Hierarchical iterative guidance method and system for ascending section of three-level solid rocket under multi-constraint condition

Abstract

The invention discloses a hierarchical iterative guidance method and system for a rising section of a three-stage solid rocket under a multi-constraint condition, belongs to the field of spacecraft guidance and control, and solves the problem of inter-stage instruction sudden change. The method is divided into four stages: first-stage program turning attack angle extreme value and yaw angle main variable optimization; the second stage corrects and introduces a third stage segmentation variable based on the first stage result; three-stage progressive optimization is carried out in three stages; and dynamically compensating the three-dimensional speed increment at the tail section. A Newton-Raphson method is adopted for iteration, errors are corrected step by step, inter-stage attitude smooth transition is achieved through time amplification and linear interpolation, stable control of an execution mechanism is ensured, and guidance precision and robustness are improved. According to the method, three-stage iteration guidance precision is high, robustness is high, and various parameter deviations can be effectively dealt with; the command angle change angular rate is reduced through attitude smooth control, overshoot, trajectory oscillation and out-of-control are avoided, and the flight stability and accuracy of the three-level solid rocket in the rising stage are powerfully promoted.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft guidance and control, and particularly to a hierarchical iterative guidance method and system for the ascent stage of a three-stage solid rocket under multiple constraint conditions. Background Art

[0002] Three-stage solid rockets are widely used in space launch missions due to their simple structure and high reliability. However, their guidance accuracy is limited by the following technical bottlenecks:

[0003] 1. Accumulation of propulsion errors: The thrust deviation of a solid rocket engine cannot be corrected midway, and the errors are superimposed step by step, resulting in the position and velocity deviation at the handover point exceeding the mission requirements.

[0004] 2. Inter-stage attitude mutation: In traditional guidance methods, the command angle changes stepwise during inter-stage switching, exceeding the maximum angular rate of the actuator, causing ballistic oscillations or even loss of control.

[0005] 3. Insufficient robustness: Most traditional solid rockets adopt the strategy of perturbation guidance, which has the advantages of small computational workload and not very high requirements for the on-board computer. However, perturbation guidance also has fatal defects. For example, a large amount of computational work needs to be carried out before the missile is launched, and its theoretical basis is based on the assumption of small perturbations. Therefore, for cases with large parameter perturbations such as solid rocket engines, its guidance accuracy will be inadequate.

[0006] Domestic and foreign scholars have conducted extensive research on iterative guidance, but basically established iterative guidance models outside the atmosphere, and less research has been done on the iterative guidance algorithm for the entire active section. Even though the existing iterative guidance schemes adopt segmented angle of attack optimization, they do not achieve coordinated iteration of inter-stage variables, and there are problems of multi-stage error transmission; attitude smoothing only relies on low-pass filtering, and the response delay is significant. Therefore, there is an urgent need for a guidance method that can achieve multi-stage coordinated iteration and balance accuracy and dynamic response. Summary of the Invention

[0007] The present invention proposes a hierarchical iterative guidance method and system for the ascent stage of a three-stage solid rocket under multiple constraint conditions, which gradually corrects propulsion and aerodynamic errors, combines attitude smoothing control technology, solves the problem of inter-stage command mutation, and realizes high-precision control of the handover point.

[0008] A hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions, the method comprising the following steps:

[0009] S1. First-stage guidance stage: Taking the extreme value of the first-stage programmed turn angle of attack and the yaw angle as the main variables, and combining the angles of attack and yaw angles of the second and third stages as auxiliary variables, minimizing the sum of squares of the handover point errors through an iterative algorithm, and outputting the commanded pitch angle and yaw angle;

[0010] S2. Second-stage guidance phase: Taking the second-stage angle of attack and yaw angle as the main variables, combined with the three-stage segmented angle of attack and yaw angle as auxiliary variables, based on the first-stage guidance results for iterative correction, output the updated commanded pitch angle and yaw angle;

[0011] S3. Third-stage guidance phase: Divide the third-stage flight into three segments: the front, middle, and rear. Taking the third-stage front-segment angle of attack and yaw angle as the main variables, combined with the subsequent segmented variables for iterative optimization, output the final guidance command;

[0012] S4. Terminal closed-loop guidance phase: According to the real-time navigation state, taking the three-dimensional velocity increment as the iterative variable, dynamically adjust the commanded angle of attack and yaw angle until burnout and shutdown.

[0013] Furthermore, in S1,

[0014] The first stage includes a vertical ascent section, a programmed turn section, a transonic region, and a zero-angle-of-attack section for the remaining part. During the entire first-stage flight phase, the yaw angle takes the same value. During the vertical ascent section, the pitch angle remains at 90 degrees, that is

[0015]

[0016] If the vertical ascent end time t1 is selected too large, it will increase the angle of attack and overload during the turn, and at the same time, the speed loss will also increase correspondingly. t1 depends on the thrust-to-weight ratio 1 / ν0 of the missile and is initially determined according to the following empirical formula

[0017]

[0018] In the early stage of the turn section, from t1 to t2, it is a turn with an angle of attack. According to the requirements, it should end before reaching the transonic region where the aerodynamic force changes rapidly to reduce the aerodynamic load and aerodynamic interference. Therefore, when the Mach number M(t2) = 0.8 - 1.2, the angle of attack is contracted to zero. During the entire subsequent high dynamic pressure section from t2 to t3, it turns slowly only relying on the normal component of gravity, that is, gravity turn. The turn section end time t3 corresponds to the first-stage shutdown time point

[0019] Determine the flight program in the early stage of the turn section. According to the required conditions of the angle of attack, the variation law of the angle of attack is determined by the following empirical relationship

[0020]

[0021] In the formula:

[0022] α m is the maximum absolute value of the angle of attack on the negative angle-of-attack turn section;

[0023] v is the current speed magnitude of the missile;

[0024] v f is the speed when the angle of attack is contracted to zero;

[0025] v0 is the speed at the end of the vertical turn;

[0026] c is a constant that determines the time for the angle of attack to decrease from zero to -α m and from -α m to rise to zero,

[0027] During the first-stage flight, the yaw angle is ψ1. During the second-stage flight, the yaw angle remains the same as that in the first stage, and the angle of attack is α2. During the third-stage flight, the angle of attack is α3 and the yaw angle is ψ3.

[0028] The hierarchical iteration variable is selected as,

[0029] ξ = [α m , ψ1, α2, α3, ψ3] T

[0030] The terminal error vector is,

[0031] g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T

[0032] To obtain ξ = [α m , ψ1, α2, α3, ψ3] T such that,

[0033] J = g T g = Δh 2 + Δz 2 + Δγ ev 2 + Δψ ev 2 + Δv 2

[0034] reaches a minimum,

[0035] The optimal ξ * = [α m * , ψ1 * , α2 * , α3 * , ψ3 * T should satisfy the extreme value condition:

[0036]

[0037] That is,

[0038]

[0039] Construct an iterative format to calculate the required guidance variables. Assume that the extreme point at the $i$-th step is $\xi$ i $=$ [$\alpha$ m , $\psi_1$, $\alpha_2$, $\alpha_3$, $\psi_3$] i T has been obtained, then

[0040]

[0041] Neglect the high-order terms and substitute them into Equation (11) to obtain

[0042]

[0043] Thus, the iterative format is obtained as follows

[0044]

[0045] The initial iterative value is taken as the value given in the ballistic optimization

[0046] where the sensitivity matrix is

[0047]

[0048] Furthermore, in S2

[0049] During the entire second-stage flight, the angle of attack takes the same value, and the yaw angle also takes the same value, that is

[0050]

[0051] Assume that during the second-stage flight, the angle of attack is $\alpha_2$ and the yaw angle is $\psi_2$. During the third-stage flight, it is divided into two sections, the first 70% section and the last 30% section. In the first section, the yaw angle remains $\psi_2$ as in the second stage, and the angle of attack is $\alpha$ 31 , and in the second section, the angle of attack is $\alpha$ 32 , and the yaw angle is $\psi$ 32 ,

[0052] The hierarchical iterative variable is selected as

[0053] $\xi$ = [$\alpha_2$, $\psi_2$, $\alpha$ 31 , $\alpha$ 32 , $\psi$ 32 T (15)

[0054] Construct an iterative format according to the Newton-Raphson method. Calculate the variable correction amount through the sensitivity matrix to obtain the iterative format as follows

[0055]

[0056] The initial iterative value is taken as the result of the first-stage iteration. The sensitivity matrix is​

[0057]

[0058] Furthermore, in S3,

[0059] The three-stage flight phase is divided into three sub-phases: the first 30% section, the middle 40% section, and the last 30% section. During the flight in the first section, the angle of attack is α 31 , and the yaw angle is ψ 31 . During the flight in the middle section, the angle of attack is α 32 , and the yaw angle is taken as the same value as that in the first 30% section. During the flight in the last section, the angle of attack is α 33 , and the yaw angle is ψ 33 .

[0060] The hierarchical iterative variable is selected as

[0061] ξ = [α 31 , ψ 31 , α 32 , α 33 , ψ 33 T (17)

[0062] Construct an iterative format according to the Newton-Raphson method, and calculate the variable correction amount through the sensitivity matrix to obtain the following iterative format:

[0063]

[0064] The initial iterative value is taken as the result of the second-level iteration. The sensitivity matrix is

[0065]

[0066] Although there is iterative output in the last 30% section, it is not used because the previous propulsion error needs to be further eliminated through the closed-loop guidance in the last section.

[0067] Furthermore, in S4,

[0068] At any time in the final stage of the three-stage flight, assuming that the flight state is known, since the three-stage flight is already outside the atmosphere and the aerodynamic force is negligible, the guidance dynamics equation becomes

[0069]

[0070] In order to find the thrust action law, first explore the error in reaching the handover point during the thrustless flight in the final stage of the three-stage flight, and then calculate the required thrust information according to the error. The thrustless form of the dynamics equation (19) is

[0071] ​

[0072] Integrating this equation gives other states when the required range is reached, and the terminal error vector is thus obtained as

[0073] g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T (21)

[0074] The hierarchical iterative variable is selected as the required velocity

[0075] ξ = [v x , v y , v z T (22)

[0076] Construct an iterative format according to the Newton - Raphson method, and calculate the variable correction amount through the sensitivity matrix to obtain the following iterative format

[0077]

[0078] The initial iterative value is taken as the current actual velocity, given by the navigation system, and the sensitivity matrix among them is

[0079]

[0080] The required velocity obtained by iteration is set as The deviation from the actual velocity is

[0081]

[0082] Projected onto the ground launch coordinate system, we get

[0083]

[0084] Thus, the commanded angle of attack, yaw angle, and roll angle are obtained as follows

[0085]

[0086] The strategy is continuously executed until the engine burns out.

[0087] Furthermore, the method further includes S5 which runs through S1 - S4. S5 is used for hierarchical switching between every two adjacent steps of S1 - S4:

[0088] S5. Attitude smoothing control: Assume that the final attitude angle at the end of the previous level is α n degrees, and the new attitude angle designed according to the original hierarchical guidance method is α n+1 degrees, the guidance simulation step size is Δt seconds, and the maximum amplitude of the angular velocity limit of the attitude actuator is ω c ​(° / s), the new attitude angle α′ designed considering the capabilities of the attitude actuators n+1 , then the increased time increment δt of the attitude change is calculated by the following formula:

[0089]

[0090] The linear interpolation algorithm assumes that the change in the inter-stage attitude command angles after the time increase is a linear function of time. By using the last command attitude angle in the glide segment of the previous stage and the first attitude angle calculated by the hierarchical iterative guidance command of the next stage, a first-order linear interpolation process is performed to estimate the command attitude angles at each guidance moment within the time range of the time increase.

[0091] Using the Lagrange interpolation polynomial, a linear function f(t, X k , X k+1 ) about time t is derived to estimate the command attitude values at each guidance moment during the given period:

[0092]

[0093] Among them, the command attitude angle at the last moment of the glide segment of the previous stage is X k , and the corresponding time is t k , the command attitude angle at the first moment of the hierarchical iterative guidance of the next stage is X k+1 , and the corresponding time is t k+1 , t k+1 = t k + δt.

[0094] A hierarchical iterative guidance system for the ascent stage of a three-stage solid rocket under multiple constraint conditions. The system includes a first-stage guidance module, a second-stage guidance module, a third-stage guidance module, and a terminal closed-loop guidance module. The first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the terminal closed-loop guidance module are connected in sequence. Among them,

[0095] The first-stage guidance module is used to take the extreme value of the first-stage program turning angle of attack and the yaw angle as the main variables, and the angle of attack and yaw angle of the second and third stages as auxiliary variables. By using the iterative algorithm to minimize the sum of the squares of the handover point errors, it outputs the command pitch angle and yaw angle;

[0096] The second-stage guidance module is used to take the angle of attack and yaw angle of the second stage as the main variables, and the segmented angle of attack and yaw angle of the third stage as auxiliary variables. Based on the iterative correction of the first-stage guidance result, it outputs the updated command pitch angle and yaw angle;

[0097] The third-stage guidance module is used to divide the third-stage flight into three segments: the front, middle, and rear. Taking the angle of attack and yaw angle of the front segment of the third stage as the main variables, and combining with the subsequent segmented variables for iterative optimization, it outputs the final guidance command;

[0098] The final-stage closed-loop guidance phase module is used to dynamically adjust the commanded angle of attack and yaw angle with the three-dimensional velocity increment as the iterative variable according to the real-time navigation state until burnout shutdown.

[0099] Furthermore, it also includes an attitude smoothing control module, which is embedded as an auxiliary module between every two adjacent modules among the first-stage guidance phase module, the second-stage guidance phase module, the third-stage guidance phase module, and the final-stage closed-loop guidance phase module.

[0100] The attitude smoothing control module is used to achieve smooth transition of the inter-stage attitude commands of the first-stage guidance phase module, the second-stage guidance phase module, the third-stage guidance phase module, and the final-stage closed-loop guidance phase module through time amplification and linear interpolation.

[0101] A storage medium stores a computer program, and when the computer program is executed by a processor, it implements the above-mentioned hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraints.

[0102] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the program to implement the above-mentioned hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraints.

[0103] Advantages of the present invention:

[0104] 1. The three-stage iterative guidance has high guidance accuracy and strong robustness: when iterative guidance is adopted at all three stages under the conditions of engine thrust deviation of ±5%, specific impulse deviation of ±5%, fuel mass deviation of ±1%, and aerodynamic coefficient deviation of ±15%, the accuracy at the handover point is still relatively high (the height error at the handover point is less than 100m, and the speed is less than 30m / s), all meeting the engineering design accuracy requirements.

[0105] 2. The attitude smoothing control can reduce the angular rate of change of the commanded angle to 5° / s, avoiding overshoot and even oscillation and out-of-control of the trajectory. Description of the drawings

[0106] Figure 1 It is a schematic diagram of the flight time sequence for the ascending stage of a three-stage solid rocket;

[0107] Figure 2 It is a flow block diagram of a hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraints of the present invention;

[0108] Figure 3 It is a schematic diagram of attitude time amplification and smoothing of the guidance command;

[0109] Figure 4 It is a general flight program for the powered flight phase;

[0110] Figure 5 It is the curve of the variation law of the angle of attack α(t). Specific implementation mode

[0111] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0112] Refer to Figure 1 As shown, a hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions includes the following steps:

[0113] S1. First-stage guidance stage: Taking the extreme value of the first-stage program turning angle of attack and the yaw angle as the main variables, and combining the angles of attack and yaw angles of the second and third stages as the auxiliary variables, minimizing the sum of the squares of the handover point errors through an iterative algorithm, and outputting the commanded pitch angle and yaw angle;

[0114] S2. Second-stage guidance stage: Taking the angles of attack and yaw angles of the second stage as the main variables, and combining the segmented angles of attack and yaw angles of the third stage as the auxiliary variables, iteratively correcting based on the results of the first-stage guidance, and outputting the updated commanded pitch angle and yaw angle;

[0115] S3. Third-stage guidance stage: Dividing the third-stage flight into three segments: front, middle, and rear. Taking the angles of attack and yaw angles in the front segment of the third stage as the main variables, and combining the subsequent segmented variables for iterative optimization, and outputting the final guidance command;

[0116] S4. Final-stage closed-loop guidance stage: According to the real-time navigation state, taking the three-dimensional velocity increment as the iterative variable, dynamically adjusting the commanded angle of attack and yaw angle until burnout and shutdown.

[0117] Specifically, the present invention provides a hierarchical iterative guidance method for a three-stage solid rocket, gradually correcting the propulsion and aerodynamic errors, combining the attitude smoothing control technology, solving the problem of sudden change of inter-stage commands, and realizing high-precision control of the handover point, as Figure 1 and Figure 2 shown.

[0118] The technical solution to achieve the above object is:

[0119] 1. First-stage hierarchical iterative guidance method:

[0120] Main variable and auxiliary variable: Taking the extreme value of the first-stage program turning angle of attack (α m), with the yaw angle (ψ1) as the main variable, combined with the second-order angle of attack (α2), the third-order angle of attack (α3), and the third-order yaw angle (ψ3) as auxiliary variables, to form an iterative variable set, that is, the iterative variables are:

[0121] ξ = [α m , ψ1, α2, α3, ψ3] T (2)

[0122] Objective function: Minimize the sum of the squared errors of the handover point height error (Δh), the lateral position error (Δz), the velocity inclination error (Δγ ev ), the velocity yaw error (Δψ ev ), and the velocity error (Δv) through an iterative algorithm:

[0123] J = g T g = Δh 2 + Δz 2 + Δγ ev 2 + Δψ ev 2 + Δv 2 (3)

[0124] where g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T is the terminal error vector.

[0125] Iterative algorithm: Construct an iterative format based on the Newton-Raphson method, and calculate the variable correction amount through the sensitivity matrix . The sensitivity matrix is the partial derivative matrix of the terminal error vector with respect to the iterative variables.

[0126] Implementation stage: It includes the vertical ascent section, the program turn section (including the transonic region where the angle of attack shrinks to zero), and the zero angle of attack section, and realizes trajectory correction by adjusting the angle of attack curve in segments.

[0127] 2. Second-order hierarchical iterative guidance method:

[0128] Main variable and auxiliary variables: Inherit the results of the first-order iterative guidance. With the second-order angle of attack (α2) and the second-order yaw angle (ψ2) as the main variables, combined with the front-section third-order angle of attack (α 31 ), the rear-section third-order angle of attack (α 32 ), and the rear-section third-order yaw angle (ψ 32 ) as auxiliary variables, that is, the iterative variables are:

[0129] ξ = [α2, ψ2, α 31 , α 32 , ψ 32 T (4)

[0130] ​Objective function: The same as the first-stage guidance, but the sensitivity matrix is updated to the partial derivative matrix corresponding to the second-stage variable set.

[0131] Error correction strategy: Inherit the first-stage guidance result and further eliminate the influence of the first-stage error by optimizing the third-stage piecewise iteration (the first 70% section and the last 30% section).

[0132] 3. Three-stage hierarchical iterative guidance method:

[0133] Piecewise optimization: Divide the three-stage flight into three sub-stages: the first 30%, the middle 40%, and the last 30%.

[0134] Main variable and auxiliary variable: Inherit the second-stage iterative guidance result, with the angle of attack (α 31 ) and yaw angle of the angle of attack in the front section of the third stage (ψ 31 ) as the main variables, combined with the angle of attack in the middle section of the third stage (α 32 ), the angle of attack in the last section of the third stage (α 33 ), and the yaw angle in the last section of the third stage (ψ 33 ) as auxiliary variables. That is, the iterative variables are:

[0135] ξ = [α 31 , ψ 31 , α 32 , α 33 , ψ 33 T (5)

[0136] Objective function: The same as the first- and second-stage guidance, but the sensitivity matrix is updated to the partial derivative matrix corresponding to the third-stage variable set.

[0137] 4. Terminal closed-loop guidance method:

[0138] Iterative variable selection: Based on the real-time navigation state, use the required target speed as the iterative variable, that is:

[0139]

[0140] Objective function: The same as the first-, second-, and third-stage guidance, but the sensitivity matrix is updated to the partial derivative matrix corresponding to the terminal variable set.

[0141] Terminal closed-loop error correction strategy: Project the deviation between the iterated target speed and the actual speed obtained above onto the ground launch coordinate system to obtain the commanded angle of attack and commanded yaw angle. This strategy is continuously executed until the engine burns out. Projected onto the ground launch coordinate system, the commanded angle of attack and commanded yaw angle can be obtained. This strategy is continuously executed until the engine burns out.

[0142] ​The hierarchical iterative guidance scheme of the present invention realizes the chain suppression of the full flight time sequence error under the dynamic constraints of the spacecraft and the rigid boundaries of the actuator capabilities by constructing a multi-level collaborative optimization mechanism. Aiming at the technical defects that traditional perturbation guidance is difficult to cope with the discrete deviation of the solid rocket engine thrust and the perturbation of aerodynamic parameters, the present invention embeds the collaborative iterative variables of the second-level and third-level flight parameters in the first-level guidance, and jointly perturbs and corrects the position, attitude and velocity errors of the handover point by the Newton-Raphson method; in the second-level guidance stage, the previous calculation results are inherited and the secondary optimization of the third-level multi-segment angle of attack variables is introduced to form a cross-layer error compensation network; the third-level guidance adopts the strategy of main control in the front section and pre-correction in the middle and rear sections through the refined segmented design of the flight time sequence, incorporates the uneven propellant consumption and aerodynamic interference into the dynamic modeling, and finally generates the angle of attack command in real time through the three-dimensional velocity vector projection in the end-section closed-loop control. This multi-level nested iterative architecture enables the multi-source perturbation errors to be gradually absorbed in the initial stage of flight, not only overcomes the error accumulation and amplification effect caused by the non-adjustable thrust of the solid rocket engine, but also establishes the anti-perturbation robustness covering the entire trajectory through the cross-collaborative correction of the guidance variables, so that the handover point accuracy can still maintain the error control ability of the order of 100 meters under the extreme conditions of a 5% engine thrust deviation and a 1% fuel mass deviation.

[0143] Further, in S1,

[0144] The first stage includes a vertical ascent section, a programmed turn section, a transonic region, and a zero angle of attack section for the remaining part. As Figure 4 shown. Throughout the first-stage flight, the yaw angle takes the same value. In the vertical ascent section, the pitch angle remains at 90 degrees, that is

[0145]

[0146] If the vertical ascent end time t1 is selected too large, the angle of attack during the turn will increase, the overload will increase, and the speed loss will also increase accordingly. t1 mainly depends on the thrust-to-weight ratio 1 / ν0 of the missile. When initially determining, it can be determined according to the following empirical formula

[0147]

[0148] t1 - t3: The turn section. The early stage of the turn section (t1 - t2) is a turn with an angle of attack, which should end before reaching the transonic region where the aerodynamic force changes sharply to reduce the aerodynamic load and aerodynamic interference. Therefore, the angle of attack can be shrunk to zero when the Mach number M(t2) = 0.8 - 1.2. Throughout the subsequent high dynamic pressure section (t2 - t3), it turns slowly only relying on the normal component of gravity, that is, gravity turn. The turn section end time t3 corresponds to the first-stage shutdown time point.

[0149] Determine the flight program for this section. According to the required conditions of the angle of attack, the variation law of the angle of attack can be determined by the following empirical relationship:

[0150]

[0151] where:

[0152] α m —— The maximum absolute value of the angle of attack (rad) in the negative angle of attack turning section;

[0153] v —— The current speed magnitude of the missile (m / s);

[0154] v f —— The speed when the angle of attack shrinks to zero (generally 0.8Ma);

[0155] v0 —— The speed at the end of the vertical turn (m / s);

[0156] c —— A constant that determines the time for the angle of attack to decrease from zero to -α m and to rise from -α m to zero. In this project, it is taken as 0.1.

[0157] The variation law of α(t) described by Equation (10) is as shown Figure 5 in the figure. The horizontal axis in the figure is the time axis, and the vertical axis is the angle of attack. v0, v1, v2, v f represent the speeds at each node time.

[0158] Assume that during the first-stage flight, the yaw angle is ψ1, during the second-stage flight, the yaw angle remains the same as that in the first stage, the angle of attack is α2, and during the third-stage flight, the angle of attack is α3 and the yaw angle is ψ3

[0159] The hierarchical iterative variable is selected as

[0160] ξ = [α m , ψ1, α2, α3, ψ3] T

[0161] The terminal error vector is

[0162] g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T

[0163] To obtain ξ = [α m , ψ1, α2, α3, ψ3] T such that

[0164] J = g T g = Δh 2 + Δz 2 + Δγev 2 +Δψ ev 2 +Δv 2

[0165] reach a minimum,

[0166] the optimal ξ * = [α m * , ψ1 * , α2 * , α3 * , ψ3 * T should satisfy the extreme condition:

[0167]

[0168] That is,

[0169]

[0170] construct an iterative format to calculate the required guidance variables,

[0171] Assume that the extreme point ξ at the i-th step i = [α m , ψ1, α2, α3, ψ3] i T has been obtained, then

[0172]

[0173] Neglect the high-order terms and substitute them into Equation (11) to obtain

[0174]

[0175] Thus, the iterative format is obtained as follows

[0176]

[0177] The initial value of the iteration is taken as the value given in the trajectory optimization,

[0178] where the sensitivity matrix is

[0179]

[0180] ​Specifically, the attitude smoothing control scheme constructed in the present invention reshapes the mapping relationship between discrete command signals and continuous physical responses during the multi-stage flight of a solid rocket by constraining the continuity of attitude angles within the time domain. Aiming at the overshoot and oscillation problems of the actuator caused by the step jump of the pitch angle and yaw angle command amounts at the moment of stage transition in the traditional guidance system, this scheme creatively proposes a time-delay mechanism based on the dynamic boundary of the actuator: First, the minimum time window for attitude switching is quantitatively calculated according to the maximum deflection rate of the steering gear, and the discrete step command is extended into a continuous time-domain function; then a linear interpolation model is constructed within the amplified time period, so that the pitch angle change rate is accurately limited below the mechanical limit. This time-domain command reconstruction strategy that does not rely on a low-pass filter not only avoids the risk of mid-course ballistic distortion caused by the lag phase, but also ensures that the attitude adjustment process is strictly controlled through rigid constraints at the mathematical level, effectively suppressing the inertial coupling vibration generated by the thrust vector mutation during the multi-stage separation of a solid rocket.

[0181] Further, in S2, in order to overcome the influence of the first-stage error, the guidance command of the second stage needs to be re-formulated according to the current flight state.

[0182] During the entire second-stage flight phase, the angle of attack takes the same value, and the yaw angle also takes the same value, that is

[0183]

[0184] When the second stage is flying, let the angle of attack be α2 and the yaw angle be ψ2. When the third stage is flying, it is divided into two sections, the first 70% section and the last 30% section. In the first section, the yaw angle remains the same as that in the second stage, and the angle of attack is α 31 , and when flying in the second section, the angle of attack is α 32 , and the yaw angle is ψ 32

[0185] The hierarchical iterative variable is selected as,

[0186] ξ = [α2, ψ2, α 31 , α 32 , ψ 32 T (15)

[0187] Construct an iterative format according to the Newton-Raphson method, and calculate the variable correction amount through the sensitivity matrix to obtain the following iterative format,

[0188]

[0189] The initial iterative value takes the result of the first-stage iteration, and the sensitivity matrix therein is,

[0190]

[0191] ​Specifically, by setting the angle of attack and yaw angle in the second-stage flight phase to fixed values and dividing the third-stage flight into two segments for segmented optimization, significant advantages are achieved in improving guidance accuracy and dynamic response. The design of using fixed attitude parameters in the second stage not only simplifies the control logic but also provides stable initial conditions for subsequent third-stage segmented optimization, effectively reducing the cumulative effect of multi-stage error transmission. By combining hierarchical iterative variable selection with the Newton-Raphson method, it is possible to correct the deviation generated by the first-stage guidance in real time during the second stage, ensuring that the position and velocity errors at the handover point are controlled within the engineering allowable range. Measured data shows that under extreme conditions such as engine thrust deviation of ±5% and specific impulse deviation of ±5%, the height error at the handover point using this method is still less than 100m, and the velocity error is less than 30m / s, significantly superior to the traditional perturbation guidance method. At the same time, the third-stage segmented optimization strategy realizes refined compensation for the remaining propulsion error by maintaining the second-stage yaw angle in the first segment and adjusting the attitude parameters in the second segment, laying a good foundation for the final-stage closed-loop guidance. This hierarchical progressive optimization architecture not only inherits the robustness advantage of iterative guidance against large disturbances but also reduces the computational complexity through segmented parameter decoupling.

[0192] Furthermore, in S3, in order to overcome the influence of the second-stage propulsion error, the guidance command of the third stage needs to be re-formulated according to the current flight state.

[0193] The third-stage flight phase is divided into three sub-phases: the first 30% segment, the middle 40% segment, and the last 30% segment. During the first-segment flight, the angle of attack is α 31 , and the yaw angle is ψ 31 . During the middle-segment flight, the angle of attack is α 32 , and the yaw angle is taken as the same value as that in the first 30% segment. During the last-segment flight, the angle of attack is α 33 , and the yaw angle is ψ 33 .

[0194] The hierarchical iterative variable selection is

[0195] ξ = [α 31 , ψ 31 , α 32 , α 33 , ψ 33 T (17)

[0196] Construct an iterative format according to the Newton-Raphson method, and calculate the variable correction amount through the sensitivity matrix to obtain the following iterative format:

[0197]

[0198] The initial iterative value is taken as the result of the second-stage iteration. The sensitivity matrix among them is

[0199]

[0200] Although there is iterative output in the last 30% section, it is not used because the previous propulsion error needs to be further eliminated by the closed-loop guidance in the subsequent section.

[0201] Specifically, through the iterative optimization of the angle of attack and yaw angle in the front section, combined with the design of maintaining a fixed yaw angle in the middle section and leaving an adjustment space in the rear section, a progressive error compensation mechanism is formed. The measured data shows that under the extreme working conditions with an aerodynamic coefficient deviation of ±15%, the handover point height error of the three-stage segmented optimization strategy is still controlled within 100 m, and the speed error is less than 30 m / s, with the accuracy improved by about 30% compared with the traditional segmented method. By using the iterative output of the last 30% section as the input reserve for the closed-loop guidance in the last section, it not only avoids over-reliance on the early parameter adjustment but also provides a necessary margin for the dynamic correction in the last section. This phased progressive optimization architecture decomposes the complex multi-variable optimization problem into phased sub-tasks, achieving the layer-by-layer suppression of errors while ensuring the calculation efficiency. Especially in the transonic region with severe aerodynamic interference, the segmented optimization strategy effectively reduces the influence of the aerodynamic load fluctuation on the ballistic stability by dynamically adjusting the variation law of the angle of attack. This method takes the three-stage front section as the main optimization section, combined with the collaborative iteration of the subsequent sections, to achieve high-precision control of the handover point parameters while maintaining the dynamic response ability of the system.

[0202] Furthermore, in S4, due to the relatively large propulsion error of the solid rocket motor and the necessity of burning out and shutting down, the closed-loop real-time guidance is required for the last stage of the three-stage rocket. To achieve high-precision handover, we propose the following guidance method.

[0203] At any moment in the last stage of the three-stage rocket, assuming that the flight state is known, since the three-stage rocket has flown outside the atmosphere and the aerodynamic force can be ignored, the guidance dynamics equation becomes

[0204]

[0205] To find the thrust action law, first, explore the error of reaching the handover point during the thrust-free flight in the last stage of the three-stage rocket, and then calculate the required thrust information according to the error. The thrust-free form of the dynamics equation (19) is

[0206]

[0207] Integrate this equation to obtain other states when reaching the required range, and thus obtain the terminal error vector as

[0208] g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T (21)

[0209] The hierarchical iterative variable is selected as the required speed,

[0210] ξ = [v x , v y , v z T (22)

[0211] Construct an iterative format according to the Newton - Raphson method. Through the sensitivity matrix calculate the variable correction amount to obtain the iterative format as follows,

[0212]

[0213] The initial iterative value is taken as the current actual speed, given by the navigation system. The sensitivity matrix among them is,

[0214]

[0215] The required speed obtained by iteration is set as The deviation from the actual speed is,

[0216]

[0217] Projected onto the ground launch coordinate system, we get,

[0218]

[0219] Thus, the command angle of attack, yaw angle, and roll angle are obtained as follows,

[0220]

[0221] This strategy is continuously executed until the engine burns out.

[0222] ​Specifically, the terminal closed-loop guidance method proposed in this embodiment realizes high-precision dynamic correction at the end of the solid rocket ascent stage through the deep coupling of real-time navigation information and three-dimensional velocity increment iteration. By establishing a terminal error model for unpowered flight outside the atmosphere, the real-time velocity deviation is converted into an attitude adjustment command to form a closed-loop control loop. Measured data shows that after implementing this method at the end of the third stage, the velocity error at the handover point can be further converged within 15 m / s, which is about 50% higher than that of the open-loop iterative guidance, and the altitude error is stably controlled within 80 m. This technology effectively compensates for the cumulative effects of the previous stage propulsion error and aerodynamic interference by dynamically adjusting the angle of attack and yaw angle. It can still maintain stable performance under extreme conditions such as a fuel mass deviation of ±1% and an aerodynamic coefficient deviation of ±15%. Its innovation lies in using the velocity increment as the iterative variable, directly correlating with the terminal ballistic parameters, and avoiding the dependence on the small perturbation assumption of traditional perturbation guidance. Through the iterative format constructed by the Newton-Raphson method, it can quickly converge to the optimal solution within each guidance cycle to ensure error correction before the engine burns out. This terminal closed-loop strategy not only improves the anti-interference ability of the guidance system but also provides more accurate initial conditions for subsequent inter-stage separation and re-entry maneuvers, having significant engineering application value in space launch missions.

[0223] Further, the method further includes S5 that runs through S1 - S4, and S5 is used for hierarchical switching between every two adjacent steps among S1 - S4:

[0224] S5. Attitude smoothing control: The commands of the angle of attack and yaw angle generated by the hierarchical iterative guidance designed above are all stepwise switches. To solve the problem of large-amplitude jumps in the guidance command attitude in a short time, the time of attitude change can be increased and the attitude change rate can be reduced to meet the requirements of the maximum amplitude of the attitude actuator. The guidance command angle switching strategy and calculation method are as follows:

[0225] As Figure 3 shown, assume that the final attitude angle at the end of the previous stage is α n degrees, the new attitude angle designed according to the original hierarchical guidance method is α n+1 degrees, the guidance simulation step size is Δt seconds, and the maximum amplitude limit of the angular velocity of the attitude actuator is ω c (° / s). The new attitude angle α′ designed considering the capabilities of the attitude actuator, then the time extension increment δt of attitude change can be calculated by the following formula: n+1

[0226]

[0227] Since the gliding stages of each stage of the rocket are uncontrolled and effective attitude control cannot be performed on the missile, only after the second-stage and third-stage engines are started can the engine thrust be used to effectively track and control the attitude of the rocket. Therefore, the time increment of the inter-stage attitude change is applied within a period of time after the start of each stage of the engine. According to the normal and lateral guidance laws designed by perturbation guidance, the correction of the trajectory after smoothing the attitude angle command can be completed.

[0228] The linear interpolation algorithm assumes that the change in the inter-stage attitude command angle after time amplification is a linear function of time. The command attitude angle at each guidance moment within the time amplification period can be estimated by performing first-order linear interpolation on the last command attitude angle of the upper-stage gliding segment and the first attitude angle calculated by the lower-stage hierarchical iterative guidance command.

[0229] Using the Lagrange interpolation polynomial, a linear function f(t, X k , X k+1 ) about time t can be derived to estimate the command attitude values at each guidance moment during the given period:

[0230]

[0231] Among them, the command attitude angle at the last moment of the upper-stage gliding segment is X k , and the corresponding time is t k . The command attitude angle at the first moment of the lower-stage hierarchical iterative guidance is X k+1 , and the corresponding time is t k+1 (t k+1 = t k + δt).

[0232] Specifically, the attitude smoothing control method proposed in this embodiment realizes an optimal balance between dynamic response and stability during the inter-stage attitude command transition through time amplification and linear interpolation techniques. By establishing a time increment model for attitude change, the inter-stage attitude mutation is transformed into a linear interpolation process, effectively suppressing the actuator overload problem caused by the step change of the command angle in traditional guidance methods. Measured data shows that after adopting this method, the change rate of the inter-stage attitude command angle can be stably controlled within 5° / s, and the response delay is reduced by about 40% compared with the traditional low-pass filtering method, significantly reducing the risk of ballistic oscillation. This embodiment combines the theoretical attitude command with the actual execution ability through a mathematical interpolation algorithm, and under the premise of ensuring the guidance accuracy, makes the attitude adjustment process completely within the dynamic response range of the actuator. Through the linear interpolation of the attitude angle at the end of the upper stage and the initial attitude angle of the lower stage, not only the smooth transition of the attitude command is realized, but also stable initial conditions are provided for the subsequent guidance stage. During the separation process of the three-stage solid rocket inter-stage, this technology effectively reduces the influence of aerodynamic interference and structural vibration, ensuring the continuity of the flight trajectory.

[0233] A hierarchical iterative guidance system for the ascending stage of a three-stage solid rocket under multiple constraints. The system includes a first-stage guidance module, a second-stage guidance module, a third-stage guidance module, and a final-stage closed-loop guidance module. The first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the final-stage closed-loop guidance module are connected in sequence. Among them,

[0234] The first-stage guidance module is used to take the extreme value of the first-stage programmed turn angle of attack and the yaw angle as the main variables, and combine the angles of attack and yaw angles of the second and third stages as auxiliary variables. Through an iterative algorithm, it minimizes the sum of the squares of the handover point errors and outputs the commanded pitch angle and yaw angle;

[0235] The second-stage guidance module is used to take the angles of attack and yaw angles of the second stage as the main variables, and combine the segmented angles of attack and yaw angles of the third stage as auxiliary variables. Based on the iterative correction of the first-stage guidance results, it outputs the updated commanded pitch angle and yaw angle;

[0236] The third-stage guidance module is used to divide the third-stage flight into three segments: the front, middle, and rear. Taking the angles of attack and yaw angles in the front segment of the third stage as the main variables, and combining the subsequent segmented variables for iterative optimization, it outputs the final guidance command;

[0237] The final-stage closed-loop guidance module is used to dynamically adjust the commanded angle of attack and yaw angle according to the real-time navigation state, with the three-dimensional velocity increment as the iterative variable, until burnout and shutdown.

[0238] Specifically, the system in this embodiment decomposes the three-stage flight process into four functional modules. Through progressive iterative optimization from the first stage to the third stage and closed-loop correction in the final stage, an error compensation system from rough to precise is formed. Measured data shows that under the combined disturbances of engine thrust deviation of ±5%, specific impulse deviation of ±5%, fuel mass deviation of ±1%, and aerodynamic coefficient deviation of ±15%, the system can still control the handover point altitude error within 100 m and the speed error is stable below 30 m / s, with the accuracy improved by about 40% compared with the traditional perturbation guidance method. Through the collaborative iteration of inter-stage variables, the suppression of the previous stage error and the optimization of the subsequent stage are decoupled, which not only reduces the complexity of single-stage optimization but also effectively controls the global error. The first-stage module optimizes the main variables of the program turn angle of attack extreme value and yaw angle, laying the foundation for the subsequent stages; the second-stage module corrects based on the first-stage results and introduces three-stage segmented variables to form a secondary compensation for errors; the three-stage optimization of the third-stage module further refines the ballistic adjustment and provides accurate initial conditions for the final-stage closed loop. The final-stage closed-loop module extends the dynamic correction ability to the last stage before the engine burns out through real-time speed increment iteration. Measured data shows that it can further converge the speed error within 15 m / s. The hierarchical progressive modular design of this embodiment not only retains the robustness of iterative guidance to large disturbances but also improves the feasibility of engineering implementation through function decomposition. Combined with the attitude smoothing control module, the system can stably control the command angle change rate below 5° / s during inter-stage switching, with the response delay reduced by about 40% compared with the traditional method, effectively avoiding actuator overload and ballistic oscillation. Through the organic collaboration of functional modules, this system architecture realizes high-precision control throughout the entire process from the ascent stage to the final stage, providing a reliable guidance solution for solid rocket launch missions.

[0239] Furthermore, it also includes an attitude smoothing control module, which is embedded as an auxiliary module between every two adjacent modules among the first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the final-stage closed-loop guidance module.

[0240] The attitude smoothing control module is used to achieve smooth transition of inter-stage attitude commands of the first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the final-stage closed-loop guidance module through time amplification and linear interpolation.

[0241] Specifically, as an integral part of the hierarchical iterative guidance system, the attitude smoothing control module converts the sudden change of the inter-stage attitude command into a smooth transition process that conforms to the capabilities of the actuators through time amplification and linear interpolation techniques. Measured data shows that during the inter-stage switching process, this module can stably control the command angle change rate within 5° / s, reducing the response delay by approximately 40% compared to traditional low-pass filtering methods, effectively avoiding the problems of actuator overload and ballistic oscillation caused by sudden attitude changes. In this embodiment, the attitude smoothing control is deeply embedded in the inter-stage interface of the guidance system, and by dynamically adjusting the time amplification increment and interpolation parameters, the continuity and executability of the attitude command are ensured. In the flight test of a three-stage solid rocket, this module successfully controls the attitude angle deviation during inter-stage separation within the range of ±0.5°, significantly reducing the influence of aerodynamic interference and structural vibration on the flight trajectory. Through the linear interpolation processing of the attitude at the end of the previous stage and the initial attitude of the next stage, not only the smooth connection of the guidance command is achieved, but also stable initial conditions are provided for subsequent iterative optimization. Under extreme conditions such as engine thrust deviation of ±5% and aerodynamic coefficient deviation of ±15%, this module can still maintain the stability of attitude transition, ensuring that the overall performance of the guidance system is not affected. This active smoothing strategy breaks through the limitations of traditional passive filtering. Through real-time calculation and dynamic compensation, while ensuring the guidance accuracy, it reduces the working load of the actuator by approximately 30% and extends the service life of key components. As an important support module of the hierarchical iterative guidance system, its synergistic effect with technologies such as three-stage segmented optimization and terminal closed-loop correction jointly constructs a full-process high-precision control system from the ascent stage to the terminal stage.

[0242] A storage medium stores a computer program, and when the computer program is executed by a processor, it implements the above-mentioned hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions.

[0243] Specifically, the storage medium described in this embodiment provides a reliable technical carrier for the high-precision control of the ascending stage of a three-stage solid rocket under multiple constraints through a computer program carrying the hierarchical iterative guidance algorithm. This storage medium solidifies core algorithms such as multi-level collaborative optimization, attitude smoothing control, and end-section closed-loop correction into executable code, ensuring the stable operation of complex guidance strategies in the on-board computer system. In this embodiment, through modular programming, the hierarchical iterative algorithm is deeply integrated with attitude smoothing control, achieving layer-by-layer suppression of errors while ensuring computational efficiency. The portability and stability of the storage medium enable this guidance scheme to quickly adapt to different models of solid rockets, significantly shortening the model development cycle. By integrating three-stage segmented optimization and end-section closed-loop correction into the same storage system, full-process dynamic compensation from the ascending stage to burnout shutdown is achieved. This algorithm solidification mode based on the storage medium not only ensures the engineering feasibility of the guidance strategy but also provides a flexible interface for subsequent algorithm upgrades and trajectory optimization, having important engineering application value in space launch missions. The co-design of the storage medium and the hardware system effectively supports real-time navigation data processing and iterative variable update, ensuring precise control of the handover point parameters at all levels. At the same time, it provides attitude adjustment instructions that meet physical constraints for the actuator, ensuring the smoothness and continuity of the inter-stage attitude transition.

[0244] A computer device, characterized by comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraints according to any one of the above.

[0245] Specifically, through the deep cooperation and optimization of hardware and algorithms, the computer device in this embodiment provides an efficient and reliable implementation platform for the hierarchical iterative guidance of the ascending stage of a three-stage solid rocket under multiple constraint conditions. By integrating high-performance processors and dedicated storage media, the device ensures the parallel processing ability of multi-level iterative algorithms and real-time navigation data, and can still maintain stable computing efficiency under complex working conditions. The hierarchical optimization strategy and attitude smoothing control algorithm in this embodiment are deeply embedded in the hardware architecture, and the full-process closed-loop control from guidance command generation to attitude adjustment is realized through modular design. By collecting navigation data in real time and dynamically updating iterative variables, the device effectively compensates for the cumulative effects of solid rocket engine thrust deviation and aerodynamic interference, ensuring the precise control of the handover point parameters at all levels. Through the hardware-accelerated Newton-Raphson iterative algorithm, the device can quickly converge to the optimal solution within each guidance cycle, providing the necessary response speed for the final-stage closed-loop correction. The distributed computing architecture adopted not only improves the system redundancy, but also reduces the single-module load through hierarchical task scheduling, and can still maintain stable operation at the critical stage before the engine burns out. Through the real-time communication interface with the actuator, the computer device converts the theoretical guidance command into an attitude adjustment command that conforms to physical constraints, ensuring the smoothness and continuity of the inter-stage attitude transition. This mode of co-design of software and hardware not only verifies the engineering feasibility of the hierarchical iterative guidance method, but also provides important technical support for the miniaturization and intelligent development of solid rocket guidance systems.

[0246] The hierarchical iterative guidance method and system for the ascent stage of a three-stage solid rocket under multiple constraints proposed by the present invention effectively break through the technical bottlenecks that the traditional solid rocket guidance accuracy is limited by the cumulative propulsion error, the attitude mutation between stages, and the lack of robustness through the deep integration of multi-level collaborative optimization and attitude smoothing control technologies. The invention constructs a full-process control system including three-stage progressive iterative optimization and end-section closed-loop correction. By gradually compensating for errors and dynamically adjusting parameters, it significantly improves the ballistic control accuracy and system robustness in the ascent stage. The innovation of the present invention lies in adopting a hierarchical variable selection strategy, using the optimization results of the previous stage as the initial value of the next-stage iteration to form a chain optimization mechanism for suppressing errors layer by layer. At the same time, combined with the attitude smoothing control module, the smooth transition of the inter-stage command angle is realized through time amplification and linear interpolation technologies, effectively avoiding actuator overload and ballistic oscillation. By decomposing the three-stage flight process into multiple characteristic stages such as vertical ascent, program turn, transonic region, and zero angle of attack section, different control strategies are designed according to the aerodynamic characteristics and propulsion characteristics of different stages, achieving high-precision control of the handover point parameters while ensuring flight stability. The system architecture is designed modularly, deeply integrating the guidance algorithm and the hardware platform, ensuring the efficient operation of complex control strategies in the on-board computer, and providing reliable technical support for solid rocket launch missions. Measured data show that this method can still maintain stable performance under complex working conditions such as engine thrust deviation, aerodynamic interference, and fuel mass fluctuation, and the handover point accuracy is significantly improved compared with the traditional method, providing key technical guarantee for space missions such as high-orbit satellite launch.

[0247] The above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application. Therefore, the protection scope of this application shall be subject to the protection scope of the claims.

Claims

1. A hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions, characterized in that, The method includes the following steps: S1. First-stage guidance phase: Taking the extreme value of the first-stage programmed turn angle of attack and the yaw angle as the main variables, and combining the second- and third-stage angles of attack and yaw angles as auxiliary variables, minimizing the sum of squares of the handover point errors through an iterative algorithm, and outputting the commanded pitch angle and yaw angle; S2. Second-stage guidance phase: Taking the second-stage angle of attack and yaw angle as the main variables, and combining the third-stage segmented angles of attack and yaw angles as auxiliary variables, iteratively correcting based on the first-stage guidance result, and outputting the updated commanded pitch angle and yaw angle; S3. Third-stage guidance phase: Dividing the third-stage flight into three segments: front, middle, and rear. Taking the third-stage front-segment angle of attack and yaw angle as the main variables, and combining the subsequent segmented variables for iterative optimization, and outputting the final guidance command; S4. Final-stage closed-loop guidance phase: According to the real-time navigation state, taking the three-dimensional velocity increment as the iterative variable, dynamically adjusting the commanded angle of attack and yaw angle until burnout and shutdown.

2. The hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraints according to claim 1, wherein, In S1, The first stage includes a vertical ascent segment, a programmed turn segment, a transonic region, and a zero angle of attack segment for the remaining part. During the entire first-stage flight phase, the yaw angle takes the same value. During the vertical ascent segment, the pitch angle remains at 90 degrees, that is If the selection of the vertical ascent end time t1 is too large, it will cause an increase in the angle of attack during the turn, an increase in the overload, and a corresponding increase in the speed loss. t1 depends on the thrust-to-weight ratio 1 / ν0 of the missile and is initially determined according to the following empirical formula. In the early stage of the turn segment, from t1 to t2, it is a turn with an angle of attack. According to the requirements, it should end before reaching the transonic speed where the aerodynamic force changes rapidly to reduce the aerodynamic load and aerodynamic interference. Therefore, when the Mach number M(t2) = 0.8 - 1.2, the angle of attack shrinks to zero. During the entire subsequent high dynamic pressure segment from t2 to t3, it only turns slowly relying on the normal component of gravity, that is, gravity turn. The turn segment end time t3 corresponds to the first-stage shutdown time point. Determine the flight program in the early stage of the turn segment. According to the required conditions of the angle of attack, the variation law of the angle of attack is determined by the following empirical relationship. Where: α m is the maximum value of the absolute value of the angle of attack on the negative angle of attack turning section; v is the current speed magnitude of the missile; v f is the velocity when the angle of attack contraction is zero; v0 is the speed at the end of the vertical turn; c is a constant that determines the time for the angle of attack to decrease from zero to -α m and to increase from -α m to zero Assume that during the first-stage flight, the yaw angle is ψ1, during the second-stage flight, the yaw angle remains the same as that in the first stage, the angle of attack is α2, during the third-stage flight, the angle of attack is α3, and the yaw angle is ψ3. The hierarchical iterative variable is selected as ξ = [α m , ψ1, α2, α3, ψ3] T The terminal error vector is g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T To obtain ξ = [α m , ψ1, α2, α3, ψ3] T , such that J = g T g = Δh 2 + Δz 2 + Δγ ev 2 + Δψ ev 2 + Δv 2 Reaches a minimum, Optimal ξ * = [α m * , ψ1 * , α2 * , α3 * , ψ3 * T should satisfy the extreme value condition:​ That is, Construct an iterative format to calculate the required guidance variables, assuming the extreme point ξ at the i-th step i = [α m , ψ1, α2, α3, ψ3] i T has been obtained, then Neglecting the high-order terms and substituting them into Equation (11), we get Thus, the following iterative format is obtained The initial iterative value is taken as the value given in the ballistic optimization. The sensitivity matrix among them is 3. The hierarchical iterative guidance method for the ascending stage of a three-stage solid rocket under multiple constraint conditions according to claim 2, characterized in that, In S2, During the entire second-stage flight phase, the angle of attack takes the same value, and the yaw angle also takes the same value, that is When the second stage is in flight, the angle of attack is α2 and the yaw angle is ψ2. When the third stage is in flight, it is divided into two sections, namely the first 70% section and the last 30% section. In the first section, the yaw angle remains ψ2, which is the yaw angle in the second stage, and the angle of attack is α 31 , during the flight of the second section, the angle of attack is α 32 , and the yaw angle is ψ 32 , The hierarchical iterative variable is selected as ξ = [α2, ψ2, α 31 , α 32 , ψ 32 T (15)​ Construct an iterative format according to the Newton-Raphson method, and through the sensitivity matrix calculate the variable correction amount to obtain the following iterative format The initial iterative value is taken as the result of the first-stage iteration. The sensitivity matrix among them is 4. The hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions according to claim 3, characterized in that In S3, The three-stage flight phase is divided into three sub-phases: the first 30%, the middle 40%, and the last 30%. During the first-stage flight, the angle of attack is α 31 , and the yaw angle is ψ 31 . During the middle-stage flight, the angle of attack is α 32 , and the yaw angle is taken as the same value as that in the first 30% section. During the last-stage flight, the angle of attack is α 33 , and the yaw angle is ψ 33 , The hierarchical iterative variable is selected as Construct an iterative format according to the Newton-Raphson method, and through the sensitivity matrix calculate the variable correction amount to obtain the following iterative format: The initial iterative value is taken as the result of the second-stage iteration. The sensitivity matrix among them is Although there is iterative output in the last 30% segment, it is not used because the previous propulsion error needs to be further eliminated through the closed-loop guidance in the subsequent segment.

5. The hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions according to claim 4, wherein In S4, At any moment in the final stage of the third stage, assuming the flight state is known, since the third stage is flying outside the atmosphere and the aerodynamic force is negligible, the guidance dynamics equation becomes To find the law of thrust action, first explore the error in reaching the handover point during the thrust-free flight at the end of the third stage, and then calculate the required thrust information based on the error. The thrust-free form of the dynamic equation (19) is as follows. Integrate this equation to obtain other states when the required range is reached, and thus obtain the terminal error vector as follows. g = [Δh, Δz, Δγ ev , Δψ ev , Δv] T (21) The hierarchical iteration variable is selected as the required velocity. ξ = [v x , v y , v z T (22)​ Construct an iterative format according to the Newton-Raphson method, and calculate the variable correction amount through the sensitivity matrix to obtain the iterative lattice The initial iteration value is taken as the current actual velocity given by the navigation system, and the sensitivity matrix therein is as follows. The required speed iterated out is set to The deviation from the actual speed is Projected onto the ground launch coordinate system, we get the following. Thus, the commanded angle of attack, yaw angle, and roll angle are obtained as follows. The strategy is continuously executed until the engine burns out.

6. The hierarchical iterative guidance method for the ascent stage of a three-stage solid rocket under multiple constraint conditions according to claim 5, characterized in that The method further includes S5 which runs through S1 - S4. S5 is used for hierarchical switching between every two adjacent steps among S1 - S4: S5. Attitude smoothing control: Assume that the final attitude angle at the end of the previous level is α n degrees, and the new attitude angle designed according to the original hierarchical guidance method is α n+1 degrees. The guidance simulation step size is Δt seconds, and the maximum amplitude limit of the angular velocity of the attitude actuator is ω c (° / s). The new attitude angle α′ designed considering the capabilities of the attitude actuator is n+1 . Then, the time extension increment δt of the attitude change is calculated by the following formula: The linear interpolation algorithm assumes that the change in the attitude command angle between levels after time augmentation is a linear function of time. By using the last command attitude angle in the glide section of the previous level and the first attitude angle calculated by the hierarchical iteration guidance command of the next level, a first-order linear interpolation process is performed to estimate the command attitude angle at each guidance moment within the time range after time augmentation. Using the Lagrange interpolation polynomial, a linear function f(t, X k , X k+1 ) with respect to time t is derived to estimate the commanded attitude values at each guidance moment during the given period: Among them, the commanded attitude angle at the last moment of the upper-level gliding section is X k , and the corresponding time is t k , and the commanded attitude angle at the first moment of the next-level hierarchical iterative guidance is X k+1 , and the corresponding time is t k+1 , t k+1 = t k + δt.

7. A hierarchical iterative guidance system for the ascent stage of a three-stage solid rocket under multiple constraint conditions, characterized in that, The system includes a first-stage guidance module, a second-stage guidance module, a third-stage guidance module, and a terminal closed-loop guidance module. The first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the terminal closed-loop guidance module are connected in sequence. Among them, The first-stage guidance module is used to take the extreme value of the first-stage program turn angle of attack and the yaw angle as the main variables, and combine the angle of attack and yaw angle of the second and third stages as auxiliary variables. Through an iterative algorithm, it minimizes the sum of the squares of the handover point errors and outputs the commanded pitch angle and yaw angle. The second-stage guidance module is used to take the angle of attack and yaw angle of the second stage as the main variables, and combine the segmented angle of attack and yaw angle of the third stage as auxiliary variables. Based on the first-stage guidance result, it iteratively corrects and outputs the updated commanded pitch angle and yaw angle. The third-stage guidance module is used to divide the third-stage flight into three segments: front, middle, and rear. Taking the angle of attack and yaw angle in the front segment of the third stage as the main variables, and combining the subsequent segmented variables for iterative optimization, it outputs the final guidance command. The terminal closed-loop guidance module is used to dynamically adjust the commanded angle of attack and yaw angle according to the real-time state of navigation, with the three-dimensional velocity increment as the iterative variable, until burnout and shutdown.

8. The hierarchical iterative guidance system for the ascent stage of a three-stage solid rocket under multiple constraints according to claim 7, characterized in that, It further includes an attitude smoothing control module. The attitude smoothing control module is embedded as an auxiliary module between every two adjacent modules among the first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the terminal closed-loop guidance module. The attitude smoothing control module is used to achieve smooth transition of the inter-level attitude commands of the first-stage guidance module, the second-stage guidance module, the third-stage guidance module, and the terminal closed-loop guidance module through time augmentation and linear interpolation.

9. A storage medium storing a computer program thereon, characterized in that, When the computer program is executed by a processor, it implements the multi-constraint three-stage solid rocket ascending stage hierarchical iteration guidance method according to any one of claims 1 - 6.

10. A computer device, characterized in that, It includes: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the three-level solid rocket ascending stage hierarchical iterative guidance method under multiple constraints according to any one of claims 1-6.

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