Robustness evaluation method for antisymmetric coupling system
By building a system simulation model of the rolling aircraft, calculating amplitude margin and phase margin, and evaluating pure delay time, the problem of robustness evaluation of the rolling aircraft is solved, and real-time stability evaluation and robustness improvement on the aircraft are achieved.
Patent Information
- Application Number
- CN202510202679.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-24
- Publication Date
- 2025-07-08
AI Technical Summary
The existing robustness evaluation methods of rolling vehicles lack effective means, and it is difficult to achieve robust optimization control of multi-input and multi-output linear systems, resulting in reduced dynamic instability and control accuracy.
Build a system simulation model, including body dynamics, servo dynamics and static decoupling dynamics links of servo. By obtaining amplitude margin, phase margin and amplitude crossing frequency of 0dB, the pure delay time is calculated and mapped to the robustness evaluation of the system.
A robustness evaluation method with small computing capacity and reliable computing capacity is provided, which can calculate stability margins in real time on the aircraft onboard computer and improve the reliability of the system's robustness evaluation.
Smart Images
Figure CN120276246A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for evaluating the robustness of an anti-symmetric coupling system, and belongs to the technical field of flight control. Background Art
[0002] A rolling aircraft refers to a type of aircraft that continuously rolls around its own longitudinal axis during flight. Dynamic stability is one of the primary issues to be considered in the design of a rolling aircraft. If the rotating aircraft exhibits dynamic instability during flight, it will not only reduce its control stability but may also lead to a decrease in guidance accuracy and even the possibility of losing control and crashing during flight.
[0003] There are various delays in a rolling aircraft system, including: the dynamic characteristics of the aircraft autopilot have dynamic delays, the servo has delays in responding to control signals, there are delays when the aircraft actuator generates control torque, delays introduced during the signal processing and transmission in the control system, and processing delays generated when the system processes target information and generates guidance commands. These delays result in various delay errors between the actual system and the ideal system, which are important reasons for the instability of the rolling aircraft. Therefore, the maximum tolerable delay time of the system can be used as an evaluation index for its robustness.
[0004] For a single-input single-output system, the amplitude margin and phase margin (cut-off frequency) can usually be obtained using the open-loop transfer function, and then the maximum tolerable delay time of the system can be analytically obtained. However, due to channel coupling in a rolling aircraft, for a multi-input multi-output linear system, there is a lack of theoretical analysis or evaluation means for system robustness, making it difficult to achieve robust optimal control.
[0005] Existing evaluation methods for the dynamic stability of rolling aircraft can only determine the stability of rolling aircraft, but lack an evaluation of the robustness of rolling aircraft.
[0006] Therefore, it is necessary to conduct a more in-depth study on the existing evaluation methods for the dynamic stability of rolling aircraft to solve the above problems. Summary of the Invention
[0007] To overcome the above problems, in-depth research has been carried out, and a method for evaluating the robustness of an anti-symmetric coupling system is proposed, including the following steps:
[0008] S1. Build the system simulation model architecture, where the system simulation model includes an airframe dynamics link, a servo dynamics link, and a servo static decoupling dynamics link;
[0009] S2. Set the transfer functions of the servo dynamics link, the servo static decoupling dynamics link, and the airframe dynamics link in the system simulation model:
[0010] S3. Obtain the amplitude margin, phase margin, and amplitude crossover frequency at 0 dB of the system simulation model, and then obtain the pure delay time of the simulation system;
[0011] S4. Map the obtained pure delay time to the robustness evaluation of the system.
[0012] In a preferred embodiment, the servo static decoupling dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to the pitch angle command or yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the link output.
[0013] In a preferred embodiment, the servo dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to the pitch angle command or yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the link output.
[0014] In a preferred embodiment, in S2, a quasi-body coordinate system is established, and the transfer functions of the servo static decoupling dynamics link and the servo dynamics link are obtained in the quasi-body coordinate system.
[0015] The quasi-body coordinate system Ox4y4z4 is as follows: The origin O is taken as the center of mass of the aircraft; The Ox4 axis coincides with the longitudinal axis of the airframe, and the direction pointing to the head of the airframe is positive; The Oy4 axis is located in the vertical plane containing the longitudinal axis of the airframe and is perpendicular to the Ox4 axis, and the direction pointing upward is positive; The Oz4 axis forms a right-handed coordinate system with the other two axes.
[0016] In a preferred embodiment, the transfer function G s (s) of the main channel of the servo dynamics link is set as:
[0017]
[0018] The transfer function G sco (s) of the coupling channel of the servo dynamics link is set as:
[0019]
[0020] Among them, ω x represents the roll angular velocity of the aircraft.
[0021] In a preferred embodiment, the transfer function of the servo dynamics link is simplified, and the transfer function G s (s) of the main channel of the simplified servo dynamics link is:
[0022]
[0023] The transfer function G of the coupled channel of the simplified servo dynamics link sco (s) is expressed as:
[0024]
[0025] In a preferred embodiment, the transfer function G of the main channel of the servo static decoupling dynamics link sd (s) is set to:
[0026]
[0027] The transfer function G of the coupled channel of the servo static decoupling dynamics link scod (s) is set to:
[0028]
[0029] In a preferred embodiment, the transfer function G of the airframe dynamics link m (s) is set to:
[0030]
[0031] where K θ represents the airframe gain, T α is the time constant of the airframe dynamics, τ m is the time constant of the natural frequency of the system, μ m is the damping ratio of the airframe dynamics.
[0032] In a preferred embodiment, in S3, the Bode plot analysis method is used to obtain the amplitude margin, phase margin and amplitude crossover frequency at 0 dB of the system simulation model.
[0033] In a preferred embodiment, the pure delay time of the simulation system is expressed as:
[0034]
[0035] where τ represents the pure delay time, Gm represents the amplitude margin, Pm represents the phase margin, and W cp represents the amplitude crossover frequency at 0 dB.
[0036] The beneficial effects of the present invention include:
[0037] (1) According to the robustness evaluation method for the roll missile control coupling anti-symmetric system provided by the present invention, the amount of computation is small, and the stability margin can be calculated in real time on the aircraft on-board computer to measure the system robustness;
[0038] (2) The robustness evaluation method for the roll control coupling anti-symmetric system provided by the present invention has high reliability. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 FIG. shows a schematic flow chart of a robustness evaluation method for an anti-symmetric coupling system according to a preferred embodiment of the present invention;
[0040] Figure 2 FIG. shows a system simulation model in the robustness evaluation method for an anti-symmetric coupling system according to a preferred embodiment of the present invention;
[0041] Figure 3 FIG. shows a schematic structural diagram of a servo static decoupling dynamics link in the robustness evaluation method for an anti-symmetric coupling system according to a preferred embodiment of the present invention;
[0042] Figure 4 FIG. shows a schematic structural diagram of a servo dynamics link in the robustness evaluation method for an anti-symmetric coupling system according to a preferred embodiment of the present invention;
[0043] Figure 5 FIG. shows the system simulation models before and after adding the delay time to the servo static decoupling dynamics link of the system simulation model in Example 1;
[0044] Figure 6 FIG. shows the output curve of the pitch angular velocity obtained in Example 1;
[0045] Figure 7 FIG. shows the output curve of the yaw angular velocity obtained in Example 1;
[0046] Figure 8 FIG. shows a system simulation model in the robustness evaluation method for an anti-symmetric coupling system according to a preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0047] The present invention will be further described in detail below with reference to the drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become more clearly defined.
[0048] As used herein, the term "exemplary" means "serving as an example, embodiment, or illustration". Any embodiment described herein as "exemplary" is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless specifically noted.
[0049] A robustness evaluation method for an anti-symmetric coupling system provided by the present invention, as Figure 1 shown, includes the following steps:
[0050] S1. Build the system simulation model architecture, where the system simulation model includes an airframe dynamics link, a servo dynamics link, and a servo static decoupling dynamics link;
[0051] S2. Set the transfer functions of the servo dynamics link, the servo static decoupling dynamics link, and the airframe dynamics link in the system simulation model:
[0052] S3. Obtain the amplitude margin, phase margin, and amplitude crossover frequency at 0 dB of the system simulation model, and then obtain the pure delay time of the simulation system;
[0053] S4. Map the obtained pure delay time to the robustness evaluation of the system.
[0054] Preferably, there is also a step:
[0055] S5. Set time delay links in both the control input channel and its coupling channel of the simulation system. Use the bisection method to obtain the threshold of the time delay link according to the obtained pure delay time, and compare the delay time of the actual system with this threshold to determine the stability of the actual system.
[0056] In S1, the structure of the system simulation model is as Figure 2 shown,
[0057] wherein, the airframe dynamics link is used to simulate the motion state of the rolling aircraft during flight, including the position, speed, and attitude of the airframe, and provides the basic motion information of the airframe for the entire simulation system.
[0058] In the present invention, the specific structure of the airframe dynamics link is not limited, and those skilled in the art can set it according to the structure of the actual rolling aircraft to be simulated.
[0059] The servo static decoupling dynamics link is used to decouple the coupled rudder deflection commands. The decoupled rudder deflection commands will be used in the servo dynamics link to drive the servo to generate the desired control torque.
[0060] Further, the rudder deflection commands include a pitch angle command and a yaw angle command.
[0061] Further, as Figure 3 shown, the servo static decoupling dynamics link includes a main channel and a coupling channel. The main channel generates the desired control torque according to the pitch angle command or the yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or the pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the output of the link.
[0062] The servo dynamics link is used to simulate the dynamic response process of the servo after receiving a control command, including the deflection angle and deflection speed of the servo, providing a control torque for the airframe, and transmitting the simulated parameters to the airframe dynamics link as the input parameters of the airframe dynamics link.
[0063] Preferably, as Figure 4 shown, the servo dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to the pitch angle command or yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the output of the link.
[0064] In S2, a quasi-airframe coordinate system is established, and the transfer functions of the servo static decoupling dynamics link and the servo dynamics link are obtained in the quasi-airframe coordinate system.
[0065] The quasi-airframe coordinate system Ox4y4z4 is as follows: The origin O is taken as the center of mass of the aircraft; The Ox4 axis coincides with the longitudinal axis of the airframe, and the direction pointing to the head of the airframe is positive; The Oy4 axis is located in the vertical plane containing the longitudinal axis of the airframe and is perpendicular to the Ox4 axis, and the direction pointing upward is positive; The Oz4 axis forms a right-handed coordinate system with the other two axes.
[0066] Furthermore, the conversion relationship between the equivalent rudder deflection angle in the quasi-airframe coordinate system and the rudder command in the airframe coordinate system is:
[0067]
[0068] where is the rudder deflection angle command in the airframe coordinate system, is the equivalent rudder deflection angle command in the quasi-airframe coordinate system, δ y (t) is the equivalent pitch angle command, δ z (t) is the equivalent yaw angle command.
[0069] In the airframe coordinate system, the transfer function G act (s) of the dynamic process of the servo can be expressed as
[0070]
[0071] where T s is the time constant of the servo, which is the reciprocal of the natural frequency of the servo, μ s is the damping coefficient of the servo, and s is the transfer parameter.
[0072] According to the conversion relationship between the quasi-airframe coordinate system and the airframe coordinate system, the transfer function G s (s) of the main channel of the servo dynamics link in the quasi-airframe coordinate system is:
[0073]
[0074] Among them, ω x represents the roll angular velocity of the aircraft.
[0075] Preferably, the transfer function of the main channel of the servo dynamics link in the quasi-body coordinate system is also simplified to reduce the amount of calculation and improve the calculation speed.
[0076] More preferably, during the rotation of the rolling aircraft, the rotational angular velocity ω x of the rolling aircraft can be regarded as a constant. Then, the transfer function G s (s) of the main channel of the simplified servo dynamics link is:
[0077]
[0078] In a preferred embodiment, the transfer function of the coupling channel of the servo dynamics link in the quasi-body coordinate system is set as:
[0079]
[0080] Preferably, the transfer function of the coupling channel of the servo dynamics link in the quasi-body coordinate system is also simplified to reduce the amount of calculation and improve the calculation speed.
[0081] More preferably, the transfer function of the simplified coupling channel of the servo dynamics link is expressed as:
[0082]
[0083] Furthermore, in the quasi-body coordinate system, the equivalent transfer function matrix G(s) of the servo dynamics is:
[0084]
[0085] It is an anti-symmetric link.
[0086] Preferably, the transfer function G sd (s) of the main channel of the static decoupling dynamics link of the servo is set as:
[0087]
[0088] Preferably, the transfer function G scod (s) of the coupling channel of the static decoupling dynamics link of the servo is set as:
[0089]
[0090] According to the present invention, the body dynamics link is set in the body coordinate system.
[0091] Preferably, the transfer function G m (s) of the body dynamics link is set as:
[0092]
[0093] where K θ represents the body gain, T α is the time constant of the body dynamics, τ m is the time constant of the natural frequency of the system, and μ m is the damping ratio of the body dynamics.
[0094] In S3, the Bode plot analysis method is used to obtain the amplitude margin, phase margin and 0dB amplitude crossover frequency of the system simulation model.
[0095] The Bode plot analysis method is a commonly used method for system stability analysis, and its specific process will not be elaborated in this invention.
[0096] Furthermore, in this invention, by disconnecting the transfer connection before the static decoupling dynamics link of the servo, the amplitude margin, phase margin and 0dB amplitude crossover frequency of the system simulation model are obtained by using the Bode plot analysis method.
[0097] According to this invention, the pure delay time of the simulation system is expressed as:
[0098]
[0099] where τ represents the pure delay time, Gm represents the amplitude margin, Pm represents the phase margin, and W cp represents the 0dB amplitude crossover frequency.
[0100] The pure delay time obtained in this invention is the maximum tolerable value of the system at the single-channel servo link.
[0101] In S4, the length of the obtained pure delay time is used as the evaluation criterion for the system robustness. The longer the pure delay time, the better the robustness of the system; conversely, the shorter the pure delay time, the worse the robustness of the system.
[0102] In this invention, the specific manner of the mapping is not limited, and those skilled in the art can freely set it according to actual needs. For example, for a roll aircraft with a specific structure, a specific threshold is set. When the obtained pure delay time is greater than the threshold, it is considered that the roll aircraft has good robustness; when the obtained pure delay time is less than the threshold, it is considered that the roll aircraft has poor robustness.
[0103] In S5, preferably, the time delay link of the control input channel of the simulation system is the same as the time delay link of its coupling channel.
[0104] The dichotomy method is a common solution method in control systems and will not be elaborated in this invention.
[0105] In the actual control system of an aircraft, there is a certain physical delay from the control input to the servo action, that is, there is also a time delay in the coupling channel of the control input channel. As Figure 8 shown, in this invention, by adding the same time delay to the control input channel and the coupling channel, the physical delay can be simulated, making the control system closer to the actual physical process.
[0106] Based on the pure delay time of the maximum tolerable value of the system at the single-channel servo link, by solving with the dichotomy method, the maximum delay threshold of a single channel when the system is critically stable can be obtained. Comparing the delay time of the actual system with this threshold, when the delay time is less than the threshold, it indicates that the system is stable, otherwise it indicates that the system is unstable, thereby determining the stability of the actual system.
[0107] Embodiment
[0108] Embodiment 1
[0109] For a certain rolling aircraft, a robustness evaluation experiment is carried out, including the following steps:
[0110] S1. Build the system simulation model architecture, and the system simulation model includes the airframe dynamics link, the servo dynamics link, and the servo static decoupling dynamics link;
[0111] S2. Set the transfer functions of the servo dynamics link, the servo static decoupling dynamics link, and the airframe dynamics link in the system simulation model:
[0112] S3. Obtain the amplitude margin, phase margin, and amplitude crossover frequency at 0 dB of the system simulation model, and then obtain the pure delay time of the simulation system;
[0113] The servo static decoupling dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to the pitch angle command or yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the link output;
[0114] The servo dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to the pitch angle command or yaw angle command. The coupling channel generates a compensation command according to the yaw angle command or pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the link output.
[0115] In S2, establish a quasi-body coordinate system, and obtain the transfer functions of the servo static decoupling dynamics link and the servo dynamics link in the quasi-body coordinate system.
[0116] The transfer function G of the main channel of the servo dynamics link s (s) is set as:
[0117]
[0118] The transfer function G of the coupling channel of the servo dynamics link sco (s) is set as:
[0119]
[0120] The transfer function G of the main channel of the static decoupling dynamics link of the servo sd (s) is set as:
[0121]
[0122] The transfer function G of the coupling channel of the static decoupling dynamics link of the servo scod (s) is set as:
[0123]
[0124] The transfer function G of the airframe dynamics link m (s) is set as:
[0125]
[0126] Among them, the time constant T of the servo s is 0.05 s, the damping coefficient μ of the servo s is 0.9, the roll angular rate ω x is 40 rad / s, the gain K θ is 1.2, the time constant T α is 1.25, the time constant τ m is The damping ratio μ m is 0.1.
[0127] In S3, the Bode plot analysis method is used to obtain the amplitude margin, phase margin and amplitude crossover frequency at 0 dB of the system simulation model. The obtained amplitude margin Gm = 25.7 dB (at 200 rad / s), phase margin Pm = 83.9 deg (at 24.2 rad / s) and amplitude crossover frequency W cp = 24.2132 rad / s, and then the pure delay time can be calculated
[0128]
[0129] To determine whether the pure delay time obtained from the experiment is the maximum tolerable value of the system at the single-channel servo link, the delay time is added before the static decoupling dynamics link of the servo in the system simulation model, as Figure 5 shown. The simulation system is run, and the output curve of the pitch angular velocity is as Figure 6 shown, and the output curve of the yaw angular velocity is as Figure 7 shown.
[0130] From Figure 6 , Figure 7 , it can be seen that the output curves of the pitch angular velocity and the yaw angular velocity are both equi-amplitude oscillations, indicating that the system simulation is in a critically stable state, that is, it shows that the obtained pure delay time is the maximum tolerable value of the system at the single-channel servo link. Then, the longer the pure delay time, the stronger the robustness of the corresponding system, thus indicating that this method can effectively evaluate the robustness of the system.
[0131] The present invention has been described above in combination with preferred embodiments, but these embodiments are only exemplary and only serve an illustrative role. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.
Claims
1. A robustness evaluation method for an anti-symmetric coupling system, characterized in that, It includes the following steps: S1. Build the system simulation model architecture, where the system simulation model includes an airframe dynamics link, a servo dynamics link, and a servo static decoupling dynamics link; S2. Set the transfer functions of the servo dynamics link, the servo static decoupling dynamics link, and the airframe dynamics link in the system simulation model: S3. Obtain the amplitude margin, phase margin, and amplitude crossover frequency at 0 dB of the system simulation model, and then obtain the pure delay time of the simulation system; S4. Map the obtained pure delay time to the robustness evaluation of the system.
2. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that the servo static decoupling dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to a pitch angle command or a yaw angle command. The coupling channel generates a compensation command according to a yaw angle command or a pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the output of the link.
3. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that the servo dynamics link includes a main channel and a coupling channel. The main channel generates a desired control torque according to a pitch angle command or a yaw angle command. The coupling channel generates a compensation command according to a yaw angle command or a pitch angle command to correct the control torque output by the main channel, and uses the corrected command as the output of the link.
4. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that in S2, establish a quasi-airframe coordinate system, and obtain the transfer functions of the servo static decoupling dynamics link and the servo dynamics link in the quasi-airframe coordinate system, where the quasi-airframe coordinate system Ox4y4z4 is: the origin O is taken as the center of mass of the aircraft; the Ox4 axis coincides with the longitudinal axis of the airframe, and the direction pointing to the head of the airframe is positive; the Oy4 axis is located in the vertical plane containing the longitudinal axis of the airframe and is perpendicular to the Ox4 axis, and the direction pointing upward is positive; the Oz4 axis forms a right-handed coordinate system with the other two axes.
5. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that The transfer function G of the main channel of the servo dynamics link s (s) is set as: The transfer function G of the coupling channel of the servo dynamics link sco (s) is set as: Among them, ω x represents the roll angular velocity of the aircraft.
6. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that Simplify the transfer function of the servo dynamics link. The transfer function G s (s) of the main channel of the simplified servo dynamics link is as follows: The transfer function G of the coupling channel of the simplified servo dynamics link sco (s) is expressed as:
7. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that The transfer function G of the main channel of the static decoupling dynamics link of the servo sd (s) is set as follows: The transfer function G of the coupling channel of the static decoupling dynamic link of the servo scod (s) is set as:
8. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that The transfer function G m (s) of the described body dynamics link is set as: Among them, K θ represents the body gain, T α is the time constant of the body dynamics, τ m is the time constant of the system natural frequency, μ m is the damping ratio of the body dynamics.
9. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that in S3, use the Bode plot analysis method to obtain the amplitude margin, phase margin, and amplitude crossover frequency at 0 dB of the system simulation model.
10. The robustness evaluation method for an anti-symmetric coupling system according to claim 1, characterized in that the pure delay time of the simulation system is expressed as: Among them, τ represents the pure delay time, Gm represents the amplitude margin, Pm represents the phase margin, and W cp represents the amplitude crossover frequency at 0 dB.