CN102508945A - Aviation nitrogen-filling vehicle gas circuit system dynamic electric simulation method and device - Google Patents

Abstract

The invention discloses a dynamic electrical simulation method and device for the gas circuit system of an aviation nitrogen-charging vehicle. Using the equivalent correspondence between the gas system and the electrical system, the gas cylinder pipeline network is transformed into a dynamic circuit topology. By using the aviation nitrogen-charging vehicle electrical simulation method and device of the present invention, the initial air pressure values of each gas cylinder are set, and then only the state of each switch valve is collected to dynamically simulate the gas-filling process of the nitrogen-charging vehicle. The invention has practical value and significance for operators to be familiar with the gas charging process of the nitrogen charging vehicle, to understand the working principle of each process, to train the operator's ability to respond to sudden accidents, and to locate and analyze faults.

Description

Method and device for dynamic electrical simulation of gas circuit system of aviation nitrogen-filled vehicle

Technical field:

The invention relates to a dynamic simulation device and method, in particular to a dynamic electrical simulation method and device for the gas circuit system of an aviation nitrogen-charging vehicle.

Background technique:

With the continuous development of modern aviation technology and aviation weaponry, nitrogen and oxygen have been widely used in civil and military aircraft flight and ground maintenance support. According to my country's current flight support system, nitrogen and oxygen for flight are mainly produced by ground oxygen and nitrogen production equipment and stored in gas cylinders. Before flight, oxygen and nitrogen charging vehicles are used to fill aircraft cylinders for backup.

As the main equipment on the ground of the airport, the nitrogen-filled vehicle has a direct impact on the quality of supply guarantee and flight safety. At the same time, the technical proficiency of operators plays a decisive role in airport production safety, equipment efficiency, and service life. In view of the increasing cost of nitrogen filling vehicle equipment, complex inflation process, and strict operating procedures, the requirements for the quality of operators are getting higher and higher.

Aeronautical nitrogen charging vehicles are mainly divided into four filling processes: ground gas station filling nitrogen into the vehicle cylinders, transferring nitrogen between the vehicle cylinders, filling nitrogen outside the vehicle cylinders and cyclic work. The actual nitrogen-charging vehicle equipment is used in flight support or training, and the real-time working status is mainly judged by the relevant barometer and valve switch status, such as gas flow direction, inflation process, and changes in the pressure of each cylinder. However, if the start and stop positions of the valves of the nitrogen filling vehicle are abnormal or the air gauge is damaged, the operator will have no way of judging the working state, which will lead to serious operational accidents. Moreover, artificial faults are not allowed in actual production, and informal operations are generally not allowed. It shows that we do not understand the phenomenon of abnormal work, so we cannot train the experience of correct handling of emergencies. If the dynamic simulation method of the gas circuit system of the nitrogen filling vehicle can be developed, the gas flow direction and the filling process in the pipeline can be clearly observed and understood. This is the necessity of the research on the simulation system of the nitrogen charging vehicle of the present invention.

The actual nitrogen-charging vehicle is often limited by the venue, funds and equipment maintenance conditions during training, but the training based on the simulation system of the present invention can be safe, economical, controllable, repeated, risk-free, and Due to the limitation of weather conditions and site space, it can not only conduct routine operation training, but also train operators to deal with various accidents and analyze and locate faults. This is of great practical value and practical significance to help operators understand and master the filling process of nitrogen-filled vehicles, improve the professional level of operators, and enhance the safety of airport ground support.

Contents of the invention

In view of the deficiencies in the prior art, the purpose of the present invention is to study a dynamic electrical simulation method for the gas circuit system of an aeronautical nitrogen-charging vehicle to simulate the gas-filling process of an aeronautical nitrogen-charging vehicle.

The present invention is realized by following method:

The dynamic electrical simulation method of the gas circuit system of the aviation nitrogen filling vehicle uses the equivalent correspondence between the gas circuit system and the electrical system to transform the pipeline network of high-pressure gas cylinders into a dynamic circuit model, and uses the dynamic response of the circuit model to simulate the gas flow direction and inflation in real time. process, changes in gas cylinder pressure, etc.; the components and gas pipelines in the high-pressure gas cylinder pipeline network system correspond to the following electrical components and branches:

1). The gas cylinder is equivalent to the capacitor in the circuit topology;

2). Pipeline flow resistance is equivalent to corresponding circuit resistance;

3). The gas circuit topology is equivalent to the corresponding circuit topology;

4). The switch valve is equivalent to the corresponding circuit switch;

5). The controlled current source of the equivalent corresponding circuit of the gas compressor;

6). The equivalent corresponding circuit diode of the check valve;

7). Pressure gauge equivalent corresponding circuit voltmeter;

8). The pressure reducing valve is equivalent to the corresponding circuit voltage regulator tube;

The schematic diagram of the gas circuit system and the equivalent dynamic circuit diagram are shown in attached drawings 1 and 2 respectively, and the supplementary details are as follows:

① When the gas valve is closed, the resistance in the corresponding circuit is an infinite value; when each valve is opened, the resistance value in the corresponding circuit represents the flow resistance of the pipeline;

② When the M pipeline of the gas compressor is equivalent to the circuit, the intake pipeline is equivalently grounded through a resistor R0, and the resistance value of R0 represents the throttle of the compressor; the compressor and the gas outlet pipeline are equivalent to the controlled current of the negative ground Source CCCS, whose control quantity is the current flowing through the resistor R0;

③The air pressure gauge and air inlet nozzle in the air circuit system do not need to make their equivalent components in the circuit model, and the air pressure representation number is equal to the voltage value of the corresponding node in the circuit;

④ For the ground gas cylinder joint J1 of the gas system of the nitrogen-filled vehicle and the aircraft inflation joints J2 and J3: when a ground gas cylinder is connected to J1, it is equivalent to connecting the ground gas cylinder at the same position on the circuit model. Capacitance Cd; when no ground gas cylinder is connected to J1, the connector on the equivalent circuit device is directly grounded. Similarly, when J2 and J3 are connected to the aircraft, they are equivalently connected to the equivalent capacitor Cf of the aircraft gas cylinder at the same position in the circuit device; when J2 and J3 are not connected to the aircraft, they are equivalent to being directly grounded at the joint. For the above-mentioned equivalent grounding states of J1, J2, and J3, it is equivalently simulated by assigning infinite values to Cd and Cf.

The purpose of the present invention is also to establish a dynamic electrical simulation model of the air system of an aviation nitrogen-charging vehicle, so that operators can be familiar with the gas-charging process of the nitrogen-charging vehicle, understand the working principles of each process, and train the operator's ability to respond to sudden accidents and failures. A simulation training platform for positioning analysis.

Utilizing the simulation method and device for aviation nitrogen-charging vehicles of the present invention, it is only necessary to set the initial air pressure values of each gas cylinder, and then only need to collect the states of each switch valve to dynamically simulate the gas-filling process of the nitrogen-charging vehicle. The invention has practical value and significance for operators to be familiar with the gas charging process of the nitrogen charging vehicle, to understand the working principle of each process, to train the operator's ability to respond to sudden accidents, and to locate and analyze faults.

Description of drawings:

Figure 1 is a flow chart of the pipeline principle of the aviation nitrogen charging vehicle.

Fig. 2 is an equivalent dynamic circuit diagram of the gas circuit system of a nitrogen-filled vehicle.

Detailed ways

As shown in Figure 1, the gas circuit system of an aviation nitrogen charging vehicle consists of a high-pressure gas cylinder, a diaphragm compressor, a pipeline, a refill valve, an additional supply valve, an inflation valve, a deflation valve, a barometer, a safety valve, a check valve, It is composed of pressure reducing valve, pressure regulating valve, air inlet nozzle and so on.

The equivalent rules of the above gas system and electrical system are studied as follows:

1). The gas cylinder equivalent in the high-pressure gas cylinder pipeline network system corresponds to the capacitor in the circuit topology: the pressure of the gas cylinder corresponds to the capacitor voltage; the gas volume of the gas cylinder corresponds to the capacitor charge; the air flow of the gas cylinder corresponds to the capacitor current; capacitance.

2). Pipeline flow resistance is equivalent to corresponding circuit resistance.

3). The gas circuit topology is equivalent to the corresponding circuit topology.

4). The switch valve is equivalent to the corresponding circuit switch.

5). The current control current source of the equivalent corresponding circuit of the gas compressor.

6). The equivalent circuit diode of the check valve.

7). The pressure gauge is equivalent to the corresponding circuit voltmeter.

8). The pressure reducing valve is equivalent to the voltage regulator tube of the corresponding circuit.

According to the above equivalent rules, the equivalent circuit symbols corresponding to the specific gas path symbols in Figure 1 are shown in the table below:

Table 1 Equivalent corresponding relationship between the gas system of the nitrogen-filled vehicle and the circuit model

It should be noted that due to the complexity of the nonlinear circuit characteristics of diodes D1~D5, voltage regulator Dz, safety valves AQ1, AQ2 and voltage regulator TF in the equivalent circuit when establishing the state equation of the system, the practical experience sums up the available software The algorithm realizes the above-mentioned component circuit characteristics. In addition, the equivalent details in the supplementary equivalent modeling process are:

① When the gas valve is closed, the resistance in the corresponding circuit is an infinite value; when each valve is opened, the resistance value in the corresponding circuit represents the flow resistance of the pipeline.

② When the M pipeline of the gas compressor is equivalent to the circuit, the intake pipeline is equivalently grounded through a resistor R0, and its resistance represents the throttle of the compressor; the compressor and the gas outlet pipeline are equivalent to a controlled current source with negative grounding CCCS, the control quantity is the current flowing through the resistor R0.

③The air pressure gauges B1~B7 and the air inlet nozzles J1, J2, and J3 in the air circuit system do not need to make their equivalent components in the circuit model, and the air pressure representation number is equal to the voltage value of the corresponding node in the circuit;

④ In the equivalent circuit, the negative poles of the capacitors C1_1~C3_3, the negative poles of the controlled current source CCCS, and the negative poles of the resistor R0 should be grounded.

⑤ For the ground gas cylinder joint J1 of the gas system of the nitrogen-filled vehicle and the aircraft inflation joints J2 and J3: when a ground gas cylinder is connected to J1, it is equivalent to connecting the ground gas cylinder at the same position on the circuit model Capacitor Cd (see Figure 2); when no ground gas cylinder is connected to J1, since the corresponding intake branch contains a check valve, the connector on the equivalent circuit model is directly grounded. Similarly, when J2 and J3 are connected to the aircraft, they are equivalent to connecting to the equivalent capacitance Cf of the aircraft cylinder at the same position in the circuit model; when J2 and J3 are not connected to the aircraft, they are equivalent to being directly grounded at the joint. For the above-mentioned equivalent grounding states of J1, J2, and J3, it is equivalently simulated by assigning infinite values to the capacitors Cd, Cf.

Through the above steps, the gas circuit system of the nitrogen-filled vehicle is equivalent to a dynamic circuit model containing components such as resistors, capacitors, and current sources, which is the equivalent circuit device of the gas circuit system of the nitrogen-filled vehicle shown in Figure 2. As shown in the figure, the resistor-capacitor branches I, II, and III are respectively composed of three sets of series resistors and capacitors connected in parallel; the following branches are connected across the two ends of the equivalent capacitor Cd: the resistor R0 representing the throttle of the compressor, the rotation Charging resistors R1, R2, R3 are connected in series with the resistance-capacitor branches I, II, and III respectively, the series connection of the circulation resistor R7, the charging resistor R10 and the equivalent capacitance Cf of the aircraft cylinder; the controlled current source The series branch of CCCS and diode D2 is connected in parallel with the series branch of the charging resistor R10 and the equivalent capacitance Cf of the aircraft cylinder; one end of the additional supply resistors R4, R5, and R6 is connected to the output end of D2, and the other end is respectively connected to the transfer charging resistor R1, R2, R3 are connected.

The circuit model and the gas path system have similar topologies, and both are non-planar graphs in graph theory. The circuit component labels correspond to the device symbols in the gas circuit system: the resistance R(i) in the circuit corresponds to the valve K(i) in the gas circuit; the capacitor C(i) corresponds to the gas cylinder P(i) (i is the label of each component in the figure) ; Diodes D1 and D2 correspond to check valves Z1 and Z2 respectively; where Cd is the equivalent capacitance of the ground gas cylinder, indicating that the gas circuit system J1 has ground gas cylinders connected; Cf is the equivalent capacitance of the aircraft gas cylinder, indicating that the gas path J2 and J3 in the system are connected with aircraft gas cylinders. Specifically, if J1, J2, and J3 are not connected to the ground and aircraft cylinders, then make the capacitors Cd, Cf in the figure equal to an infinite value equivalently grounded state. R0 is used to characterize the throttle of the compressor, and the current i flowing through it represents the intake air flow of the compressor. The current i is also used as the control quantity of the controlled current source, and the controlled current source represents the model compressor, so the working principle of the compressor It can be simulated by the current i flowing through R0 and the controlled current source CCCS.

Combining the circuit model obtained above, the change of the voltage value of the capacitor reflects the pressure change of the gas cylinder in the gas circuit system; the branch current reflects the gas flow in the gas circuit system pipeline; the resistance R0 and the current i in the controlled current source CCCS represent the operation of the compressor Condition. This circuit model, together with the circuit characteristics of diodes D1~D5, regulator tube Dz, safety valves AQ1, AQ2 and voltage regulator TF realized by software, achieves the design goal of completely simulating the working process of the gas circuit system of the nitrogen filling vehicle.

Then the state equation of the equivalent dynamic circuit is established.

Using the knowledge of graph theory, each component in the circuit corresponds to a branch, and the directed graph of the circuit in Figure 2 is made. Choose a tree as a unique tree, its branches are: 11 branches of capacitors Cd, Cf, C1_1~C33, 5 branches of resistors R0, R10, R1_1, R2_1, R3_1; and the rest of the directed graph The current source branch and the resistance branch are connected branches. For the branch where the capacitor is located, the basic cut set matrix Q _f and the basic circuit matrix B _f are made according to the column writing order of connecting the branch first and then the tree branch, and the following formula is obtained:

Q _f =[Q ₁₁ |E] _(n-1)×b (1)

B _f ＝[E|B ₁₂ ] _(b-n+1×b (2)

Among them, E represents the identity matrix. I _K , _IT represent the column vectors of the currents of the branches and branches; U _K , U _T represent the column vectors of the voltages of the branches and branches. and thus get:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

For the basic cut set matrix Q _f has Q _f I _b ＝0

Substitute the above formula into (1) to get I _T ＝-Q ₁₁ I _K (5)

For the basic circuit matrix B _f has B _f U _b ＝0

Substitute the above formula into (2) to get U _K ＝-B ₁₂ U _T (6)

And the relationship between Q _f and B _f in graph theory $B_{12}=-Q_{11}^T---\left(7\right)$

Substituting (7) into the above formulas, we can simplify $u_K=Q_{11}^T{u}_T$

I _T ＝-Q ₁₁ I _K

Thus, the state equation matrix form is obtained

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

微分项都包含在矩阵方程的左边，i_s，u_C，i_R、

这些状态变量和常量都包含在矩阵方程右边。从矩阵方程中只列写出含

微分项的方程，并且方程两边都同除以各自电容C系数，得到如下状态方程形式：so all

Differential terms are included in the left side of the matrix equation, i _s , u _C , i _R ,

These state variables and constants are included on the right side of the matrix equation. From the matrix equation, write only the

The equation of the differential term, and both sides of the equation are divided by the respective capacitance C coefficients, and the following state equation form is obtained:

$\left[\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="du\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">du</figure-callout></span><figure-callout\; id="1"\; label="du\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\\ \frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ \frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; r</span>}}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}& & \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; nr</span>}}\end{array}\right]<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

微分项的方程来表达出来：在未包含微分项的方程中，让电阻作为元素的矩阵A_r×r乘以i_r×1列向量，等于u_c1～u_cn表达式组成的列向量U_r×1。即：In the above formula (9), the current column vector i _r×1 is used by the rest not included

The equation of the differential item is expressed: in the equation that does not contain the differential item, let the matrix A _r×r of the resistance as an element be multiplied by the i _r×1 column vector, which is equal to the column vector U _r composed of u _c1 ~u _cn expressions _×1 . Right now:

$\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; r</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}& & \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; rr</span>}}\end{array}\right]<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

In the above formula _, the column vector g _{r×1 can} be expressed as:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; c"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="L\; p"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="1"\; label="L\; p"\; filenames="HDA0000097921260000011.png"\; state="\{\{state\}\}">\; </figure-callout>}& {\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}& & \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; L</span>}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; rn</span>}}\end{array}\right]<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; cn</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In summary, the final expression of the state equation is deduced from the state matrix:

${<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; du</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Finally, the algorithm for solving the state equation is given.

的第i行乘以状态向量[u_c]_n×1的值得到第i个微分方程的函数值，然后更新函数自变量[u_c]_n×1得到四阶龙格库塔算法系数k1、k2、k3、k4，完成第i行微分方程的求解。类似可依次求解出每一行的微分方程的状态变量值。Through the above steps, the state equation of the 11th-order dynamic circuit (the circuit contains 11 independent capacitors, that is, the gas circuit system contains 9 gas cylinders on the vehicle, plus ground gas cylinders and aircraft gas cylinders) can be obtained. The state equation is the first-order differential equations in mathematics, and the common Runge-Kutta (Runge-Kutta) algorithm is only for a differential equation. The present invention improves the fourth-order Runge-Kutta algorithm to adapt to the first-order differential equations. Solving of equations. For the first-order differential equations shown in formula (12), the differential equations of each row are solved sequentially: Let the state matrix

Multiply the i-th row of the state vector [u _c ] _n×1 to get the function value of the i-th differential equation, and then update the function independent variable [u _c ] _n×1 to get the fourth-order Runge-Kutta algorithm coefficient k1, k2, k3, k4, complete the solution of the i-th line differential equation. Similarly, the state variable values of the differential equations of each row can be solved sequentially.

Here is a method to use software to realize the circuit characteristics of diodes, Zener tubes, and ideal transformers in the circuit and the gas path characteristics of safety valves in the gas path system:

1). Since the first-order differential of the capacitor voltage of the state variable is equal to the current of the capacitor branch, for a branch containing a diode, the first-order differential of the state variable is used to represent the current of the branch. In this way, before solving the state equation with Runge-Kutta each time, it is detected whether the branch current direction is reversed. If it is reversed, the resistance of the branch is assigned an infinite value, so that the branch is equivalent to turning off in the circuit, so that the unidirectional conduction characteristic of the equivalent diode is used.

2). For a branch circuit containing a voltage regulator tube and an ideal transformer, when the input voltage of the voltage regulator tube is lower than the set value of the pressure reducing valve, the input branch is considered to be open; when the input voltage of the voltage regulator tube is greater than the set value of the pressure reducing valve , which is equivalent to the cut-off of the input branch, and an infinite value is assigned to the branch resistance to make it shut off. The ideal transformer is actually a Zener tube with adjustable voltage value. Firstly, the voltage stabilization value of the ideal transformer is calculated from the collected voltage regulation parameters, and then the circuit characteristics of the ideal transformer can be equivalent to the circuit characteristics of the ideal transformer according to the software implementation method of the Zener tube.

3). For the safety valve connected to the gas circuit system, because the working principle of the gas circuit system safety valve is that when the pressure of the node exceeds or is equal to the set value of the safety valve, even the gas is discharged into the atmosphere to realize the pressure relief function. Therefore, the voltage value of this node is calculated in real time in the circuit model. If the real voltage is greater than the set value of the safety valve, it is only necessary to invalidate the current flowing into this position, that is, the gas cylinder pressure value flowing into the current from this node remains at the current value, and The cylinder that inputs current to this node changes according to the original change.

Claims (2)

1. the dynamic electric analogy method of aviation Nitrogen filling vehicle air-channel system; Utilize the equivalent corresponding relation of air-channel system and electric system; The gas cylinder piping network is converted into the dynamic circuit model, goes out situation such as real-time gas flow, inflation flow process, gas cylinder air pressure change with the dynamic response real time modelling of circuit model; Components and parts and gas path pipe in the said gas cylinder pipeline network system correspond to following electric components and branch road:

1). the electric capacity in the gas cylinder equivalence corresponding circuits topology;

2). channel flow dynamic resistance equivalence corresponding circuits resistance;

3). gas circuit topoligical equivalence corresponding circuits topology;

4). controlled valve equivalence corresponding circuits switch;

5). the controlled current source of gas compressor equivalence corresponding circuits;

6). non-return valve equivalence corresponding circuits diode;

7). tensimeter equivalence corresponding circuits voltage table;

8). reduction valve equivalence corresponding circuits stabilivolt;

And:

1. during the shutoff of gas valve, the resistance in the corresponding circuits is infinitely large quantity; During each valve open, the resistance value size expression valve opening degree and the gas circuit resistance of ducting in the corresponding circuits;

When 2. the equivalence of gas compressor M pipeline was in circuit, the air inlet pipeline equivalence was through resistance R 0 ground connection, and R0 resistance size characterizes compressor throttle size; Compressor and outlet pipe equivalence are the controlled current source CCCS of minus earth, and its controlled quentity controlled variable is the electric current that flows through resistance R 0;

3. the respective nodes magnitude of voltage is represented in the rain glass available circuit in the air-channel system;

4. the inflation that connects mouth J1 and aircraft bottle for the air inlet of ground gas cylinder in the air-channel system meets mouth J2, J3: when the ground gas cylinder inserted J1, equivalence same position on circuit model inserted the equivalent capacity Cd of ground gas cylinder; When no ground gas cylinder inserts J1, connect outspoken ground connection on the equivalent-circuit model; As J2, when J3 inserts aircraft, equivalence same position in circuit model inserts the equivalent capacity Cf of aircraft bottle; When J2, J3 do not insert aircraft, equivalence is connecing the direct ground connection in mouth place; For the equivalent ground state of above-mentioned J1, J2, J3, through coming equivalent simulation for Cd, Cf compose infinitely large quantity.

2. the dynamic electric copying device of aviation Nitrogen filling vehicle air-channel system is characterized in that, resistance capacitance branch road I, II, III are made up of three groups of resistance in series electric capacity of parallel connection respectively; Be connected across the following branch road that has at equivalent capacity Cd two ends: characterize compressor throttle size resistance R 0, change charging resistance R1, R2, R3 respectively with the series arm of the equivalent capacity Cf of three branch roads, circulation resistance R 7 and inflation resistance R 10 and aircraft bottle after resistance capacitance branch road I, II, III connects; Controlled current source CCCS and diode D2 series arm are in parallel with aircraft bottle equivalent capacity Cf series arm with inflation resistance R 10; An end that increases resistive R4, R5, R6 links to each other with the output terminal of D2, and its other end links to each other with commentaries on classics charging resistance R1, R2, R3 respectively.

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