Parameter optimization design method based on non-static error tilt stable loop
Patent Information
- Application Number
- CN202411492442.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-24
- Publication Date
- 2026-10-13
AI Technical Summary
但是，当系统达到稳态时，这种回路结构必然会存在稳态误差
[0029]根据本发明提供的具体实施例，本发明公开了以下技术效果：针对常规倾斜角速度比例积分回路不能有效消除战术导弹滚动通道存在复杂扰动的问题，本发明提出一种无静差倾斜稳定回路结构，采用极点配置方法，推导了期望特征多项式系数与无静差倾斜稳定回路控制参数之间的解析关系，通过带有非线性自适应惯性因子的粒子群优化算法，对期望特征多项式系数进行优化设计，优化结果能够同时满足时域和频域指标要求。该回路结构能够快速消除由初始扰动产生的倾斜角误差，克服各项滚动干扰，保证导弹在飞行过程中倾斜角误差始终为零或尽可能小，满足对倾斜角误差的工程应用要求。
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Figure CN122902198A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of missile rolling channel design technology, and in particular to a parameter optimization design method based on a zero-static-error tilt stabilization loop. Background Technology
[0002] For tactical missile flight control systems, it is typically required that the missile's tilt angle be zero or maintained within a certain range during flight, and that the tilt angular velocity be stabilized or limited to a certain value. To meet these requirements, the missile's roll path is generally designed as a proportional-integral (PI) tilt angular velocity structure, where the tilt angle is stabilized only by the stabilization control system, without actual control—a tilt stabilization loop structure. Existing literature indicates that this control loop structure is effective for missiles with small conventional disturbances. However, when the system reaches steady state, this loop structure inevitably introduces steady-state error. Therefore, when there are large and complex disturbances in the roll path, simply using a PI control loop structure will not effectively eliminate the tilt angle error under the influence of disturbances, thus failing to maintain the tilt angle at zero or as small as possible. To address this problem, existing technologies employ online estimation of the roll disturbance torque and subsequent feedforward compensation in the loop to reduce the steady-state tilt angle error during missile flight. However, this design method requires that the real-time online estimated roll disturbance torque be as close as possible to the true value, which places high demands on the designer's engineering application experience. Therefore, how to design a loop structure to effectively eliminate the complex disturbances present in the rolling channel of tactical missiles is an urgent problem to be solved by those skilled in the art. Summary of the Invention
[0003] The purpose of this invention is to provide a parameter optimization design method based on a zero-steady-error tilted stable loop to solve the problems mentioned in the background art.
[0004] To achieve the above objectives, the present invention provides the following solution: a parameter optimization design method based on a zero-steady-error tilted stable loop, the specific steps of which include the following:
[0005] Design a zero-static-error tilt stabilization loop according to missile control requirements;
[0006] The pole placement method is used to solve the analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in the zero steady-state error tilted stable loop. Thus, the parameter optimization problem of the zero steady-state error tilted stable loop is transformed into using the coefficients of the desired characteristic polynomial as the variable to be optimized.
[0007] The coefficients of the desired characteristic polynomial are optimized using a particle swarm optimization algorithm with a nonlinear dynamic adaptive inertia factor.
[0008] Preferably, the zero-static-error tilt stabilization loop is a double-loop tilt stabilization loop structure.
[0009] Preferably, in the zero-steady-error tilt stabilization loop, the closed-loop transfer function from the control command to the tilt angle is:
[0010]
[0011] Where, k γ1 k γ2 k γ3 For the controller parameters in a zero-steady-state tilt steady-state loop, k dj For the rudder system transmission coefficient, u z For control commands, γ is the tilt angle, and k nt Here are the gyroscope transfer coefficients: K3 = -c3 / c1, T3 = 1 / c1. Let be the rolling damping moment coefficient, q be the dynamic pressure, s be the characteristic area of the missile, L be the characteristic length of the missile, and V be the missile's flight velocity. J is the aileron control moment coefficient. x1 It is the moment of inertia about the longitudinal axis of the projectile.
[0012] Preferably, the analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in the zero-steady-state-error tilt stabilization loop is as follows:
[0013]
[0014] Where p1, p2, p3, and p4 are the expected characteristic polynomial parameters.
[0015] Preferably, the adjustment strategy expression for the nonlinear dynamic adaptive inertia factor is:
[0016]
[0017]
[0018] Where k is the generation number, and when k = 1, f(1) can be calculated from the above formula. w max w is the maximum value of the inertia factor. min k is the minimum value of the inertia factor. min k is the number of iterations required for the inertia factor to reach its maximum value. max Let w(k) be the number of iterations when the inertia factor reaches its minimum value, and w(k) be the inertia factor.
[0019] Preferably, the specific steps for optimizing the coefficients of the desired characteristic polynomial using a particle swarm optimization algorithm with a nonlinear dynamic adaptive inertia factor are as follows:
[0020] Step 1: Set initial parameters and randomly generate initial position and velocity;
[0021] Step 2: Calculate the fitness value for each particle based on the problem to be solved;
[0022] Step 3: Calculate and update the inertia factor value;
[0023] Step 4: Calculate and update the position and velocity of each particle;
[0024] Step 5: Update the global optimal solution and the individual optimal solution;
[0025] Step 6: Determine if the termination condition is met. If not, repeat steps 2-5 for iterative optimization. If the condition is met, output the global optimal solution as the best individual.
[0026] Preferably, the fitness value corresponding to each particle is calculated using a weighted multi-objective function, the expression of which is:
[0027]
[0028] Where, x i0 For the i-th performance metric requirement, x i Let ω represent the actual performance of the i-th parameter affected by the parameters p1, p2, p3, and p4 to be optimized, where m is the number of performance metrics and ω is the value of ω. i is the weighting coefficient for the i-th performance item.
[0029] According to specific embodiments provided by the present invention, the following technical effects are disclosed: Addressing the problem that conventional tilt angular velocity proportional-integral loops cannot effectively eliminate complex disturbances in the roll channel of tactical missiles, the present invention proposes a zero-static-error tilt stabilization loop structure. Using the pole placement method, the analytical relationship between the expected characteristic polynomial coefficients and the control parameters of the zero-static-error tilt stabilization loop is derived. Through a particle swarm optimization algorithm with a nonlinear adaptive inertia factor, the expected characteristic polynomial coefficients are optimized, and the optimization result simultaneously meets the time-domain and frequency-domain performance requirements. This loop structure can quickly eliminate tilt angle errors caused by initial disturbances, overcome various roll interferences, and ensure that the tilt angle error of the missile is always zero or as small as possible during flight, meeting the engineering application requirements for tilt angle error. Attached Figure Description
[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0031] Figure 1 This is a flowchart of the method of the present invention;
[0032] Figure 2 This is a structural diagram of the tilt-stabilized loop without static error of the present invention;
[0033] Figure 3 This is a schematic diagram of the control parameter optimization process for the zero-static-error tilt stabilization loop of the present invention;
[0034] Figure 4 This is a graph showing the tilt angle response curve of the feature point unit step command of the present invention.
[0035] Figure 5 This is a graph showing the tilt angular velocity response curve under a unit step command at a feature point in this invention.
[0036] Figure 6 This is a plot of the tilt angle response curve for a unit step aileron disturbance at a characteristic point of the present invention.
[0037] Figure 7 This is a graph showing the tilt angular velocity curve of the characteristic point unit step aileron perturbation of the present invention;
[0038] Figure 8 This is a frequency domain characteristic curve of the feature points of the present invention;
[0039] Figure 9 This is a diagram showing the tilt angle response curve of the conventional tilting loop structure used in this invention.
[0040] Figure 10 This is a graph showing the variation of the projectile's rolling interference torque according to the present invention.
[0041] Figure 11 This is a graph showing the tilt angular velocity response of the six-degree-of-freedom simulated projectile of the present invention.
[0042] Figure 12 The diagram shows the tilt angle response curve of the six-degree-of-freedom simulated projectile of this invention. Detailed Implementation
[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0044] The purpose of this invention is to provide a parameter optimization design method based on a zero-steady-error tilt-stabilized loop, such as... Figure 1 As shown, the specific steps include the following:
[0045] Step 1: Design a zero-static-error tilt stabilization loop according to missile control requirements;
[0046] Step 2: Using the pole placement method, solve the analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in the zero steady-state error tilted stable loop. Thus, the parameter optimization problem of the zero steady-state error tilted stable loop is transformed into using the coefficients of the desired characteristic polynomial as the variable to be optimized.
[0047] Step 3: Optimize the coefficients of the desired characteristic polynomial using a particle swarm optimization algorithm with a nonlinear dynamic adaptive inertia factor.
[0048] Furthermore, such as Figure 2 As shown, the zero-static-error tilt stabilization loop is a double-loop tilt stabilization loop structure. In the figure, γ is the tilt angle around the longitudinal axis of the projectile, and δ... f For equivalent aileron interference, u z For control commands, e γ For tilt angle error, G dj (s) is the transfer function of the rudder system, G nt (s) is the gyroscope transfer function, k γ1 k γ2 k γ3 These are the parameters for a tilt-stabilized loop controller with no steady-state error.
[0049] Because the bandwidth of the rudder system and gyroscope is relatively large compared to the missile body bandwidth, the rudder system and gyroscope are treated as a straight-through circuit in the initial circuit design, making G... dj (s)=k dj G nt (s)=k nt .
[0050] according to Figure 2 In a steady-state loop with no static error, the control command u z The closed-loop transfer function to the tilt angle γ is:
[0051]
[0052] Where, k γ1 k γ2 k γ3 For the controller parameters in a zero-steady-state tilt steady-state loop, k dj For the rudder system transmission coefficient, u z For control commands, γ is the tilt angle, and k nt Here are the gyroscope transfer coefficients: K3 = -c3 / c1, T3 = 1 / c1. Let be the rolling damping moment coefficient, q be the dynamic pressure, s be the characteristic area of the missile, L be the characteristic length of the missile, and V be the missile's flight velocity. J is the aileron control moment coefficient. x1 It is the moment of inertia about the longitudinal axis of the projectile.
[0053] Therefore, there is.
[0054] The above formula shows that, from the input instruction u z The closed-loop amplification factor to the output γ is independent of the aerodynamic parameters of the missile itself. Even if the aerodynamic parameters of the missile are not accurately fitted, it will not affect the closed-loop amplification factor of the loop. Therefore, this loop structure theoretically results in a zero tilt angle response when the input command is zero, meaning that the requirement of zero steady-state error in the tilt angle has been met during the design process. During loop implementation, the control command u will be... z Simply set it to 0.
[0055] according to Figure 2 The interference δ caused by the equivalent aileron f To tilt angle error e γ The closed-loop transfer function is:
[0056]
[0057] By the final value theorem, the system under aileron disturbance δ can be obtained. f steady-state error e under action γss for:
[0058]
[0059] The above equation shows that when there is an equivalent aileron interference term in the system, the tilt angle is theoretically zero steady-state error.
[0060] Furthermore, the coefficients of the expected characteristic polynomial and the control parameter k are derived. γ1 k γ2 k γ3 The analytical relationship between them. From the system closed-loop transfer function formula (1), it can be seen that the closed-loop system is a third-order system, so the expected characteristic polynomial is determined to be third-order:
[0061] f q (s)=p1s 3 +p2s 2 +p3s 2 +p4; (5)
[0062] From the system closed-loop transfer function formula (1), the system closed-loop characteristic polynomial can be obtained as follows:
[0063]
[0064] According to the pole placement method, the coefficients of the desired characteristic polynomial should be equal to the coefficients of the closed-loop characteristic polynomial, which means the following system of equations should be satisfied:
[0065]
[0066] By solving the above equation, the analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in a zero-steady-state-error tilted steady loop can be obtained as follows:
[0067]
[0068] After designing the expected characteristic polynomial coefficients p1, p2, p3, and p4, k can be solved using equation (8). γ1 k γ2 k γ3 .
[0069] The problem can now be described as: how to determine the expected characteristic polynomial coefficients p1, p2, p3, and p4 based on the performance requirements of the tilted stable loop (such as stability margin, overshoot, and rise time). In this invention, an improved particle swarm optimization algorithm is used to find the optimal solution for these coefficients.
[0070] Particle Swarm Optimization (PSO) algorithms are easy to implement, but prone to getting trapped in local optima. Considering that different PSO parameters will cause the algorithm to exhibit different behavior patterns, and that the inertia factor w in the standard PSO algorithm is a fixed coefficient, the choice of its value is crucial, affecting convergence accuracy and speed. This invention presents a novel nonlinear dynamic adaptive inertia factor adjustment strategy determined by equations (9) and (10):
[0071]
[0072]
[0073] Where k is the generation number, and when k = 1, f(1) can be calculated from the above formula. w max w is the maximum value of the inertia factor. min k is the minimum value of the inertia factor. min k is the number of iterations required for the inertia factor to reach its maximum value. max Let w(k) be the number of iterations when the inertia factor reaches its minimum value, and w(k) be the inertia factor.
[0074] Furthermore, combining the basic process of the standard PSO algorithm with the nonlinear dynamic adaptive inertia factor adjustment strategy given in this invention, the process of optimizing the parameters of the tactical missile's zero-static-error tilt stabilization loop controller using the improved PSO algorithm is as follows: Figure 3 As shown. The specific steps are as follows:
[0075] Step 1: Set initial parameters and randomly generate initial position and velocity;
[0076] Step 2: Calculate the fitness value for each particle based on the problem to be solved;
[0077] Step 3: Calculate and update the inertia factor value;
[0078] Step 4: Calculate and update the position and velocity of each particle;
[0079] Step 5: Update the global optimal solution and the individual optimal solution;
[0080] Step 6: Determine if the termination condition is met. If not, repeat steps 2-5 for iterative optimization. If the condition is met, output the global optimal solution as the best individual.
[0081] In step 2 above, the fitness value of each particle is calculated using a weighted multi-objective function. The expression for the weighted multi-objective function is:
[0082]
[0083] Where, x i0 For the i-th performance metric requirement, x i Let ω represent the actual performance of the i-th parameter affected by the parameters p1, p2, p3, and p4 to be optimized, where m is the number of performance metrics and ω is the value of ω. i is the weighting coefficient for the i-th performance item.
[0084] In step 4 above, the position and velocity of each particle are updated using equation (12):
[0085]
[0086] Where j = (1,2,…,d); v ij (k) and x ij (k) represent the velocity and position of the j-th dimension variable of the i-th particle in the k-th generation, respectively; Gbest is the global optimal solution of the current population; Pbest i is the individual optimal solution for the current i-th particle; w is the inertia factor; c1 and c2 are acceleration factors greater than zero; r1 and r2 are random numbers between [0,1].
[0087] In this embodiment of the invention, the effectiveness of the algorithm is verified through digital simulation. Taking a tactical missile with significant disturbances in its rolling channel as the controlled object, firstly, an improved particle swarm optimization algorithm is used to optimize the control parameters of the steady-state tilt-stabilized loop without steady-state error at the characteristic points. Secondly, the optimization results are applied to a six-degree-of-freedom simulation model to verify the effectiveness of the algorithm and the correctness of the design results.
[0088] Based on theoretical ballistic data, representative feature points were selected for the optimization design of control parameters for the tilt stabilization loop without static error. The feature points cover both high-altitude and low-altitude ballistic trajectories, including features such as maximum dynamic pressure, minimum dynamic pressure, maximum K3, minimum K3, maximum T3, and minimum T3. Specific feature point parameters are shown in Table 1.
[0089]
[0090] Table 1
[0091] Using the above parameters, the control parameters of the zero-steady-error tilt stabilization loop are optimized at each characteristic point. The optimization results are shown in [the table below]. Figures 4-8 And Table 2. Among them... Figure 4 and Figure 5 The time-domain response curves of each feature point under a unit step command are shown below. Figure 6 and Figure 7 The time-domain response curves of each feature point under a unit step aileron disturbance command are shown below. Figure 8 The frequency domain characteristic curves for each feature point are shown. It can be seen that under a unit step command, the tilt angle at each feature point converges rapidly to 0°; under a unit step aileron disturbance, the maximum tilt angle at each feature point is less than 20° and converges rapidly to 0°, and the maximum tilt angular velocity is less than 200° / s and also converges to 0° / s, verifying the zero steady-state error characteristic of the tilt stabilization loop structure used in this invention. Furthermore, as shown in Table 2, the rise time at each feature point is less than 0.25s, the overshoot is less than 16%, the gain margin is greater than 11dB, and the phase margin is greater than 45°. Both the time domain and frequency domain indicators meet the design requirements.
[0092]
[0093] Table 2
[0094] To verify the correctness and effectiveness of the design results, a six-degree-of-freedom digital simulation was also performed on a certain control trajectory of this type of tactical missile in this embodiment of the invention. Various rolling disturbance terms were added to the simulation model (including initial disturbance at launch, aileron disturbance, disturbance caused by manufacturing and installation deviations of the control surfaces, tail fins, and missile body, engine thrust eccentricity disturbance, center of mass shift disturbance, etc.). Simulations were performed for two cases: one using a conventional tilt angle + tilt angular velocity feedback loop structure, and the other using the novel zero-static-error tilt stabilization loop structure of this invention. Figure 9 The tilt angle response curve of a missile using a conventional tilt angle + tilt angle velocity feedback loop structure is shown. It can be seen that the tilt angle of the missile is always in error (20° to 40°) during flight, indicating that the conventional loop structure cannot effectively eliminate the steady-state error of the tilt angle. Figures 10-12 The simulation curves are for a missile using the static error-free tilting stable loop structure described in this paper. Figure 10 The variation curves of the roll disturbance force caused by aileron disturbance and manufacturing / installation deviations are presented. It can be seen that the roll disturbance torque consists of a low-frequency, slowly varying component and a high-frequency, rapidly varying component. Figure 11 The missile's tilt angular velocity response curve shows that, due to the initial disturbance before launch, the missile's tilt angular velocity was relatively high, reaching 629.8° / s. Under the control of the tilt stabilization loop without static error, the tilt angle rapidly converged to around 0° / s, and the tilt angular velocity remained within ±70° / s throughout the flight. Figure 12 The missile's tilt angle response curve shows that the tilt angle at the start of control is -126.6°, and under the action of loop control, the tilt angle quickly converges to near 0°, and remains within ±10° throughout the flight. This indicates that the loop structure of the present invention can quickly eliminate the tilt angle error caused by the initial disturbance and overcome various rolling disturbance torques during flight, ensuring that the tilt angle error of the missile always meets the engineering application requirements during flight.
[0095] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A parameter optimization design method based on a zero-steady-error tilted stable loop, characterized in that, The specific steps include the following: Design a zero-static-error tilt stabilization loop according to missile control requirements; The pole placement method is used to solve the analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in the zero steady-state error tilted stable loop. Thus, the parameter optimization problem of the zero steady-state error tilted stable loop is transformed into using the coefficients of the desired characteristic polynomial as the variable to be optimized. The coefficients of the desired characteristic polynomial are optimized using a particle swarm optimization algorithm with a nonlinear dynamic adaptive inertia factor.
2. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 1, characterized in that, The zero-static-error tilt stabilization loop is a double-loop tilt stabilization loop structure.
3. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 1, characterized in that, In the aforementioned zero-steady-error tilt stabilization loop, the closed-loop transfer function from the control command to the tilt angle is: Where, k γ1 k γ2 k γ3 For the controller parameters in a zero-steady-state tilt steady-state loop, k dj For the rudder system transmission coefficient, u z For control commands, γ is the tilt angle, and k nt Here are the gyroscope transfer coefficients: K3 = -c3 / c1, T3 = 1 / c1. Let be the rolling damping moment coefficient, q be the dynamic pressure, s be the characteristic area of the missile, L be the characteristic length of the missile, and V be the missile's flight velocity. J is the aileron control moment coefficient. x1 It is the moment of inertia about the longitudinal axis of the projectile.
4. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 3, characterized in that, The analytical relationship between the controller parameters and the coefficients of the desired characteristic polynomial in the zero steady-state error tilted stable loop is as follows: Where p1, p2, p3, and p4 are the expected characteristic polynomial parameters.
5. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 1, characterized in that, The adjustment strategy expression for the nonlinear dynamic adaptive inertia factor is as follows: Where k is the generation number, and when k = 1, f(1) can be calculated from the above formula. w max w is the maximum value of the inertia factor. min k is the minimum value of the inertia factor. min k is the number of iterations required for the inertia factor to reach its maximum value. max Let w(k) be the number of iterations when the inertia factor reaches its minimum value, and w(k) be the inertia factor.
6. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 1, characterized in that, The specific steps for optimizing the coefficients of the desired characteristic polynomial using a particle swarm optimization algorithm with a nonlinear dynamic adaptive inertia factor are as follows: Step 1: Set initial parameters and randomly generate initial position and velocity; Step 2: Calculate the fitness value for each particle based on the problem to be solved; Step 3: Calculate and update the inertia factor value; Step 4: Calculate and update the position and velocity of each particle; Step 5: Update the global optimal solution and the individual optimal solution; Step 6: Determine if the termination condition is met. If not, repeat steps 2-5 for iterative optimization. If the condition is met, output the global optimal solution as the best individual.
7. The parameter optimization design method based on a zero-steady-error tilted stable loop according to claim 6, characterized in that, The fitness value for each particle is calculated using a weighted multi-objective function, the expression of which is: Where, x i0 For the i-th performance metric requirement, x i Let ω represent the actual performance of the i-th parameter affected by the parameters p1, p2, p3, and p4 to be optimized, where m is the number of performance metrics and ω is the value of ω. i is the weighting coefficient for the i-th performance item.