CN118149657A - Constant time convergence guidance rocket projectile angle constraint guidance law design method - Google Patents
Constant time convergence guidance rocket projectile angle constraint guidance law design method Download PDFInfo
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Abstract
The invention discloses a design method of a guided rocket projectile angle constraint guidance law with fixed time convergence, which comprises the steps of firstly designing a fixed time state observer based on a consistent accurate robust differentiator algorithm to estimate an unmeasurable system state; then designing an integral sliding mode surface converging at fixed time and providing a fixed time guidance law; compared with the traditional limited time angle constraint guidance law, the method can not only ensure that the upper bound of convergence time is not influenced by an initial state, but also simplify the hardware composition of a guidance system by adopting a partial state feedback strategy, is convenient for engineering application, and effectively solves the two problems of the angle constraint guidance law. Finally, the effectiveness of the method is verified through simulation.
Description
Technical Field
The invention belongs to the technical field of rockets, and particularly relates to a guided rocket projectile angle constraint guidance law design method with fixed time convergence.
Background
The proportional guidance law is widely applied to the design of guidance systems of various guided rocket projectiles as a classical guidance method. However, the traditional proportional guidance law has the problems of weak sudden prevention capability, weak robustness and the like, and the problems have higher requirements on the performance of a guidance algorithm. If the target is hit by adopting a terminal constraint angle mode, on one hand, the outburst prevention effect can be improved, and in addition, the damage efficiency can be optimized, and the angle constraint guidance law is an important means for realizing the attack mode.
In order to improve the angle constraint guidance law performance, many researches have been conducted based on advanced control theory. In order to improve the robust performance of the angle constraint guidance law under uncertain disturbances such as target maneuver, unmodeled dynamics and the like, the angle constraint guidance law based on methods such as sliding mode control, self-adaptive control and the like appears. In recent years, with the development of a finite time control theory, an angle constraint guidance law based on a finite time stabilization method also appears. Compared with the traditional progressive stabilization method, the limited time angle constraint guidance law can realize the limited time of the guidance error, and the rapidity and the high precision of convergence are ensured. Compared with the traditional finite time control, the upper limit of the convergence time of the fixed time control method is irrelevant to the initial value of the system, so that the problem that the convergence speed is influenced by the initial value of the system in the traditional finite time control can be effectively solved. On the other hand, the development of observer technology provides a basis for developing guidance law designs with part of states being measurable.
At present, two main problems exist, so that the limited time angle constraint guidance law is difficult to realize in engineering: 1) The convergence time is related to the initial state of the bullet, and when the initial value is large, the system convergence speed cannot be ensured; 2) The existing methods all adopt full state feedback for guidance, and in fact, partial states are difficult to realize due to high measurement cost.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a design method of guided rocket projectile angle constraint guidance law with fixed time convergence, which comprises the steps of firstly designing a fixed time state observer to estimate an unmeasurable system state based on a consistent accurate robust differentiator algorithm; then designing an integral sliding mode surface converging at fixed time and providing a fixed time guidance law; compared with the traditional limited time angle constraint guidance law, the method can not only ensure that the upper bound of convergence time is not influenced by an initial state, but also simplify the hardware composition of a guidance system by adopting a partial state feedback strategy, is convenient for engineering application, and effectively solves the two problems of the angle constraint guidance law. Finally, the effectiveness of the method is verified through simulation.
The technical scheme adopted for solving the technical problems is as follows:
step 1: building a system 1:
Wherein the method comprises the steps of Is to uncertainty interference and meet/>，/>Is a positive constant; /(I)For the system state of system 1,/>、/>/>Is a positive constant; /(I)Representing a sign function;
If it is And/>While satisfying the following parameter fields/>：
Then/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>WhereinIs a normal number and is associated with initial state/>/>Is irrelevant;
Step 2: building a system 2:
Wherein the method comprises the steps of Is the system state of system 2; if the constant parameter/>Satisfy/>，/>，/>，/>，/>，/>，/>And/>While the initial state/>, of system 2Is bounded, the system state of system 2 converges in a fixed time:
Wherein, A system state convergence time for system 2; /(I)Is a normal number independent of the initial state of the system;
step 3: establishing a guidance system equation;
Step 4: guidance law design.
Further, the step3 specifically includes the following steps:
Is provided with Representing the object,/>Representing a guided rocket projectile, the position of the guided rocket projectile being/>The target position is；/>Representing the flight speed of a guided rocket projectile,/>For the speed of the target,/>And/>Ballistic inclination angles of guided rocket projectile and target respectively,/>For the relative distance of the bullet and the mesh,/>Is the angle of sight,/>And/>Normal control acceleration of the guided rocket projectile and the target are respectively controlled;
the relative equations of motion of the guided rocket projectile and the target are as follows:
Is provided with Let the angle error/>, for the desired angleLet/>The guidance system equation is obtained as follows:
Wherein, Representing an angular velocity error; /(I)Indicating interference.
Further, the step 4 specifically includes the following steps:
step 4-1: a fixed time state observer is designed;
Based on the system 1, a fixed time state observer is designed as follows:
Wherein the method comprises the steps of Is a normal number,/>/>Respectively/>And/>Is a function of the estimated value of (2); /(I)And/>The expression is as follows:
Selecting parameters And/>And/>Satisfies the following parameter domain/>Then estimate error/>And/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>Wherein/>Is a normal number and is associated with initial state/>/>Independent of:
Wherein, Representing an upper interference bound;
Step 4-2: angle constraint guidance law design based on fixed time stabilization and partial state feedback;
Based on the estimate of the fixed time state observer, in combination with the system 2, a fixed time converging slip plane is designed as follows:
Wherein the method comprises the steps of ，/>，/>And/>；/>Is a differential operator; /(I)、/>、/>、/>Is a design parameter;
For a pair of Obtaining a derivative:
Wherein:
Finally, the design part state feedback fixed time guidance law is as follows:
Wherein the method comprises the steps of 、/>/>Is a normal number, and/>Then the system state fixed time converges:
Wherein, Representing state convergence time; /(I)Is a normal number independent of the initial state of the system.
The beneficial effects of the invention are as follows:
The method solves the engineering problem that the convergence time of the guidance system is influenced by the initial state; the method does not depend on full-state feedback, reduces the requirement of a guided rocket projectile loading measurement system, and is beneficial to simplifying the composition and reducing the cost; meanwhile, guidance is realized through an analytic formula, large-scale operation is avoided, and the real-time resolving power requirement of the missile-borne computer is reduced.
Drawings
FIG. 1 is a schematic diagram of the relative movement relationship of the bullet mesh according to the method of the present invention;
FIG. 2 (a) is a simulation result angle error of scenario 1 according to an embodiment of the present invention A comparison chart;
FIG. 2 (b) is a view angle rate of simulation results of scenario 1 of the present invention A comparison chart;
FIG. 2 (c) is a diagram of a scenario 1 simulation result estimation error according to an embodiment of the present invention A comparison chart;
FIG. 3 (a) is a view of the simulation result angle error of scenario 2 of the present invention A comparison chart;
FIG. 3 (b) is a view angle rate of the simulation result of scenario 2 of the present invention A comparison chart;
FIG. 3 (c) is a view of the simulation result estimation error of scenario 2 of the present invention Comparison graph.
Detailed Description
The invention will be further described with reference to the drawings and examples.
In order to solve the two problems at the same time, the method provides an angle constraint guidance law with fixed time convergence under the condition that the line of sight angular rate and the relative distance change rate are not measurable.
Step 1: building a system 1:
If it is And/>While satisfying the following parameter fields/>：
Then/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>WhereinIs a normal number and is associated with initial state/>/>Is irrelevant;
Step 2: building a system 2:
Wherein the method comprises the steps of Is the system state of system 2; if the constant parameter/>Satisfy/>，/>，/>，/>，/>，/>，/>And/>While the initial state/>, of system 2Is bounded, the system state of system 2 converges in a fixed time:
step 3: establishing a guidance system equation;
as shown in fig. 1, the relative equations of motion of the guided rocket projectile and the target are as follows:
The guidance system equation is obtained as follows:
Step 4: designing a guidance law;
The design target is as follows: at the angular rate of line of sight Relative distance rate of change/>Under the condition of no measurement, designing an angle constraint guidance law meeting the convergence characteristic of fixed time;
step 4-1: a fixed time state observer is designed;
Based on the system 1, a fixed time state observer is designed as follows:
Selecting parameters And/>And/>Satisfies the following parameter domain/>Then estimate error/>And/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>Wherein/>Is a normal number and is associated with initial state/>/>Independent of:
Step 4-2: angle constraint guidance law design based on fixed time stabilization and partial state feedback;
Based on the estimate of the fixed time state observer, in combination with the system 2, a fixed time converging slip plane is designed as follows:
For a pair of Obtaining a derivative:
Wherein:
Finally, the design part state feedback fixed time guidance law is as follows:
the system state fixed time converges:
Examples:
1. Setting a simulation scene;
Developing the trajectory simulation of the guided rocket projectile, wherein the initial guidance position of the rocket projectile is set as follows />The target position is set to/>/>Initial ballistic inclination angles of the guided rocket projectile and the target are respectively set as，/>Initial speeds are set to/>, respectively/>The rate of change of speed is set to/>/>. Target maneuver acceleration is set to/>。
The finite time slip film face was designed as follows:
Meanwhile, the following limited time guidance laws are designed:
Wherein parameters are selected ，/>，/>，/>，/>，/>，/>，；/>、/>、/>；/>、/>、/>、/>、/>; Partial state feedback fixed time guidance law parameter is selected as/>、/>、/>. In order to eliminate the buffeting problem, sign functions in the guidance law are replaced by sigmoid functions, and the expression is as follows: /(I)Wherein/>Get 80,/>Is an argument of the sigmoid function.
The partial state feedback fixed time guidance law (guidance law 1) and the full state feedback fixed time guidance law (guidance law 2) and the traditional limited time guidance law (guidance law 3) adopting the method of the invention are subjected to comparison simulation in the following two scenes:
Scene 1 (small initial error): the desired angle is Initial angle error/>。
Scene 2 (large initial error): the desired angle isInitial angle error/>。
The initial angle error of scene 2 is approximately 6 times that of scene 1.
2. Simulation result analysis
Simulation results of scene 1 and scene 2 are shown in fig. 2 (a) to 2 (c) and fig. 3 (a) to 3 (c), respectively, and convergence time is summarized in table 1, and miss distance is summarized in table 2.
TABLE 1 convergence time
| Guidance method | Guidance law 1 | Guidance law 2 | Guidance law 3 |
| Scene 1(s) | 4.1 | 4.1 | 4.15 |
| Scene 2(s) | 5 | 5 | \ |
TABLE 2 off-target quantity
| Guidance method | Guidance law 1 | Guidance law 2 | Guidance law 3 |
| Scene 1 (m) | 0.2646 | 0.232 | 0.1918 |
| Scene 2 (m) | 0.2963 | 0.2231 | 8.488 |
Scene 1 simulation result analysis: from the data of FIG. 2 (a), FIG. 2 (b) and Table 1, it can be seen that the three methods can ensure angle errorsLine of sight angular rate error/>Converging to 0 within 5 s. From fig. 2 (c), it can be seen that the proposed fixed time state observer can ensure that the estimation error converges to 0 within 0.1 s. Meanwhile, as can be seen from the table 1, the three methods can ensure that the target-off amount of the guided rocket projectile is not higher than 0.25m, and can meet the requirement of striking precision. Therefore, the three guidance methods can obtain similar control effects in the scene 1.
Scene 2 simulation result analysis: as can be seen from FIGS. 3 (a), 3 (b) and Table 1, when the initial angle error is enlarged toAfterwards, the proposed fixed time guidance law can still guarantee the angle error/>Line of sight angular rate error/>Convergence to 0 within 5s, whereas a limited time guidance law cannot guarantee an angular error/>, during the guidance periodAnd the view angle rate converges to 0, because the convergence time of the finite time guidance law is related to the initial error, the convergence time is increased when the initial error is increased, and the upper limit of the convergence time can be always ensured to be irrelevant to the initial error by the fixed time guidance law. It can also be seen from table 2 that the amount of off-target for the limited time guidance law is much greater than the fixed time guidance law because the guidance error cannot converge to 0. From fig. 3 (c), it can be seen that the proposed fixed time state observer can still guarantee that the estimation error converges to 0 within 0.1 s. In addition, for the two methods of the fixed time guidance law adopting the partial state feedback and the fixed time guidance law adopting the full state feedback, the guidance error convergence effect and the miss distance are basically the same, so that the proposed method can realize the fixed time guidance effect under the condition of using only the partial state feedback.
Claims (3)
1. The design method of the guided rocket projectile angle constraint guidance law with fixed time convergence is characterized by comprising the following steps of:
step 1: building a system 1:
；
Wherein the method comprises the steps of Is to uncertainty interference and meet/>，/>Is a positive constant; /(I)For the system state of system 1,/>、/>/>Is a positive constant; /(I)Representing a sign function;
If it is And/>While satisfying the following parameter fields/>：
；
Then/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>Wherein/>Is a normal number and is associated with initial state/>/>Is irrelevant;
Step 2: building a system 2:
；
Wherein the method comprises the steps of Is the system state of system 2; if the constant parameter/>Satisfy the following requirements，/>，/>，/>，/>，/>，/>And/>While the initial state/>, of system 2Is bounded, the system state of system 2 converges in a fixed time:
；
；
Wherein, A system state convergence time for system 2; /(I)Is a normal number independent of the initial state of the system;
step 3: establishing a guidance system equation;
Step 4: guidance law design.
2. The method for designing the guided rocket projectile angle constraint guidance law with fixed time convergence according to claim 1, wherein the step 3 is specifically as follows:
Is provided with Representing the object,/>Representing a guided rocket projectile, the position of the guided rocket projectile being/>Target position is/>；/>Representing the flight speed of a guided rocket projectile,/>For the speed of the target,/>And/>Ballistic inclination angles of guided rocket projectile and target respectively,/>For the relative distance of the bullet and the mesh,/>Is the angle of sight,/>And/>Normal control acceleration of the guided rocket projectile and the target are respectively controlled;
the relative equations of motion of the guided rocket projectile and the target are as follows:
；
Is provided with Let the angle error/>, for the desired angleLet/>The guidance system equation is obtained as follows:
；
Wherein, Representing an angular velocity error; /(I)Indicating interference.
3. The method for designing the guided rocket projectile angle constraint guidance law with fixed time convergence according to claim 2, wherein the step 4 is specifically as follows:
step 4-1: a fixed time state observer is designed;
Based on the system 1, a fixed time state observer is designed as follows:
；
Wherein the method comprises the steps of Is a normal number,/>/>Respectively/>And/>Is a function of the estimated value of (2); /(I)And/>The expression is as follows:
；
Selecting parameters And/>And/>Satisfies the following parameter domain/>Then estimate error/>And/>Will be at a finite time/>Inner convergence to 0; at the same time, convergence time/>Upper bound meets/>Wherein/>Is a normal number and is associated with initial state/>/>Independent of:
；
Wherein, Representing an upper interference bound;
Step 4-2: angle constraint guidance law design based on fixed time stabilization and partial state feedback;
Based on the estimate of the fixed time state observer, in combination with the system 2, a fixed time converging slip plane is designed as follows:
；
Wherein the method comprises the steps of ，/>，/>And/>；/>Is a differential operator; /(I)、/>、/>、/>Is a design parameter;
For a pair of Obtaining a derivative:
；
Wherein:
；
Finally, the design part state feedback fixed time guidance law is as follows:
；
Wherein the method comprises the steps of 、/>/>Is a normal number, and/>Then the system state fixed time converges:
；
；
Wherein, Representing state convergence time; /(I)Is a normal number independent of the initial state of the system.
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| 许琛等: "基于固定时间稳定与部分状态反馈的角度约束制导律", 弹箭与制导学报, vol. 44, no. 1, 9 January 2024 (2024-01-09), pages 13 - 19 * |
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