure to be analyzed;
The second, carry out topological analysis, the method and the content of topological analysis comprise:
1) the unified reference direction of having stipulated voltage in electric network; For elements such as resistance, electric capacity, inductance, when the components and parts horizontal positioned left side for just, right for negative, when components and parts are vertically placed, go up to being to bear just, down; For voltage source, current source element, the default voltage reference direction is consistent with the placement location of voltage source, current source;
2) after the drafting electric network is finished, next carry out Analysis of Topological Structure, at first obtain a tree, determine that tree props up and chord.Default voltage source, capacitor prop up for tree, and current source, inductor are chord; When there being plenary capacitance device loop, then one of them capacitor is set to chord; When there being full inductor cut set, then one of them inductor is set to set and props up; Resistor is defaulted as chord, inquires about the resistance two ends then and whether has the tree forehearth limb, if there is no set forehearth limb then resistance be set to the tree;
When 3) writing a circuit matrix or cut set matrix, set earlier and prop up and the chord numbering; In the topological structure relation, be provided with the piecemeal of voltage and current vector, and write the kirchhoff voltage equation of fundamental circuit matrix and the kirchhoff current equation of fundamental cutset.
Three, generate state equation and output equation, concrete grammar is: select branch electric capacity and chord inductance as state variable, output variable is selected as required.
Four, carry out the structural property analysis, concrete grammar is: the structural property in this method mainly is meant structural controllability and structure controllability.By controllability matrix T
c=[B A*B], whether the structure of calculating electric network is controlled, and A, B refer to the coefficient matrix of electric network equation here; By the controllability matrix T
o=[C; C*A], whether the output of calculating electric network is considerable, and C refers to the coefficient matrix of electric network output equation here.
Five, carry out electric network emulation;
In the method, symbol has been adopted in the electric network analysis, has avoided the participation of concrete parameter value, thereby the result who analyzes has generality, has represented the structural property of electric network; This method can realize electric network emulation simultaneously, for state equation and output equation in the 4th step of entering, just can obtain the structural property of special parameter electric network to concrete parameter value.
In above-mentioned the 4th step and the 5th step, after electric network carried out symbolic operation, the structural property that obtains can not change because of the change of parameter, and in electric network emulation, structural property depends on electric network structure and electric network element set parameter simultaneously.
Six, provide analysis result.
Above-mentioned several steps is an integral body, and the purpose of drawing electric network figure to be analyzed is to analyze the structural property of electric network, and has stipulated the reference direction of voltage.The key of topological analysis is to select a tree, and topological analysis provides the basis for the generation of state equation.When generating state equation, need set condition variable and output variable, this method is arranged state variable, and output variable is then selected as required.By controllability matrix T
c=[B A*B], whether the structure that can calculate electric network is controlled; By the controllability matrix T
o=[C; C*A], whether the output that can calculate electric network is considerable.The purpose of electric network emulation is to verify concrete electric network, the parameter value of electric network element set is imported into the structural property that can obtain the special parameter electric network.
Advantage of the present invention and good effect:
Superiority of the present invention is: adopt the electric network symbolic operation, can directly analyze the structural behaviour of electric network, have generality; When giving the concrete parameter of electric network element set, can realize the simulation of electric network.
[description of drawings]:
Fig. 1 is the flow chart of the analytical method of electric network structural property.
Fig. 2 is the electric network schematic diagram.
Fig. 3 is the electric network topological analysis.
Fig. 4 is that state equation shows and the controllability analysis.
[embodiment]:
Embodiment 1:
(1) draw electric network (as shown in Figure 2) to be analyzed, its structure has certain symmetry, and two branch roads on the right have a resistive element and a capacity cell respectively.Analysis by present case will illustrate the superiority of this method in the electric network structural property is analyzed.
(2) carry out topological analysis (Fig. 3)
1) the unified reference direction of having stipulated voltage in electric network.For elements such as resistance, electric capacity, inductance, when the components and parts horizontal positioned left side for just, right for negative, when components and parts are vertically placed, go up to being to bear just, down.For voltage source, current source element, the default voltage reference direction is consistent with the placement location of voltage source, current source.
2) default voltage source, capacitor prop up for tree, and current source, inductor are chord; When there being plenary capacitance device loop, then one of them capacitor is set to chord; When there being full inductor cut set, then one of them inductor is set to set and props up; Resistor is defaulted as chord, inquires about the resistance two ends then and whether has the tree forehearth limb, if there is no set forehearth limb then resistance be set to the tree.
When 3) writing a circuit matrix or cut set matrix, earlier tree is propped up and the chord numbering.In the topological structure relation, be provided with the piecemeal of voltage and current vector, and write the kirchhoff voltage equation of fundamental circuit matrix and the kirchhoff current equation of fundamental cutset.
According to the above description, voltage source V 1 is set to that tree, capacitor C 1 and C2 are set to tree, all resistance all are defaulted as chord.Because resistance R 1 two ends do not set forehearth limb, thereby R1 is set is tree, and resistance R 2 and R3 two ends have all formed the tree forehearth limb, thereby still be chord.
(3) generate state equation and output equation (Fig. 4)
Because capacitor C 1 and C2 are positioned on the tree, thereby program all is state variable and has constituted state vector their voltage.This example selects C1 electric current and C2 voltage as output variable.According to the topological analysis of (2), program has provided state equation and output equation:
(4) structural property analysis (controllability and controllability analysis)
We are by controllability matrix T then
c=[B A*B], A, B refer to the coefficient matrix of electric network equation here.State equation and output according to (3) can obtain T
c=2, and the exponent number of A also is 2, both equate that the structural property of this explanation electric network is controlled.Also can obtain the controllability matrix T
o=[C; C*A], C refers to the coefficient matrix of electric network output equation here.Through computing T
o=2, and the exponent number of A also is 2, both equate that the structural property of this explanation electric network is considerable.
(5) electric network emulation
In the method, symbol has been adopted in the electric network analysis, has avoided the participation of concrete parameter value, thereby the result who analyzes has generality, has represented the structural property of electric network.Simultaneously this method can realize electric network emulation, if concrete parameter value for entering, can obtain the structural property of special parameter electric network.We carry out assignment to the parameter of these elements now, establish R
1=R
2=R
3=10k Ω, C
1=C
2=33 μ F, the so above-mentioned coefficient matrix of input voltage 1V just becomes:
(6) analysis result
This coefficient matrix is carried out computing, obtain controllability matrix T
cWith the controllability matrix T
oOrder be respectively 1 and 2, and its state variable number is 2.Because controllability matrix T
cOrder and state variable number unequal, so this electric network is uncontrollable.And controllability matrix T
oOrder equate that with the state variable number so this electric network is considerable.Although be uncontrollable under parameter current, for analog element, this possibility is zero, because can not guarantee R
1=R
2=R
3, C
1=C
2, and also can be because of the reason of computational accuracy when calculating, thereby obtain uncontrollable but considerable conclusion.If the symbolization computing just can be avoided the interference of circuit parameter, directly analyze its structural property.After electric network carried out symbolic operation, the structural property that obtains can not change because of the change of parameter, and in electric network emulation, structural property depends on the electric network structure and parameter simultaneously.Therefore, this method provides a kind of analysis means of electric network structural property, and this is very easily for research structure, and can also carry out electric network emulation by this method.
This method is analyzed its state equation of design and output equation based on electric network theory, analyzes the structural property of electric network by research state equation and output equation.In order to study the structural property of general electric network, we have adopted the method for symbolic operation, just directly adopt the electric network element set name code to carry out computing.So the coefficient matrix of state equation and output equation also is symbolically, the computing of back also all is symbolically, the result of electric network analysis has just avoided the participation of concrete parameter value thus, thereby the result who analyzes has generality, has represented the structural property of electric network.On the other hand, if concrete parameter value generation is entered, we just can obtain the common conclusions of certain electric network configuration character, also are that this method can be carried out electric network emulation.By this method, we combine the topological structure of electric network analysis and the structural property of electric network, can analyze the general characteristic of electric network structural property, are a kind of methods of studying the electric network structure, have generality and generality.
Claims (6)
1. the analytical method of a RLC electric network structural property is characterized in that it by drawing electric network figure and electric network topological analysis, generates the state equation and the output equation of electric network, analyzes and electric network emulation thereby carry out the electric network control performance; This method is by studying the structural property of electric network to the topological structure property analysis of electric network, thereby provides new approach for the research of research electric network structural property; This method comprises:
The first, draw electric network figure to be analyzed;
The second, carry out topological analysis;
Three, generate state equation and output equation;
Four, carry out the structural property analysis;
Five, carry out electric network emulation;
Six, provide analysis result.
2. method according to claim 1 is characterized in that the method and the content of described topological analysis of second step comprises:
1) the unified reference direction of having stipulated voltage in electric network; For elements such as resistance, electric capacity, inductance, when the components and parts horizontal positioned left side for just, right for negative, when components and parts are vertically placed, go up to being to bear just, down; For voltage source, current source element, the default voltage reference direction is consistent with the placement location of voltage source, current source;
2) default voltage source, capacitor prop up for tree, and current source, inductor are chord; When there being plenary capacitance device loop, then one of them capacitor is set to chord; When there being full inductor cut set, then one of them inductor is set to set and props up; Resistor is defaulted as chord, inquires about the resistance two ends then and whether has the tree forehearth limb, if there is no set forehearth limb then resistance be set to the tree;
When 3) writing a circuit matrix or cut set matrix, set earlier and prop up and the chord numbering; In the topological structure relation, be provided with the piecemeal of voltage and current vector, and write the kirchhoff voltage equation of fundamental circuit matrix and the kirchhoff current equation of fundamental cutset.
3. method according to claim 1, it is characterized in that the method for described generation state equation of the 3rd step and output equation is: select branch electric capacity and chord inductance as state variable, output variable is selected as required.
4. method according to claim 1 is characterized in that described method of carrying out the structural property analysis of the 4th step is: by controllability matrix T
c=[B A*B], whether the structure of calculating electric network is controlled, and A, B refer to the coefficient matrix of electric network equation here; By the controllability matrix T
o=[C; C*A], whether the output of calculating electric network is considerable, and C refers to the coefficient matrix of electric network output equation here.
5. method according to claim 1 is characterized in that the 5th goes on foot the described electric network emulation of carrying out, in the method, symbol has been adopted in the electric network analysis, avoided the participation of concrete parameter value, thereby the result who analyzes has generality, represented the structural property of electric network; This method can realize electric network emulation simultaneously, for entering, just can obtain the structural property of special parameter electric network to concrete parameter value.
6. method according to claim 1, it is characterized in that in the 4th step and the 5th step, after electric network carries out symbolic operation, the structural property that obtains can not change because of the change of parameter, and in electric network emulation, structural property depends on electric network structure and electric network element set parameter simultaneously.
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|---|---|---|---|---|
| CN103268377A (en) * | 2013-05-10 | 2013-08-28 | 定西师范高等专科学校 | Radio link control (RLC) series second-order circuit model analysis method based on matrix laboratory (MATLAB) |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103268377A (en) * | 2013-05-10 | 2013-08-28 | 定西师范高等专科学校 | Radio link control (RLC) series second-order circuit model analysis method based on matrix laboratory (MATLAB) |
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Open date: 20100602 |