A Frequency Domain Analysis Method for Adaptive Augmented Controllers for Launch Vehicle Applications

Abstract

This invention discloses a frequency domain analysis method for an adaptive augmented controller (AAC) for launch vehicle applications, comprising: further simplifying the nonlinear damping module of an improved AAC controller to obtain a frequency domain model of the AAC controller; inputting a sinusoidal characteristic signal to obtain an analytical solution for the AAC controller output value; removing higher-order harmonics from the analytical solution to obtain an output signal in the same frequency band as the input signal; using the frequency domain response of the integrator in the low-frequency band as an integral filter to simplify the output signal, and using the linear part of the result as the frequency domain analytical model of the AAC controller; evaluating the accuracy and applicability of the AAC controller frequency domain analytical model through frequency sweep testing, and giving the applicable range of the AAC controller; integrating the obtained AAC controller frequency domain analytical model into the launch vehicle control model, and improving the frequency domain margin of the launch vehicle control system in both high-frequency and low-frequency bands by adjusting the control parameters.

Description

Technical Field

[0001] This invention relates to an adaptive augmented controller frequency domain analysis method for launch vehicle applications, belonging to the field of spacecraft control technology. Background Technology

[0002] Due to the harsh flight environment and extremely high reliability requirements, the development of control systems for large launch vehicles generally relies on rigorous forward design and stability assessment. In the application of Adaptive Augmentation Control (AAC) to launch vehicle control systems, simplifying its nonlinear structure and obtaining a reasonable and reliable frequency domain model of the AAC controller through mathematical processing are prerequisites for conducting stability assessments and margin calculations.

[0003] To date, frequency domain analysis of AAC controllers remains a global academic challenge. Scholars generally employ methods based on describing functions to obtain the AAC frequency domain response and rely on frequency sweeping and mechanistic analysis to perform qualitative analysis of the AAC controller's frequency domain output. This method has poor engineering adaptability and is very inefficient. In publicly available domestic literature, no literature has yet proposed a frequency domain analytical model for AAC controllers and applied it to the development of launch vehicle control systems. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a frequency domain analysis method for adaptive augmented controllers for launch vehicle applications. By combining local linearization and the describing function method, the frequency domain model of the AAC controller is obtained, thereby solving the problem of frequency domain analysis and stability evaluation of adaptive augmented controllers for large launch vehicle applications, achieving the effects of simple calculation, reliable accuracy, and flexible and convenient engineering applications.

[0005] The technical solution of this invention is: an adaptive augmented controller frequency domain analysis method for launch vehicle applications, comprising:

[0006] The frequency domain model of the adaptive augmenting controller is obtained by adjusting the nonlinear damping module of the improved adaptive augmenting controller; the adaptive augmenting controller is denoted as the AAC controller.

[0007] By inputting a sinusoidal characteristic signal into the frequency domain model of the AAC controller, the output value k of the AAC controller can be obtained. t The analytical solution; the analytical solution of the AAC controller output value is used to remove higher-order harmonics and obtain the output signal in the same frequency band as the input signal;

[0008] Using the frequency domain response of the integrator in the low-frequency band as an integral filter, the output signal is adjusted based on its characteristic that the amplitude approaches positive infinity at 0Hz. At the same time, combined with the output limiting of the AAC controller, the results are organized into a nonlinear part and a linear part. After confirming the stability of the nonlinear part, the remaining linear part is the frequency domain analytical model of the AAC controller.

[0009] The accuracy and applicability of the frequency domain analytical model of the AAC controller are evaluated through frequency sweep testing, and the applicability of the AAC controller is given according to the characteristics of the controlled object.

[0010] The obtained frequency domain analytical model of the AAC controller was integrated into the launch vehicle control model. By adjusting the control parameters, the frequency domain margin of the launch vehicle control system was improved in both high and low frequency bands.

[0011] The preferred mathematical formula for the improved adaptive augmentation controller is:

[0012]

[0013] k t =k a +k0

[0014] Where, k t To adapt the final output coefficients, k a k is the integral part of the output coefficients, and k0 is the constant part of the output coefficients; For k a The derivative of k tmax e represents the upper limit of the output coefficient amplitude. r As the reference model deviation value, y s Here are the filter values ​​for the spectral damper; a is the weight of the error term, c is the weight of the damping term, and β is the weight of the regression term; k tmin ,k tmax These are the upper and lower limits of the AAC controller output, respectively.

[0015] Preferably, the nonlinear damping module in the mathematical formula of the improved adaptive augmentation controller is -c·k t and The method for adjusting the nonlinear damping module is as follows:

[0016]

[0017] Wherein, γ1 and γ2 are constant coefficients;

[0018] The mathematical formula for the adaptive augmentation controller after adjusting the nonlinear damping module is as follows:

[0019]

[0020] The above formula is the frequency domain model of the AAC controller.

[0021] Preferably, a sinusoidal characteristic signal i = A·sin(ωt) is input to the frequency domain model of the adaptive augmented controller to obtain the AAC controller output value k. t The analytical solution is:

[0022]

[0023] Where A is the amplitude of the input signal, ω is the frequency of the input signal, t is time, and γ1 and γ2 are constant coefficients. For the frequency domain response of the integrator in the extremely low frequency range, A Gt A represents the high-pass filter amplitude of the AAC controller. Dt This refers to the low-pass filter amplitude of the AAC controller. This represents the amplitude response of the low-pass filter in the extremely low frequency range. This is the filtering phase of the low-pass filter. Here, A represents the high-pass filter phase, 'a' represents the error term weight, and A' represents the error term weight. G′ Let α be the frequency domain response of the integrator, and α be the weighting coefficient of the damping term of the AAC controller.

[0024] Preferably, the AAC controller output value k t The analytical solution removes higher-order harmonics, yielding an output signal in the same frequency band as the input signal, specifically:

[0025] The frequency domain model of the AAC controller and the output value k of the AAC controller are used to... t Multiplying the analytical solutions, ignoring harmonics above three times ω, we obtain the AAC controller output signal o:

[0026]

[0027] Where Q1 and Q2 are coefficients that are related to the frequency of the input signal, ω is the frequency of the input signal, and t is time.

[0028] Preferably, the frequency domain response of the integrator in the low-frequency band is used as an integral filter. Based on its characteristic that the amplitude approaches positive infinity at 0Hz, the output signal is adjusted. At the same time, combined with the output limiting of the AAC controller, the following is obtained:

[0029]

[0030] k t ∈[k tmin ,k tmax ]

[0031] Where Q1 and Q2 are coefficients, which are related to the frequency of the input signal, k tmin ,ktmax These represent the upper and lower limits of the AAC controller output amplitude, respectively, where A is the input signal amplitude, ω is the input signal frequency, t is time, and γ1 and γ2 are constant coefficients. For the frequency domain response of the integrator in the extremely low frequency range, A Dt This refers to the low-pass filter amplitude of the AAC controller. To represent the amplitude response of the low-pass filter in the extremely low frequency range, A Gt Here, α is the high-pass filter amplitude of the AAC controller, a is the error term weight, α is the damping term weight coefficient of the AAC controller, and k is the high-pass filter amplitude of the AAC controller. t is the output value of the AAC controller, and i is the sinusoidal characteristic signal input to the frequency domain model of the AAC controller.

[0032] Preferably, the nonlinear part is: A 2 It only generates additional amplitude and is not connected in series with other modules, and is represented as:

[0033] N(A)=A 2 , A>0.

[0034] Preferably, the linear part is an AAC controller frequency domain analytical model:

[0035]

[0036] Among them, F aac For the amplitude of the frequency domain analytical model, This represents the phase of the frequency domain analytical model.

[0037] Preferably, the results of the frequency sweep test are as follows:

[0038] The AAC controller experiences a gain transition from low to high frequency bands. At this gain transition point, the relative accuracy of the frequency domain analytical model is lower than that of other frequency bands. The remaining frequency bands are within the applicable range of the AAC controller.

[0039] The position of the gain inflection point can be adjusted by designing the AAC controller parameters.

[0040] Preferably, the frequency domain analytical model of the AAC controller is integrated into the launch vehicle control model. The control parameters that need to be adjusted include:

[0041] a: Increasing this value significantly increases the turning frequency;

[0042] α: Increasing this value significantly reduces the transition frequency;

[0043] A Gt Increasing this value slightly increases the inflection frequency.

[0044] A Dt Increasing this value slightly reduces the inflection frequency.

[0045] By first adjusting a and α, and then adjusting A Gt A Dt The approach of fine-tuning enables the design of an AAC controller based on frequency domain response.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] (1) The present invention obtains a frequency domain analytical model of the AAC controller, which is simple to calculate, intuitive and flexible in design, and reliable in accuracy.

[0048] (2) After frequency sweep verification and correction, the present invention corrects the accuracy and applicable boundaries of the frequency domain analytical model, so that the frequency domain model can accurately represent the characteristics of the AAC controller.

[0049] (3) This invention combines the AAC controller with the traditional control system, performs closed-loop design in the frequency domain, greatly improves design efficiency, and can accurately evaluate the improvement level of the AAC controller on the system control capability. Attached Figure Description

[0050] Figure 1 The curves represent the frequency domain analytical model of the AAC controller involved in this invention.

[0051] Figure 2 This is a comparison diagram between the frequency domain model of the AAC controller obtained by this invention and the traditional PD frequency domain model;

[0052] Figure 3 This is the low-frequency sweep result of the AAC controller according to the present invention;

[0053] Figure 4 This is the high-frequency sweep result of the AAC controller according to the present invention. Detailed Implementation

[0054] An adaptive augmented controller frequency domain analysis method for launch vehicle applications includes the following steps:

[0055] 1) The design is carried out using the mathematical formula of the improved adaptive augmentation controller, and the nonlinear damping module is further simplified to obtain the frequency domain model of the adaptive augmentation controller.

[0056] 2) Input a sinusoidal characteristic signal into the frequency domain model of the adaptive augmentation controller to obtain the output value k of the adaptive augmentation controller. t The analytical solution expression for the output value k of the adaptive augmentation controller; t The analytical solution is processed by neglecting higher-order harmonics to obtain an output signal in the same frequency band as the input signal;

[0057] 3) The frequency domain response of the integrator in the low-frequency band is used as an integral filter to further simplify the output signal. At the same time, the output limiting of the adaptive augmentation controller is considered to obtain the frequency domain analytical model of the AAC controller.

[0058] 4) Based on sinusoidal signal frequency sweep, the accuracy and applicability of the frequency domain analytical model are evaluated, and the applicability of the adaptive augmenting controller is given according to the characteristics of the controlled object.

[0059] 5) Integrate the obtained AAC controller frequency domain analytical model into the launch vehicle control model. By adjusting the amplitude and frequency of the input signal, control the frequency band position where the AAC controller frequency domain response changes from low-frequency characteristics to high-frequency characteristics. Thus, for a specific launch vehicle, design reasonable control parameters to reduce the adaptability of the launch vehicle control system in the high-frequency band and increase it in the low-frequency band, while increasing the rigidity and elasticity margins.

[0060] Referring to the accompanying drawings, the present invention provides a frequency domain analysis method for an adaptive augmentation control (AAC) for launch vehicle applications. The specific implementation steps are as follows:

[0061] In step 1), the design is carried out using the improved AAC controller mathematical formula, the specific formula of which is as follows:

[0062]

[0063] k t =k a +k0 (2)

[0064] Where, k t To adapt the final output coefficients, k a k is the integral part of the output coefficients, and k0 is the constant part of the output coefficients. For k a The derivative of k tmax e represents the upper limit of the output coefficient amplitude. r As the reference model deviation value, y s Here are the filter values ​​for the spectral damper. a is the weight of the error term, c is the weight of the damping term, and β is the weight of the regression term; k tmin ,k tmax These are the upper and lower limits of the AAC controller output, respectively.

[0065] c·k t There are two nonlinear damping modules, corresponding to k respectively. a The increasing and decreasing trends of [the variable / increase]. Using an improved AAC controller model, its nonlinearity can be reduced, making frequency domain analysis near the equilibrium position simpler.

[0066] Based on this, the two nonlinear damping modules in the above formula are further simplified, and the specific method is as follows:

[0067]

[0068] Where γ1 and γ2 are constant coefficients. After the above simplification, the mathematical formula for the AAC controller becomes as follows:

[0069]

[0070] Formula (5) is the frequency domain model of the adaptive augmentation controller.

[0071] In step 2), the frequency domain model is solved mathematically to obtain the analytical solution of the adaptive augmentation controller's frequency domain model. Furthermore, based on the physical mechanism, the singular parts of the analytical solution are corrected. Specifically:

[0072] First, based on the simplified formula, the derivation is performed using the describing function method. Assume the frequency domain input i of the AAC controller is:

[0073] i=A·sin(ωt) (6)

[0074] Where A is the amplitude of the input signal, ω is the frequency of the input signal, and t is time. Substituting the above formula (6) into the AAC frequency domain model (5), the output value k of the AAC controller can be obtained through mathematical derivation. t The analytical solution expression is shown below:

[0075]

[0076] In the above formula, This represents the frequency domain response of the integrator in the extremely low frequency range, typically taken as 10. 5 The maximum value of the order of magnitude. A Dt The low-pass filter amplitude of the AAC controller, A Gt This refers to the high-pass filter amplitude of the AAC controller. This is the filtering phase of the low-pass filter. This is the filtering phase of the high-pass filter.

[0077] Multiplying formula (7) by formula (5) for the input signal i yields the output signal o of the AAC controller. Ignoring harmonics above three times ω and further simplifying it, we obtain:

[0078] o=Q1 sin(ωt)+Q2cos(ωt) (8)

[0079] Where Q1 and Q2 are coefficients, which are related to the frequency of the input signal. Using the auxiliary angle formula, the above result can be transformed into:

[0080]

[0081] The final frequency domain amplitude of the AAC controller can be obtained. The phase is arctan(Q2 / Q1).

[0082] Where Q1 and Q2 are coefficients, their expressions are:

[0083]

[0084] After processing, the output signal expression of this stage can be used to obtain the AAC frequency domain analytical model.

[0085] In step 3), k tmin ,k tmax These are the upper and lower limits of the AAC controller output, respectively, and the adaptive augmentation controller output limit k is set accordingly. tmin ,k tmax By incorporating formula (9), the output signal of the stage is further modified, and can be rewritten as the product of a linear part and a nonlinear part. Limit cycle analysis is then performed on the nonlinear part of the product. Specifically:

[0086] Using A G 0 ′ (The frequency domain response of the integrator in the extremely low frequency band) As an integral filter, its amplitude approaches positive infinity at 0Hz. Formula (9) is further simplified, and the output limiting of the AAC controller is taken into consideration, finally obtaining:

[0087]

[0088] Meanwhile, for the nonlinear module A in the AAC process... 2 It is assumed that it only generates additional amplitude and does not have a series module, and the formula is:

[0089] N(A)=A 2 A>0 (12)

[0090] After limit cycle analysis based on classical control theory, it is concluded that this module only generates stable limit cycles, with minimal impact on the system. The remaining linear part is an AAC frequency domain analytical model.

[0091]

[0092] Among them, F aac For the amplitude of the frequency domain analytical model, This represents the phase of the frequency domain analytical model.

[0093] In step 4), based on the frequency sweep of the sinusoidal signal, the accuracy and applicability of the frequency domain analytical model formula (13) are evaluated, and the applicability of the frequency domain analytical model is given according to the characteristics of the controlled object.

[0094] Specifically:

[0095] By changing the amplitude A and frequency ω of the input signal i, a frequency sweep test was performed on the AAC frequency domain analytical model formula (13). The frequency sweep revealed that the AAC controller's frequency domain characteristic is a forward gain, which is greater than 1 in the low-frequency range and less than 1 in the high-frequency range; simultaneously, the AAC controller generates almost no phase. The frequency sweep results are as follows: Figure 3 and Figure 4 As shown, in the low-frequency range, the input signal is greater than the output signal, indicating that the AAC gain is greater than 1; in the high-frequency range, the input signal is less than the output signal, indicating that the AAC gain is less than 1. The response curves for different frequency bands can be summarized as follows: Figure 1 As shown in the diagram, it can be seen that the AAC controller experiences a gain transition during the shift from low to high frequencies. The relative accuracy of the frequency domain analytical model is lower at this transition point. Apart from this point, the remaining frequency bands are within the applicable range of the AAC controller. The location of this transition point can be artificially designed by adjusting the AAC controller parameters; therefore, the applicable range of the AAC controller should be adjusted according to the task requirements.

[0096] In step 5), the analytical frequency domain model formula (13) is integrated into the launch vehicle control model. It is found that after deformation, the AAC controller can be equivalently added to the control system as a series link. This can simultaneously increase the rigidity and elasticity margin of the traditional launch vehicle system. By analyzing the design parameters a, α, and A... Gt A Dt Adjustments can be made to artificially control the frequency band where the AAC controller's frequency domain response transitions from low-frequency to high-frequency characteristics, thereby allowing for the design of reasonable control parameters a, α, and A for a specific launch vehicle. Gt A Dt Based on the above design concept, frequency domain analysis is performed on the device with adaptive augmented control to assist in the design of control parameters.

[0097] The final result of integrating the AAC controller into the frequency domain model is as follows: Figure 2 As shown, due to the special frequency domain characteristics of the AAC controller, compared with the traditional PD controller, the frequency domain margin of the launch vehicle control system is improved in both high and low frequency bands, thereby improving the overall control quality of the rocket.

[0098] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A frequency domain analysis method for an adaptive augmented controller for launch vehicle applications, characterized in that... include: By adjusting the nonlinear damping module of the improved adaptive augmentation controller, the frequency domain model of the adaptive augmentation controller is obtained. The adaptive augmentation controller is referred to as the AAC controller; By inputting a sinusoidal characteristic signal into the frequency domain model of the AAC controller, the output value of the AAC controller can be obtained. The analytical solution; The higher-order harmonics are removed from the analytical solution of the AAC controller output value to obtain an output signal with the same frequency band as the input signal. Using the frequency domain response of the integrator in the low-frequency band as an integral filter, the output signal is adjusted based on its characteristic that the amplitude approaches positive infinity at 0Hz. At the same time, combined with the output limiting of the AAC controller, the results are organized into a nonlinear part and a linear part. After confirming the stability of the nonlinear part, the remaining linear part is the frequency domain analytical model of the AAC controller. The accuracy and applicability of the frequency domain analytical model of the AAC controller are evaluated through frequency sweep testing, and the applicability of the AAC controller is given according to the characteristics of the controlled object. The obtained frequency domain analytical model of the AAC controller is integrated into the launch vehicle control model. By adjusting the control parameters, the frequency domain margin of the launch vehicle control system is improved in both high and low frequency bands. Using the integrator's frequency domain response in the low-frequency range as an integral filter, and adjusting the output signal based on its amplitude approaching positive infinity at 0Hz, while simultaneously combining this with the output limiting of the AAC controller, we obtain: in, , This is a coefficient that is related to the frequency of the input signal. These are the upper and lower limits of the AAC controller output, respectively. For the input signal amplitude, For input signal frequency, For time, and These are constant coefficients. This represents the frequency domain response of the integrator in the extremely low frequency range. This refers to the low-pass filter amplitude of the AAC controller. This represents the amplitude response of the low-pass filter in the extremely low frequency range. This refers to the high-pass filter amplitude of the AAC controller. For the error term weights, For the AAC controller damping term weighting coefficient, For the output value of the AAC controller, To input a sinusoidal characteristic signal into the frequency domain model of the AAC controller; The nonlinear part is: It only generates additional amplitude and is not connected in series with other modules, and is represented as: ； The linear part is the frequency domain analytical model of the AAC controller: in, For the amplitude of the frequency domain analytical model, This represents the phase of the frequency domain analytical model.

2. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 1, characterized in that: The mathematical formula for the improved adaptive augmentation controller is: in, To adapt the final output coefficients, This is the integral part of the output coefficients. This refers to the constant part of the output coefficients; for The derivative, This is the upper limit of the output coefficient amplitude. As a reference model deviation value, This is the filter value for the spectrum damper; For the error term weights, For the weight of the damping term, The weights of the regression terms; These are the upper and lower limits of the AAC controller output, respectively.

3. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 2, characterized in that: The nonlinear damping module in the mathematical formula of the improved adaptive augmented controller is: and The method for adjusting the nonlinear damping module is as follows: in, , These are constant coefficients; The mathematical formula for the adaptive augmentation controller after adjusting the nonlinear damping module is as follows: The above formula is the frequency domain model of the AAC controller.

4. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 1, characterized in that: Input a sinusoidal characteristic signal to the frequency domain model of the adaptive augmented controller. Obtain the output value of the AAC controller. The analytical solution is: in, For the input signal amplitude, For input signal frequency, For time, and These are constant coefficients. This represents the frequency domain response of the integrator in the extremely low frequency range. This refers to the high-pass filter amplitude of the AAC controller. This refers to the low-pass filter amplitude of the AAC controller. This represents the amplitude response of the low-pass filter in the extremely low frequency range. This is the filtering phase of the low-pass filter. This is the filtering phase of the high-pass filter. For the error term weights, This is the frequency domain response of the integrator. This represents the weighting coefficient of the damping term in the AAC controller.

5. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 1, characterized in that: AAC controller output value The analytical solution removes higher-order harmonics, yielding an output signal in the same frequency band as the input signal, specifically: The frequency domain model of the AAC controller and the output value of the AAC controller. Multiply the analytical solutions, ignoring the factor of three. The above harmonics are used to obtain the output signal of the AAC controller. : in, , This is a coefficient that is related to the frequency of the input signal. For input signal frequency, For time.

6. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 1, characterized in that: The results of the frequency sweep test are as follows: The AAC controller experiences a gain transition from low to high frequency bands. At this gain transition point, the relative accuracy of the frequency domain analytical model is lower than that of other frequency bands. The remaining frequency bands are within the applicable range of the AAC controller. The position of the gain inflection point can be adjusted by designing the AAC controller parameters.

7. The frequency domain analysis method for an adaptive augmented controller for launch vehicle applications according to claim 1, characterized in that: When integrating the AAC controller frequency domain analytical model into the launch vehicle control model, the control parameters that need to be adjusted include: Increasing the value significantly increases the turning frequency. Increasing the frequency of transitions significantly reduces the frequency of transitions. Increasing the value slightly increases the turning frequency. Increasing the frequency of transitions slightly decreases the frequency of transitions. By adjusting first , After adjustment , The approach of fine-tuning enables the design of an AAC controller based on frequency domain response.

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