A method for constructing longitudinal short-period frequency and damping ratio

Abstract

The present application provides a method for constructing a longitudinal short-period frequency and a damping ratio, comprising: 1) using a longitudinal linearized small-disturbance aircraft equation to obtain the longitudinal short-period modal characteristics of the aircraft body and the longitudinal pitch rate expression, based on the longitudinal pitch rate expression, constructing a longitudinal stabilization control law containing three parts of expected operating torque, incorporating the constructed rudder expected operating torque expression into the longitudinal pitch rate expression to obtain a control law structure with a second-order equivalent dynamic response characteristic; 2) determining an initial value of a target parameter; 3) solving the target parameter short-period frequency, and constructing a longitudinal short-period closed-loop simulation model together with a short-period longitudinal linearized small-disturbance aircraft equation model through the determined control law structure and the target parameter initial value of the control law feedback gain; and adjusting based on the initial value of the short-period frequency, the short-period frequency is increased so that the short-period frequency when the longitudinal short-period stability reserve meets the requirement is the determined value of the final target parameter short-period frequency.

Description

Technical Field

[0001] The present application belongs to the field of flight control technology, and in particular relates to a method for constructing a longitudinal short-period frequency and a damping ratio. Background Art

[0002] The main goal of the aircraft control and stability augmentation design is to obtain satisfactory flight quality and meet the relevant requirements of the flight quality specifications. When evaluating the longitudinal flight quality of the aircraft, the main parameters involved are the aircraft longitudinal short-period frequency and damping ratio. Therefore, when designing the aircraft control and stability augmentation, it is necessary to obtain satisfactory short-period frequency and damping ratio.

[0003] In the current design of stability augmentation control laws, the design method based on root locus parameter adjustment and the inspection method in time domain and frequency domain are mainly used. Although satisfactory short-period frequency and damping ratio can be obtained, the design process is complicated and cannot be directly solved as the target parameter.

[0004] Therefore, it is necessary to find a simple method to optimize the design with the expected short-period frequency and damping ratio as the target parameters in the control system stabilization design. Summary of the invention

[0005] The purpose of the present application is to provide a method for constructing a longitudinal short-period frequency and a damping ratio to solve or alleviate at least one problem in the background technology.

[0006] The present application provides a method for constructing a longitudinal short-period frequency and a damping ratio, comprising:

[0007] 1) Constructing the longitudinal stability augmentation control law

[0008] The longitudinal short-period modal characteristics of the aircraft body and the longitudinal pitch rate expression are obtained by using the longitudinal linearized small disturbance aircraft equation:

[0009] Based on the longitudinal pitch rate expression, a longitudinal stabilization control law including three parts of expected operating torque is constructed, wherein the first part of the expected operating torque is used to offset the dynamic characteristics of the aircraft body, so that the short-period modal characteristics become a pure integral response, the second part of the expected operating torque is used to construct the expected dynamic response, and the third part of the expected torque makes the control system constitute a zero-static error control;

[0010] The constructed desired operating torque expression of the rudder surface is incorporated into the longitudinal pitch rate expression to obtain a control law structure of the second-order equivalent dynamic response characteristics;

[0011] 2) Determine the initial value of the target parameter

[0012] Among them, the initial value of the short-period damping ratio ξ is selected in the range of 0.35<ξ<1.3;

[0013] Integral gain coefficient P 0 The initial value satisfies

[0014] The initial value of the short-period frequency ω satisfies ω=max(ω 1 ,ω 2 ),in, The solution is ω 21 and ω 22 ,ω 2 =max(ω 21 ,ω 22 );

[0015] 3) Solve the short-period frequency of the target parameter

[0016] The control law structure and the target parameter initial value of the control law feedback gain determined by the above steps are used together with the short-period longitudinal linearized small disturbance aircraft equation model to construct a longitudinal short-period closed-loop simulation model;

[0017] The short-cycle frequency is adjusted based on the initial value of the short-cycle frequency. The short-cycle frequency is increased so that the longitudinal short-cycle stability reserve meets the requirements, which is the determined value of the final target parameter short-cycle frequency.

[0018] Furthermore, the method of obtaining the longitudinal short-period modal characteristics of the aircraft body by using the longitudinal linearized small-disturbance aircraft equation includes:

[0019]

[0020]

[0021]

[0022] Where α is the angle of attack; ω z is the pitch angle rate; is the pitch angle; δ z is the horizontal tail; A is the state matrix; B is the input matrix; Y α is the derivative of lift with respect to angle of attack; g is the acceleration due to gravity; v is the true airspeed; is the derivative of the pitching moment with respect to the angle of attack; is the differential derivative of the pitch moment with respect to the angle of attack; is the derivative of the pitch moment with respect to the pitch angular rate; is the derivative of the pitch moment with respect to the horizontal tail; is the derivative of lift with respect to the horizontal tail.

[0023] Furthermore, the longitudinal pitch rate expression is obtained based on the longitudinal linearized small disturbance aircraft equation:

[0024]

[0025] Furthermore, the expression of the expected operating torque in the first part is:

[0026]

[0027] The expression of the expected operating torque in the second part is:

[0028]

[0029] The expression of the expected operating torque in the third part is:

[0030]

[0031] Where: M z0 is the pitching moment at zero angle of attack; K Ξ is the control column transfer coefficient; X p To provide driving displacement signal.

[0032] Furthermore, the control law structure of the second-order equivalent dynamic response characteristic is:

[0033]

[0034] Furthermore, the short-period damping ratio limit value is: 0.35<ξ<1.3.

[0035] Furthermore, in the formula In the equation, coefficient a = ξP0, coefficient

[0036] Furthermore, when increasing the short cycle frequency, the following constraints must be met:

[0037] a) The longitudinal short-period stability reserve meets the requirement that the amplitude reserve is greater than 6dB and the phase reserve is greater than 45°;

[0038] b) Longitudinal short-period time domain response characteristics: rise time, overshoot, steady-state error, and oscillation times meet standard requirements;

[0039] c) The longitudinal short-period frequency domain matching error meets the standard requirements.

[0040] The method provided in the present application can significantly reduce the complexity of parameter adjustment in the design process of the longitudinal inner-loop stabilization control law, and transform the parameter adjustment process of each branch of the control law into directly optimizing and solving the target parameters with the expected short-period frequency and damping ratio, thereby simplifying the design process and ensuring that the obtained control law parameters meet the longitudinal short-period design requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0042] Figure 1 This is a flow chart of the method for constructing the longitudinal short-period frequency and damping ratio of the present application.

[0043] Figure 2 This is a schematic curve of the short-period characteristics with an initial value of ω=1.8 in the embodiment of the present application.

[0044] Figure 3 This is a schematic curve of the short-period characteristics with a final value of ω=3.9 in the embodiment of the present application.

[0045] Figure 4 A comparison of unit step responses according to an embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0047] like Figure 1 As shown, the method for constructing the aircraft longitudinal short-period frequency and damping ratio provided by the present application specifically includes the following steps:

[0048] S1. Constructing the longitudinal stability augmentation control law

[0049] The longitudinal short-period modal characteristics of the aircraft body are obtained using the longitudinal linearized small disturbance aircraft equation. The formula is as follows:

[0050]

[0051]

[0052]

[0053] The expression of the longitudinal pitch rate ωz is obtained from the longitudinal linearized small disturbance aircraft equation:

[0054]

[0055] Based on the longitudinal pitch rate expression, the longitudinal stabilization control law is constructed through the δz term. The control law contains three parts of expected operating torque. The first part of the expected operating torque is used to offset the dynamic characteristics of the aircraft body and make the short-period modal characteristics become a pure integral response. The second part of the expected operating torque is used to construct the expected dynamic response. The third part of the expected operating torque makes the control system form a zero-static control. The three parts of the expected operating torque are as follows:

[0056]

[0057]

[0058]

[0059] The desired operating torque of the rudder constructed above is combined and substituted into the longitudinal pitch rate expression (4), and the control law structure of the second-order equivalent dynamic response characteristics is obtained:

[0060]

[0061] For example, in one embodiment of the present application, the longitudinal short-period aircraft body large derivatives in Table 1 are provided, and the aircraft short-period longitudinal small disturbance equations are solved and the longitudinal short-period modal equations A and B can be obtained through the aircraft longitudinal short-period body large derivatives, and the longitudinal stabilization control law is constructed through δz1, δz2, and δz3:

[0062]

[0063]

[0064] Table 1 Longitudinal short-period large derivatives of the aircraft body

[0065]

[0066] S2. Determine the initial value of the target parameter

[0067] Short period damping ratio:

[0068] The short-period damping ratio is selected according to the equivalent short-period damping ratio limit requirements of the national military standard. The limit value that meets the first-level requirements is: 0.35<ξ<1.3. ξ=0.8 can be selected as the initial value according to the empirical value.

[0069] Integral gain coefficient P_0:

[0070] To ensure that the pitch rate branch feedback gain is greater than zero, P_0+M_z^(ω_z)>0 is required. Generally, P_0=-M_z^(ω_z)+0.5 can be taken. The value of P_0 can be determined by the pitch damping derivative M_z^(ω_z).

[0071] Short cycle frequency:

[0072] The short-period frequency is selected according to the longitudinal short-period CAP criterion, that is, ω_1>√(0.28n_y^α), where n_y^α=v_0 / gY^α.

[0073] To ensure that the feedback gain in the angle of attack feedback branch is greater than zero, it is required

[0074] ω_2^2+aω_2+b>0, where a=ξP_0, b=-P_0Y^α+M_z^α. If there exists a solution ω_21, ω_22, and the requirement is: ω_2=max(ω_21, ω_22), then the initial value of the short-period frequency takes the maximum value of the above two constraints: ω=max(ω_1, ω_2).

[0075] For example, the initial values ​​of the target parameters through the above process are as follows:

[0076] a) Short-period damping ratio:

[0077] ξ=0.8.

[0078] b) Integral gain coefficient:

[0079]

[0080] c) Short cycle frequency

[0081] That is ω 1 >1.8.

[0082] exist

[0083] a=ξP0=2.4099,

[0084]

[0085] ω21=-2.4126, ω22=0.0047, ω2=max(ω21,ω22)=0.0047.

[0086] Short-period frequency: ω=max(ω1,ω2)=max(1.8,0.0047), that is, the initial value ω=1.8.

[0087] S3. Solve the short-period frequency of the target parameter

[0088] The control law structure and initial value of the control law feedback gain determined by the above steps, together with the short-period longitudinal linearized small disturbance aircraft equation model, are constructed into a longitudinal short-period closed-loop simulation model. Based on the short-period initial frequency, increasing the short-period frequency will significantly improve the rapidity of the aircraft response and obtain better short-period time domain response characteristics, but it will reduce the longitudinal short-period stability reserve. Therefore, when increasing the short-period frequency, the following constraints must be met:

[0089] a) The longitudinal short-period stability reserve meets the requirement that the amplitude reserve is greater than 6dB and the phase reserve is greater than 45°;

[0090] b) Longitudinal short-period time domain response characteristics: rise time, overshoot, steady-state error, and oscillation times meet the requirements of national military standards;

[0091] c) The longitudinal short-period frequency domain matching error meets the national military standard requirements.

[0092] The short-period frequency that meets the above requirements is the final target parameter value.

[0093] For example, in this embodiment, the initial value of the target parameter is determined to be ω=1.8, and is substituted into the longitudinal short-period model to obtain the stability reserve and time domain response as follows: Figure 2 As shown, at this time, the amplitude reserve is 18.22dB and the phase reserve is 55.8°. The short cycle frequency can be further increased and adjusted until one of the amplitude reserve or the phase reserve reaches a critical value, such as Figure 3 It is shown that when the phase reserve reaches the critical value, ω=3.9, which is the final determined value of the target parameter short-cycle frequency.

[0094] Substituting the short-period frequency ω = 3.9 and the damping ratio ξ = 0.8 into the control law structure of equation (8), the obtained time domain response is compared with the constructed short-period closed-loop time domain response, as shown in Figure 4 As shown in the figure, when the time domain response is consistent with the constructed short-period closed-loop time domain response, it is proved that the equivalent fitting results of the control law system constructed with the expected short-period frequency and damping ratio are very consistent with the theoretical model.

[0095] The method of the present application can significantly reduce the complexity of parameter adjustment in the design process of the longitudinal inner-loop stabilization control law, and transform the parameter adjustment process of each branch of the control law into directly optimizing and solving the target parameters with the desired short-period frequency and damping ratio, thereby simplifying the design process and ensuring that the obtained control law parameters meet the longitudinal short-period design requirements.

[0096] Explanation of symbols:

[0097] α is the angle of attack;

[0098] ω z is the pitch angle rate;

[0099] is the pitch angle;

[0100] δ z For the flat tail;

[0101] Y α is the derivative of lift with respect to angle of attack;

[0102] g is the acceleration due to gravity;

[0103] v is true air speed;

[0104] is the derivative of the pitching moment with respect to the angle of attack;

[0105] is the differential derivative of the pitch moment with respect to the angle of attack;

[0106] is the derivative of the pitch moment with respect to the pitch angular rate;

[0107] is the derivative of the pitch moment with respect to the horizontal tail;

[0108] is the derivative of lift with respect to the horizontal tail;

[0109] M z0 is the pitching moment at zero angle of attack;

[0110] K Ξ is the control column transfer coefficient;

[0111] X p Provide displacement signals for driving;

[0112] ξ is the short-period damping ratio;

[0113] ω is the short-period frequency;

[0114] P 0 is the integral proportional coefficient of the pitch loop;

[0115] is the derivative of the angle of attack with respect to overload;

[0116] A is the state matrix;

[0117] B is the input matrix.

[0118] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for constructing longitudinal short-period frequency and damping ratio, It is characterized in that include: 1) Constructing the longitudinal stability augmentation control law The longitudinal short-period modal characteristics of the aircraft body and the longitudinal pitch rate expression are obtained by using the longitudinal linearized small disturbance aircraft equation: Based on the longitudinal pitch rate expression, a longitudinal stabilization control law including three parts of expected operating torque is constructed, wherein the first part of the expected operating torque is used to offset the dynamic characteristics of the aircraft body, so that the short-period modal characteristics become a pure integral response, the second part of the expected operating torque is used to construct the expected dynamic response, and the third part of the expected torque makes the control system constitute a zero-static error control; The constructed desired operating torque expression of the rudder surface is incorporated into the longitudinal pitch rate expression to obtain a control law structure of the second-order equivalent dynamic response characteristics; 2) Determine the initial value of the target parameter Among them, the initial value of the short-period damping ratio ξ is selected in the range of 0.35<ξ<1.3; Integral gain coefficient P 0 The initial value satisfies The initial value of the short-period frequency ω satisfies ω=max(ω 1 ,ω 2 ),in, The solution is ω 21 and ω 22 ,ω 2 =max(ω 21 ,ω 22 ); is the derivative of the angle of attack with respect to overload; 3) Solve the short-period frequency of the target parameter The control law structure and the target parameter initial value of the control law feedback gain determined by the above steps are used together with the short-period longitudinal linearized small disturbance aircraft equation model to construct a longitudinal short-period closed-loop simulation model; The short-cycle frequency is adjusted based on the initial value of the short-cycle frequency. The short-cycle frequency when the short-cycle frequency is increased and the vertical short-cycle stability reserve meets the requirements is the determined value of the final target parameter short-cycle frequency. The method of obtaining the longitudinal short-period modal characteristics of the aircraft body by using the longitudinal linearized small-disturbance aircraft equation includes: Where α is the angle of attack; ω z is the pitch angle rate; is the pitch angle; δ z is the horizontal tail; A is the state matrix; B is the input matrix; Y α is the derivative of lift with respect to angle of attack; g is the acceleration due to gravity; v is the true airspeed; is the derivative of the pitching moment with respect to the angle of attack; is the differential derivative of the pitch moment with respect to the angle of attack; is the derivative of the pitch moment with respect to the pitch angular rate; is the derivative of the pitch moment with respect to the horizontal tail; is the derivative of lift with respect to the horizontal tail; The longitudinal pitch rate expression is obtained according to the longitudinal linearized small disturbance aircraft equation: The expression of the expected operating torque in the first part is: The expression of the expected operating torque in the second part is: The expression of the expected operating torque in the third part is: Where: M z0 is the pitching moment at zero angle of attack; K Ξ is the control column transfer coefficient; X p Provide displacement signals for driving; The control law structure of the second-order equivalent dynamic response characteristic is:

2. The method for constructing longitudinal short-period frequency and damping ratio as claimed in claim 1, It is characterized in that The short-period damping ratio limit value is: 0.35<ξ<1.

3.

3. The method for constructing longitudinal short-period frequency and damping ratio as claimed in claim 2, It is characterized in that In the formula In the equation, coefficient a = ξP0, coefficient 4. The method for constructing the longitudinal short-period frequency and damping ratio according to any one of claims 1 to 3, It is characterized in that When increasing the short cycle frequency, the following constraints must be met: a) The longitudinal short-period stability reserve meets the requirement that the amplitude reserve is greater than 6dB and the phase reserve is greater than 45°; b) Longitudinal short-period time domain response characteristics: rise time, overshoot, steady-state error, and oscillation times meet standard requirements; c) The longitudinal short-period frequency domain matching error meets the standard requirements.

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