High-speed wind tunnel virtual flight test control similarity criterion determination method

Abstract

The invention provides a high-speed wind tunnel virtual flight test control similarity criterion determination method. The method comprises the following steps: analyzing open-loop and closed-loop motion similarities of virtual flight respectively; when the closed-loop motion similarity of the virtual flight is analyzed, standardized transformation is carried out on the state feedback control structure, then similarity transformation is carried out on control parameters of the standardized state feedback control structure, and the control parameters are feedback gains; and finally, analyzing closed-loop control time domain response characteristics and frequency domain characteristics, namely stability margin, of the aircraft through wind tunnel virtual flight, and determining time domain and frequency domain characteristic similarity analysis criteria of closed-loop control of the scaling aircraft and the real aircraft. The method is suitable for a high-speed wind tunnel virtual flight test, and under the condition that a certain similarity criterion is met, simulation of open-loop / closed-loop dynamic response and control characteristics of a real aircraft is achieved through the open-loop / closed-loop dynamic response and control characteristics of the scaling aircraft in the wind tunnel virtual flight test.

Description

Technical Field

[0001] The invention belongs to the field of aircraft overall technology and guidance control technology, and relates to a method for determining a control similarity criterion for a high-speed wind tunnel virtual flight test. Background Art

[0002] High-speed flight itself faces flight environments such as strong aerodynamic uncertainty and dynamic coupling. During large maneuvering flights, the changes in the flow field structure caused by the changes in the motion state of the aircraft cause significant unsteady effects, which puts forward extremely stringent requirements for high-speed flight stability control. Traditional high-speed flight control design mainly relies on wind tunnel tests and CFD simulations to obtain quasi-steady aerodynamic data modeling, and verifies and evaluates through mathematical simulation and semi-physical simulation. For unsteady aerodynamic effects and aerodynamic uncertainties, they are mainly covered by setting pull-off conditions. This processing method has two disadvantages: first, the pull-off of aerodynamic parameters has limited simulation capabilities for nonlinear and strongly coupled aerodynamic characteristics, making it difficult to truly and accurately reflect the actual flight motion state, bringing risks to subsequent flight tests; second, in order to ensure that the full envelope flight environment can be covered, the pull-off conditions are usually set more harshly, which increases the conservatism of the control system design and is not conducive to the improvement of the maneuverability of the aircraft.

[0003] At present, in the case of incomplete and inadequate understanding of the unsteady aerodynamic mechanism and modeling during high-speed flight, wind tunnel virtual flight tests have become an effective means to verify flight performance and stability control. It has the functions of simulating the real flight flow field environment, aircraft dynamics characteristics, and open-loop / closed-loop control laws. By constructing a mapping relationship between the model's motion process in the wind tunnel virtual flight test and the real aircraft motion process, the goal of evaluating and analyzing flight performance can be achieved.

[0004] For large-sized aircraft, scaled-down tests must be conducted in wind tunnel virtual flight tests due to the limitations of test conditions. Considering that the aerodynamic, dynamic and control characteristics of the aircraft will change after scaling down, relevant similarity criteria must be considered when conducting scaled-down wind tunnel virtual flight tests. The prior art (see Li Hao. Similarity Criteria and Simulation Methods for Wind Tunnel Virtual Flight Tests [D]. Mianyang: Graduate School of China Aerodynamics Research and Development Center, 2012.) proposed a wind tunnel virtual test simulation method under scaled-down test conditions. However, the prior art mainly focuses on the similarity simulation of the aerodynamic and dynamic characteristics of the scaled model, and gives the above relationship to preliminarily give the similarity change relationship of typical control loop parameters. The similarity relationship between the open-loop / closed-loop control response characteristics of the scaled system and the real system has not been studied in depth, which is precisely the most critical link to support the wind tunnel virtual flight test to verify the control characteristics. Summary of the invention

[0005] The present invention aims to solve at least one of the problems existing in the prior art.

[0006] To this end, the present invention provides a method for determining control similarity criteria for high-speed wind tunnel virtual flight tests, which is applicable to high-speed wind tunnel virtual flight tests. Under the condition of meeting certain similarity criteria, the open-loop / closed-loop dynamic response and control characteristics of the scaled-down aircraft in the wind tunnel virtual flight test can be used to simulate the open-loop / closed-loop dynamic response and control characteristics of the real aircraft.

[0007] The technical solution of the present invention is:

[0008] A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test, the method is:

[0009] Step 1: Determine the similarity dimensional relationship between the scaled aircraft and the real aircraft;

[0010] Step 2: Analyze the similarity of the open-loop motion of the virtual flight: Analyze the open-loop dynamic time domain response characteristics and frequency domain transfer function characteristics of the aircraft through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the open-loop motion of the scaled aircraft and the real aircraft;

[0011] Step 3: Analyze the similarity of closed-loop motion of virtual flight:

[0012] Step 3-1, performing a standardized transformation on the state feedback control structure;

[0013] Step 3-2, performing similarity transformation on the control parameter of the state feedback control structure after being standardized in step 3-1, where the control parameter is the feedback gain;

[0014] Step 3-3, analyze the time domain response characteristics and frequency domain characteristics of the closed-loop control of the aircraft, that is, the stability margin, through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the closed-loop control of the scaled aircraft and the real aircraft.

[0015] Furthermore, in the first step, the similarity dimensional relationship between the scaled aircraft and the real aircraft is as follows:

[0016] The physical quantity y1 representing the motion of the real aircraft and the physical quantity y2 representing the motion of the scaled aircraft satisfy the following proportional relationship:

[0017] y2(t2)=k y y1(t1) (1)

[0018] Where t1 is the movement time of the real aircraft, t2 is the movement time of the scaled aircraft, and k y is the similarity proportionality coefficient of the physical quantity;

[0019] If the physical quantity is written in vector form y1∈R n , y2∈R n , then the corresponding similarity ratio coefficient diagonal matrix k y =diag(k y1 …k yn ), and still satisfy y2(t2)=k y y1(t1).

[0020] Furthermore, for the high-speed wind tunnel virtual flight test, the speed proportionality coefficient k is selected V , density proportionality coefficient k ρ , length ratio coefficient k L As a proportionality coefficient of a basic physical quantity;

[0021] And, k V =V SO1 / V SO2 , k L =1 / N,k ρ =μ2 / (k V k L μ1), where V SO1 、V SO2 represent the speed of sound in real flight and wind tunnel respectively, μ1 and μ2 represent the gas viscosity in real flight and wind tunnel respectively, and N is the scale factor of the wind tunnel test model;

[0022] The other motion parameter proportional coefficients include: Angle proportional coefficient k θ , time proportional coefficient k t , angular velocity proportionality coefficient k ω , mass proportionality coefficient k m , moment of inertia proportional coefficient k J , acceleration proportionality coefficient k g , force proportionality coefficient k F , torque proportionality coefficient k M ;

[0023] And, k θ =1, k t =k L / k V , k ω =k V / k L ,

[0024] Furthermore, in the second step, before analyzing the open-loop dynamics time domain response characteristics and frequency domain transfer function characteristics of the aircraft, the open-loop dynamics system of the real aircraft is simplified and converted into the following state space expression:

[0025]

[0026] Among them, A1 is the state matrix, B1 is the input matrix, C1 is the output matrix, and D1 is the feedforward matrix; the state quantity x1 = [x 11 ,…x 1n ] T ∈R n 、Input u1=[u 11 ,…u 1m ] T ∈R m , output y1 = [y 11 ,…y 1p ] T ∈R p .

[0027] Furthermore, the specific process of the second step is as follows:

[0028] For the open-loop dynamics system of the real aircraft, that is, the open-loop dynamics system of the scaled aircraft corresponding to the real system, that is, the scaled system, the state quantity, input quantity, and output quantity of the scaled system are recorded as x2, u2, and y2 respectively; according to the dimensional relationship in the first step, the similarity ratio coefficient matrix of the state quantity, input quantity, and output quantity vector is calculated respectively: k x , k u , k y , then the real system and the scaled system satisfy the following similarity criteria:

[0029] (1) Similarity analysis criterion for open-loop control time domain characteristics: Let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), if all subsequent corresponding moments t2 = k t t1, external input satisfies the similarity relation u2(t2)=k u u1(t1), then the time domain response of the scaled-down aircraft at any corresponding time in the future will satisfy the following similarity relationship:

[0030]

[0031] Therefore, formula (3) is the similarity analysis criterion of the open-loop control time domain characteristics. By applying the criterion determined by formula (3), the open-loop dynamic response characteristics of the real aircraft can be inversely deduced based on the open-loop dynamic response of the virtual flight test in the wind tunnel of the scaled aircraft;

[0032] (2) Similarity analysis criteria for open-loop control frequency domain characteristics: For the open-loop dynamic system of a real aircraft as shown in equation (2), in the case of single input and single output, it can be written as the following transfer function:

[0033]

[0034] Where K' is the transfer function gain, q and w are orders, and z j is the zero point of the transfer function, p i are the poles of the transfer function, a1,…,a w-1 、a w and b1, ..., b q-1 、b q All are parameter values;

[0035] Then the transfer function of the scaled-down system corresponding to the open-loop dynamics system of the real aircraft has the following form:

[0036]

[0037] in, is the angular velocity proportionality coefficient k ω to the power of (wq);

[0038] The scaled system is based on the real system, and all poles and zeros are scaled by k at the same time. ω times, therefore, formula (5) is the similarity analysis criterion for the open-loop control frequency domain characteristics. By applying the criterion determined by formula (5), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and then the transfer function model of the real aircraft can be inferred to evaluate the open-loop stability characteristics of the open-loop aircraft.

[0039] Furthermore, in step 3-1, the process of standardizing the state feedback control structure is as follows:

[0040] (1) For attitude PID control and closed-loop control of overload pilot, the control command is expressed in the following state feedback form:

[0041] u=v-Kx (6)

[0042] Among them, u is the control instruction, that is, the input quantity, v is the reference input, K is the feedback gain matrix, and x is the state quantity; on this basis, the motion state equation of the closed-loop system can be written in the following standard form:

[0043]

[0044] Among them, A is the state matrix, B is the input matrix, C is the output matrix, and y is the output quantity;

[0045] (2) For a control structure with a state observer, the state observer dynamic equation and control input are written as follows:

[0046]

[0047] Among them, z is the observation vector of the state observer, A x A is the state matrix of the observer for the state quantity of the original system, z is the state matrix of the observer for the observed part, K x is the feedback control gain matrix for the state quantity of the original system, K z is the feedback control gain matrix for the observation part;

[0048] Defining the expansion state The motion state equation of the control structure with a state observer is converted into the following state feedback form:

[0049]

[0050] Furthermore, in step 3-2, the process of performing similarity transformation on the feedback gain is as follows:

[0051] According to the similarity dimensional relationship given in step 1, calculate the similarity proportional coefficient matrix k of the state quantity, input quantity and output quantity vector x , k u , k y ;

[0052] If the feedback gain matrix of the state of the real aircraft is K1, then in the wind tunnel virtual flight test, while the controller structure of the scaled aircraft is consistent with the real one, the feedback gain matrix K2 of the scaled aircraft should be strictly transformed according to the following formula:

[0053]

[0054] Therefore, the feedback gain of the scaled aircraft is obtained by similarity transformation according to formula (10).

[0055] Furthermore, the specific process of step 3-3 is as follows:

[0056] (1) Similarity analysis criterion for closed-loop control time domain characteristics: Let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), at the corresponding time t2 = kt At t1, the reference input satisfies the similarity relation v2(t2)=k u v1(t1), then the closed-loop dynamic equation of the scaled-down system satisfies:

[0057]

[0058] Among them, C2 is the output matrix of the scaling system;

[0059] The scaled closed-loop system can be regarded as the real system scaled by time scale k. t times, the state quantity and output quantity at the corresponding moment strictly meet the criterion of formula (3), that is, x2(t2)=k x x1(t1),y2(t2)=k y y1(t1);

[0060] Therefore, formula (3) and formula (11) are the similarity analysis criteria of closed-loop control time domain characteristics. By applying the criteria determined by formula (3) and formula (11), the closed-loop control time domain response of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and the closed-loop control time domain response of the real aircraft can be inferred;

[0061] (2) Similarity analysis criteria for closed-loop control frequency domain characteristics: Under the premise of satisfying the closed-loop control similarity transformation, the closed-loop transfer function of the system The following similarity relationship is satisfied:

[0062] ①If the closed-loop transfer function of the real system is:

[0063]

[0064] Then the transfer function of the scaled system has the following form:

[0065]

[0066] And for any s = jω2 = jk ω ω1, exists

[0067] ②The amplitude margin and phase margin of the scaled-down system are exactly the same as those of the real system, and the cutoff frequency of the system is ω c When the following similarity ratio relationship is met:

[0068] ω c2 =k ω ω c1 (14)

[0069] Then the frequency domain characteristics of the scaled-down system closed-loop control are completely similar to those of the real system; where ω c2 is the cutoff frequency of the scaled system, ω c1is the cutoff frequency of the real system.

[0070] Therefore, equations (13) and (14) are similarity analysis criteria for closed-loop control frequency domain characteristics. By applying the criteria determined by equations (13) and (14), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and then the transfer function model of the real aircraft can be inferred to evaluate the closed-loop stability characteristics of the closed-loop aircraft.

[0071] By applying the above technical solution, the present invention has the following beneficial effects:

[0072] (1) The present invention proposes a method for determining similarity criteria of open-loop / closed-loop control characteristics under conditions of a scaled-down high-speed wind tunnel virtual flight test, which is suitable for overall performance analysis of aircraft and verification and evaluation of control systems. The criteria determined based on this method can realize similarity transformation of control parameters with a type of formal control law in a wind tunnel virtual flight test. On this basis, the open-loop / closed-loop control characteristics of the scaled-down model and the real aircraft will have similarities, which can be used to guide the design of high-speed wind tunnel virtual flight test schemes and comprehensive verification of control performance.

[0073] (2) The present invention provides an open-loop control similarity criterion, which has the advantage that the open-loop dynamic equations and transfer function parameters of the scaled-down system and the real system satisfy a simple proportional relationship.

[0074] (3) The present invention also provides a closed-loop control similarity criterion, which has the advantage of ensuring that the closed-loop control stability margin of the scaled-down system is the same as that of the real system. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0076] Figure 1 It is a high-speed wind tunnel virtual flight test control similarity analysis flow chart of the present invention;

[0077] Figure 2 This is a comparison diagram between the closed-loop control response of the angle of attack of the scaled-down aircraft and the real aircraft after the control parameters are scaled-down;

[0078] Figure 3 This is a comparison diagram between the attitude angular velocity closed-loop control response of the scaled-down aircraft and the real aircraft after the control parameter scaling transformation;

[0079] Figure 4This is a comparison chart between the amplitude / phase stability margin of the scaled-down aircraft and the real aircraft. DETAILED DESCRIPTION

[0080] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0081] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0082] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0083] Embodiment 1:

[0084] This embodiment provides a method for determining a control similarity criterion for a high-speed wind tunnel virtual flight test, the method comprising:

[0085] Step 1: Determine the similarity dimensional relationship between the scaled aircraft and the real aircraft;

[0086] Step 2: Analyze the similarity of the open-loop motion of the virtual flight: Analyze the open-loop dynamic time domain response characteristics and frequency domain transfer function characteristics of the aircraft through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the open-loop motion of the scaled aircraft and the real aircraft;

[0087] Step 3: Analyze the similarity of closed-loop motion of virtual flight:

[0088] Step 3-1, performing a standardized transformation on the state feedback control structure;

[0089] Step 3-2, performing similarity transformation on the control parameter of the state feedback control structure after being standardized in step 3-1, where the control parameter is the feedback gain;

[0090] Step 3-3, analyze the time domain response characteristics and frequency domain characteristics of the closed-loop control of the aircraft, that is, the stability margin, through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the closed-loop control of the scaled aircraft and the real aircraft.

[0091] Embodiment 2:

[0092] This embodiment provides a method for determining a control similarity criterion for a high-speed wind tunnel virtual flight test based on Embodiment 1. Figure 1 , the specific steps are as follows:

[0093] Step 1: Determine the similar dimensional relationship of the scaled aircraft:

[0094] According to the wind tunnel virtual flight test method proposed in the prior art, the scaled aircraft and the real aircraft should meet the requirements of geometric similarity, flow similarity and kinematic similarity. In this embodiment, except for a1, ..., a2 in equations (4) and (5), w-1 、a w and b1, ..., b q-1 、b q In addition, all parameters with a subscript of "1" represent the physical quantities of the real aircraft, and all parameters with a subscript of "2" represent the physical quantities of the scaled aircraft;

[0095] On this basis, the physical quantity y1 representing the motion of the real aircraft and the physical quantity y2 representing the motion of the scaled aircraft satisfy the following proportional relationship:

[0096] y2(t2)=k y y1(t1) (1)

[0097] Where t1 is the movement time of the real aircraft, t2 is the movement time of the scaled aircraft, and k y is the similarity proportionality coefficient of the physical quantity.

[0098] After a set of proportionality coefficients of basic physical quantities is given, the remaining physical quantities are determined strictly according to the relationship of similar dimensions. In particular, if the physical quantity is written in vector form y1∈R n y2∈R n , R n represents an n-dimensional vector, then its corresponding similarity ratio coefficient diagonal matrix k y =diag(k y1 ,…,k yn ), and still satisfy y2(t2)=k y y1(t1); where k y1 , …, k yn is the similarity scale coefficient diagonal matrix k y The diagonal elements of ;

[0099] For high-speed wind tunnel virtual flight tests, the speed proportionality coefficient k is optimized V , density proportionality coefficient k ρ , length ratio coefficient k L Three proportional coefficients are used as the proportional coefficients of basic physical quantities, among which k V , k ρ , k L are similar proportion coefficients in the diagonal matrix k y The values ​​of V can be determined by wind tunnel test condition parameters and actual flight parameters, as shown in Table 1. SO1 、V SO2 They represent the speed of sound in real flight and wind tunnel flow respectively, μ1 and μ2 represent the gas viscosity in real flight and wind tunnel flow respectively, and N is the scale factor of the wind tunnel test model.

[0100] Table 1 Basic physical quantities and calculation methods of similarity relations of scaled aircraft

[0101] Similarity ratio coefficient dimension expression <![CDATA[Speed proportionality coefficient k V > m / s <![CDATA[V SO1 In SO2 ]]> <![CDATA[Length ratio coefficient k L > m 1N <![CDATA[Density proportionality coefficient k ρ > <![CDATA[kg / m 3 ]]> <![CDATA[μ2(k V k L μ1)]]>

[0102] The proportional coefficients of other motion parameters can be calculated based on the similar proportional coefficients of the basic physical quantities in Table 1. Table 2 gives the calculation formulas for the similar proportional coefficients of the commonly used physical quantities in aircraft dynamics analysis and control design.

[0103] Table 2 Calculation method of similarity ratio parameters of main motion physical quantities

[0104]

[0105] Step 2: Similarity analysis of virtual flight open-loop motion

[0106] The open-loop motion characteristics of the aircraft are analyzed and studied through wind tunnel virtual flight, which mainly includes two parts: open-loop dynamic time domain response characteristics analysis and frequency domain transfer function characteristics analysis. This step gives the similarity analysis criteria of the time domain and frequency domain characteristics of the open-loop motion of the scaled aircraft and the real aircraft in turn.

[0107] For the open-loop dynamic system of a real aircraft, after appropriate simplification, it can be transformed into the following state space expression:

[0108]

[0109] Among them, A1 is the state matrix, B1 is the input matrix, C1 is the output matrix, and D1 is the feedforward matrix; the state quantity x1 = [x 11 ,…x 1n ] T ∈R n 、Input u1=[u 11 ,…u 1m ] T ∈R m , output y1 = [y 11 ,…y 1p ] T ∈R p For the open-loop dynamics system of the scaled aircraft (hereinafter referred to as the scaled system) corresponding to the open-loop dynamics system of the real aircraft (hereinafter referred to as the real system), the state quantity, input quantity, and output quantity of the scaled system are recorded as x2, u2, and y2 respectively. According to the dimensional relationship in step 1, the similarity ratio coefficient matrix of the state quantity, input quantity, and output quantity vector can be calculated respectively: x , k u , k y , then the real system and the scaled system satisfy the following similarity criteria:

[0110] (2) Similarity analysis criterion for open-loop control time domain characteristics: For the typical motion process of the real aircraft to be studied, let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), as long as all subsequent corresponding moments t2 = k t t1, external input satisfies the similarity relation u2(t2)=k u u1(t1), then the time domain response of the scaled-down aircraft at any subsequent corresponding time satisfies the following similarity relationship.

[0111]

[0112] Therefore, formula (3) is the similarity analysis criterion of the open-loop control time domain characteristics. By applying the criterion determined by formula (3), the open-loop dynamic response characteristics of the real aircraft can be inversely deduced based on the open-loop dynamic response of the virtual flight test in the wind tunnel of the scaled aircraft.

[0113] (2) Similarity analysis criteria for open-loop control frequency domain characteristics: For the open-loop dynamic system of a real aircraft as shown in equation (2), under the condition of single input and single output (i.e., both the input u and the output y are one-dimensional parameters), it can be written as the following transfer function:

[0114]

[0115] Where K′ is the transfer function gain, q and w are orders, and z j is the zero point of the transfer function, p i are the poles of the transfer function, a1,…,a w-1 、a w and b1, ..., b q-1 , b q All are parameter values;

[0116] Then the transfer function of the scaled-down system corresponding to the open-loop dynamics system of the real aircraft has the following form:

[0117]

[0118] in, is the angular velocity proportionality coefficient k ω to the power of (wq);

[0119] The scaled system is based on the real system, and all poles and zeros are scaled by k at the same time. ω times, due to k ω is a positive number, so the scaling system does not change the positions of the zeros and poles in the left and right half planes of the complex plane, that is, it does not change the open-loop stability of the system.

[0120] Therefore, formula (5) is the similarity analysis criterion of the open-loop control frequency domain characteristics. By applying the criterion determined by formula (5), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and the transfer function model of the real aircraft can be inversely deduced to evaluate the open-loop stability characteristics of the open-loop aircraft.

[0121] Step 3: Standardize the state feedback control structure

[0122] In order to further carry out similarity analysis after considering closed-loop control, the linear closed-loop control system needs to be rewritten into a standardized structure in the form of state feedback control.

[0123] (1) For closed-loop control forms commonly used in engineering, such as attitude PID control and overload autopilot, the control instructions can all be expressed in the following state feedback form:

[0124] u=v-Kx (6)

[0125] Among them, u is the control instruction, that is, the input quantity, v is the reference input, K is the feedback gain matrix, and x is the state quantity; on this basis, the motion state equation of the closed-loop system can be written in the following standard form:

[0126]

[0127] Among them, A is the state matrix, B is the input matrix, C is the output matrix, and y is the output quantity.

[0128] (2) For control structures with state observers such as LESO and LADRC, the state observer dynamic equations and control inputs can be written as follows:

[0129]

[0130] Among them, z is the observation vector of the state observer, A x A is the state matrix of the observer for the state quantity of the original system, z is the state matrix of the observer for the observed part, K x is the feedback control gain matrix for the state quantity of the original system, K z is the feedback control gain matrix for the observation part;

[0131] Defining the expansion state Then the motion state equation of the control structure with state observer can be transformed into the following state feedback form:

[0132]

[0133] (3) Other linear closed-loop control structures can be standardized by referring to the method of (1) or (2), which will not be repeated here.

[0134] Step 4: Control parameter similarity transformation

[0135] Based on the state feedback control structure obtained in step 3, the similarity proportional coefficient matrix k of the state quantity, input quantity and output quantity vector is calculated according to the similarity dimensional relationship given in step 1 x , k u , k y This process is a prior art and will not be described in detail in this embodiment;

[0136] If the state feedback gain matrix of the real aircraft is K1, then in the wind tunnel virtual flight test, while the controller structure of the scaled aircraft is consistent with the real one, the feedback gain matrix K2 of the scaled aircraft should be strictly transformed according to the following formula:

[0137]

[0138] Under the condition of meeting the requirements of geometric similarity, flow similarity and kinematic similarity, when the feedback gain of the scaled aircraft is transformed similarly according to formula (10), the closed-loop motion similarity between the scaled system and the real system can be guaranteed.

[0139] Step 5: Similarity analysis of virtual flight closed-loop control

[0140] The closed-loop control characteristics of the aircraft are analyzed and studied through wind tunnel virtual flight, which mainly includes two parts: closed-loop control time domain response characteristics analysis and frequency domain characteristics (stability margin) analysis. This step gives the similarity analysis criteria of the time domain and frequency domain characteristics of the closed-loop control of the scaled aircraft and the real aircraft in turn.

[0141] (1) Similarity analysis criterion for closed-loop control time domain characteristics: Let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), at the corresponding time t2 = k t At t1, the reference input satisfies the similarity relation v2(t2)=k u v1(t1), then the closed-loop dynamic equation of the scaled-down system satisfies:

[0142]

[0143] Among them, C2 is the output matrix of the scaling system;

[0144] The scaled closed-loop system can be regarded as the real system scaled by time scale k. t times, the state quantity and output quantity at the corresponding moment strictly meet the criterion of formula (3), that is, x2(t2)=k x x1(t1),y2(t2)=k y y1(t1), that is, formula (3);

[0145] Therefore, equations (3) and (11) are similarity analysis criteria for closed-loop control time-domain characteristics. By applying the criteria determined by equations (3) and (11), the closed-loop control time-domain response of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and the closed-loop control time-domain response of the real aircraft can be inferred.

[0146] (2) Similarity analysis criteria for closed-loop control frequency domain characteristics: Under the premise of satisfying the closed-loop control similarity transformation, the closed-loop transfer function of the system The following similarity relationship is satisfied:

[0147] ①If the closed-loop transfer function of the real system is:

[0148]

[0149] Then the transfer function of the scaled system has the following form:

[0150]

[0151] And for any s = jω2 = jk ω ω1, exists

[0152] ②The amplitude margin and phase margin of the scaled-down system are exactly the same as those of the real system, and the cutoff frequency of the system is ω c When the following similarity ratio relationship is met:

[0153] ω c2 =k ω ω c1 (14)

[0154] Then the frequency domain characteristics of the scaled-down system closed-loop control are completely similar to those of the real system; where ω c2 is the cutoff frequency of the scaled system, ω c1 is the cutoff frequency of the real system.

[0155] Therefore, equations (13) and (14) are similarity analysis criteria for closed-loop control frequency domain characteristics. By applying the criteria determined by equations (13) and (14), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and then the transfer function model of the real aircraft can be inferred to evaluate the closed-loop stability characteristics of the closed-loop aircraft.

[0156] Combining the above five steps, the similarity analysis criteria for open-loop motion, the similarity transformation method for closed-loop control parameters, and the similarity analysis criteria for closed-loop control are given under wind tunnel virtual flight test conditions. Under the guidance of this criterion, the wind tunnel virtual flight test data of the scaled aircraft can be used to support the open / closed-loop dynamic response characteristics and stability analysis and evaluation of the aircraft under real flight conditions.

[0157] Embodiment 3:

[0158] In order to verify the effectiveness of the closed-loop control similarity criteria proposed in Example 1 and Example 2, this embodiment performs numerical simulation on the closed-loop control flight process of a high-speed deformable aircraft and its scaled test model. The simulation process is performed according to the following steps:

[0159] Step 1: After satisfying the geometric similarity, flow similarity and kinematic similarity conditions between the wind tunnel virtual flight test and the real flight, determine the proportional coefficient relationship of the basic physical quantities of the similarity relationship of the scaled aircraft: k V =1.0, k ρ =1.0, k L =1 / 3, and then calculate the similar proportional coefficient relationship of other physical quantities according to Table 2:

[0160]

[0161] Step 2: On this basis, the open-loop dynamic characteristics of the scaled aircraft and the real aircraft have the following similarity:

[0162] (1) At the initial time t 20 =t 10 = 0, the aircraft's attitude angle θ, angle of attack α, and pitch angle δ z , that is, the attitude angle θ2, angle of attack α2, and pitch rudder deflection angle δ of the scaled aircraft z2 And the attitude angle θ1, angle of attack α1, pitch rudder angle δ of the real aircraft z1 Satisfy between: θ2(t 20 )=θ1(t 10 ), α2(t 20 )=α1(t 10 ),δ z2 (t 20 )=δ z1 (t 10 ), and at all subsequent moments, the input rudder deviation is guaranteed to satisfy δ z2 (t2) = δ z1 (3t2), the open-loop motion state always satisfies the following similarity relationship:

[0163]

[0164] Among them, ω z is the pitch angular velocity, ω z1 is the pitch angular velocity of the real aircraft, ω z2 is the pitch velocity of the scaled aircraft;

[0165] (2) The open-loop system is based on the pitch rudder deflection angle δ z The transfer function to the angle of attack α has the form

[0166]

[0167] After satisfying the similarity relationship mentioned in step 2 of embodiment 2, the open-loop transfer function of the scaling system is in the following form:

[0168]

[0169] Step 3: The real aircraft uses LADRC to perform pitch attitude control. For a given angle of attack command α c , rudder angle control command δ zc The expression is as follows:

[0170]

[0171] Where K P1 =8, K D1 =3, K1=-7 is the control gain, ω o1 =10 is the observer parameter, z1 and z2 are the observer state variables.

[0172] According to the state feedback control structure normalization and control parameter similarity transformation method given in steps 3 and 4 of Example 2, the control structure of the scaled system still maintains the form of formula (19), but the control gain and observer parameters need to be similarly transformed. The scaled system control parameters after transformation are: K P2 =K P1 =8, K D2 =K D1 / k ω =1, ω o2 =k ω ω o1 =30.

[0173] Step 4: After completing the similarity transformation of the control parameters, a comparative simulation is performed on the wind tunnel virtual flight and the real flight process. When the input angle of attack command satisfies α c2 (t2) = α c1 (t1), that is, when the time scale is compressed by 3 times, the angle of attack α and the pitch angular velocity ω z Closed-loop control response curve Figure 2 , Figure 3 As shown, it can be seen that the closed-loop control response satisfies α2(t2)=α1(t1), ω z2 (t2) = 3ω z1 (t1) is similar to the

[0174] Figure 4The simulation results of the amplitude margin and phase margin of the scaled system and the real aircraft are given. It can be seen that the amplitude margin of the scaled system is 10.8dB and the phase margin is 52.8°, which are consistent with the real aircraft. The cutoff frequency of the real system is 31.2rad / s, and the cutoff frequency of the scaled system is 93.6rad / s, which meets the cutoff frequency ω c2 =3ω c1 relation.

[0175] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0176] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0177] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for determining control similarity criteria for high-speed wind tunnel virtual flight tests, characterized in that: The method is: Step 1: Determine the similarity dimensional relationship between the scaled aircraft and the real aircraft; Step 2: Analyze the similarity of the open-loop motion of the virtual flight: Analyze the open-loop dynamic time domain response characteristics and frequency domain transfer function characteristics of the aircraft through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the open-loop motion of the scaled aircraft and the real aircraft; Step 3: Analyze the similarity of closed-loop motion of virtual flight: Step 3-1, performing a standardized transformation on the state feedback control structure; Step 3-2, performing similarity transformation on the control parameter of the state feedback control structure after being standardized in step 3-1, where the control parameter is the feedback gain; Step 3-3, analyze the time domain response characteristics and frequency domain characteristics of the closed-loop control of the aircraft, that is, the stability margin, through wind tunnel virtual flight, and determine the similarity analysis criteria of the time domain and frequency domain characteristics of the closed-loop control of the scaled aircraft and the real aircraft.

2. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test according to claim 1, characterized in that: In the first step, the similarity dimensional relationship between the scaled aircraft and the real aircraft is as follows: The physical quantity y1 representing the motion of the real aircraft and the physical quantity y2 representing the motion of the scaled aircraft satisfy the following proportional relationship: y2(t2)=k y y1(t1) (1) Where t1 is the movement time of the real aircraft, t2 is the movement time of the scaled aircraft, and k y is the similarity proportionality coefficient of the physical quantity; If the physical quantity is written in vector form y1∈R n , y2∈R n , then the corresponding similarity ratio coefficient diagonal matrix k y =diag(k y1 …k yn ), and still satisfy y2(t2)=k y y1(t1).

3. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test according to claim 2, characterized in that: For high-speed wind tunnel virtual flight tests, the speed proportionality factor k is selected V , density proportionality coefficient k ρ , length ratio coefficient k L As a proportionality factor of basic physical quantities; And, k V =V SO1 / V SO2 , k L =1 / N,k ρ =μ2 / (k V k L μ1), where V SO1 、V SO2 represent the sound speed of real flight and wind tunnel flow, μ1 and μ2 represent the gas viscosity of real flight and wind tunnel flow, respectively, and N is the scale factor of the wind tunnel test model; The other motion parameter proportional coefficients include: Angle proportional coefficient k θ , time proportional coefficient k t , angular velocity proportionality coefficient k ω , mass proportionality coefficient k m , moment of inertia proportional coefficient k J , acceleration proportionality coefficient k g , force proportionality coefficient k F , torque proportionality coefficient k M ; And, k θ =1, k t =k L / k V , k ω =k V / k L , 4. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test as claimed in claim 2, characterized in that: In the second step, before analyzing the open-loop dynamics time domain response characteristics and frequency domain transfer function characteristics of the aircraft, the open-loop dynamics system of the real aircraft is simplified and converted into the following state space expression: Among them, A1 is the state matrix, B1 is the input matrix, C1 is the output matrix, and D1 is the feedforward matrix; the state quantity x1 = [x 11 ,…x 1n ] T ∈R n 、Input u1=[u 11 ,…u 1m ] T ∈R m , output y1 = [y 11 ,…y 1p ] T ∈R p .

5. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test as claimed in claim 4, characterized in that: The specific process of the second step is as follows: For the open-loop dynamics system of the real aircraft, that is, the open-loop dynamics system of the scaled aircraft corresponding to the real system, that is, the scaled system, the state quantity, input quantity, and output quantity of the scaled system are recorded as x2, u2, and y2 respectively; according to the dimensional relationship in the first step, the similarity ratio coefficient matrix of the state quantity, input quantity, and output quantity vector is calculated respectively: k x , k u , k y , then the real system and the scaled system satisfy the following similarity criteria: (1) Similarity analysis criterion for open-loop control time domain characteristics: Let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), if all subsequent corresponding moments t2 = k t t1, external input satisfies the similarity relation u2(t2)=k u u1(t1), then the time domain response of the scaled-down aircraft at any corresponding time in the future will satisfy the following similarity relationship: Therefore, formula (3) is the similarity analysis criterion of the open-loop control time domain characteristics. By applying the criterion determined by formula (3), the open-loop dynamic response characteristics of the real aircraft can be inversely deduced based on the open-loop dynamic response of the virtual flight test in the wind tunnel of the scaled aircraft; (2) Similarity analysis criteria for open-loop control frequency domain characteristics: For the open-loop dynamic system of a real aircraft as shown in equation (2), in the case of single input and single output, it can be written as the following transfer function: Where K' is the transfer function gain, q and w are orders, and z j is the zero point of the transfer function, p i are the poles of the transfer function, a1,…,a w-1 、a w and b1, ..., b q-1 , b q All are parameter values; Then the transfer function of the scaled-down system corresponding to the open-loop dynamics system of the real aircraft has the following form: in, is the angular velocity proportionality coefficient k ω to the power of (wq); The scaled system is based on the real system, and all poles and zeros are scaled by k at the same time. ω times, therefore, formula (5) is the similarity analysis criterion for the open-loop control frequency domain characteristics. By applying the criterion determined by formula (5), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and then the transfer function model of the real aircraft can be inferred to evaluate the open-loop stability characteristics of the open-loop aircraft.

6. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test as claimed in claim 2, characterized in that: In step 3-1, the process of standardizing the state feedback control structure is as follows: (1) For attitude PID control and closed-loop control of overload pilot, the control command is expressed in the following state feedback form: u=v-Kx (6) Among them, u is the control instruction, that is, the input quantity, v is the reference input, K is the feedback gain matrix, and x is the state quantity; on this basis, the motion state equation of the closed-loop system can be written in the following standard form: Among them, A is the state matrix, B is the input matrix, C is the output matrix, and y is the output quantity; (2) For a control structure with a state observer, the state observer dynamic equation and control input are written as follows: Among them, z is the observation vector of the state observer, A x A is the state matrix of the observer for the state quantity of the original system, z is the state matrix of the observer for the observed part, K x is the feedback control gain matrix for the state quantity of the original system, K z is the feedback control gain matrix for the observation part; Defining expansion states The motion state equation of the control structure with a state observer is converted into the following state feedback form:

7. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test according to claim 6, characterized in that: In step 3-2, the process of performing similarity transformation on the feedback gain is as follows: According to the similarity dimensional relationship given in step 1, calculate the similarity proportional coefficient matrix k of the state quantity, input quantity and output quantity vector x , k u , k y ; If the feedback gain matrix of the state of the real aircraft is K1, then in the wind tunnel virtual flight test, while the controller structure of the scaled aircraft is consistent with the real one, the feedback gain matrix K2 of the scaled aircraft should be strictly transformed according to the following formula: Therefore, the feedback gain of the scaled aircraft is obtained by similarity transformation according to formula (10).

8. A method for determining control similarity criteria for a high-speed wind tunnel virtual flight test as claimed in claim 7, characterized in that: The specific process of step 3-3 is: (1) Similarity analysis criterion for closed-loop control time domain characteristics: Let the initial time of the real aircraft be t 20 , the initial time of the scaled-down aircraft is t 10 , assuming that at the initial time t 20 =t 10 = 0, then the initial motion state of the scaled aircraft satisfies the similarity ratio relationship x2(t 20 ) = k x x1(t 10 ), at the corresponding time t2 = k t At t1, the reference input satisfies the similarity relation v2(t2)=k u v1(t1), then the closed-loop dynamic equation of the scaled-down system satisfies: Among them, C2 is the output matrix of the scaling system; The scaled closed-loop system can be regarded as the real system scaled by time scale k. t times, the state quantity and output quantity at the corresponding moment strictly meet the criterion of formula (3), that is, x2(t2)=k x x1(t1),y2(t2)=k y y1(t1); Therefore, formula (3) and formula (11) are the similarity analysis criteria of closed-loop control time domain characteristics. By applying the criteria determined by formula (3) and formula (11), the closed-loop control time domain response of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and the closed-loop control time domain response of the real aircraft can be inferred; (2) Similarity analysis criteria for closed-loop control frequency domain characteristics: Under the premise of satisfying the closed-loop control similarity transformation, the closed-loop transfer function of the system The following similarity relationship is satisfied: ①If the closed-loop transfer function of the real system is: Then the transfer function of the scaled system has the following form: And for any s = jω2 = jk ω ω1, exists ②The amplitude margin and phase margin of the scaled-down system are exactly the same as those of the real system, and the cutoff frequency of the system is ω c When the following similarity ratio relationship is met: oh c2 =k ω oh c1 (14) Then the frequency domain characteristics of the scaled-down system closed-loop control are completely similar to those of the real system; where ω c2 is the cutoff frequency of the scaled system, ω c1 is the cutoff frequency of the real system. Therefore, equations (13) and (14) are similarity analysis criteria for closed-loop control frequency domain characteristics. By applying the criteria determined by equations (13) and (14), the transfer function model of the scaled aircraft can be obtained according to the virtual flight test of the scaled aircraft wind tunnel, and then the transfer function model of the real aircraft can be inferred to evaluate the closed-loop stability characteristics of the closed-loop aircraft.

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