Face symmetry rocket multivariable PD control parameter adjustment method based on frequency response

Abstract

The invention discloses a plane symmetry rocket multivariable PD control parameter adjustment method based on frequency response, and belongs to the field of automatic control. Firstly, a transfer function matrix model is obtained according to a state-space equation of a plane symmetry rocket multivariable system; then, a reference model structure is determined, and an unexpected coupling effect is suppressed by enabling a closed-loop system to track a diagonal reference model matrix; then, obtaining a frequency domain model of a compensation controller required by the tracking reference model matrix by utilizing a sensitivity function matching condition of a closed-loop system and an expected closed-loop system; finally, a control gain calculation formula in a compensation controller matrix under PD control is comprehensively obtained based on the frequency response data; and a selection criterion of key variables in the frequency domain parameter adjustment method is designed. According to the method, mutual coupling among multiple channels of the plane-symmetric rocket can be processed, so that the response performance of a rocket multivariable system is improved, and the flight reliability is improved.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a method for tuning parameters of multivariable PD control for symmetrical rockets based on frequency response. Background Technology

[0002] Symmetric rockets often have large boosters mounted in parallel on both sides of the core stage, or additional wings, such as those found on Starships, to enhance payload capacity and mission adaptability. Compared to axisymmetric rockets, symmetric rockets face a more complex flow field structure during flight, with relatively stronger coupling of three-axis motion around the center of mass, inertia, and three-channel control. The aerodynamic characteristics and control capabilities of the pitch and yaw channels are not perfectly symmetrical, and lateral aerodynamic disturbances have a far greater impact on rocket stability and control than on axisymmetric rockets. Therefore, the controller parameter design for symmetric rockets needs to fully consider the rocket's characteristics and the effects of multi-channel coupling to suppress coupling effects, thereby ensuring the stability of the multivariable control system and the accuracy of attitude control.

[0003] Decoupled single-channel control design methods neglect the mutual coupling between multiple channels and cannot fully utilize the measurement information from other channels, making it difficult to compensate for interference caused by coupling in a timely manner. Therefore, the controller of a symmetrical rocket needs to consider the effects of coupling and adopt a multi-channel joint control design to enable the controller to have coupling suppression capabilities.

[0004] Because engineering practice tends to favor controllers with low structural complexity and ease of implementation, and emphasizes frequency response, PID control remains widely used in most industrial process controls. To address the impact of multi-channel coupling on system response performance, multivariable PID control frequency domain design methods can handle multivariable cross-coupled processes and meet certain stability margin requirements. Previous research on frequency domain control design methods has rarely addressed specific variable design methods, yet the selection of these variables in frequency domain design is crucial to the controller's effectiveness and implementation. Summary of the Invention

[0005] This invention provides a frequency response-based method for tuning the multivariable PD control of a symmetrical rocket, improving upon a PI control frequency domain tuning method and providing a detailed variable design method to solve the multi-channel coupled control problem of a symmetrical rocket.

[0006] This invention provides a method for tuning the multivariable PD control parameters of a surface-symmetric rocket based on frequency response, comprising the following steps:

[0007] Step 1: Ignore external disturbances in the attitude control system of the symmetrical rocket and establish a small-deviation attitude dynamics model of the symmetrical rocket for frequency domain analysis.

[0008] Step 2: Using the three-channel attitude angle as the output and the three-channel equivalent swing angle command as the input, establish the state-space equation of the multivariable system of the surface-symmetric rocket.

[0009] Step 3: Based on Step 2, considering the characteristics of the servo mechanism, the state-space equations of the symmetric rocket multivariable system are converted into a transfer function matrix model.

[0010] Step 4: Determine the reference model structure and make the closed-loop system track the diagonal reference model matrix to suppress unwanted coupling effects;

[0011] Step 5: Define the closed-loop system sensitivity function before and after parameter tuning. By using the matching condition of the sensitivity function, obtain the transfer function matrix model of the compensation controller required for the tracking reference model matrix.

[0012] Step 6: Based on the PD control structure, take the real and imaginary parts of the frequency domain model of the compensation controller, use the frequency response at N frequency points, and consider the weight of the corresponding frequency points to calculate the proportional gain and derivative gain of each element in the compensation controller matrix.

[0013] Optionally, in one embodiment of the present invention, in step 1, the small-deviation attitude dynamics model of the surface-symmetric rocket used for frequency domain analysis is:

[0014]

[0015] In the formula, θ and σ are the velocity inclination angle and the track yaw angle, respectively; These are the projected components of the arrow body's angular velocity about its center of mass on the three axes; ψ and γ represent the pitch angle, yaw angle, and roll angle, respectively; α and β represent the angle of attack and sideslip angle, respectively. β = ψ - σ; The core-level equivalent swing angle for the pitch, yaw, and roll channels; The boost equivalent swing angle for pitch, yaw, and roll channels is given. One point on the parameter represents the first derivative of the parameter, and two points on the parameter represent the second derivative of the parameter. and This is the control force coefficient regarding the magnitude of the thrust. and The gravitational coefficient is related to the acceleration due to gravity. For the aerodynamic coefficients related to lift, The aerodynamic coefficient with respect to lateral forces; The pitch channel core stage engine oscillation control force coefficient. The yaw channel core stage engine oscillation control force coefficient. The pitch channel booster engine oscillation control force coefficient. The yaw channel booster engine oscillation control force coefficient; The pitch channel core stage engine oscillation inertial force coefficient. The yaw channel core stage engine oscillation inertial force coefficient. The pitch channel booster engine oscillation inertial force coefficient, The yaw channel booster engine oscillation inertial force coefficient; and Let be the inertia coupling coefficient with respect to the moment of inertia. This is the aerodynamic damping moment coefficient for the pitch channel. This is the aerodynamic damping moment coefficient of the yaw channel; The normal aerodynamic moment coefficient is... This is the lateral aerodynamic moment coefficient; The pitch channel core stage engine oscillation control torque coefficient. The yaw channel core stage engine oscillation control torque coefficient. The pitch channel booster engine oscillation control torque coefficient. The yaw channel booster engine oscillation control torque coefficient; The pitch channel core stage engine oscillation moment coefficient, The yaw channel core stage engine oscillation inertial moment coefficient. The pitch channel booster engine's oscillation inertial moment coefficient, d1 is the yaw channel booster engine oscillation inertial moment coefficient; d2 is the roll channel aerodynamic damping moment coefficient. 3xj For the oscillation control torque coefficient of the core stage engine in the roll channel, d 3zt The oscillation control torque coefficient of the booster engine, d″ 3xj d″ is the oscillating inertia moment coefficient of the core stage engine in the roll channel. 3zt The oscillating moment coefficient of the booster engine;

[0016] The engine vibration equation is as follows:

[0017]

[0018] In the formula: ξ is the equivalent angular acceleration of the engine. n and ω n These are the damping ratio and natural frequency of the engine vibration characteristics, respectively. The control commands output by the controller are converted into linear displacement by the servo actuator, which is equivalent to the yaw angle deflection of the engine. m = xj, zt.

[0019] Optionally, in one embodiment of the present invention, in step 2, the three-channel attitude angle is... ψ and γ are outputs, representing the three-channel equivalent swing angle command. As input, combined with the angle transformation equation β=ψ-σ, the state-space equations of the surface-symmetric rocket multivariable system are:

[0020]

[0021] In the formula: For the input vector, This is a three-channel equivalent swing angle command; For state vectors, This is the output vector; matrices T, A, B, E, and C are respectively:

[0022]

[0023]

[0024] In the formula, a 21 =cosγ / cosψ, a 24 =sinγ / cosψ, a 51 =-sinγ, a 54 =cosγ, a 81 =tanψcosγ,a 84 =tanψsinγ;ξ n and ω n These represent the damping ratio and natural frequency of the engine vibration characteristics, respectively; in the E matrix: k xj k zt These are the control commands output by the controller to the engine yaw angle on the core stage and booster. The allocation ratio.

[0025] Optionally, in one embodiment of the present invention, in step 3, the transfer function matrix model is:

[0026]

[0027] In the formula, G0(s) is from u c The transfer function matrix from y(s) to y(s); G cn (s) represents the characteristics of the servo mechanism; W n (s) represents the engine vibration characteristics; I is the identity matrix, G cn (s), W n (s) are respectively:

[0028]

[0029] In the formula, ξ rω r These are the damping ratio and natural frequency, respectively, representing the characteristics of the servo mechanism.

[0030] Optionally, in one embodiment of the present invention, in step 4, the reference model structure is as follows:

[0031]

[0032] In the formula, T r (s) is a diagonal reference model matrix; i = 1, 2, 3, representing pitch, yaw, and roll channels respectively; a0, a1, b0, and b1 are the reference model parameters to be designed, all of which are positive constants, and the specific values ​​are determined based on the required T. ri The time-domain performance index of (s) is determined; T ri The time-domain performance indicators of (s) are designed according to the different effects of the three channels on the rocket attitude and trajectory and the different requirements of the three control channels for tracking response performance.

[0033] Optionally, in one embodiment of the present invention, in step 5, the closed-loop system and its sensitivity function before parameter tuning are defined as follows:

[0034] T(s) = [I + G(s)C(s)] -1 G(s)C(s),S(s)=IT(s)=[I+G(s)C(s)] -1

[0035] In the formula: T(s) is the initial closed-loop system; C(s) is the initial PD controller; S(s) is the sensitivity function of T(s);

[0036] The defined closed-loop system after parameter tuning and its sensitivity function are as follows:

[0037]

[0038] In the formula: This is the closed-loop system after parameter tuning; The PD controller after parameter tuning; for The sensitivity function; ΔC(s) is the compensation controller;

[0039] The desired sensitivity function of the closed-loop system is S r (s)=IT r (s), the target being tracked is Based on the sensitivity function matching condition The transfer function matrix model of the compensation controller is obtained as follows:

[0040]

[0041] In the formula, each element in the ΔC(s) matrix is ​​a PD controller:

[0042] ΔC ij (s)=Δk pij +Δk dij s

[0043] In the formula: Δk pij Δk dij These are the proportional gain and derivative gain relative to the initial controller, i = 1, 2, 3, j = 1, 2, 3.

[0044] Optionally, in one embodiment of the present invention, in step 6, for the transfer function matrix model of the compensation controller, s is replaced with jω, and for each element ΔC in the ΔC(jω) matrix... ij (jω) takes the real and imaginary parts respectively, and uses the PD controller Δk pij +Δk dij The equation relating the real and imaginary parts of jω, combined with frequency response data from N frequency points, yields the formulas for calculating the proportional gain and differential gain of each element in the ΔC(s) matrix:

[0045]

[0046] In the formula: Operators This means: if p = [p1, ..., p] N ] T , q = [q1,...,q N ] T , N∈Z + ,but Re[·] denotes taking the real part, Im[·] denotes taking the imaginary part; auxiliary variables A set of frequency points selected by the designer, ω N For the Nth frequency point, It is a set of weighting coefficients corresponding to the selected frequency points, λ N The weighting coefficient corresponding to the Nth frequency point; Given frequency response data at N frequency points, They are respectively:

[0047]

[0048] The frequency response-based multivariable PD control parameter tuning method for symmetrical rockets according to embodiments of the present invention has the following beneficial effects:

[0049] 1. Compared with traditional PD / PID control, this invention considers the coupling effect of multivariable systems in the controller design and designs multiple control channels jointly. It can make full use of system measurement information to coordinate multiple variables and achieve decoupled command tracking without active decoupling, thereby effectively suppressing the cross-coupling effect between multiple control channels.

[0050] 2. This invention derives analytical formulas for PD control parameters based on the expected closed-loop reference model matching relationship and frequency response data. It also provides design methods for key variables such as reference model, frequency point selection, and weighting coefficients. This eliminates the need for repeated parameter adjustments to improve control performance, reduces controller design complexity, and the method is easy to implement in engineering.

[0051] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0052] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0053] Figure 1 A flowchart illustrating a frequency response-based multivariable PD control parameter tuning method for a symmetrical rocket according to an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of the control design for a multivariable PD control parameter tuning method for a symmetrical rocket based on frequency response, according to an embodiment of the present invention.

[0055] Figure 3 This is a comparison curve of the step response of the principal component (1,1) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0056] Figure 4 This is a comparison curve of the step response of the principal component (2,2) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0057] Figure 5 This is a comparison curve of the step response of the principal component (3,3) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0058] Figure 6 This is a comparison curve of the step response of auxiliary element (1,2) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0059] Figure 7 This is a comparison curve of the step response of auxiliary element (2,1) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0060] Figure 8This is a comparison curve of the step response of the auxiliary element (3,1) of the closed-loop system before and after parameter tuning in an embodiment of the present invention.

[0061] Figure 9 The diagram shows the closed-loop time-domain response curves of the pitch channel before and after parameter adjustment in an embodiment of the present invention. Detailed Implementation

[0062] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0063] like Figure 1 and Figure 2 As shown, the frequency response-based method for tuning the multivariable PD control parameters of a surface-symmetric rocket includes the following steps:

[0064] Step 1: Ignore external disturbances in the attitude control system of the symmetrical rocket and establish a small-deviation attitude dynamic model of the symmetrical rocket for frequency domain analysis.

[0065] In step 1, ignoring wind and structural interference, the small-deviation attitude dynamics model of the surface-symmetric rocket established for frequency domain analysis is as follows:

[0066]

[0067] In the formula: θ and σ are the velocity inclination angle and the track yaw angle, respectively; These are the projected components of the arrow body's angular velocity about its center of mass on the three axes; ψ and γ represent the pitch angle, yaw angle, and roll angle, respectively; α and β represent the angle of attack and sideslip angle, respectively. β = ψ - σ; The core-level equivalent swing angle for the pitch, yaw, and roll channels; The boost equivalent swing angle for pitch, yaw, and roll channels is given. One point on the parameter represents the first derivative of the parameter, and two points on the parameter represent the second derivative of the parameter. and This is the control force coefficient regarding the magnitude of the thrust. and The gravitational coefficient is related to the acceleration due to gravity. For the aerodynamic coefficients related to lift, The aerodynamic coefficient with respect to lateral forces; The pitch channel core stage engine oscillation control force coefficient. The yaw channel core stage engine oscillation control force coefficient. The pitch channel booster engine oscillation control force coefficient. The yaw channel booster engine oscillation control force coefficient; The pitch channel core stage engine oscillation inertial force coefficient. The yaw channel core stage engine oscillation inertial force coefficient. The pitch channel booster engine oscillation inertial force coefficient, The yaw channel booster engine oscillation inertial force coefficient; and Let be the inertia coupling coefficient with respect to the moment of inertia. This is the aerodynamic damping moment coefficient for the pitch channel. This is the aerodynamic damping moment coefficient of the yaw channel; The normal aerodynamic moment coefficient is... This is the lateral aerodynamic moment coefficient; The pitch channel core stage engine oscillation control torque coefficient. The yaw channel core stage engine oscillation control torque coefficient. The pitch channel booster engine oscillation control torque coefficient. The yaw channel booster engine oscillation control torque coefficient; The pitch channel core stage engine oscillation moment coefficient, The yaw channel core stage engine oscillation inertial moment coefficient. The pitch channel booster engine's oscillation inertial moment coefficient, d1 is the yaw channel booster engine oscillation inertial moment coefficient; d2 is the roll channel aerodynamic damping moment coefficient. 3xj For the oscillation control torque coefficient of the core stage engine in the roll channel, d 3zt The oscillation control torque coefficient of the booster engine, d″ 3xj d″ is the oscillating inertia moment coefficient of the core stage engine in the roll channel. 3zt The oscillating inertial moment coefficient of the booster engine.

[0068] The engine vibration equation is:

[0069]

[0070] In the formula: ξ n ω n These are the damping ratio and natural frequency of the engine vibration characteristics, respectively. The control commands output by the controller are converted into linear displacement by the servo actuator, which is equivalent to the yaw angle deflection of the engine. m = xj, zt.

[0071] Step 2: Using the three-channel attitude angle as output and the three-channel equivalent swing angle command as input, establish the state-space equation of the surface-symmetric rocket multivariable system.

[0072] In step 2, the three-channel attitude angle is used. ψ and γ are outputs, providing a three-channel equivalent swing angle command. As input, combined with simplified angle transformation equations β=ψ-σ, the state-space equations of the surface-symmetric rocket multivariable system are:

[0073]

[0074] y = Cx

[0075] In the formula: It is the input vector; It is a state vector. This is the output vector; matrices T, A, B, E, and C are respectively:

[0076]

[0077] In the formula: In matrix A1: a 21 =cosγ / cosψ, a 24 =sinγ / cosψ, a 51 =-sinγ, a 54 =cosγ, a 81 =tanψcosγ,a 84 =tanψsinγ; In the E matrix: k xj k zt These are the control commands output by the controller to the engine yaw angle on the core stage and booster. The allocation ratio.

[0078] Step 3: Based on Step 2, considering the characteristics of the servo mechanism, the state-space equation of the multivariable system is converted into a transfer function matrix model.

[0079] Based on the state-space equations obtained in step 2, when deriving the frequency domain model of the symmetric rocket attitude control system, the engine vibration characteristics are considered as intermediate variables. The engine vibration equations are eliminated and the servo mechanism characteristics are considered when calculating the frequency domain model. The resulting transfer function matrix model is as follows:

[0080]

[0081] In the formula: G0(s) is from u cThe transfer function matrix from y(s) to y(s); G cn (s) represents the characteristics of the servo mechanism; W n (s) represents the engine vibration characteristics; G cn (s), W n (s) are respectively:

[0082]

[0083] In the formula: ξ r ω r These are the damping ratio and natural frequency, respectively, representing the characteristics of the servo mechanism.

[0084] Step 4: Determine the reference model structure and suppress unwanted coupling effects by making the closed-loop system track the diagonal reference model matrix.

[0085] In step 4, considering that the elements off-diagonal of the closed-loop transfer function matrix represent undesirable cross-coupling effects, it is desirable to design the closed-loop system as a diagonal reference model matrix. Given that the decoupled dynamics around the center of mass consist of three independent second-order systems, and that the PD controller introduces a zero into the system, the reference model structure is designed as a second-order transfer function with a zero:

[0086]

[0087] In the formula: T r (s) is a diagonal reference model matrix; i = 1, 2, 3, representing pitch, yaw, and roll channels respectively; a0, a1, b0, and b1 are the reference model parameters to be designed, all of which are positive constants, and the specific values ​​are determined based on the required T. ri The time-domain performance indicators of (s) are determined, including overshoot σ%, peak time t. p Adjustment time t s wait.

[0088] T ri The time-domain performance indicators of (s) are designed according to the different requirements of the tracking response performance of the three control channels: the pitch channel has a direct impact on the rocket's flight trajectory, requiring high control accuracy and stability, and a fast response to adapt to the rocket's rapidly changing dynamic environment; the yaw channel requires a moderate response speed to correct the heading deviation, and needs to maintain high stability to avoid large heading deviations; the roll channel affects the rocket's stability in the pitch and yaw channels, and needs to correct roll errors with a relatively fast response speed.

[0089] Step 5: Define the closed-loop system sensitivity function before and after parameter tuning. By using the matching condition of the sensitivity function, obtain the transfer function matrix model of the compensation controller required for the tracking reference model matrix.

[0090] In step 5, the closed-loop system and its sensitivity function before parameter tuning are defined as follows:

[0091] T(s) = [I + G(s)C(s)] -1 G(s)C(s),S(s)=IT(s)=[I+G(s)C(s)] -1

[0092] In the formula: T(s) is the initial closed-loop system; C(s) is the initial PD controller; S(s) is the sensitivity function of T(s).

[0093] The elements on the main diagonal of the C(s) matrix are all PD controllers:

[0094] C ii (s)=k pii +k dii s

[0095] In the formula: k pii k dii This is the initial control gain, i = 1, 2, 3; k pii k dii The control gain matrix is ​​as follows:

[0096]

[0097] The defined closed-loop system after parameter tuning and its sensitivity function are as follows:

[0098]

[0099] In the formula: This is the closed-loop system after parameter tuning; The PD controller after parameter tuning; for The sensitivity function. ΔC(s) is the compensation controller.

[0100] According to the definition of the closed-loop system sensitivity function before and after parameter tuning, we have:

[0101]

[0102] Considering that the desired sensitivity function of the closed-loop system is S r (s)=IT r (s), the target being tracked is Based on the sensitivity function matching condition have:

[0103]

[0104] The transfer function matrix model of the compensation controller can be obtained as follows:

[0105]

[0106] In the formula: each element in the ΔC(s) matrix is ​​a PD controller.

[0107] ΔC ij (s)=Δk pij +Δk dij s

[0108] In the formula: Δk pij Δk dij It is the gain increment relative to the initial controller, i = 1, 2, 3, j = 1, 2, 3; Δk pij Δk dij The PD control gain matrix is ​​as follows:

[0109]

[0110] Step 6: Based on the PD control structure, take the real and imaginary parts of the frequency domain model of the compensation controller, use the frequency response at N frequency points, and consider the weight of the corresponding frequency points to calculate the proportional gain and differential gain calculation formulas for each element in the compensation controller matrix.

[0111] The ΔC(s) obtained in step 5 is a high-order transfer function and cannot be directly used in the actual rocket control system. The proportional gain and derivative gain values ​​need to be solved for feedback control. Replacing s with jω yields the frequency response data ΔC(jω) of the compensation controller matrix. For each element ΔC(jω) in the ΔC(jω) matrix... ij (jω) takes the real and imaginary parts respectively, and uses them in conjunction with the PD controller Δk pij +Δk dij The equation relating the real and imaginary parts of jω can be used to calculate the PD control gain required for the system to track the reference model by selecting a set of frequency points that have a key impact on the system's dynamic characteristics and synthesizing the frequency response data. First, regarding ΔC... ij (jω) can be obtained by finding the real and imaginary parts:

[0112]

[0113] Then, the auxiliary variables are taken as follows:

[0114]

[0115] In the formula: These are a set of frequency points selected by the designer. It is a set of weighting coefficients corresponding to the selected frequency points.

[0116] The frequency range for selecting frequency points is determined based on the frequency response characteristics of the rocket process model, and the specific frequency points and weighting coefficients are selected according to the bandwidth standard of the rocket control system. The selection rules are as follows:

[0117] (1) Frequency band of the frequency point: For a rigid body model of a symmetrical launch vehicle, the controller design mainly focuses on the low-frequency response, which is usually between a few tenths of a rad / s and a few rad / s, generally not exceeding 10 rad / s. In this example, since the bouncing frequency of the object under study is low, the right boundary of the frequency band is selected to the left of the minimum value of the bouncing mode frequency.

[0118] (2) Bandwidth at frequency points: Based on initial controller design experience, the system cutoff frequency needs to be kept near the standard cutoff frequency, which is determined by the system bandwidth under the controller adjusted at the moment of maximum aerodynamic torque coefficient. Therefore, the bandwidth of the pitch and yaw channels is about 1.8 to 2 rad / s, while the roll channel requires stronger anti-interference capability and has a bandwidth of about 3.0 to 3.5 rad / s. A relatively dense frequency point should be selected near the bandwidth frequency, and other frequency points should be selected on the left and right sides of the bandwidth frequency respectively.

[0119] (3) Number of frequency points: In order to accurately track the reference model, the number of frequency points is generally no less than 5. Selecting more than 15 frequency points has little effect on improving the tracking accuracy.

[0120] (4) Frequency point weighting coefficients: When densely selecting points near the bandwidth frequency, a larger weighting coefficient can be set for them. When sparsely selecting points on both sides of the bandwidth, a smaller weighting coefficient can be set. Only the relative magnitude between the weighting coefficients of different frequency points needs to be considered; no specific numerical values ​​need to be designed.

[0121] Finally, the frequency response at N frequency points is used:

[0122]

[0123] In the formula: For the frequency response data at the selected frequency points:

[0124]

[0125] according to Operation rules: p = [p1, ..., p N ] T , q = [q1, ..., q N ] T , The formulas for calculating the proportional gain and differential gain of each element in the ΔC(s) matrix can be obtained as follows:

[0126]

[0127] In the formula:

[0128] The effectiveness of this invention is verified through simulation below. The simulation parameters are as follows:

[0129] The coefficients of the rigid body dynamics model of a rocket at a certain moment are: d 3xj =0.667,d 3zt =4.39, d″ 3xj =5.22E-04, d″ 3zt =3.43E-03; ξ n =0.3, ω n =65; ξ r =0.3, ω r =32;k xj :k zt =1:1.

[0130] Reference model matrix T r The structure and parameters of (s) are:

[0131]

[0132] The corresponding time-domain performance metrics are: pitch channel σ% = 28%, t p =1.28s,t s =2.34s; yaw channel σ% = 25.9%, t p =1.36s,t s =2.52s; Roll channel σ% = 22.1%, t p =1s,t s =1.94s.

[0133] In this invention, the reference model T ri (s) describes the dynamic characteristics of a standard closed-loop system, while the rocket reference model in engineering describes the desired dynamic characteristics of the closed-loop transfer function from the program angle to the attitude angle. The differences between the two are as follows:

[0134]

[0135] PD controller before parameter tuning:

[0136]

[0137] Frequency points and weighting coefficients: The frequency band of the frequency points is [0.1, 6] rad / s, and a set of selected frequency points is [ω1, ..., ω]. NThe frequency point weighting coefficients are [λ1,...,λ] = [0.1, 1, 1.85, 1.9, 1.95, 2.0, 2.05, 2.1, 2.2, 2.5, 3.0, 3.2, 3.4, 4.6, 6]. N ] = [1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1].

[0138] The PD controller after parameter tuning:

[0139]

[0140] Controller Matrix Whether there are values ​​on the off-diagonal lines directly depends on whether there is cross-coupling in the process model G(s). Considering small deviations in attitude angles for yaw and roll channels, as well as small deviations in velocity tilt and yaw angles, pitch-yaw coupling exists in the process model G(s), and there is interference from the pitch channel to the roll channel. A multivariable PD control parameter tuning algorithm based on frequency response is used to achieve this. Under the influence of parameter tuning, the closed-loop system Tracking expected closed-loop system T r The effect of (s) is as follows Figures 3-8 As shown.

[0141] in Figure 3 , Figure 4 , Figure 5 The figure shows the unit feedback step response curve of the principal component of the closed-loop system. As can be seen from the figure, the pitch, yaw, and roll channels all tracked the designed reference model with high accuracy. The peak time of the initial closed-loop system, as well as the overshoot of the yaw and roll channels, did not meet the design specifications. However, the overshoot and response speed of the parameter-tuned closed-loop system both meet the given time-domain performance specifications. Figure 6 , Figure 7 and Figure 8 The figure shows the unit feedback step response curve of the auxiliary element of the closed-loop system. T(1,2) and T(2,1) represent the mutual interference between the pitch and yaw channels. As can be seen from the figure, the undesirable cross-coupling effect is effectively suppressed. T(3,1) represents the interference effect of the pitch channel on the roll channel. The response of T(3,1) is also weakened to a certain extent. The peak values ​​of the three oscillations are reduced, and the final convergence time is also shortened. Figure 9 For the pitch channel closed-loop transfer function The step response and the overshoot of the pitch angle response before and after parameter tuning both meet the industry standard of σ%≤20%, but the response speed after parameter tuning is faster, which meets the performance requirements of the pitch channel for fast response.

[0142] In summary, simulation results verify the effectiveness of the frequency response-based multivariable PD control parameter tuning algorithm. By using multivariable joint control to feedback the states of other control channels, it fully utilizes all measurement information and reduces the impact of control coupling. The derived compensation controller is based on the matching conditions required for the entire multivariable system to track the desired closed-loop system. Therefore, the obtained controller can guarantee the stability of the entire multivariable system and coordinate the relationship between multiple inputs and outputs.

[0143] This invention presents a frequency-response-based multivariable PD control parameter tuning method for symmetrical rockets. Considering the coupling effects between multiple channels in a symmetrical rocket attitude dynamics model, a multivariable PD controller is obtained through frequency response data synthesis. This controller enables the closed-loop system to track a diagonal reference model matrix to suppress channel coupling. First, the transfer function matrix model is obtained based on the state-space equations of the symmetrical rocket's multivariable system. Then, the reference model structure is determined, and undesirable coupling effects are suppressed by making the closed-loop system track the diagonal reference model matrix. Next, the frequency domain model of the compensation controller required to track the reference model matrix is ​​obtained using the sensitivity function matching condition between the closed-loop system and the desired closed-loop system. Finally, the control gain calculation formula in the compensation controller matrix under PD control is obtained based on frequency response data synthesis. Selection criteria for key variables in the frequency domain parameter tuning method are also designed. This invention can handle the mutual coupling between multiple channels of a symmetrical rocket, thereby improving the response performance of the rocket's multivariable system and enhancing flight reliability.

[0144] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0145] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0146] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

Claims

1. A method for tuning the multivariable PD control parameters of a surface-symmetric rocket based on frequency response, characterized in that, Includes the following steps: Step 1: Ignore external disturbances in the attitude control system of the symmetrical rocket and establish a small-deviation attitude dynamics model of the symmetrical rocket for frequency domain analysis. Step 2: Using the three-channel attitude angle as the output and the three-channel equivalent swing angle command as the input, establish the state-space equation of the multivariable system of the surface-symmetric rocket. Step 3: Based on Step 2, considering the characteristics of the servo mechanism, the state-space equations of the symmetric rocket multivariable system are converted into a transfer function matrix model. Step 4: Determine the reference model structure and make the closed-loop system track the diagonal reference model matrix to suppress unwanted coupling effects; Step 5: Define the closed-loop system sensitivity function before and after parameter tuning. By using the matching condition of the sensitivity function, obtain the transfer function matrix model of the compensation controller required for the tracking reference model matrix. Step 6: Based on the PD control structure, take the real and imaginary parts of the frequency domain model of the compensation controller, use the frequency response at N frequency points, and consider the weight of the corresponding frequency points to calculate the proportional gain and derivative gain of each element in the compensation controller matrix.

2. The method according to claim 1, characterized in that, In step 1, the small-deviation attitude dynamics model of the surface-symmetric rocket used for frequency domain analysis is as follows: In the formula, θ and σ are the velocity inclination angle and the track yaw angle, respectively; These are the projected components of the arrow body's angular velocity about its center of mass on the three axes; ψ and γ represent the pitch angle, yaw angle, and roll angle, respectively; α and β represent the angle of attack and sideslip angle, respectively. β = ψ - σ; The core-level equivalent swing angle for the pitch, yaw, and roll channels; The boost equivalent swing angle for pitch, yaw, and roll channels is given. One point on the parameter represents the first derivative of the parameter, and two points on the parameter represent the second derivative of the parameter. and This is the control force coefficient regarding the magnitude of the thrust. and The gravitational coefficient is related to the acceleration due to gravity. For the aerodynamic coefficients related to lift, The aerodynamic coefficient with respect to lateral forces; The pitch channel core stage engine oscillation control force coefficient. The yaw channel core stage engine oscillation control force coefficient. The pitch channel booster engine oscillation control force coefficient. The yaw channel booster engine oscillation control force coefficient; The pitch channel core stage engine oscillation inertial force coefficient. The yaw channel core stage engine oscillation inertial force coefficient. The pitch channel booster engine oscillation inertial force coefficient, The yaw channel booster engine oscillation inertial force coefficient; and Let be the inertia coupling coefficient with respect to the moment of inertia. This is the aerodynamic damping moment coefficient for the pitch channel. This is the aerodynamic damping moment coefficient of the yaw channel; The normal aerodynamic moment coefficient is... This is the lateral aerodynamic moment coefficient; The pitch channel core stage engine oscillation control torque coefficient. The yaw channel core stage engine oscillation control torque coefficient. The pitch channel booster engine oscillation control torque coefficient. The yaw channel booster engine oscillation control torque coefficient; The pitch channel core stage engine oscillation moment coefficient, The yaw channel core stage engine oscillation inertial moment coefficient. The pitch channel booster engine's oscillation inertial moment coefficient, d1 is the yaw channel booster engine oscillation inertial moment coefficient; d2 is the roll channel aerodynamic damping moment coefficient. 3xj For the oscillation control torque coefficient of the core stage engine in the roll channel, d 3zt The oscillation control torque coefficient of the booster engine, d″ 3xj d″ is the oscillating inertia moment coefficient of the core stage engine in the roll channel. 3zt The oscillating moment coefficient of the booster engine; The engine vibration equation is as follows: In the formula: ξ is the equivalent angular acceleration of the engine. n and ω n These are the damping ratio and natural frequency of the engine vibration characteristics, respectively. The control commands output by the controller are converted into linear displacement by the servo actuator, which is equivalent to the yaw angle deflection of the engine. m = xj, zt.

3. The method according to claim 2, characterized in that, In step 2, the three-channel attitude angle is used. ψ and γ are outputs, representing the three-channel equivalent swing angle command. As input, combined with the angle transformation equation β=ψ-σ, the state-space equations of the surface-symmetric rocket multivariable system are: y = Cx In the formula: For the input vector, This is a three-channel equivalent swing angle command; For state vectors, This is the output vector; matrices T, A, B, E, and C are respectively: In the formula, a 21 =cosγ / cosψ, a 24 =sinγ / cosψ, a 51 =-sinγ, a 54 =cosγ, a 81 =tanψcosγ,a 84 =tanψsinγ;ξ n and ω n These represent the damping ratio and natural frequency of the engine vibration characteristics, respectively; in the E matrix: k xj k zt These are the control commands output by the controller to the engine yaw angle on the core stage and booster. The allocation ratio.

4. The method according to claim 3, characterized in that, In step 3, the transfer function matrix model is as follows: In the formula, G0(s) is from u c The transfer function matrix from y(s) to y(s); G cn (s) represents the characteristics of the servo mechanism; W n (s) represents the engine vibration characteristics; I is the identity matrix, G cn (s), W n (s) are respectively: In the formula, ξ r ω r These are the damping ratio and natural frequency, respectively, representing the characteristics of the servo mechanism.

5. The method according to claim 1, characterized in that, In step 4, the reference model structure is as follows: In the formula, T r (s) is a diagonal reference model matrix; i = 1, 2, 3, representing pitch, yaw, and roll channels respectively; a0, a1, b0, and b1 are the reference model parameters to be designed, all of which are positive constants, and the specific values ​​are determined based on the required T. ri The time-domain performance index of (s) is determined; T ri The time-domain performance indicators of (s) are designed according to the different effects of the three channels on the rocket attitude and trajectory and the different requirements of the three control channels for tracking response performance.

6. The method according to claim 5, characterized in that, In step 5, the closed-loop system and its sensitivity function before parameter tuning are defined as follows: T(s)=[I+G(s)C(s)] -1 G(s)C(s),S(s)=I-T(s)=[I+G(s)C(s)] -1 In the formula: T(s) is the initial closed-loop system; C(s) is the initial PD controller; S(s) is the sensitivity function of T(s); The defined closed-loop system after parameter tuning and its sensitivity function are as follows: In the formula: This is the closed-loop system after parameter tuning; The PD controller after parameter tuning; for The sensitivity function; ΔC(s) is the compensation controller; The desired sensitivity function of the closed-loop system is S r (s)=IT r (s), the target being tracked is Based on the sensitivity function matching condition The transfer function matrix model of the compensation controller is obtained as follows: In the formula, each element in the ΔC(s) matrix is ​​a PD controller: ΔC ij (s)=Δk pij +Δk dij s In the formula: Δk pij Δk dij These are the proportional gain and derivative gain relative to the initial controller, i = 1, 2, 3, j = 1, 2, 3.

7. The method according to claim 6, characterized in that, In step 6, for the transfer function matrix model of the compensation controller, s is replaced with jω, and for each element ΔC(jω) in the matrix... ij (jω) takes the real and imaginary parts respectively, and uses the PD controller Δk pij +Δk dij The equation relating the real and imaginary parts of jω, combined with frequency response data from N frequency points, yields the formulas for calculating the proportional gain and differential gain of each element in the ΔC(s) matrix: In the formula: Operators This means: if p = [p1, ..., p] N ] T , q = [q1, ..., q N ] T , N∈Z + ,but Re[·] denotes taking the real part, Im[·] denotes taking the imaginary part; auxiliary variables A set of frequency points selected by the designer, ω N For the Nth frequency point, It is a set of weighting coefficients corresponding to the selected frequency points, λ N The weighting coefficient corresponding to the Nth frequency point; Given frequency response data at N frequency points, They are respectively:

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