A fixed-time convergence guidance control method with impact angle constraint

Abstract

The application discloses a fixed-time convergence guidance control method with a landing angle constraint, and the method comprises the following steps: designing an approaching law based on a fixed-time convergence theory, obtaining a control instruction by using a sliding mode guidance law, and flying an aircraft according to the control instruction. The fixed-time convergence guidance control method with the landing angle constraint has a constant ratio of an upper limit of a convergence time of a system state to a whole guidance time, and the upper limit of the convergence time is irrelevant to an initial value of the system state, so that the problems of excessively long or excessively short convergence time and sensitivity to the initial value of the system state are effectively solved.

Description

Technical Field

[0001] This invention relates to a fixed-time convergence guidance and control method with landing angle constraints, belonging to the field of aircraft guidance and control. Background Technology

[0002] As a core technology of precision guidance, terminal guidance is used to control the flight direction of high-speed aircraft so that it can accurately strike the target in a specific attitude.

[0003] In the terminal guidance phase, due to the close proximity of the aircraft and its high speed, the time available for terminal guidance is often very short. This requires the guidance and control methods for high-speed aircraft to have finite-time convergence characteristics.

[0004] Traditional finite-time convergence algorithms are highly sensitive to the initial state of the system and are independent of the overall guidance time. This can easily lead to excessively long or short convergence times. In specific environments, especially complex environments such as high-speed target movement, this can easily cause deviations between the actual collision angle and the actual collision angle, or even guidance failure.

[0005] Based on the above problems, it is necessary to propose a guidance and control method in which the upper bound of the system state convergence time is independent of the initial value of the system state, so as to effectively solve the problem of excessively long or short convergence time and thus improve guidance accuracy. Summary of the Invention

[0006] To overcome the above problems, the inventors conducted in-depth research and proposed a fixed-time convergence guidance and control method with landing angle constraints. The method obtains the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target. The control command u is obtained using a sliding mode guidance law. The aircraft controls the servo motors to adjust its flight attitude according to the control command.

[0007] Furthermore, the sliding surface s1 of the sliding mode guidance law is:

[0008] s1 = x1 + k|x2| α sgn(x2)

[0009]

[0010] Where x1 and x2 are system variables, and q is the target's line-of-sight angle relative to the aircraft. Let q be the target's angular rate relative to the aircraft's line of sight. F Let be the desired landing angle, and k and α be the parameters to be designed, where k > 0 and 1 < α < 2.

[0011] According to the present invention, the reaching law of the sliding mode guidance law for:

[0012]

[0013] Where c1, c2, q1, and q2 are the parameters to be designed, s1 represents the sliding surface, and t go This indicates the remaining flight time of the aircraft.

[0014] According to the present invention, the convergence time T of the sliding mode guidance law satisfies:

[0015] T≤T m =0.8t f

[0016] Among them, T m This represents the upper bound of the system state convergence time, t. f This indicates the total flight time of the aircraft.

[0017] In a preferred embodiment, in the guidance and control method, the dynamic characteristics of the autopilot are expressed as follows to represent the impact of the autopilot's hysteresis on the aircraft:

[0018]

[0019] Among them, a M The overload command for the aircraft is determined by the sliding mode surface and the approach law; ξ represents the damping ratio of the autopilot, ω n This represents the inherent frequency of the autopilot, and u represents the control command.

[0020] In a preferred embodiment, control command u is obtained based on the dynamic characteristics of the autopilot, such that control command u can compensate for the impact of autopilot lag on the aircraft. The control command is expressed as:

[0021]

[0022] x3=a M

[0023]

[0024] Where λ2 is the parameter to be designed, x3 and x4 are system variables, and x 4d Let s1 be the virtual control law of system variable x4, and s2 be the virtual control law of system variable x4. 4d The error variable is s3 = x4 - x 4d .

[0025] In a preferred embodiment, the virtual control law x of system variable x4 4d Obtained through the following methods:

[0026] The virtual control quantity x of system variable x3 is obtained based on the sliding surface and the reaching law.3c :

[0027]

[0028] Where, θ M The velocity tilt angle of the aircraft is represented by r, and the distance between the aircraft and the target is represented by r.

[0029] Virtual control quantity x for system variable x3 3c Filtering is performed to obtain its virtual control law x. 3d ;

[0030] Establish the system variable x3 and its virtual control law x 3d The error variable s2;

[0031] Obtain the virtual control quantity x of system variable x4 4c This makes the system variable x3 and its virtual control law x 3d The error variable s2→0;

[0032] Virtual control quantity x for system variable x4 4c Filtering is performed to obtain its virtual control law x. 4d .

[0033] In a preferred embodiment, the filtering is a first-order low-pass filter.

[0034] In a preferred embodiment, the overload command a for the aircraft M Apply constraints:

[0035]

[0036] Among them, a Mmax This indicates the upper limit of the aircraft's acceleration.

[0037] The present invention also provides a fixed-time convergence guidance and control system with landing constraints, comprising:

[0038] The measurement module is used to obtain the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target.

[0039] The processing module is configured to obtain control command u according to the sliding mode guidance law using the method described in any one of claims 1-9;

[0040] The execution module is used to control the servos according to control commands, thereby controlling the attitude of the aircraft.

[0041] The beneficial effects of this invention include:

[0042] (1) A unique approach law based on fixed-time convergence theory was designed, which makes the ratio of the upper bound of the system state convergence time to the overall guidance time a constant, and the upper bound of the convergence time is independent of the initial value of the system state, effectively solving the problems of excessively long or short convergence time and sensitivity to the initial value of the state.

[0043] (2) The dynamic characteristics of the autopilot were considered and expressed, and it was approximated as a second-order element. Based on the dynamic surface control method, the control quantity was designed so that the actual output deflection command could compensate for the lag effect of the autopilot's dynamic characteristics and improve the guidance accuracy.

[0044] (3) The acceleration saturation constraint brought about by the physical constraints of the actuator is increased, so that the actual acceleration and deflection commands are closer to the actual engineering situation. Attached Figure Description

[0045] Figure 1 A schematic flowchart of a fixed-time convergence guidance and control method with landing angle constraints according to a preferred embodiment of the present invention is shown.

[0046] Figure 2 The simulated trajectory curve of the aircraft in the simulation results of Example 1 is shown;

[0047] Figure 3 The simulation results of Example 1 show the convergence curve of the aircraft's line-of-sight angle.

[0048] Figure 4 The convergence curve of the aircraft's line-of-sight angular rate in the simulation results of Example 1 is shown.

[0049] Figure 5 The simulation results of Example 1 show the change curve of the aircraft control command. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0051] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0052] This invention provides a fixed-time convergence guidance and control method with landing angle constraints. It obtains the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target. It uses a sliding mode guidance law to obtain the control command u, and the aircraft controls the servo motors to adjust its flight attitude according to the control command.

[0053] In this invention, the specific method for obtaining the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target is not limited. Any existing method can be used to obtain them, such as obtaining them through a laser sensor or through radar.

[0054] The relative motion model between the aircraft and the target can be represented as:

[0055]

[0056] Where q is the target's line-of-sight angle relative to the aircraft. Let a be the target's angular rate relative to the aircraft's line-of-sight. M V indicates the overload command for the aircraft. M θ represents the speed of the aircraft. M The velocity tilt angle of the aircraft is represented by r, and the distance between the aircraft and the target is represented by r.

[0057] Furthermore, the rate of change of the target's angular velocity relative to the aircraft's line-of-sight can be obtained. It can be represented as:

[0058]

[0059] According to the present invention, the sliding surface s1 of the sliding mode guidance law is:

[0060] s1 = x1 + k|x2| α sgn(x2)

[0061]

[0062] Where x1 and x2 are system variables, and q is the target's line-of-sight angle relative to the aircraft. Let q be the target's angular rate relative to the aircraft's line of sight. F Let be the desired landing angle, and k and α be the parameters to be designed, where k > 0 and 1 < α < 2.

[0063] The sliding surface designed in this invention is a non-singular terminal sliding surface. Compared with the sliding surface in traditional sliding mode guidance laws, it has the advantages of finite-time convergence, high accuracy, and strong robustness.

[0064] In a preferred embodiment, the parameters to be designed in the sliding surface are k = 5 and α = 1.5. These values ​​were determined by the inventors based on experience and a large number of experiments, and they can achieve better convergence results compared to other parameters.

[0065] In traditional finite-time convergence theory, the upper bound of the convergence time of the system state is related to the initial value of the system state. Therefore, different guidance parameters need to be selected under different guidance scenarios, and the parameters need to be continuously tuned. This has weak engineering applicability, and when the initial error is large, it may even lead to the failure of the guidance mission.

[0066] Meanwhile, in traditional finite-time convergence theory, the upper bound of the convergence time of the system state is an absolute quantity compared with the guidance time. It is only related to the parameters and does not change with the guidance time. Therefore, it may cause the convergence time to be too long or too short. When the ratio of the upper bound of the convergence time to the guidance time is too large, or even exceeds the guidance time, it may cause guidance failure. When the ratio is too small, it will cause large jitter.

[0067] To address the aforementioned problems, this invention designs a novel reaching law based on fixed-time convergence theory, specifically the reaching law of the sliding mode guidance law. for:

[0068]

[0069] Where c1, c2, q1, and q2 are the parameters to be designed, and t go This indicates the remaining flight time of the aircraft. Furthermore,

[0070] Preferably, in this invention, the parameters to be designed are c1=c2=4 / ln5, q1=0.7, q2=2.5. These values ​​were determined by the inventors based on experience and a large number of experiments, and compared with other parameters, they can achieve better convergence results.

[0071] Furthermore, according to the aforementioned convergence law, the convergence time of the system state can be expressed as:

[0072]

[0073]

[0074] Under the aforementioned design parameters, the convergence time T of the sliding mode guidance law satisfies:

[0075] T≤T m =0.8t f

[0076] Among them, T m t represents the upper limit of the convergence time. f This indicates the total flight time of the aircraft.

[0077] The inventors discovered that during the terminal guidance phase, the hysteresis of the autopilot has a significant impact on guidance accuracy. In this invention, the dynamic characteristics of the autopilot are expressed in the guidance control method as follows, which effectively expresses the impact of the autopilot's hysteresis on the aircraft:

[0078]

[0079] Among them, a M The overload command for the aircraft is determined by the sliding surface and the approach law; ξ represents the damping ratio of the autopilot, which is a constant parameter; ω n The autopilot's inherent frequency is a constant parameter, and u represents the control command.

[0080] Specifically, the overload command a of the aircraft M By differentiating the sliding surface and relating it to the reaching law, we can immediately obtain the expression:

[0081]

[0082] In this invention, control command u is obtained based on the dynamic characteristics of the autopilot, so that control command u can compensate for the impact of autopilot lag on the aircraft, thereby eliminating the impact of autopilot lag on guidance accuracy.

[0083] According to the present invention, the control command can be obtained by a dynamic surface control method, and the control command is expressed as follows:

[0084]

[0085] x3=a M

[0086]

[0087] Where λ2 is the parameter to be designed, which is generally a positive constant, and x3 and x4 are system variables, x 4d Let s1 be the virtual control law of system variable x4, and s2 be the virtual control law of system variable x4. 4d The error variable is s3 = x4 - x 4d .

[0088] In this invention, during the process of obtaining control commands, two new states x3 and x4 are established, where x3 = a. M , By dynamically controlling the overload command and the rate of change of the overload command of the aircraft, the actual output control command can compensate for the lag effect of the autopilot's dynamic characteristics and improve guidance accuracy.

[0089] Furthermore, the virtual control law x of system variable x44d Obtained through the following methods:

[0090] The virtual control quantity x of system variable x3 is obtained based on the sliding surface and the reaching law. 3c Specifically, by taking the first derivative of the sliding surface and combining it with the reaching law, the virtual control quantity x of the system variable x3 can be obtained. 3c :

[0091]

[0092] Where, θ M The velocity tilt angle of the aircraft is represented by r, and the distance between the aircraft and the target is represented by r.

[0093] Virtual control quantity x for system variable x3 3c Filtering is performed to obtain its virtual control law x. 3d ;

[0094] Preferably, the filtering is a first-order low-pass filter. The filtered virtual control law x can be obtained through a first-order low-pass filter with a time constant τ3 > 0. 3d :

[0095]

[0096] Where τ3 is a time constant.

[0097] Establish the system variable x3 and its virtual control law x 3d The error variable s2, i.e., s2 = x3 - x 3d ;

[0098] Obtain the virtual control quantity x of system variable x4 4c This makes the system variable x3 and its virtual control law x 3d The error variable s2→0;

[0099] Specifically, by taking the first derivative of the error variable s2 and making s2→0, the virtual control quantity x of the system variable x4 can be obtained. 4c :

[0100]

[0101] Where λ1 is a positive real number.

[0102] Virtual control quantity x for system variable x4 4c Filtering is performed to obtain its virtual control law x. 4d :

[0103] Preferably, the filtering is a first-order low-pass filter. The filtered virtual control law x can be obtained through a first-order low-pass filter with a time constant τ4 > 0. 4d :

[0104]

[0105] Furthermore, according to the present invention, the control command can be obtained by establishing the system variable x4 and its virtual control law x. 4d The error variable s3, i.e., s3 = x4 - x 4d ;

[0106] The control command u can be obtained by taking the first derivative of the error variable s3 with respect to time t and making s3→0.

[0107]

[0108] In this invention, the overload command a for the aircraft is also specified. M Apply constraints:

[0109]

[0110] Among them, a Mmax This indicates the upper limit of the aircraft's acceleration.

[0111] The present invention also provides a fixed-time convergence guidance and control system with landing constraints, comprising:

[0112] The measurement module is used to obtain the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target.

[0113] The processing module is used to obtain control commands u based on the sliding mode guidance law;

[0114] The execution module is used to control the servo motor according to the control command to achieve control of the aircraft attitude. Preferably, the servo motor is a proportional electric servo motor, which has better resistance to high overload than traditional pneumatic servo motors. Especially under the high speed and high maneuverability conditions of the aircraft, it can achieve precise control of the aircraft attitude.

[0115] Preferably, the processing module includes a sliding surface unit, a reaching law unit, and a control command acquisition unit;

[0116] The sliding surface unit is used to set the sliding surface of the guidance law, and is represented as follows:

[0117] s = x1 + k|x2| α sgn(x2)

[0118]

[0119] Where x1 and x2 are system variables, and q is the target's line-of-sight angle relative to the aircraft. Let q be the target's angular rate relative to the aircraft's line of sight. FLet k be the desired landing angle, and α be the parameters to be designed, where k > 0 and 1 < α < 2.

[0120] The approach law unit is used to set the approach law of the guidance law, expressed as:

[0121]

[0122] Where c1, c2, q1, and q2 are the parameters to be designed;

[0123] The control command acquisition unit obtains control commands based on the sliding surface unit and the reaching law unit:

[0124]

[0125] x3=a M

[0126]

[0127] Where λ2 is the parameter to be designed, which is generally a positive constant, and x3 and x4 are system variables, x 4d Let s1 be the virtual control law of system variable x4, and s2 be the virtual control law of system variable x4. 4d Error variables.

[0128] Example

[0129] Example 1

[0130] A simulation experiment was set up to conduct aircraft guidance and control in a scenario with a fixed target.

[0131] Where the target coordinates are x t =5000m, y t =0, initial aircraft velocity V m =300m / s, the launch angle is θ = 90°, and the terminal landing angle is set to q. F = -30°, -60°, -90°.

[0132] In the guidance law of an aircraft, the sliding surface s is:

[0133] s = x1 + k|x2| α sgn(x2)

[0134]

[0135] Where k = 5, α = 1 . 5;

[0136] Approach Law for:

[0137]

[0138] Where c1 = c2 = 4 / ln5, q1 = 0.7, q2 = 2.5

[0139] The dynamic characteristics of the autopilot can be expressed as follows:

[0140]

[0141] Thus, control commands are obtained, which are expressed as follows:

[0142]

[0143] x3=a M

[0144]

[0145] Furthermore, the overload command a for the aircraft is given by the following formula. M Apply constraints:

[0146]

[0147] Among them, a Mmax =80m / s 2 , λ2=10.

[0148] Simulation results are as follows Figures 2-5 And as shown in Tables 1 and 2, where, Figure 2 The simulated trajectory curve of the aircraft is shown; Figure 3 The convergence curve of the aircraft's line-of-sight angle is shown; Figure 4 The convergence curve of the aircraft's line-of-sight angular rate is shown. Figure 5 The control command variation curves of the aircraft are shown; Table 1 shows the relationship between the convergence time of the line-of-sight angle q and the guidance time; Table 2 shows the line-of-sight angular rate. Relationship between convergence time and guidance time.

[0149] Table 1

[0150]

[0151] Table 2

[0152]

[0153] from Figure 2 It can be seen that the aircraft is capable of accurately striking fixed targets with different designated terminal angles;

[0154] from Figures 3-5 As can be seen from Tables 1 and 2, under different specified terminal landing angles, i.e., different initial conditions, the convergence time of the aircraft satisfies: T ≤ T m=0.8t f The upper bound of the convergence time is independent of the initial value of the system state, effectively solving the problems of excessively long or short convergence time and sensitivity to the initial value of the state.

[0155] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0156] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0157] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A fixed-time convergence guidance and control method with landing angle constraints, characterized in that, The target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target are obtained. The control command u is obtained using the sliding mode guidance law. The aircraft controls the servos to adjust its flight attitude according to the control command. The sliding surface s1 of the sliding mode guidance law is: s1=x1+k|x2| α sgn(x2) Where x1 and x2 are system variables, and q is the target's line-of-sight angle relative to the aircraft. Let q be the target's angular rate relative to the aircraft's line of sight. F Let k be the desired landing angle, and α be the parameters to be designed, where k > 0 and 1 < α < 2. The reaching law of the sliding mode guidance law for: Where c1, c2, q1, and q2 are the parameters to be designed, and t go Indicates the remaining flight time of the aircraft; The convergence time T of the sliding mode guidance law satisfies: T≤T m =0.8t f Among them, T m This represents the upper bound of the system state convergence time, t. f This indicates the total flight time of the aircraft.

2. The fixed-time convergence guidance and control method with landing angle constraint according to claim 1, characterized in that, In guidance and control methods, the dynamic characteristics of the autopilot are expressed by the following formula to represent the impact of the autopilot's hysteresis on the aircraft: Among them, a M The overload command for the aircraft is determined by the sliding mode surface and the approach law; ξ represents the damping ratio of the autopilot, ω n This represents the inherent frequency of the autopilot, and u represents the control command.

3. The fixed-time convergence guidance and control method with landing angle constraint according to claim 2, characterized in that, The control command u is obtained based on the dynamic characteristics of the autopilot, so that the control command u can compensate for the impact of the autopilot's lag on the aircraft. The control command is expressed as: x3=a M Where λ2 is the parameter to be designed, x3 and x4 are system variables, and x 4d Let s1 be the virtual control law of system variable x4, and s2 be the virtual control law of system variable x4. 4d The error variable is s3 = x4 - x 4d .

4. The fixed-time convergence guidance and control method with landing angle constraint according to claim 3, characterized in that, Virtual control law x of system variable x4 4d Obtained through the following methods: The virtual control quantity x of system variable x3 is obtained based on the sliding surface and the reaching law. 3c : Where, θ M The velocity tilt angle of the aircraft is represented by r, and the distance between the aircraft and the target is represented by r. Virtual control quantity x for system variable x3 3c Filtering is performed to obtain its virtual control law x. 3d ; Establish the system variable x3 and its virtual control law x 3d The error variable s2; Obtain the virtual control quantity x of system variable x4 4c This makes the system variable x3 and its virtual control law x 3d The error variable s2→0; Virtual control quantity x for system variable x4 4c Filtering is performed to obtain its virtual control law x. 4d .

5. The fixed-time convergence guidance and control method with landing angle constraint according to claim 4, characterized in that, The filtering method is a first-order low-pass filter.

6. The fixed-time convergence guidance and control method with landing angle constraint according to claim 2, characterized in that, Overload command a for the aircraft M Apply constraints: Among them, a M max This indicates the upper limit of the aircraft's acceleration.

7. A fixed-time convergence guidance and control system with landing constraints, characterized in that, include: The measurement module is used to obtain the target's line-of-sight angle relative to the aircraft, the aircraft's velocity tilt angle, and the distance between the aircraft and the target. The processing module is configured to obtain control command u according to the sliding mode guidance law using the method described in any one of claims 1-6; The execution module is used to control the servos according to control commands, thereby controlling the attitude of the aircraft.

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