A Pre-defined Sliding Mode Control Method for Unmanned Aerial Vehicles Based on MRPs to Combat Wind Disturbance

Abstract

A wind-disturbance-resistant sliding mode control method for unmanned aerial vehicles (UAVs) based on mechanical performance parameters (MRPs) is disclosed. The method includes: establishing a UAV position dynamics model based on MRPs; calculating the position tracking error based on the position dynamics model and determining the position tracking error limit satisfying the preset performance function using a preset performance function; performing an inverse function operation on the position tracking error to convert it into an unconstrained transformation error; calculating an improved super-torsional sliding mode surface using the transformation error; and calculating the preset sliding mode control input for the UAV based on the super-torsional sliding mode surface. The advantages of this invention are: considering complex wind disturbances, establishing an MRP-based UAV position dynamics model, introducing preset performance control to effectively limit UAV position deviation, and combining this with the improved super-torsional sliding mode control method, which can improve the robustness and tracking accuracy of UAV trajectory tracking control under complex wind disturbance conditions.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, and specifically relates to a UAV preset sliding mode anti-wind disturbance control method based on MRPs (Modified Rodriguez parameters). Background Technology

[0002] With the rapid development of unmanned aerial vehicle (UAV) technology, drones have become indispensable tools widely used in various fields. Using drones for damage detection of aircraft skin can significantly improve detection efficiency. However, in complex external environments such as wind disturbances, the drone's flight position can deviate significantly during aircraft skin damage detection, potentially causing collisions and resulting in safety issues and property damage. Therefore, while improving controller robustness, it is crucial to constrain the drone's position deviation through control methods to ensure flight safety.

[0003] To address the position tracking and control problem of UAVs under wind disturbances, the H∞-based backstepping sliding mode control method can handle the modeling uncertainties and upper bounds of wind disturbances, and the designed position control method has a certain degree of robustness. However, in reality, complex wind disturbances pose challenges to the position offset limits of UAVs in the three axes, and existing control methods are insufficient to effectively solve this problem. Therefore, the safety of UAVs cannot be effectively guaranteed during flight operations such as inspection missions. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a method for controlling wind disturbance in a UAV based on a pre-defined sliding mode using MRPs.

[0005] To achieve the above objectives, the MRP-based UAV pre-sliding mode wind disturbance control method provided by the present invention includes the following steps performed in sequence:

[0006] 1) Based on the MRPs attitude representation method, establish a position dynamics model of the UAV under complex wind disturbance conditions;

[0007] 2) Based on the above position dynamics model, calculate the position tracking error of the UAV, and use the preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV;

[0008] 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error;

[0009] 4) Differentiate the above conversion error with respect to time and introduce the power-law approach to calculate the improved super-torsional sliding surface, thereby ensuring the stability of the UAV under complex wind disturbance conditions;

[0010] 5) Based on the above-mentioned super-torsional sliding mode surface, the constant velocity approach law and the exponential approach law are introduced to calculate the preset sliding mode control output of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller for the UAV.

[0011] In step 1), the method for establishing the position dynamics model of the UAV based on the MRPs attitude representation method is as follows:

[0012] First, a position dynamics model of the UAV under complex wind disturbance conditions is established based on MRPs:

[0013]

[0014] Where x represents the position coordinate of the UAV's center of mass in the x-axis direction of the global coordinate system O-xyz. The x-axis represents the acceleration; y represents the position coordinate of the UAV's center of mass in the y-axis direction within the global coordinate system O-xyz. The y-axis represents the acceleration; z represents the position coordinates of the UAV's center of mass along the z-axis in the global coordinate system O-xyz. Let σ1, σ2, and σ3 represent the acceleration along the z-axis, and σ1, σ2, and σ3 represent the transformation angles along the x, y, and z axes in the body coordinate system O-x'y'z' and the global coordinate system O-xyz, respectively. σ = [σ1 σ2 σ3] T This is a vector representation of the MRP parameters, where U1 represents the total thrust in the z' direction in the body coordinate system, and vector F... T =[F Tx F Ty F Tz ] T The wind force is expressed in N, m represents the mass of the drone in kg, and g represents the acceleration due to gravity.

[0015] In step 2), the method of calculating the UAV's position tracking error based on the aforementioned position dynamics model and determining the position tracking error limit that satisfies the preset performance function using a preset performance function, thereby limiting the UAV's position tracking error, is as follows:

[0016] First, the position tracking error of the UAV is expressed as:

[0017] e x =xx d (2)

[0018] Where x represents the position coordinate of the UAV's centroid in the x-axis direction of the global coordinate system O-xyz, x d Indicates the desired target location of the drone;

[0019] Then, a preset performance function ρ is constructed to limit the position tracking error, with the following formula:

[0020]

[0021] Where, k j The convergence velocity parameters, ρ0,ρ, represent the position transient response. ∞ These represent the initial and steady-state values ​​of the preset performance function, respectively.

[0022] Then, using a preset performance function ρ, the limit of the position tracking error is expressed as:

[0023]

[0024] in, δ represents the preset performance control parameters.

[0025] In step 3), the method for performing an inverse function calculation on the aforementioned position tracking error to obtain the unconstrained conversion error is as follows:

[0026] Regarding the above tracking error e x Performing an inverse function calculation yields the unconstrained transformation error, as shown in the formula:

[0027]

[0028] Where Λ represents the position tracking error that meets the preset performance control parameters.

[0029] In step 4), the method of differentiating the above-mentioned conversion error with respect to time and introducing a power-law approach to calculate the improved super-torsional sliding surface, thereby ensuring the stability of the UAV under complex wind disturbance conditions, is as follows:

[0030] First, calculate the conversion error ε. x The derivative with respect to time is given by the formula:

[0031]

[0032] Then, by introducing the power-law approaching law, the improved supertorsion sliding surface is calculated, and the formula is:

[0033]

[0034] Where μ,c and The constant representing the conversion error that satisfies the improved design requirements for the accuracy and stability of the supertorsion slip surface, sgn(ε) x )|ε x | 1-μ This represents the power-law approaching condition that makes the sliding surface satisfy the rapid stability condition.

[0035] In step 5), the method for calculating the preset sliding mode control output of the UAV based on the above-mentioned super-torsional sliding mode surface, by introducing the constant velocity approach law and the exponential approach law, and thus completing the design of the UAV's preset sliding mode anti-wind disturbance controller is as follows:

[0036] First, by introducing the constant velocity approach law and the exponential approach law, the preset sliding mode control output of the UAV is calculated using the following formula:

[0037]

[0038] in, and represent control gain, This represents the constant velocity approaching law that ensures the stability of the sliding mode control system. This represents the exponential approach law that ensures the stability of the sliding mode control system.

[0039] The MRP-based UAV pre-sliding mode wind disturbance control method provided by this invention has the following advantages:

[0040] Considering the forces exerted on each axis of the UAV by complex wind disturbances in real-world environments, a mathematical model based on modified Rogorges parameters is established, and an improved super-torsional sliding mode controller is designed. This enables the UAV to strictly limit its position deviation within a preset range under complex wind disturbances. It allows the UAV to maintain small positional deviations and rapid response capabilities during flight, ensuring flight stability. Furthermore, it takes into account complex wind disturbances in real-world environments, allowing for pre-setting of system performance control conditions to achieve robustness of the UAV's flight process under wind disturbance conditions in real-world application scenarios. Attached Figure Description

[0041] Figure 1 The flowchart of the MRP-based UAV pre-sliding mode anti-wind disturbance control method provided by the present invention is shown below.

[0042] Figure 2 This is a structural diagram of a preset sliding mode wind disturbance resistance controller for a drone provided in an embodiment of the present invention;

[0043] Figure 3 A three-dimensional position tracking diagram under complex wind disturbance combined with preset performance control parameters, provided in an embodiment of the present invention;

[0044] Figure 4 This is a three-dimensional position tracking error diagram under complex wind disturbance combined with preset performance control parameters, provided as an embodiment of the present invention. Detailed Implementation

[0045] The following describes in detail the MRP-based UAV pre-sliding mode anti-wind disturbance control method provided by the present invention, with reference to the accompanying drawings and specific embodiments.

[0046] like Figure 1As shown, the MRP-based UAV preset sliding mode wind disturbance control method provided by the present invention includes the following steps performed in sequence:

[0047] 1) Based on the MRPs attitude representation method, establish a position dynamics model of the UAV under complex wind disturbance conditions;

[0048] First, a position dynamics model of the UAV under complex wind disturbance conditions is established based on MRPs:

[0049]

[0050] Where x represents the position coordinate of the UAV's center of mass in the x-axis direction of the global coordinate system O-xyz. The x-axis represents the acceleration; y represents the position coordinate of the UAV's center of mass in the y-axis direction within the global coordinate system O-xyz. The y-axis represents the acceleration; z represents the position coordinates of the UAV's center of mass along the z-axis in the global coordinate system O-xyz. Let σ1, σ2, and σ3 represent the acceleration along the z-axis, and σ1, σ2, and σ3 represent the transformation angles along the x, y, and z axes in the body coordinate system O-x'y'z' and the global coordinate system O-xyz, respectively. σ = [σ1 σ2 σ3] T This is a vector representation of the MRP parameters, where U1 represents the total thrust in the z' direction in the body coordinate system, and vector F... T =[F Tx F Ty F Tz ] T The wind force is expressed in N, m represents the mass of the drone in kg, and g represents the acceleration due to gravity.

[0051] 2) Based on the above position dynamics model, calculate the position tracking error of the UAV, and use the preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV;

[0052] First, the position tracking error of the UAV is expressed as:

[0053] e x =xx d (2)

[0054] Where x represents the position coordinate of the UAV's centroid in the x-axis direction of the global coordinate system O-xyz, x d Indicates the desired target location of the drone;

[0055] Then, a preset performance function ρ is constructed to limit the position tracking error, with the following formula:

[0056]

[0057] Where, k j The convergence velocity parameters, ρ0,ρ, represent the position transient response. ∞ These represent the initial and steady-state values ​​of the preset performance function, respectively.

[0058] Then, using a preset performance function ρ, the limit of the position tracking error is expressed as:

[0059]

[0060] in, δ represents the preset performance control parameters.

[0061] 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error;

[0062] Regarding the above tracking error e x Performing an inverse function calculation yields the unconstrained transformation error, as shown in the formula:

[0063]

[0064] Where Λ represents the position tracking error that meets the preset performance control parameters.

[0065] 4) Differentiate the above conversion error with respect to time and introduce the power-law approach to calculate the improved super-torsional sliding surface, thereby ensuring the stability of the UAV under complex wind disturbance conditions;

[0066] First, calculate the conversion error ε. x The derivative with respect to time is given by the formula:

[0067]

[0068] Then, by introducing the power-law approaching law, the improved supertorsion sliding surface is calculated, and the formula is:

[0069]

[0070] Where μ,c and The constant representing the conversion error that satisfies the improved design requirements for the accuracy and stability of the supertorsion slip surface, sgn(ε) x )|ε x | 1-μ This represents the power-law approaching condition that makes the sliding surface satisfy the rapid stability condition.

[0071] 5) Based on the above-mentioned super-torsional sliding mode surface, the constant velocity approach law and the exponential approach law are introduced to calculate the preset sliding mode control output of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller for the UAV.

[0072] First, by introducing the constant velocity approach law and the exponential approach law, the preset sliding mode control output of the UAV is calculated using the following formula:

[0073]

[0074] in, 'l' represents the control gain. This represents the constant velocity approaching law that ensures the stability of the sliding mode control system. This represents the exponential approach law that ensures the stability of the sliding mode control system.

[0075] The effects of this invention can be further illustrated by the following simulation results.

[0076] Experimental setup: First, based on the UAV's rotational inertia and mass parameters, the wind disturbance velocity was set to a range of [-10, 10] m / s, with a preset maximum error boundary of ±0.5 m. The preset performance control parameters were set as follows: δ = 1 and the steady-state value ρ of the preset performance function ∞ =0.5. Design in Matlab as follows: Figure 2 The UAV shown is equipped with a preset sliding mode wind disturbance control system, simulating the limited position offset control performance of the UAV under complex wind disturbance conditions on all axes. The UAV parameter settings for this experiment are shown in Table 1:

[0077] Table 1. UAV Model Parameters

[0078]

[0079] Figure 3 This is a three-dimensional position tracking diagram provided by an embodiment of the present invention, which combines wind disturbance with preset performance control. Figure 4 This is a three-dimensional position tracking error diagram under wind disturbance combined with preset performance control, provided as an embodiment of the present invention.

[0080] from Figure 3 As can be seen, within a 40-second simulation period, the UAV can reach the desired position in 2 seconds in the x-axis, y-axis, and z-axis directions. Furthermore, under continuous complex wind disturbances, the actual position of the UAV is consistent with the desired position, achieving effective position tracking.

[0081] from Figure 4 As can be seen, within the 40-second simulation time, the position error of the UAV can reach 0 in the x-axis, y-axis and z-axis directions in 2 seconds. Moreover, under continuous complex wind disturbance, the position error has almost no fluctuation and will not exceed the performance envelope.

[0082] This positional constraint ensures the safety of the inspected aircraft and UAV during the aircraft skin inspection process. It can be seen that the method of the present invention can limit the positional deviation of the UAV under complex external wind disturbances and has strong robustness.

[0083] The method of the present invention was verified by building a simulation model. The simulation results show that the method of the present invention can quickly and stably track the input signal under complex wind disturbance conditions and has good anti-interference ability.

Claims

1. A method for controlling wind disturbance in a UAV based on pre-defined sliding mode using MRPs, characterized in that: The method includes the following steps performed in sequence: 1) Based on the MRPs attitude representation method, establish a position dynamics model of the UAV under complex wind disturbance conditions; 2) Based on the above position dynamics model, calculate the position tracking error of the UAV, and use the preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV; 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error; 4) Differentiate the above conversion error with respect to time and introduce the power-law approach to calculate the improved super-torsional sliding surface, thereby ensuring the stability of the UAV under complex wind disturbance conditions; 5) Based on the above-mentioned super-torsional sliding mode surface, the constant velocity approach law and the exponential approach law are introduced to calculate the preset sliding mode control output of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller for the UAV. In step 1), the method for establishing the position dynamics model of the UAV based on the MRPs attitude representation method is as follows: First, a position dynamics model of the UAV under complex wind disturbance conditions is established based on MRPs: Where x represents the position coordinate of the UAV's center of mass in the x-axis direction of the global coordinate system O-xyz. The x-axis represents the acceleration; y represents the position coordinate of the UAV's center of mass in the y-axis direction within the global coordinate system O-xyz. y represents the acceleration along the y-axis; z represents the position coordinates of the UAV's center of mass along the z-axis in the global coordinate system O-xyz. Let σ1, σ2, and σ3 represent the acceleration along the z-axis, and σ1, σ2, and σ3 represent the transformation angles along the x, y, and z axes in the body coordinate system O-x'y′z′ and the global coordinate system O-xyz, respectively. σ = [σ1σ2 σ3] T This is a vector representation of the MRP parameters, where U1 represents the total thrust in the z′ direction in the body coordinate system, and vector F... T =[F Tx F Ty F Tz ] T The wind force is expressed in N, m represents the mass of the drone in kg, and g represents the acceleration due to gravity.

2. The method for wind disturbance mitigation control of UAVs based on MRPs according to claim 1, characterized in that: In step 2), the method of calculating the UAV's position tracking error based on the aforementioned position dynamics model and determining the position tracking error limit that satisfies the preset performance function using a preset performance function, thereby limiting the UAV's position tracking error, is as follows: First, the position tracking error of the UAV is expressed as: e x =x-x d (2) Where x represents the position coordinate of the UAV's centroid in the x-axis direction of the global coordinate system O-xyz, x d Indicates the desired target location of the drone; Then, a preset performance function ρ is constructed to limit the position tracking error, with the following formula: Where, k j The convergence velocity parameters, ρ0,ρ, represent the position transient response. ∞ These represent the initial and steady-state values ​​of the preset performance function, respectively. Then, using a preset performance function ρ, the limit of the position tracking error is expressed as: in, δ represents the preset performance control parameters.

3. The method for controlling unmanned aerial vehicles (UAVs) based on pre-defined sliding mode wind disturbance according to claim 2, characterized in that: In step 3), the method for performing an inverse function calculation on the aforementioned position tracking error to obtain the unconstrained conversion error is as follows: Regarding the above position tracking error e x Performing an inverse function calculation yields the unconstrained transformation error, as shown in the formula: Where Λ represents the position tracking error that meets the preset performance control parameters.

4. The method for controlling wind disturbance in a UAV based on pre-defined sliding mode according to claim 3, characterized in that: In step 4), the method of differentiating the above-mentioned conversion error with respect to time and introducing a power-law approach to calculate the improved super-torsional sliding surface, thereby ensuring the stability of the UAV under complex wind disturbance conditions, is as follows: First, calculate the conversion error ε. x The derivative with respect to time is given by the formula: Then, by introducing the power-law approaching law, the improved supertorsion sliding surface is calculated, and the formula is: Where μ,c and The constant representing the conversion error that satisfies the improved design requirements for the accuracy and stability of the supertorsion slip surface, sgn(ε) x )|ε x | 1-μ This represents the power-law approaching condition that makes the sliding surface satisfy the rapid stability condition.

5. The method for controlling unmanned aerial vehicles based on MRPs with preset sliding mode to resist wind disturbance as described in claim 4, characterized in that: In step 5), the method for calculating the preset sliding mode control output of the UAV based on the above-mentioned super-torsional sliding mode surface, by introducing the constant velocity approach law and the exponential approach law, and thus completing the design of the UAV's preset sliding mode anti-wind disturbance controller is as follows: First, by introducing the constant velocity approach law and the exponential approach law, the preset sliding mode control output of the UAV is calculated using the following formula: in, and l represent control gain, This represents the constant velocity approaching law that ensures the stability of the sliding mode control system. This represents the exponential approach law that ensures the stability of the sliding mode control system.

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