High-mobility aircraft fixed-time sliding mode precise guidance method

Abstract

A high-mobility aircraft fixed-time sliding mode precise guidance method, the steps are as follows: 1. Given the desired line of sight angle value: give the desired line of sight angle value; Give the initial position, initial track angle of the aircraft; Give the initial position, initial track angle and acceleration of the target; 2. Fixed time sliding mode approach law calculation: calculate the sliding mode surface s1, and calculate the value of the approach law required to eliminate the error between the desired line of sight angle and the actual line of sight angle; 3. Fixed time observer estimates acceleration: use the fixed time observer to estimate the size of the acceleration component of the target in the line of sight coordinate system 4. Fixed time sliding mode control law calculation: calculate the control amount size u required to make the line of sight angle rate approach to zero. The control flow is shown in the attached figure.

Description

Technical Field

[0001] This invention provides a fixed-time sliding mode precision guidance method for high-maneuverability aircraft, which provides a fixed-time precision guidance method for high-maneuverability aircraft to strike targets with unknown acceleration in three-dimensional space, and belongs to the field of automatic control technology. Background Technology

[0002] Highly maneuverable aircraft (HMAS), as a crucial force in modern air warfare, are increasingly becoming an important means of conducting precision air strikes due to their high maneuverability and ability to rapidly approach and engage targets. Therefore, researching precision guidance technology for HMAS has significant practical implications. In precision strike missions, targets are in continuous motion, not stationary, necessitating consideration of targets with unknown acceleration. Furthermore, actual combat is subject to constraints on the line-of-sight angle and engagement time, thus requiring a precision guidance method that considers both the line-of-sight angle and convergence time.

[0003] This invention, "A Fixed-Time Sliding Mode Precision Guidance Method for High-Maneuverability Aircraft," proposes a fixed-time sliding mode precision guidance method based on the relative motion model of the aircraft and the target for high-maneuverability aircraft tasked with pursuing targets with unknown acceleration. This method combines a fixed-time state observer algorithm and sliding mode control theory. The closed-loop system controlled by this method exhibits fixed-time convergence performance, providing an effective design tool for the guidance engineering implementation of high-maneuverability aircraft. Summary of the Invention

[0004] The purpose of this invention is to provide a precise guidance method for high-maneuverability aircraft with terminal angle constraints to pursue targets. Control engineers can use this method and combine it with actual parameters to achieve precise guidance and control of high-maneuverability aircraft in environments with unknown target acceleration.

[0005] The technical solution of the present invention:

[0006] This invention, "A Precise Guidance Method for a High-Mighty Aircraft Using a Fixed-Time Sliding Mode," primarily involves calculating the first sliding surface value based on a given desired line-of-sight angle, and then calculating the required magnitude of the approach law based on a designed approach law. Next, the target's acceleration is estimated using a designed fixed-time observer. Subsequently, the magnitude of the control variable is calculated according to the definition of the second sliding surface. Finally, this control law is applied to the three-dimensional relative motion model of the aircraft and the target. In practical applications, the relative distance between the aircraft and the target, and the respective track angles of the aircraft and the target, are measured by sensors. The control variable calculated by this method is then converted into inner-loop roll angle, normal overload, and throttle commands, enabling the high-maneuverability aircraft to complete the pursuit and guidance control of a target with unknown acceleration.

[0007] The present invention, "A method for precise guidance of a high-maneuverability aircraft in a fixed-time sliding mode," comprises the following specific steps:

[0008] Step 1: Given the desired line-of-sight angle value; given the initial position and initial track angle of the aircraft; given the initial position, initial track angle, and acceleration of the target.

[0009] Step 2: Calculate the reaching law: Calculate the sliding surface s1, and calculate the reaching law required to eliminate the error between the desired viewing angle and the actual viewing angle. The value of .

[0010] Step 3: Target acceleration estimation: Estimate the magnitude of the target's acceleration components in the line-of-sight coordinate system using a fixed-time observer.

[0011] Step 4: Calculate the control law: Calculate the control quantity u required to make the line-of-sight angular rate approach zero.

[0012] Step 5: Stability analysis: Select Lyapunov candidate function V.

[0013] Wherein, the given desired viewing angle mentioned in step one is x 1d =[θ ld φ ld ] T =[c1 c2] T , x is a relative angle parameter. a0 ,y a0 ,z a0 Let x represent the initial three-dimensional position of the aircraft, and let x represent the initial track inclination angle and track yaw angle of the aircraft, respectively. t0 ,y t0 ,z t0 Let θ be the initial three-dimensional position of the target. t0 ,φ t0 These are the target's initial track inclination and track deflection, respectively. t0 The acceleration parameters of the target.

[0014] In step two, the calculation of the sliding surface s1 and the calculation of the approach law required to eliminate the error between the desired viewing angle and the actual viewing angle are described. The value of is calculated as follows:

[0015] 1) Calculate the first sliding surface value, defined as the error between the current viewing angle and the desired viewing angle.

[0016] 2) Calculate the reaching law k1,k2∈R 2×2 For control parameters, 0 < r1 < 1, r2 > 1. Defined as sig(x r )=|x| r The sgn(x) and sgn() functions are defined as follows:

[0017] In step three, the magnitude of the target's acceleration component in the line-of-sight coordinate system is estimated using a fixed-time disturbance observer. The calculation method is as follows:

[0018] 1) Calculate the current velocity-dependent state variables V for the observer. N Defined as

[0019] 2) Calculate the observation error e1 = z1 - V of the fixed-time state observer. N z1 is the V obtained by the observer N The estimated value;

[0020] Calculate the derivative of z1 l1,l2∈R 2×2 Here, z1 is the observer parameter matrix, and z2 is the target acceleration component a. t =[a tθ -a tφ ] T The estimated value,

[0021] 3) Calculate the derivative of z2. l3∈R 2×2 Here is the observer parameter matrix; calculated from the derivative of z2. The estimated value.

[0022] The calculation method for the control quantity u required to bring the line-of-sight angular rate close to zero, as described in step four, is as follows:

[0023] 1) Calculate the current sliding surface value s2, where s2 is determined by... Calculated.

[0024] 2) Calculate the aircraft acceleration control quantity u = [a aθ a aφ ] T a aθ ,a aφ Let be the acceleration components of the aircraft along the y and z axes of the line-of-sight coordinate system, respectively, which are calculated by the following formula.

[0025]

[0026] Where k3,k4∈R 2×2 For control parameters, The Hadamard product is defined as the element-wise multiplication of two matrices.

[0027]

[0028] The Lyapunov candidate function selected in the stability analysis described in step five is calculated as follows:

[0029]

[0030] The beneficial effects of this invention are:

[0031] 1) This method can estimate the acceleration of an unknown target and has fixed-time convergence.

[0032] 2) This method can intercept maneuvering targets at the desired line-of-sight angle within a fixed time, and the convergence time is independent of the initial state.

[0033] 3) This method is designed for three-dimensional relative motion models and is more suitable for practical applications.

[0034] In application, control engineers use the actual desired line-of-sight angle and convert the control quantity calculated by this method into inner-loop commands to control the aircraft in order to complete the mission of striking targets with unknown acceleration. Attached Figure Description

[0035] Figure 1 This is a flowchart of the guiding method described in this invention;

[0036] Figure 2 This is a three-dimensional positional diagram of the aircraft and the target of the present invention;

[0037] The symbols are explained as follows:

[0038] θ ld ,φ ld Desired line of sight tilt angle, desired line of sight deflection angle

[0039] θ l ,φ l Actual line of sight tilt angle, line of sight deflection angle

[0040] Acceleration components of the U-shaped aircraft along the y and z axes in the line-of-sight coordinate system

[0041] z2 target acceleration related estimates

[0042] V N Model state quantities for a fixed-time state observer

[0043] Approach Law

[0044] Ox o yo z o Reference inertial coordinate system

[0045] Ox a y a z a Aircraft track coordinate system

[0046] O t x t y t z t Target track coordinate system

[0047] Ox l y l z l Relative line-of-sight coordinate system

[0048] θ a ,φ a The aircraft's track inclination and track deflection

[0049] θ t ,φ t Target's track inclination and track deflection

[0050] θ l ,φ l Line of sight tilt and line of sight deflection

[0051] V a aircraft speed

[0052] V t target speed

[0053] V Lyapunov alternative functions Detailed Implementation

[0054] The design methods of each part of this invention will be further described below with reference to the accompanying drawings:

[0055] This invention, "A Precise Guidance Method for Fixed-Time Sliding Mode of a High-Maneuverability Aircraft," is available in [link to document]. Figure 1 As shown, the specific steps are as follows: Step 1: Give the desired line-of-sight angle value

[0056] Given the desired line of sight tilt angle and line of sight deflection angle x 1d =[θ ld φ ld ] T =[c1 c2] T , Step 2: Fixed-time sliding mode reaching law calculation

[0057] 1) Calculate the first sliding surface value, defined as the error between the current viewing angle and the desired viewing angle.

[0058] 2) Calculate the reaching law k1,k2∈R 2×2 For control parameters, 0 < r1 < 1, r2 > 1. Defined as sig(x r )=|x| r The sgn(x) and sgn() functions are defined as follows:

[0059] Step 3: Estimate acceleration using a fixed-time observer

[0060] 1) Calculate the current velocity-dependent state variables V for the observer. N Defined as

[0061] 2) Calculate the observation error e1 = z1 - V of the fixed-time state observer. N z1 is the V obtained by the observer N Estimate the value of z1; calculate the derivative of z1. l1,l2∈R 2×2 Here, z1 represents the observer parameter matrix, and z2 represents the target acceleration components. The estimated value,

[0062] 3) Calculate the derivative of z2. l3∈R 2×2 Here is the observer parameter matrix; calculated from the derivative of z2. The estimated value.

[0063] Step 4: Calculation of Fixed-Time Sliding Mode Control Law

[0064] 1) Calculate the current sliding surface value s2, where s2 is determined by... Calculated.

[0065] 2) Calculate the aircraft acceleration control quantity u = [a aθ a aφ ] T a aθ ,a aφ Let be the acceleration components of the aircraft along the y and z axes of the line-of-sight coordinate system, respectively, which are calculated by the following formula.

[0066] Where k3,k4∈R 2×2 For control parameters, The Hadamard product is defined as the element-wise multiplication of two matrices.

[0067] Step 5: Stability Analysis

[0068] 1) Select Lyapunov alternative functions

[0069] 2) Calculate the derivative with respect to V

[0070]

[0071] Therefore, convergence time T0 is the convergence time of the fixed-time observer.

Claims

1. A method for precise guidance of a high-maneuverability aircraft using a fixed-time sliding mode, characterized in that: The specific steps are as follows: Step 1: Given the desired line-of-sight angle value; given the initial position and initial track angle of the aircraft; given the initial position, initial track angle, and acceleration of the target; Step 2: Fixed-time sliding mode reaching law calculation: Calculate the sliding surface And calculate the approach law required to eliminate the error between the desired sight angle and the actual sight angle. The value; Step 3: Estimate acceleration using a fixed-time observer: Estimate the magnitude of the target's acceleration components in the line-of-sight coordinate system using a fixed-time observer. ; Step 4: Fixed-time sliding mode control law calculation: Calculate the control quantity required to make the line-of-sight angular rate approach zero. ; Step 5: Stability analysis; The calculations described in step four require the amount of control needed to bring the line-of-sight angular rate close to zero. The calculation method is as follows: 1) Calculate the current sliding surface value , Depend on Calculated; 2) Calculate the aircraft acceleration control parameters , Let be the acceleration components of the aircraft along the y and z axes of the line-of-sight coordinate system, respectively, which are calculated by the following formula. in, For control parameters, The Hadamard product is defined as the element-wise multiplication of two matrices. 。 2. The method for precise guidance of a high-maneuverability aircraft in a fixed-time sliding mode according to claim 1, characterized in that: The given desired viewing angle mentioned in step one is These are relative angle parameters. This represents the initial three-dimensional position of the aircraft. These are the initial trajectory inclination angle and trajectory deflection angle of the aircraft, respectively. Let be the initial three-dimensional position of the target. These are the target's initial trajectory inclination angle and trajectory deflection angle, respectively. Let be the acceleration parameters of the target, where , For the desired line of sight tilt angle and line of sight deflection angle.

3. The method for precise guidance of a high-maneuverability aircraft in a fixed-time sliding mode according to claim 1, characterized in that: The calculation of the sliding surface described in step two And the approach law required to eliminate the error between the desired sight angle and the actual sight angle. The value of is calculated as follows: 1) Calculate the first sliding surface value, defined as the error between the current viewing angle and the desired viewing angle. , , These are the angle of inclination and the angle of deflection of the line of sight. 2) Calculate the reaching law , For control parameters, , Defined as , , The function is defined as .

4. The method for precise guidance of a high-maneuverability aircraft in a fixed-time sliding mode according to claim 1, characterized in that: The method described in step three involves using a fixed-time disturbance observer to estimate the magnitude of the target's acceleration components in the line-of-sight coordinate system. The calculation method is as follows: 1) Calculate the current velocity-dependent state variables used by the observer. Defined as ; 2) Calculate the observation error of the fixed-time state observer. , For obtained by the observer Estimates; Calculate derivative , The observer parameter matrix, For the target acceleration component The estimated value, ; 3) Calculation derivative , The observer parameter matrix; according to The derivative is calculated to obtain The estimated value .

5. A method for precise guidance of a high-maneuverability aircraft in a fixed-time sliding mode according to claim 1, characterized in that: In the stability analysis described in step five, the Lyapunov alternative function... The calculation method is as follows: .

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