Adaptive augmentation controller frequency domain analysis method for carrier rocket application

Abstract

The invention discloses a carrier rocket application-oriented adaptive augmented controller frequency domain analysis method, which comprises the following steps of: further simplifying a nonlinear damping module of an improved AAC controller to obtain a frequency domain model of the AAC controller, inputting a sine characteristic signal into the frequency domain model to obtain an analytical solution of an output value of the AAC controller, and removing high-order harmonics from the analytical solution to obtain a frequency domain model of the AAC controller. Obtaining an output signal with the same frequency band as the input signal; frequency domain response of an integrator at a low frequency band is used as an integral filter to simplify an output signal, and a linear part of a result is used as a frequency domain analysis model of the AAC controller; the precision and the application range of the AAC controller frequency domain analysis model are evaluated through a frequency sweep test, and the application range of the AAC controller is given; the obtained AAC controller frequency domain analysis model is integrated into a carrier rocket control model, and the frequency domain margin of a carrier rocket control system is improved at high frequency and low frequency by adjusting control parameters.

Description

Technical Field

[0001] The invention relates to a frequency domain analysis method of an adaptive augmented controller for launch vehicle application, belonging to the technical field of spacecraft control. Background Art

[0002] Due to the harsh flight environment and extremely high reliability requirements, the development of control systems for large launch vehicles generally requires rigorous forward design and stability assessment. In the process of applying the adaptive augmentation controller (AAC) to the launch vehicle control system, how to simplify its nonlinear structure and obtain a reasonable and reliable AAC controller frequency domain model through mathematical processing is a prerequisite for stability assessment and margin calculation.

[0003] Up to now, the frequency domain analysis technology of AAC controller is still a worldwide academic problem. Scholars generally use the method based on description function to obtain the frequency domain response of AAC, and rely on frequency sweep and mechanism analysis to conduct qualitative analysis on the frequency domain output of AAC controller. This method has poor engineering adaptability and low efficiency. In the domestic public data, no literature has been found to propose the frequency domain analytical model of AAC controller and apply it to the field of launch vehicle control system development. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, to provide a frequency domain analysis method for an adaptive augmented controller for launch vehicle applications, to obtain a frequency domain model of the AAC controller by combining local linearization with a describing function method, thereby solving the frequency domain analysis and stability evaluation problems of an adaptive augmented controller for large launch vehicle applications, and achieving an engineering application effect with simple calculation, reliable accuracy, and flexibility and convenience.

[0005] The technical solution of the present invention is: a frequency domain analysis method of an adaptive augmented controller for launch vehicle application, comprising:

[0006] The nonlinear damping module of the improved adaptive augmented controller is adjusted to obtain a frequency domain model of the adaptive augmented controller; the adaptive augmented controller is denoted as an AAC controller;

[0007] Input the sinusoidal characteristic signal into the frequency domain model of the AAC controller to obtain the output value k of the AAC controller t The analytical solution of the AAC controller output value is used to remove high-order harmonics and obtain an output signal in the same frequency band as the input signal;

[0008] The frequency domain response of the integrator in the low frequency band is used as an integral filter. The output signal is adjusted based on the characteristic that its amplitude approaches positive infinity at 0Hz. At the same time, combined with the output limiting of the AAC controller, the obtained result is sorted 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 tests, 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 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.

[0011] Preferably, the mathematical formula of the improved adaptive augmentation controller is:

[0012]

[0013] k t =k a +k0

[0014] Among them, k t is the adaptive final output coefficient, k a is the integral part of the output coefficient, and k0 is the constant part of the output coefficient; k a The derivative of k tmax is the upper limit of the output coefficient, e r is the reference model deviation value, y s is the filter value of the spectrum 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 They are the upper and lower limit amplitudes of the AAC controller output respectively.

[0015] Preferably, the nonlinear damping module in the mathematical formula of the improved adaptive augmented controller is -c·k t and The method to adjust the nonlinear damping module is:

[0016]

[0017] Among them, γ1 and γ2 are constant coefficients;

[0018] The mathematical formula of the adaptive augmented 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 into 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 input signal amplitude, ω is the input signal frequency, t is the time, γ1 and γ2 are constant coefficients, is the frequency domain response of the integrator in the very low frequency band, A Gt A is the filtering amplitude of the AAC controller high-pass filter, A Dt is the filtering amplitude of the low-pass filter of the AAC controller, is the amplitude response of the low-pass filter in the very low frequency band, is the low-pass filter phase, is the filtering phase of the high-pass filter, a is the error term weight, A G′ is the frequency domain response of the integrator, and α is the weight coefficient of the damping term of the AAC controller.

[0024] Preferably, the AAC controller output value k t The analytical solution removes high-order harmonics and obtains 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 t Multiply the analytical solution of , ignoring harmonics above three times ω, and get the AAC controller output signal o:

[0026]

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

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

[0029]

[0030] k t ∈[k tmin ,k tmax ]

[0031] Among them, Q1 and Q2 are coefficients, which are related to the frequency of the input signal, and k tmin ,ktmax are the upper and lower limit amplitudes of the AAC controller output, respectively; A is the input signal amplitude, ω is the input signal frequency, t is the time, γ1 and γ2 are constant coefficients, is the frequency domain response of the integrator in the very low frequency band, A Dt is the filtering amplitude of the low-pass filter of the AAC controller, is the amplitude response of the low-pass filter in the very low frequency band, A Gt is the filtering amplitude of the AAC controller high-pass filter, a is the error term weight, α is the AAC controller damping term weight coefficient, k 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 , only produces additional amplitude and no modules are connected in series, expressed as:

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

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

[0035]

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

[0037] Preferably, the result of the frequency sweep test is:

[0038] The AAC controller has a gain transition in the transition stage from the low frequency band to the high frequency band. The relative accuracy of the frequency domain analytical model at this gain transition is lower than that of other frequency bands. The remaining frequency bands are all within the applicable range of the AAC controller.

[0039] The position of the gain turn 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, and the control parameters that need to be adjusted include:

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

[0042] α: If this value increases, the turning frequency will be greatly reduced;

[0043] A Gt :When this value increases, the turning frequency increases slightly;

[0044] A Dt :When this value increases, the turning frequency decreases slightly;

[0045] By adjusting a and α first, then adjusting A Gt , A Dt The idea of ​​refinement can realize the design of 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 has simple calculation, intuitive and flexible design, and reliable accuracy.

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

[0049] (3) The present invention combines the AAC controller with the traditional control system and performs closed-loop design in the frequency domain, which greatly improves the design efficiency and can accurately evaluate the improvement level of the AAC controller on the system control capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a frequency domain analytical model curve of the AAC controller involved in the present invention;

[0051] Figure 2 A comparison diagram of the AAC controller frequency domain model obtained by the present invention and the traditional PD frequency domain model;

[0052] Figure 3 The low frequency sweep result of the AAC controller of the present invention;

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

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

[0055] 1) The improved adaptive augmented controller mathematical formula is used to carry out the design, and the nonlinear damping module is further simplified to obtain the frequency domain model of the adaptive augmented controller;

[0056] 2) Input the sinusoidal characteristic signal into the frequency domain model of the adaptive augmented controller to obtain the output value k of the adaptive augmented controller t The analytical solution expression of the adaptive augmented controller output value k t The analytical solution of is processed by ignoring the high-order harmonics to obtain an output signal with 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 the sinusoidal signal frequency sweep, the accuracy and applicability of the frequency domain analytical model are evaluated, and the applicability of the adaptive augmented controller is given according to the characteristics of the controlled object;

[0059] 5) The obtained AAC controller frequency domain analytical model is integrated into the launch vehicle control model. By adjusting the amplitude and frequency of the input signal, the frequency band position where the AAC controller frequency domain response changes from low-frequency characteristics to high-frequency characteristics is controlled. Therefore, for a specific launch vehicle, reasonable control parameters are designed 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 rigid body and elastic margin.

[0060] In conjunction with the accompanying drawings, the present invention provides an adaptive augmentation controller (AAC) frequency domain analysis method for launch vehicle applications, and the specific implementation steps are as follows:

[0061] In step 1), the improved AAC controller mathematical formula is used for design, and its specific formula is as follows:

[0062]

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

[0064] Among them, k t is the adaptive final output coefficient, k a is the integral part of the output coefficient, and k0 is the constant part of the output coefficient. k a The derivative of k tmax is the upper limit of the output coefficient, e r is the reference model deviation value, y s is the filter value of the spectrum 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 They are the upper and lower limit amplitudes of the AAC controller output respectively.

[0065] c.k t are two nonlinear damping modules, corresponding to k a The improved AAC controller model can reduce its nonlinearity and make it easier to perform frequency domain analysis near the equilibrium position.

[0066] On this basis, the two nonlinear damping modules in the above formula are further simplified as follows:

[0067]

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

[0069]

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

[0071] In step 2), the frequency domain model is solved by mathematical processing to obtain the analytical solution of the frequency domain model of the adaptive augmented controller, and the singular part of the analytical solution is corrected based on the physical mechanism. Specifically:

[0072] First, based on the simplified formula, the describing function method is used for derivation, assuming that the frequency domain input i of the AAC controller is:

[0073] i=A·sin(ωt) (6)

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

[0075]

[0076] In the above formula, is the frequency domain response of the integrator in the very low frequency band, generally 10 5 The maximum value of the order of magnitude. Dt is the filtering amplitude of the low-pass filter of the AAC controller, A Gt is the filtering amplitude of the AAC controller high-pass filter, is the low-pass filter phase, is the high-pass filter phase.

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

[0078] o=Q1 sin(ωt)+Q2cos(ωt) (8)

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

[0080]

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

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

[0083]

[0084] After the output signal expression of this link is processed, the AAC frequency domain analytical model can be obtained.

[0085] In step 3), k tmin ,k tmax The output limit k of the AAC controller is tmin ,k tmax By adding it to formula (9), the link output signal can be further modified and rewritten as the product of a linear part and a nonlinear part. The limit cycle analysis is carried out on the nonlinear part of the product. Specifically:

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

[0087]

[0088] At the same time, for the nonlinear module A in the AAC link 2 , it is considered that it only produces additional amplitude and no modules are connected in series, the formula is:

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

[0090] After analyzing the limit cycle based on classical control theory, it is believed that this module will only produce a stable limit cycle, which has little impact on the system. The remaining linear part is the AAC frequency domain analytical model:

[0091]

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

[0093] In step 4), based on the sinusoidal signal frequency sweep, 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, the AAC frequency domain analytical model formula (13) is subjected to a frequency sweep test. Through the frequency sweep, it can be seen that the frequency domain characteristic of the AAC controller is a forward gain, which is greater than 1 in the low frequency band and less than 1 in the high frequency band; at the same time, the AAC controller hardly generates a phase. The frequency sweep results are shown in Figure 3 and Figure 4 As shown, it can be seen that in the low frequency band, the input signal is greater than the output signal, indicating that the AAC gain is greater than 1. In the high frequency band, the input signal is less than the output signal, indicating that the AAC gain is less than 1. The response curves of different frequency bands are summarized as follows Figure 1 From the form shown, it can be seen that the AAC controller has a gain turning point in the transition stage from the low frequency band to the high frequency band. The relative accuracy of the frequency domain analytical model at this turning point is low. Apart from this, the rest of the frequency bands are within the applicable range of the AAC controller. The position of this turning point can be artificially designed by adjusting the AAC controller parameters at the same time. 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 equivalent to a series link added to the control system. It can simultaneously increase the rigid body and elastic margin of the traditional launch vehicle system. By adjusting the design parameters a, α, A Gt , A Dt By adjusting the frequency domain response of the AAC controller, the frequency band position where the low-frequency characteristics are changed to the high-frequency characteristics can be artificially controlled, so as to design reasonable control parameters a, α, A for a specific launch vehicle. Gt , A Dt Based on the above design idea, the frequency domain analysis is carried out 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 shown in Figure 2 As shown, it can be seen that 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 the specification of the present invention belong to the prior art known to the professional and technical personnel in this field.

Claims

1. A frequency domain analysis method for adaptive augmented controller for launch vehicle applications, characterized in that include: The nonlinear damping module of the improved adaptive augmented controller is adjusted to obtain the frequency domain model of the adaptive augmented controller; The adaptive augmentation controller is denoted as AAC controller; Input the sinusoidal characteristic signal into the frequency domain model of the AAC controller to obtain the output value k of the AAC controller t The analytical solution of the AAC controller output value is used to remove high-order harmonics and obtain an output signal in the same frequency band as the input signal; The frequency domain response of the integrator in the low frequency band is used as an integral filter. The output signal is adjusted based on the characteristic that its amplitude approaches positive infinity at 0Hz. At the same time, combined with the output limiting of the AAC controller, the obtained result is sorted 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 tests, 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.

2. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: The mathematical formula of the improved adaptive augmented controller is: k t =k a +k0 Among them, k t is the adaptive final output coefficient, k a is the integral part of the output coefficient, and k0 is the constant part of the output coefficient; k a The derivative of k tmax is the upper limit of the output coefficient, e r is the reference model deviation value, y s is the filter value of the spectrum 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 They are the upper and lower limit amplitudes of the AAC controller output respectively.

3. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 2, characterized in that: The nonlinear damping module in the mathematical formula of the improved adaptive augmented controller is -c·k t and The method to adjust the nonlinear damping module is: Among them, γ1 and γ2 are constant coefficients; The mathematical formula of the adaptive augmented 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 of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: Input the sinusoidal characteristic signal i = A sin(ωt) into the frequency domain model of the adaptive augmented controller to obtain the AAC controller output value k t The analytical solution is: Where A is the input signal amplitude, ω is the input signal frequency, t is the time, γ1 and γ2 are constant coefficients, is the frequency domain response of the integrator in the very low frequency band, A Gt is the filtering amplitude of the AAC controller high-pass filter, A Dt is the filtering amplitude of the low-pass filter of the AAC controller, is the amplitude response of the low-pass filter in the very low frequency band, is the low-pass filter phase, is the filtering phase of the high-pass filter, a is the error term weight, A G′ is the frequency domain response of the integrator, and α is the weight coefficient of the damping term of the AAC controller.

5. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: The output value k of the AAC controller t The analytical solution removes high-order harmonics and obtains 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 k of the AAC controller are t Multiply the analytical solution of , ignoring harmonics above three times ω, and get the AAC controller output signal o: Among them, Q1 and Q2 are coefficients, which are related to the frequency of the input signal, ω is the input signal frequency, and t is time.

6. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: The frequency domain response of the integrator in the low frequency band is used as an integral filter. The output signal is adjusted based on the characteristic that its amplitude approaches positive infinity at 0 Hz. Combined with the output limiting of the AAC controller, the following is obtained: k t ∈[k tmin ,k tmax ] Among them, Q1 and Q2 are coefficients, which are related to the frequency of the input signal, and k tmin ,k tmax are the upper and lower limit amplitudes of the AAC controller output, respectively; A is the input signal amplitude, ω is the input signal frequency, t is the time, γ1 and γ2 are constant coefficients, is the frequency domain response of the integrator in the very low frequency band, A Dt is the filtering amplitude of the low-pass filter of the AAC controller, is the amplitude response of the low-pass filter in the very low frequency band, A Gt is the filtering amplitude of the AAC controller high-pass filter, a is the error term weight, α is the AAC controller damping term weight coefficient, k 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.

7. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 6, characterized in that: The nonlinear part is: A 2 , only produces additional amplitude and no modules are connected in series, expressed as: N(A)=A 2 ,A>0。 8. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 6, characterized in that: The linear part is the frequency domain analytical model of the AAC controller: Among them, F aac is the amplitude of the frequency domain analytical model, is the phase of the frequency domain analytical model.

9. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: The results of the frequency sweep test are: The AAC controller has a gain transition in the transition stage from the low frequency band to the high frequency band. The relative accuracy of the frequency domain analytical model at this gain transition is lower than that of other frequency bands. The remaining frequency bands are all within the applicable range of the AAC controller. The position of the gain turn can be adjusted by designing the AAC controller parameters.

10. The frequency domain analysis method of an adaptive augmented controller for launch vehicle application according to claim 1, characterized in that: 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: a: As this value increases, the turning frequency increases significantly; α: If this value increases, the turning frequency will be greatly reduced; A Gt :When this value increases, the turning frequency increases slightly; A Dt :When this value increases, the turning frequency decreases slightly; By adjusting a and α first, then adjusting A Gt , A Dt The idea of ​​refinement can realize the design of AAC controller based on frequency domain response.

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