Unmanned aerial vehicle preset performance control method and system considering time-varying position constraint

Abstract

The present application belongs to the technical field of unmanned aerial vehicle trajectory tracking control, and specifically discloses a preset performance control method and system for unmanned aerial vehicle considering time-varying position constraint. In the case that the unmanned aerial vehicle has time-varying position constraint, model uncertainty, actuator failure and wind disturbance, the method first converts the system with position constraint into an unconstrained system by using a nonlinear mapping method, then uses a preset performance control method and an adaptive backstepping technology to design a controller for the transformed system, so that the system error is kept within the preset boundary function range; the present application also designs a fuzzy logic system FLS and a nonlinear disturbance observer to estimate the model uncertainty and wind disturbance, thereby proposing a trajectory tracking control scheme combining model mapping and preset performance. Under the control of the method of the present application, the quadrotor unmanned aerial vehicle has good robustness, and even after the actuator fails, the tracking error can still be kept within the preset interval.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle trajectory tracking control, and particularly relates to an unmanned aerial vehicle preset performance control method and system considering time-varying position constraints. BACKGROUND

[0002] In recent decades, unmanned aerial vehicles have increasingly appeared in the public eye, such as rescue, agriculture, photography, etc. As one of the most popular types of winged unmanned aerial vehicles, quadrotor unmanned aerial vehicles (UAVs) have many unique advantages, such as strong flight stability and adaptability, vertical take-off and landing, and easy production. Quadrotor unmanned aerial vehicles are not only applied to wide areas, but also to constrained narrow areas such as communities and pipelines, which puts higher requirements on unmanned aerial vehicle systems. Quadrotor unmanned aerial vehicle systems with four inputs and six outputs are considered to be underactuated and highly coupled systems, which makes control more difficult. Therefore, how to design a high-adaptability and high-efficiency unmanned aerial vehicle controller with constraints has become a challenging task.

[0003] Domestic and foreign experts have conducted in-depth research on the design of complex nonlinear systems and constrained systems. Model predictive control methods are considered to be a powerful means to solve constraint control problems. This method is essentially an optimization strategy, but the strategy requires a large amount of calculation and is not easy to implement. Barrier Lyapunov function (BLF) technology is commonly used to handle state constraint problems. In previous studies, experts and scholars have proposed a non-singular fast terminal sliding mode controller based on BLF to ensure the finite time convergence of a blended wing body (BWB) aircraft system. In addition, an adaptive model-free controller based on time-varying BLF for a robotic arm has also been proposed. In the above studies, the BLF method is used, but the BLF method requires some necessary assumptions, such as the virtual control input needing to satisfy the constraint condition, which is difficult in practice. Unlike using the BLF method for constrained systems, more and more scholars have begun to study nonlinear mapping functions and coordinate transformations. At present, scholars have proposed using nonlinear mapping methods to design controllers for constrained robot systems, and some literature has introduced a new mapping function to replace the BLF method, which also eliminates the assumption that the virtual control input satisfies the constraint requirement.

[0004] In engineering practice, with the increasing demand for control performance, the prescribed performance control (PPC) emerges as the times require and gradually becomes popular. Among them, for unmanned aerial vehicles with disturbances, experts have proposed an adaptive prescribed performance controller that can ensure the system error to converge quickly within the prescribed range. The PPC method can also solve the tracking problem of vehicles with actuator faults and ensure that the tracking error converges to the prescribed region. In addition, using the prescribed performance technique to design an observer to solve the problem of frequent actuator faults of unmanned aerial vehicles can make the system more robust and adaptive. However, in the face of time-varying constraints on system states, the design of the prescribed performance function becomes complex.

[0005] It is well known that quadrotor unmanned aerial vehicles are extremely susceptible to actuator faults, which can lead to deteriorating control or even failure. Therefore, the actuator fault problem has attracted widespread attention. In previous studies, a new adaptive control method based on state estimator has been proposed to solve the actuator failure problem of uncertain delayed semi-Markov jump systems, but it does not consider the problem of time-varying position constraints. In addition, scholars have studied a fault-tolerant control method for handling unmanned aerial vehicle thrust system failures. Specifically, when the loss of control output is severe, the directional control can be abandoned to maintain attitude controllability, but this method is not highly applicable in strict position constraints. In addition, experts have designed a high-gain observer that can effectively compensate for the negative effects of actuator faults in quadrotor unmanned aerial vehicles, but this method has not been well applied to position constraint problems. SUMMARY

[0006] The purpose of the present application is to propose a quadrotor unmanned aerial vehicle prescribed performance control method considering time-varying position constraints. This method is aimed at complex systems with time-varying position constraints, model uncertainties, external wind disturbances, and actuator faults. It uses a nonlinear mapping function to convert the constraint model into a new unconstrained model. It uses prescribed performance control and adaptive backstepping control to design a quadrotor unmanned aerial vehicle prescribed performance controller to achieve stable following of the desired signal without violating the constraint conditions and to achieve high control accuracy and robustness.

[0007] To achieve the above purpose, the present application adopts the following technical solutions:

[0008] The quadrotor unmanned aerial vehicle prescribed performance control method considering time-varying position constraints comprises the following steps:

[0009] Step 1. A composite model of the unmanned aerial vehicle considering time-varying position constraints, model uncertainty and external wind disturbance is established, the composite model is mapped by using a nonlinear mapping relationship to be converted into an unconstrained model; a preset performance function is used to limit the tracking error of the unconstrained system, an error transformation function is used to process the tracking error, and is used for subsequent design of the unmanned aerial vehicle preset performance controller;

[0010] Step 2. Based on the unconstrained system of step 1, an adaptive fuzzy system is used to estimate the model uncertainty, and a disturbance observer is used to estimate and compensate the external wind disturbance and actuator fault, and a preset performance method and backstepping method are used to design the unmanned aerial vehicle preset performance controller;

[0011] Step 3. The unmanned aerial vehicle preset performance controller designed in step 2 is used to realize trajectory tracking control on the unconstrained system obtained after nonlinear mapping, and according to the nonlinear mapping relationship, the expected signal of the original constrained system can be obtained without violating the constraint condition.

[0012] In addition, on the basis of the above, the application also proposes a preset performance control method for the unmanned aerial vehicle considering time-varying position constraints, which adopts the following technical scheme:

[0013] The preset performance control system for the quad-rotor unmanned aerial vehicle considering time-varying position constraints comprises the following modules:

[0014] A model construction module is used to establish a composite model of the unmanned aerial vehicle considering time-varying position constraints, model uncertainty and external wind disturbance, to map the composite model by using a nonlinear mapping relationship to be converted into an unconstrained model; a preset performance function is used to limit the tracking error of the unconstrained system, an error transformation function is used to process the tracking error, and is used for subsequent design of the unmanned aerial vehicle preset performance controller;

[0015] A controller design module is used to estimate the model uncertainty by using an adaptive fuzzy system based on the unconstrained system, and to estimate and compensate the external wind disturbance and actuator fault by using a disturbance observer, and to design the unmanned aerial vehicle preset performance controller by using a preset performance method and backstepping method;

[0016] And an actuator fault control module is used to realize trajectory tracking control on the unconstrained system obtained after nonlinear mapping by using the unmanned aerial vehicle preset performance controller, and according to the nonlinear mapping relationship, the expected signal of the original constrained system can be obtained without violating the constraint condition.

[0017] Further, based on the unmanned aerial vehicle preset performance control method considering time-varying position constraints, the application further provides a computer device; the computer device comprises a memory and one or more processors, the memory stores executable code, and the processor executes the executable code to realize the steps of the unmanned aerial vehicle preset performance control method considering time-varying position constraints.

[0018] Further, based on the unmanned aerial vehicle preset performance control method considering time-varying position constraints, the application further provides a computer readable storage medium; the computer readable storage medium stores a program, and the program is executed by a processor to realize the steps of the unmanned aerial vehicle preset performance control method considering time-varying position constraints.

[0019] The application has the following advantages:

[0020] As described above, the application provides an unmanned aerial vehicle preset performance control method considering time-varying position constraints, which adopts a method combining nonlinear mapping and preset performance control for a quadrotor unmanned aerial vehicle under constraint conditions. The method ingeniously converts the model of the unmanned aerial vehicle with position constraints into a model without constraints by using a nonlinear mapping function. Compared with the BLF method, the method avoids the problems of complex BLF design and narrow initial output range. In addition, the unmanned aerial vehicle preset performance control method considering time-varying position constraints does not need to assume that the virtual control input satisfies the constraint boundary. For an unmanned aerial vehicle with model uncertainty and external disturbance, the application designs a fault-tolerant adaptive preset performance controller capable of adapting to actuator faults and position constraints by combining PPC with backstepping control, which can effectively keep the unmanned aerial vehicle trajectory tracking error within the preset performance boundary range. The disturbance observer and the FLS can effectively compensate for the adverse effects of external disturbance and model uncertainty, respectively, so that the quadrotor unmanned aerial vehicle controlled by the method of the application has good robustness and adaptability. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A flowchart of the unmanned aerial vehicle preset performance control method considering time-varying position constraints in the embodiment of the application;

[0022] Figure 2 A schematic diagram of the nonlinear mapping function in the embodiment of the application;

[0023] Figure 3 A system block diagram of the unmanned aerial vehicle preset performance control method considering time-varying position constraints in the embodiment of the application;

[0024] Figure 4 A schematic diagram of the actuator fault parameter in the embodiment of the application;

[0025] Figure 5A response output schematic diagram in an embodiment of the present application;

[0026] Figure 6 A 3D actual motion trajectory tracking diagram of the unmanned aerial vehicle in an embodiment of the present application;

[0027] Figure 7 An actual position state trajectory tracking diagram in an embodiment of the present application;

[0028] Figure 8 An actual position state error change schematic diagram in an embodiment of the present application;

[0029] Figure 9 A position state conversion state trajectory tracking schematic diagram in an embodiment of the present application;

[0030] Figure 10 A position state conversion state error change schematic diagram in an embodiment of the present application;

[0031] Figure 11 An actual attitude state trajectory tracking schematic diagram in an embodiment of the present application;

[0032] Figure 12 An attitude state error change schematic diagram in an embodiment of the present application. DETAILED DESCRIPTION

[0033] The present application will be further described in detail below in combination with the accompanying drawings and specific embodiments:

[0034] Embodiment 1

[0035] In combination with the deficiencies researched in the above background art, the present application aims at the control problem of quad-rotor unmanned aerial vehicle under time-varying position constraints, uses a nonlinear mapping method to avoid the “feasibility condition” assumption of the BLF method, uses a preset performance control method to design a controller, and considers the influence of actuator faults and external wind disturbances, thereby effectively ensuring the stable flight of the quad-rotor unmanned aerial vehicle under time-varying position constraints.

[0036] For the quad-rotor unmanned aerial vehicle actuator fault system with time-varying position constraints, model uncertainties and external disturbances, the present embodiment proposes a preset performance control method for unmanned aerial vehicle considering time-varying position constraints. In order to realize high-precision trajectory tracking control, the present embodiment proposes a scheme combining model nonlinear mapping and preset performance control, estimates the unknown internal dynamics of the model by using an adaptive fuzzy system, and designs a nonlinear disturbance observer to estimate the external disturbance and actuator fault, so that it is more suitable for actual application. Finally, through experimental analysis, the control performance of the quad-rotor unmanned aerial vehicle with time-varying position constraints by the method proposed in the present application is verified.

[0037] The preset performance controller of the quad-rotor unmanned aerial vehicle is designed in view of time-varying position constraint, actuator fault, model uncertainty and external wind disturbance, and the nonlinear mapping method is combined with the PPC method, so that the time-varying constraint problem of the quad-rotor unmanned aerial vehicle is effectively solved.

[0038] The control method of the application is aimed at the quad-rotor unmanned aerial vehicle, and the control target is to realize the stable following of the expected signal of the unmanned aerial vehicle under the condition of spatial position constraint by using the nonlinear function mapping and the preset performance control method.

[0039] As shown in Figure 1 , the unmanned aerial vehicle preset performance control method considering time-varying position constraint specifically includes the following steps:

[0040] Step 1. A composite model of the quad-rotor unmanned aerial vehicle considering time-varying position constraint, model uncertainty and external wind disturbance is established, the composite model is mapped and processed by using a nonlinear mapping relationship to convert it into an unconstrained model, a preset performance function is used to limit the tracking error of the unconstrained system, an error transformation function is used to process the tracking error, and the error transformation function is used for subsequent design of the unmanned aerial vehicle preset performance controller.

[0041] Let the position vector P and the Euler angle vector Θ be represented as P=[x,y,z] T ∈R 3 and Θ=[φ,θ,ψ] T ∈R 3 , wherein (x, y, z) is the position of the unmanned aerial vehicle in the inertial coordinate system, and φ, θ and ψ represent the roll angle, pitch angle and yaw angle of the unmanned aerial vehicle respectively.

[0042] For the convenience of subsequent processing of the position subsystem, let [P1(t), P2(t), P3(t)] T =[x,y,z] T , wherein P1(t) represents x, P2(t) represents y, and P3(t) represents z. P is defined here for the convenience of using subscript to represent x, y and z in subsequent design of the unmanned aerial vehicle preset performance controller.

[0043] The UAV position subsystem model is shown in equation (1a) and the UAV attitude subsystem model is shown in equation (1b):

[0044]

[0045] where A = [A1, A2, A3] T , A1 = (cosφsinθcosψ+sinφsinψ) / m, A2 = (cosφsinθsinψ-sinφcosψ) / m, A3 = cosφsinθ / m, m represents the total mass of the UAV; H a represents unknown nonlinear composite terms acting on the position subsystem, H a = [H1, H2, H3] T ∈R 3 , wherein H1, H2, H3 represent unknown nonlinear composite terms acting on the x-axis, y-axis, and z-axis directions of the position subsystem, respectively; d a (t) represents external wind disturbance received by the position subsystem, d a (t) = [d1, d2, d3] T ∈R 3 , wherein d1, d2, d3 represent external wind disturbance received by the position subsystem in the x-axis, y-axis, and z-axis directions, respectively.

[0046] J (·) represents the moment of inertia, J x , J y , J z represent the moments of inertia of the UAV about the x-axis, y-axis, and z-axis directions, respectively, and l is the distance from the propeller of the UAV to the center of mass; u Θ = [u o,2 , u o,3 , u o,4 ] T ∈R 3 , u o,1 , u o,2 , u o,3 , u o,4 represent control inputs generated by the four motor rotors of the UAV, respectively; H b represents unknown nonlinear composite terms acting on the attitude subsystem, H b = [H4, H5, H6] T ∈R 3 , wherein H4, H5, H6 represent unknown nonlinear composite terms acting on the roll angle, pitch angle, and yaw angle of the attitude subsystem, respectively; d b (t) represents external wind disturbance received by the attitude subsystem, d b (t) = [d4, d5, d6] T∈ R 3 where d4, d5, d6 represent the external wind disturbance on roll, pitch and yaw angles of the attitude subsystem respectively.

[0047] The UAV position subsystem and attitude subsystem models have asymmetric time-varying position constraint effects as shown in equation (2):

[0048]

[0049] where i1=1, 2, 3, denotes the set, is a known positive function.

[0050] H (·) = f (·) +△f (·) ;

[0051] where H (·) represents the unknown nonlinear composite terms acting on the position subsystem and the attitude subsystem.

[0052] f (·) represents the air resistance terms, where f1, f2, f3, f4, f5, f6 represent the air resistance terms in the x-axis, y-axis, z-axis, roll angle, pitch angle and yaw angle directions respectively. g is the acceleration of gravity; G (·) is the air resistance coefficient, where G x , G y , G z , G φ , G θ , G ψ represent the air resistance coefficients of the UAV in the x-axis, y-axis, z-axis, roll angle, pitch angle and yaw angle directions respectively.

[0053] △f (·) represents the model uncertainty terms, [△f1, △f2, △f3] T ∈ R 3 and [△f4, △f5, △f6] T ∈ R 3 represent the model uncertainty terms of the position subsystem and the attitude subsystem respectively, where △f1, △f2, △f3 represent the model uncertainty terms of the position subsystem in the x-axis, y-axis and z-axis directions respectively, and △f4, △f5, △f6 represent the model uncertainty terms of the attitude subsystem in the roll angle, pitch angle and yaw angle directions respectively.

[0054] u o,1 , u o,2 , u o,3 , u o,4 have the following relationship:

[0055]

[0056] where l1 is the lift coefficient, l2 is the rotor drag coefficient, w (·) is the motor rotor speed, w1, w2, w3, w4 represent the four motor rotor speeds of the unmanned aerial vehicle respectively.

[0057] In actual engineering, to avoid singularity problem, the roll angle and pitch angle should satisfy and The external wind disturbance d1, d2, d3, d4, d5, d6 is unknown and bounded; the time-varying position constraint boundary does not intersect, that is, the constraint upper limit is always greater than the constraint lower limit.

[0058] Let the desired trajectory [Υ1,Υ2,γ3] T = [x d , y d , z d ] T , where x d , y d , z d represent the desired position trajectory of the unmanned aerial vehicle in the inertial coordinate system. There are normal numbers and such that the desired trajectory and its derivative satisfy and and for the desired yaw angle ψ d only need to satisfy where i1 = 1, 2, 3, j1 = 1, 2. In addition, the system state x, y, z, θ, ψ, φ can be used for the design of the preset performance controller of the quad-rotor unmanned aerial vehicle.

[0059] When the four actuators of the unmanned aerial vehicle may be affected by faults in operation, the actual input differs from the desired input , considering the following relationship:

[0060]

[0061] where i2 = 1, 2, 3, 4, and are continuous time-varying functions, and represent partial fault factors and bias fault factors respectively, and and are unknown and bounded continuous functions.

[0062] For a quadcopter drone system with external constraints, directly designing a controller is challenging. To this end, this paper proposes a method for preprocessing the constraint model using a nonlinear mapping function, converting the constraint model into an unconstrained model. In a nonlinear system, assuming the constraint state is s, the mapped new state is set to ζ, and the constraint range is -k c1 <s<k c2 , where k c1 、k c2 are all positive numbers. Consider the following smooth nonlinear mapping expression N(k c1 ,k c2 ,s):s→ζ, where N(·) is a nonlinear mapping function and the expression of ζ is shown in formula (5):

[0063]

[0064] Depend on Figure 2 It can be seen that when s approaches the constraint boundary, ζ→∞. The range of values ​​of the mapped new state ζ is unconstrained, that is, ζ∈R.

[0065] Defining system status And suppose [x1,x3,x5] T The actual position state [x,y,z] T The conversion state obtained by the nonlinear mapping function N(·), that is, x1=N(F 11 ,F 12 ,x),x3=N(F 21 ,F 22 ,y),x5=N(F 31 ,F 32 ,z). Obviously, through the transformation of the nonlinear mapping function, we get [x1,x3,x5] T ∈R 3 .

[0066] In order to obtain the transformed unconstrained model, we need The derivative of is:

[0067]

[0068] Among them, i1=1,2,3, and The expression is as follows:

[0069]

[0070] Obviously, in the previously defined set In, μ (·)is positive and is computable for control design. Combining the UAV dynamics model shown in Equations (1a) and (1b), the time-varying position constraint shown in Equation (2), the actuator faults shown in Equation (4) and the nonlinear mapping function N(·), the unconstrained UAV position subsystem model S1 shown in Equation (9a) and the unconstrained UAV attitude subsystem model S2 shown in Equation (9b) are obtained, respectively:

[0071]

[0072] where [x1, x3, x5] T is the transformed unconstrained state, i.e., the transformed state; H (·) is given in Equation (1); u x , u y and u z represent the virtual control inputs for the x, y and z subsystems, respectively, u x = u1(cosφsinθcosψ+sinφsinψ), u y = u1(cosφsinθsinψ-sinφcosψ),

[0073] u z = u1cosφcosθ.

[0074] D (·) denotes the nonlinear terms containing disturbances, where D1, D2, D3, D4, D5, D6 denote the nonlinear terms containing disturbances in the x, y, z, roll, pitch and yaw directions, respectively, D1= d1+ A1o1- A1Γ1u1, D2= d2+ A2o1- A2Γ1u1, D3= d3+ A3o1- A3Γ1u1, D4= d4+ K2o2- K2Γ2u2, D5= d5+ K3o3- K3Γ3u3, D6= d6+ K4o4- K4Γ4u4. Note that D (·) depends on the external wind disturbance, the system state, the fault parameters and the desired inputs. The system state depends on the control inputs, and the control inputs driving the UAV depend on the rotational speeds of the four rotors. In practical engineering, it is assumed that the velocity derivatives of the four rotors are bounded, and there exists a positive constant D ( * ·) such that

[0075] The position subsystem as shown in Equation (9a) is a nonlinear mapping subsystem, and the position controller is designed based on the unconstrained state. Therefore, the desired position signal also needs to be mapped, as follows:

[0076]

[0077] where i1 = 1,2,3, [Y1,Y2,Y3] T denotes the desired position signal after mapping processing;

[0078] Assume the desired attitude signal [Y4,Y5,Y6] T = [φ d ,θ d ,ψ d ] T for the subsequent design of UAVs' preset performance controller, where φ d , θ d , ψ d represent the desired roll angle, desired pitch angle and desired yaw angle of UAVs, respectively. Meanwhile, define the position and rotation tracking error as:

[0079]

[0080] where i3 = 1,3,5,7,9,11.

[0081] The above nonlinear mapping method has some important implications. When i1 = 1,2,3, for any where t represents time, denotes the initial position of x, y, z, and if for any t, are bounded, then it can be guaranteed that for any t, In this way, the position constraint problem is reduced to the problem of guaranteeing the boundedness of

[0082] The preset performance method is as follows:

[0083] -ρ(t) < z(t) < ρ(t) (12)

[0084] where z(t) is the tracking error signal of the unconstrained system shown in equations (9a) and (9b), and ρ(t) is the preset performance function, which is selected as follows:

[0085] ρ(t) = (ρ0-ρ ∞ )e -ht +ρ ∞ (13)

[0086] where ρ0, ρ ∞ , h are normal numbers, and satisfy ρ0>ρ ∞ . To achieve the preset performance control of the tracking error, introduce the error transformation function G(ε):

[0087] z(t) = ρ(t)G(ε) (14) ​

[0088]

[0089] where G(ε) is a derivable function with positive derivative, ε is the new conversion error, and the expression of ε is:

[0090]

[0091] Taking the derivative of the new conversion error ε, we get:

[0092]

[0093] where and

[0094] Through the conversion error processing, it is to ensure that the tracking error z(t) is within the predetermined performance requirements, and it is proved that the conversion error ε(t) is bounded.

[0095] Step 2. Based on the unconstrained system of step 1, estimate the model uncertainty using an adaptive fuzzy system, and estimate and compensate for external wind disturbances and actuator faults using a disturbance observer, and design a UAV preset performance controller using the preset performance method and backstepping method.

[0096] Step 2.1. Design a fuzzy observer composed of an adaptive fuzzy system and a disturbance observer.

[0097] Since the nonlinear terms and model uncertainty terms in the model shown in formulas (9a) and (9b) are unknown, the controller cannot be designed. To solve the above problem, the composite term is fuzzy approximated, where i3=1, 3, 5, 7, 9, 11, and we get:

[0098]

[0099] where, represents the adaptive fuzzy system, represents the weight, represents the Gaussian basis function, represents the approximation error. In the process of approximating the model uncertainty term by the adaptive fuzzy system, the parameters are constantly updated, and the optimal weight represents the parameters when the approximation effect is best.

[0100] The adaptive fuzzy system is used to approximate the nonlinear term, which cannot be directly used for UAV preset performance controller design, but can be used for UAV preset performance controller design after approximating its value by a fuzzy system. This process reflects the estimation of model uncertainty.

[0101] In order to reduce the negative impact of the disturbance compound term, the present invention designs a fuzzy observer to approximate the disturbance compound term and defines Let be a bounded composite term containing perturbations, In order to conveniently express the parameters in the fuzzy observer design process, we define j o =x,y,z,2,3,4 and K o =[K1,K1,K1,K2,K3,K4] T They correspond to i3=1,3,5,7,9,11 respectively, that is, when i3=1, j o =x,K o =K1; when i3=3, j o =y,K o =K1; when i3=5, j o =z,K o =K1; when i3=7, j o =2,K o =K2; when i3=9, j o =3,K o =K3; when i3=11, j o =4,K o =K4.

[0102] Design the fuzzy observer as shown in formula (18):

[0103]

[0104] in, yes Estimates, and are the design parameters and observer states, respectively, and yes estimates;

[0105] right Taking the derivative we get:

[0106]

[0107] in, express The estimation error of

[0108] set up for The estimation error of is obtained according to formula (19):

[0109]

[0110] Using Young's inequality on the last term in equation (20), we get

[0111]

[0112] where is an unknown constant and satisfies There is an unknown constant satisfying

[0113]

[0114] Substituting equation (21) into equation (20), we get

[0115]

[0116] where Step 2.2. Design the pre-performance controller of the quadrotor UAV using the pre-performance method and the backstepping method.

[0117] When i5 = 1, 3, 5 correspond to j2 = x, y, z, consider the position subsystem shown in equation (9a) as follows:

[0118]

[0119] Define the state transformation as:

[0120]

[0121] where is a new state variable; is the tracking error error transformation, and is a virtual control input. z(t) in the above is the overall description of the pre-performance method, and here the subscripted

[0122] Select the Lyapunov function as follows:

[0123]

[0124] Through equation (15) and equation (24), the derivative of is obtained as:

[0125]

[0126] where and represents the nonlinear representation term generated in the process of the preset performance method. r and v in the above are collectively described as the preset performance method, and the subscripted and are specific applications of the method of the present application in the process of unmanned aerial vehicle control design. Since the backstepping design method is combined, the subscript is used to distinguish each step of and

[0127] The virtual control input is designed as:

[0128]

[0129] wherein is a design parameter. Substitute formula (27) into formula (26) to obtain:

[0130]

[0131] The Lyapunov function is selected as: as follows:

[0132]

[0133] The derivative of is obtained as:

[0134]

[0135] wherein

[0136] The Lyapunov function is selected as: as follows:

[0137]

[0138] The derivative of is obtained as:

[0139]

[0140] wherein represents a design parameter; and i (·) is given in formula (22), that is is an unknown normal number and satisfies There is an unknown normal number satisfying

[0141] When i5=1, 3, 5, the position subsystem controller as shown in formula (33) and the fuzzy adaptive law as shown in formula (44):

[0142]

[0143] where and are design parameters, and Substituting equations (33) and (34) into equation (32) gives

[0144]

[0145] According to Young's inequality, the following inequality holds:

[0146]

[0147] Substituting equations (36) and (37) into equation (35) gives

[0148]

[0149] where

[0150] Similar to the position subsystem controller design, consider the attitude subsystem given by equation (9b) when i6= 7, 9, 11 correspond to j3= 2, 3, 4 as follows:

[0151]

[0152] The parameters used by the attitude subsystem and the position subsystem are distinguished by different subscripts, and the controller is different because the attitude subsystem model given by equation (39) is different from the position subsystem model given by equation (23).

[0153] Define the state transformation as given by equation (40):

[0154]

[0155] where is the new state variable; is the tracking error error transformation, is the virtual control input.

[0156] Select the Lyapunov function as follows:

[0157]

[0158] By equations (15) and (40), the derivative of is obtained as:

[0159]

[0160] Design the virtual control input as:

[0161]

[0162] in, and It is a nonlinear expression term generated during the preset performance method. is the design parameter. Substituting formula (43) into formula (42), we get:

[0163]

[0164] Select the Lyapunov function as follows:

[0165]

[0166] right The derivative is:

[0167]

[0168] Select the Lyapunov function as follows:

[0169]

[0170] right Taking the derivative we get:

[0171]

[0172] in, represents the design parameters, is an unknown positive constant and satisfies There is an unknown positive constant satisfy

[0173] Design the attitude subsystem controller And the fuzzy adaptive law is as follows:

[0174]

[0175] in, and are design parameters, and Substituting formula (49) and formula (50) into formula (48) yields:

[0176]

[0177] According to Young's inequality, the following inequality holds:

[0178]

[0179] Substituting formula (52) and formula (53) into formula (51), we get:

[0180]

[0181] where,

[0182] According to the coupling between the position virtual controller and the virtual input signal as shown in formula (33), the expression of the actual total lift ui is as follows:

[0183]

[0184] The desired pitch angle and roll angle are obtained as follows:

[0185]

[0186] In step 2, after completing the design of the preset performance controller of the quadrotor unmanned aerial vehicle, the stability of the unmanned aerial vehicle controlled by the unmanned aerial vehicle preset performance controller is analyzed.

[0187] Specifically, after completing the design of the unmanned aerial vehicle preset performance controller, the stability of the quadrotor unmanned aerial vehicle controlled by the controller is analyzed. As shown in formula (9a) and formula (9b), the quadrotor unmanned aerial vehicle system considering time-varying position constraints, model uncertainties, actuator failures and external wind disturbances, under the premise of the assumption, if the actual controller of the virtual control signal shown in formula (27) and formula (43) and the fuzzy adaptive law shown in formula (34) and formula (50) is applied, the actual controller is shown in formula (33) and formula (49), then for any initial condition Tracking error Finally, it is guaranteed to be uniformly bounded, where i4=1,2,3,4,5,6.

[0188] The process of stability analysis of the quadrotor unmanned aerial vehicle controlled by the unmanned aerial vehicle preset performance controller is described in detail as follows:

[0189] a, b, c, d are real numbers, let a∈R, b∈R, c>1 and d>1, and satisfy (c-1)(d-1)=1, for any k>0, the following inequality can be obtained:

[0190]

[0191] Select the overall Lyapunov function Where i3=1,3,5,7,9,11; according to formula (38) and formula (54), the derivative of V is shown in formula (57):

[0192]

[0193] where,

[0194] By solving the inequality (57), we obtain the inequality as shown in equation (58):

[0195]

[0196] where V(0) represents the value of V zero state, p represents the sum of all This means that all closed-loop signals are bounded. In particular, according to equation (24), equation (40), equation (29) and equation (45), we have is bounded, and, ε, is also bounded. Therefore, the tracking error z(t) is bounded and kept within the pre-set performance bound, i.e., the control system converges to satisfy the pre-set performance requirement. For the position subsystem, take the x subsystem as an example, note that z1 = Y1 - xi, we have:

[0197]

[0198] is expressed as:

[0199] Q1z1 = Q2e1 (59)

[0200] where Q1 and Q2 are bounded functions, Q1 = (F 11 + x d )(F 12 - x d )(F 11 + x)(F 12 - x) > 0, Q2 = F 11 F 12 + x x d > 0; e1 is the actual tracking error, e1 = x d - x. Therefore, equation (59) is rewritten as shown in equation (60):

[0201] e1 = Qz1 (60)

[0202] where where Q is a bounded function, since Q and z1 are bounded, e1 is also bounded. Similarly to the x subsystem, the actual tracking error of other subsystems is also bounded.

[0203] Therefore, all closed-loop signals are bounded. The actual position states [x, y, z] T can stably follow the given desired signal without violating the position state constraints.

[0204] Without loss of generality, the constraints in the present application are asymmetric. For known positive functions, the designed controller can also guarantee to meet the control requirements.

[0205] In summary, considering the fault quadrotor unmanned aerial vehicle model with time-varying position constraints, model uncertainty and external wind disturbance, the virtual control law shown in formula (27) and formula (43), the fuzzy adaptive law of formula (34) and formula (50) and the actual control signal shown in formula (33) and formula (49), the tracking error will eventually converge to a small neighborhood of the origin, and in addition, all signals in the closed-loop system are bounded.

[0206] Step 3. The unmanned aerial vehicle preset controller designed in step 2 is used to realize trajectory tracking control of the mapped unconstrained quadrotor unmanned aerial vehicle system, and the mapping relationship can be used to obtain the expected signal that the original constrained system stably follows under the constraint condition, that is, the mapping relationship can be used to obtain the expected signal that the original constrained system stably follows under the constraint condition.

[0207] In addition, in order to verify the effectiveness of the method proposed in the present application, the following specific experiments are given:

[0208] The present embodiment will verify the effectiveness of the nonlinear mapping method on the original system shown in formula (1a) and formula (1b), and the effectiveness of the above-mentioned preset performance controller on the preprocessed unmanned aerial vehicle system state control shown in formula (9a) and formula (9b) through numerical simulation. In addition, in order to highlight the advantages of the proposed method, the adaptive backstepping control ABC method of the original system is compared with the method proposed in the present application.

[0209] The unmanned aerial vehicle preset performance control method considering time-varying position constraints proposed in the present application is simulated in a virtual environment to verify the feasibility of the control method proposed in the present application:

[0210] The parameters of the unmanned aerial vehicle are selected as:

[0211]

[0212] The reference trajectory is selected as:

[0213]

[0214] The initial value is given as X0:

[0215]

[0216] Wherein, (x0, y0, z0) is the initial value of the position of the unmanned aerial vehicle in the inertial coordinate system, and phi0, theta0 and psi0 respectively represent the initial values of the roll angle, the pitch angle and the yaw angle of the unmanned aerial vehicle.

[0217] The parameters of the preset performance function are:

[0218]

[0219] The constraint boundary function is selected as:

[0220]

[0221] The model uncertainty is respectively:

[0222]

[0223] The external wind disturbance is respectively:

[0224]

[0225] The parameters of the preset performance controller of the unmanned aerial vehicle are selected as i4=1, 2, 3, 4, 5, 6.

[0226]

[0227] In the simulation of the method of the application, the actuator fault parameters are as shown in Figure 4 The control input time response is as shown in Figure 5 The three-dimensional motion trajectory diagram of the quad-rotor unmanned aerial vehicle is as shown in Figure 6

[0228] Compared with the ABC method, Figure 7 The time response of the actual position trajectory (x, y, z) is shown, and some information can be obtained, although both methods keep the position state within the constraint boundary, but the control accuracy of the ABC method is obviously weaker than that of the method of the application. Figure 8 The z x , z y , z z respectively represent the tracking errors of the position subsystem x, y and z, and from Figure 8 It can be seen that although the error of the method of the application is relatively obvious at the beginning of the simulation, it quickly converges to a very small neighborhood of zero, and until the end of the simulation, the error of the ABC method is also relatively large, which shows that the error of the ABC method has greater fluctuations than the method of the application as a whole.

[0229] The converted position tracking is as shown in Figure 9 From which it can be easily obtained that the system state quickly and stably follows the reference signal. The time response of the converted position error is as shown in Figure 10 , wherein the z x1 ​、z x3 、z x5 They represent the tracking errors of the converted states of the position subsystem after x, y, and z mapping, respectively, and the errors eventually converge to zero.

[0230] The time response and error of posture tracking are as follows: Figure 11 and Figure 12 As shown. Figure 11 It can be seen that the tracking performance of the method of the present invention is better than that of the ABC method. Figure 12 Middle z φ 、z θ 、z ψ Respectively represent the tracking errors of the roll angle, pitch angle and yaw angle of the attitude subsystem. Compared with the ABC method, the method of the present invention is Figure 12 The error is smaller. Specifically, in the φ and θ subsystems, the error of the ABC method exceeds the preset bounds, while the method proposed in the present invention remains within the preset bounds. Furthermore, similar to the position subsystem, the error of the ABC method remains greater than that of the control method of the present invention until the end of the simulation. The above analysis clearly demonstrates that the method of the present invention is more effective and faster than the ABC method in the attitude subsystem.

[0231] In order to further demonstrate the superiority of the method proposed in the present invention, the following performance indicators are compared between the method proposed in the present invention and ABC to further prove the effectiveness of the method proposed in the present invention.

[0232] Absolute Error (IAE) amplitude integral:

[0233]

[0234] Among them, i4=1,2,3,4,5,6.

[0235] x y z φ θ PM 0.1890 0.3599 0.0885 0.0015 0.0017 ABC 0.0959 0.3958 0.1055 0.0240 0.0213

[0236] Table 1

[0237] The IAE indicators of the PM and ABC methods of the present invention are shown in Table 1. Except for the x subsystem, the indicators of the method proposed in the present invention are smaller than those of the ABC method. d =0, we only need to study the indicators of x, y, z, φ, and θ.

[0238] Through the above analysis, it is concluded that under the conditions of actuator failure and external interference, the control method proposed in the present invention has good tracking performance, and the tracking error is maintained within the preset performance range. The control method proposed in the present invention is significantly better than the tracking performance of the traditional ABC method.

[0239] Embodiment 2

[0240] The embodiment 2 describes a quadrotor unmanned aerial vehicle preset performance control system considering time-varying position constraints, which is based on the same inventive concept as the quadrotor unmanned aerial vehicle preset performance control considering time-varying position constraints in embodiment 1.

[0241] The quadrotor unmanned aerial vehicle preset performance control system considering time-varying position constraints comprises the following modules:

[0242] A model construction module is configured to establish a composite model of the unmanned aerial vehicle considering time-varying position constraints, model uncertainties and external wind disturbances, map the composite model using a nonlinear mapping relationship to convert it into an unconstrained model, limit the tracking error of the unconstrained system using a preset performance function, process the tracking error using an error transformation function, and use it for subsequent design of the unmanned aerial vehicle preset performance controller.

[0243] A controller design module is configured to estimate the model uncertainties using an adaptive fuzzy system based on the unconstrained system, estimate and compensate the external wind disturbances and actuator faults using a disturbance observer, and design the unmanned aerial vehicle preset performance controller using the preset performance method and the backstepping method.

[0244] An actuator fault control module is configured to realize trajectory tracking control of the unconstrained system obtained after nonlinear mapping using the unmanned aerial vehicle preset performance controller, and obtain the expected signal of the original constrained system following stably without violating the constraint condition according to the nonlinear mapping relationship.

[0245] It should be noted that the functions and effects of each functional module in the system described in the embodiment are implemented in the implementation process of the corresponding steps in the method of embodiment 1, which will not be described here.

[0246] Embodiment 3

[0247] The embodiment 3 describes a computer device comprising a memory and one or more processors. The executable code is stored in the memory, and when the processor executes the executable code, the steps of the quadrotor unmanned aerial vehicle preset performance control method considering time-varying position constraints in embodiment 1 are implemented.

[0248] The computer device in the embodiment is any device or apparatus with data processing capability, which will not be described here.

[0249] Embodiment 4

[0250] The embodiment 4 describes a computer readable storage medium, which stores a program. The program is executed by a processor to implement the steps of the UAV preset performance control method considering time-varying position constraints in the embodiment 1. The computer readable storage medium can be an internal storage unit of any device or apparatus with data processing capability, such as a hard disk or a memory, or an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc.

[0251] Of course, the above description is merely preferred embodiments of the present application, and the present application is not limited to the above-described embodiments. It should be noted that any equivalent replacements, obvious modifications made by any person skilled in the art under the teaching of the present specification shall fall within the scope of the present specification, and shall be protected by the present application.

Claims

1. A method for controlling the preset performance of a UAV considering time-varying position constraints, characterized in that: The steps include: Step 1. Establish a composite model of the UAV that takes into account time-varying position constraints, model uncertainty, and external wind disturbances. Use a nonlinear mapping relationship to map the composite model and convert it into an unconstrained model. Use a preset performance function to limit the tracking error of the unconstrained system. Use an error transformation function to process the tracking error and use it in the subsequent design of the UAV's preset performance controller. Step 2. Based on the unconstrained system in step 1, the model uncertainty is estimated using an adaptive fuzzy system, and the external wind disturbance and actuator failure are estimated and compensated using a disturbance observer. The preset performance method and backstepping method are used to design the preset performance controller of the UAV. Step 3. Use the preset controller of the UAV designed in step 2 to realize trajectory tracking control of the unconstrained system obtained after nonlinear mapping, and according to the nonlinear mapping relationship, the expected signal of the original constrained system can be obtained to stably follow without violating the constraints.

2. The method for controlling the preset performance of a drone considering time-varying position constraints according to claim 1, characterized in that: In step 1, the process of establishing a composite model of the UAV that considers time-varying position constraints, model uncertainty, and external wind disturbances is as follows: Assume that the position vector P and the Euler angle vector Θ are expressed as: P=[x,y,z] T ∈R 3 and Θ = [φ,θ,ψ] T ∈R 3 ; Where (x, y, z) is the position of the UAV in the inertial coordinate system, φ, θ, ψ represent the roll angle, pitch angle, and yaw angle of the UAV respectively; let [P1(t), P2(t), P3(t)] T =[x,y,z] T ; Establish the UAV position subsystem model as shown in formula (1a) and the UAV attitude subsystem model as shown in formula (1b): Where A=[A1,A2,A3] T , A1=(cosφsinθcosψ+sinφsinψ) / m, A2=(cosφsinθsinψ-sinφcosψ) / m, A3=cosφsinθ / m, m represents the total mass of the UAV; H a represents the unknown nonlinear composite term acting on the position subsystem, H a =[H1,H2,H3] T ∈R 3 , where H1, H2, and H3 represent the unknown nonlinear composite terms acting on the x-axis, y-axis, and z-axis directions of the position subsystem, respectively; d a (t) represents the external wind disturbance to the position subsystem, d a (t) = [d1, d2, d3] T ∈R 3 , where d1, d2, and d3 represent the external wind disturbances experienced by the position subsystem in the x-axis, y-axis, and z-axis directions, respectively; J x 、J y 、J z Respectively represent the UAV's moment of inertia about the x-axis, y-axis, and z-axis, l is the distance from the UAV propeller to the center of mass; u Θ =[u o,2 ,u o,3 ,u o,4 ] T ∈R 3 ,u o,1 、u o,2 、u o,3 、u o,4 Represents the control inputs generated by the four motor rotors of the drone; H b represents the unknown nonlinear composite term acting on the attitude subsystem, H b =[H4,H5,H6] T ∈R 3 , where H4, H5, and H6 represent the unknown nonlinear composite terms acting on the roll angle, pitch angle, and yaw angle of the attitude subsystem, respectively; d b (t) represents the external wind disturbance to the attitude subsystem, d b (t) = [d4, d5, d6] T ∈R 3 , where d4, d5, and d6 represent the external wind disturbances on the roll angle, pitch angle, and yaw angle of the attitude subsystem, respectively; The UAV position subsystem and attitude subsystem models have the influence of asymmetric time-varying position constraints as shown in formula (2): Among them, i1=1,2,3, Represents a collection, is a known positive function; H (·) =f (·) +△f (·) ; Among them, H (·) represents the unknown nonlinear composite term acting on the position subsystem and attitude subsystem; f (·) represents the air resistance term, where f1, f2, f3, f4, f5, and f6 represent the air resistance in the x-axis, y-axis, z-axis, roll angle, pitch angle, and yaw angle directions, respectively; g is the acceleration due to gravity; G x , G y , G z , G φ , G θ , G ψ Respectively represent the air resistance coefficient of the drone in the x-axis, y-axis, z-axis, roll angle, pitch angle and yaw angle directions; △f () represents model uncertainty, [△f1,△f2,△f3] T ∈R 3 and [△f4,△f5,△f6] T ∈R 3 Represent the model uncertainties of position subsystem and attitude subsystem respectively; u o,1 、u o,2 、u o,3 、u o,4 The relationship is: Among them, l1 is the lift coefficient, l2 is the rotor drag coefficient, w1, w2, w3, w4 are the motor rotor speeds; To avoid singularity problems, the roll angle and pitch angle should satisfy and The external wind disturbance is unknown and bounded; the time-varying position constraint boundaries do not cross, that is, the upper constraint bound is always greater than the lower constraint bound; Let the expected trajectory [Υ1,γ2,Υ3] T =[x d ,y d ,z d ] T ; where x d 、y d 、z d Represents the expected position trajectory of the UAV in the inertial coordinate system; there is a positive constant and Make the expected trajectory and its derivative satisfies and And for the desired yaw angle ψ d Just need to satisfy Where j1=1,2; In addition, the system states x, y, z, θ, ψ, and φ can be used to design the controller for the preset performance of the UAV; When the four actuators of the drone are affected by a fault during operation, the actual input With expected input There are differences, considering the relationship shown in formula (4): Among them, i2=1,2,3,4, and is a continuous time-varying function, and represent the partial fault factor and bias fault factor respectively, and and are all unknown and bounded continuous functions.

3. The method for controlling the preset performance of a drone considering time-varying position constraints according to claim 2, characterized in that: In step 1, the process of mapping the composite model using a nonlinear mapping relationship to convert it into an unconstrained model is as follows: In a nonlinear system, assume that the constraint state is s, the mapped new state is set to ζ, and the constraint range is -k c1 <s<k c2 , where k c1 、k c2 are all positive numbers; consider the smooth nonlinear mapping expression N(k c1 ,k c2 ,s):s→ζ, where N(·) is a nonlinear mapping function and the expression of ζ is shown in formula (5): When s approaches the constraint boundary, ζ→∞; the value range of the mapped new state ζ is unconstrained, that is, ζ∈R; Defining system status And suppose [x1,x3,x5] T The actual position state [x,y,z] T The conversion state obtained by the nonlinear mapping function N(·), that is, x1=N(F 11 ,F 12 ,x),x3=N(F 21 ,F 22 ,y),x5=N(F 31 ,F 32 ,z); through the transformation of the nonlinear mapping function, we get [x1,x3,x5] T ∈R 3 ; In order to obtain the transformed unconstrained model, Taking the derivative we get: in and The expression of is shown in formula (7), The expression formula (8) is shown as follows: In the previously defined collection middle, is a positive number and can be calculated; combined with the UAV dynamics model shown in formula (1a) and formula (1b), the time-varying position constraint shown in formula (2), the actuator fault shown in formula (4), and the nonlinear mapping function N(·), we can obtain the UAV position subsystem model S1 of the unconstrained system shown in formula (9a) and the UAV attitude subsystem model S2 of the unconstrained system shown in formula (9b): Among them, [x1,x3,x5] T is the unconstrained state after the transformation; u x 、u y and u z Represents the virtual control input of x-subsystem, y-subsystem and z-subsystem respectively, u x =u1(cosφsinθcosψ+sinφsinψ), u y =u1(cosφsinθsinψ-sinφcosψ), u z =u1cosφcosθ; D (·) Denotes the nonlinear term containing disturbance, where D1, D2, D3, D4, D5, and D6 represent the nonlinear terms containing disturbance in the x-axis, y-axis, z-axis, roll angle, pitch angle, and yaw angle directions, respectively. D1 = d1 + A1o1 - A1Γ1u1, D2 = d2 + A2o1 - A2Γ1u1, D3 = d3 + A3o1 - A3Γ1u1, D4 = d4 + K2o2 - K2Γ2u2, D5 = d5 + K3o3 - K3Γ3u3, and D6 = d6 + K4o4 - K4Γ4u4; (·) Depends on external wind disturbance, system state, fault parameters and expected input; the system state depends on the control input, and the control input that drives the drone depends on the speed of the four rotors of the drone. The speed derivatives of the four rotors are bounded and there is a positive constant Make The position subsystem shown in formula (9a) is a nonlinear mapping subsystem, and the position controller is designed based on the unconstrained state; therefore, the desired position signal also needs to be mapped as shown in formula (10): [Y1,Y2,Y3] T represents the expected position signal after mapping processing; Assume that the expected posture signal [Y4, Y5, Y6] T =[φ d ,θ d ,ψ d ] T And used in the design of subsequent UAV preset performance controller, where φ d ,θ d , ψ d Represent the desired roll angle, desired pitch angle, and desired yaw angle of the drone respectively; at the same time, define the position and rotation tracking error for: Where i3 = 1, 3, 5, 7, 9, 11; When i1=1,2,3, for any If for any t, are all bounded, then we can ensure that for any t, Where t represents time, represents the initial position of x, y, and z; the position constraint problem is reduced to ensuring The boundedness problem; In step 1, the tracking error of the unconstrained system is limited by using a preset performance function, and the tracking error is processed by using an error transformation function as follows: The preset performance method is shown in formula (12): -ρ(t) <z(t)<ρ(t) (12) Where z(t) represents the tracking error signal of the unconstrained system shown in formulas (9a) and (9b), and ρ(t) is the preset performance function. The preset performance function is selected as shown in formula (13): ρ(t)=(ρ0-ρ ∞ )e -ht +r ∞ (13) Among them, ρ0, ρ ∞ , h is a positive constant, and satisfies ρ0>ρ ∞ ; In order to achieve the preset performance control of tracking error, the error transformation function G(ε) is introduced: z(t)=ρ(t)G(ε) (14) Among them, G(ε) is a differentiable function with a positive derivative, ε is the new conversion error, and the expression of ε is: Taking the derivative of the new conversion error ε, we get: in and By processing the conversion error, we ensure that the tracking error z(t) is within the preset performance requirement range, proving that the conversion error ε is bounded.

4. The method for controlling the preset performance of a UAV considering time-varying position constraints according to claim 3, characterized in that: The step 2 is specifically as follows: Step 2.

1. Design a fuzzy observer consisting of an adaptive fuzzy system and a disturbance observer. For compound items Perform fuzzy approximation and get: in, represents an adaptive fuzzy system, represents the weight, represents the Gaussian basis function, represents the approximation error; Design a fuzzy observer to approximate the disturbance compound term, define Let be a bounded composite term containing perturbations, Define j o =x,y,z,2,3,4 and K o =[K1,K1,K1,K2,K3,K4] T Corresponding to i3=1,3,5,7,9,11 respectively, design the fuzzy observer as shown in formula (18): in, yes Estimates, and are the design parameters and observer states, respectively, and yes estimates; right Taking the derivative we get: in, express The estimation error of set up for The estimation error of is obtained according to formula (19): Applying Young's inequality to the last term in equation (20) yields: in, is an unknown positive constant and satisfies There is an unknown positive constant satisfy Substituting formula (21) into formula (20), we get: in, Step 2.

2. Design the UAV preset performance controller using the preset performance method and backstepping method. When i5 = 1, 3, 5 correspond to j2 = x, y, z respectively, consider the position subsystem shown in formula (9a), as shown in formula (23): Define the state transformation as shown in formula (24): in, is the new state quantity; Tracking error The error conversion, is the virtual control input; Select the Lyapunov function shown in formula (25) By using formula (15) and formula (24), we can get The derivative of is: in, and It is a nonlinear expression term generated during the preset performance method; Design the virtual control input as: in is the design parameter. Substituting formula (27) into formula (26), we get: Choose the Lyapunov function as shown in formula (29) right Taking the derivative we get: in, Choose the Lyapunov function as shown in formula (31) right Taking the derivative we get: in, represents the design parameters, is an unknown positive constant and satisfies There is an unknown positive constant satisfy Design the position subsystem controller as shown in formula (33) Design the fuzzy adaptive law as shown in formula (34): in, and are design parameters, and Substituting formula (33) and formula (34) into formula (32) yields: According to Young's inequality, the inequalities of formula (36) and formula (37) hold: Substituting formula (36) and formula (37) into formula (35), we obtain: in, When i6=7,9,11 corresponds to j3=2,3,4, the attitude subsystem shown in formula (9b) is as shown in formula (39): The state transformation is defined as shown in formula (40): in, is the new state quantity; Tracking error The error conversion, is the virtual control input; Select the Lyapunov function shown in formula (41) By using formula (15) and formula (40), we can get The derivative of is: Design the virtual control input as: in, and It is a nonlinear expression term generated during the preset performance method. is the design parameter. Substituting formula (43) into formula (42), we get: Choose the Lyapunov function as shown in formula (45) right Taking the derivative we get: Choose the Lyapunov function as shown in formula (47) right Taking the derivative we get: in, represents the design parameters, is an unknown positive constant and satisfies There is an unknown positive constant satisfy Design the attitude subsystem controller as shown in formula (49) And the fuzzy adaptive law shown in formula (50): in, and are design parameters, and Substituting formula (49) and formula (50) into formula (48) yields: According to Young's inequality, the inequalities of formula (52) and formula (53) hold: Substituting formula (52) and formula (53) into formula (51), we obtain: in, According to the obtained coupling between the position virtual controller and the virtual input signal as shown in formula (33), the expression of the actual total lift u1 is shown in formula (55): Get the desired pitch angle θ d and the desired roll angle φ d As shown in formula (56):

5. The method for controlling the preset performance of a drone considering time-varying position constraints according to claim 1, characterized in that: In step 2, after the design of the drone preset performance controller is completed, a stability analysis is performed on the drone controlled by the drone preset performance controller.

6. The method for controlling the preset performance of a UAV considering time-varying position constraints according to claim 4, characterized in that: For the new unconstrained system after mapping, its dynamic model is shown in formula (9a) and formula (9b), considering the quadratically differentiable expected tracking signal Y i If the virtual control signals shown in formula (27) and formula (43) and the fuzzy adaptive laws shown in formula (34) and formula (50) are used, and the actual control signals shown in formula (33) and formula (49) and the fuzzy observer shown in formula (18) are used, the trajectory tracking error of the UAV system after mapping processing will be guaranteed to be uniformly bounded, and the expected signal of the original constraint system that can stably follow without violating the constraint conditions can be obtained according to the nonlinear mapping relationship.

7. The method for controlling the preset performance of a UAV considering time-varying position constraints according to claim 2, characterized in that: In step 1, when o i2 = 0, the actuator only has a bias fault, and when o i2 When ≠0, the actuator has a bias and gain fault.

8. A UAV preset performance control system considering time-varying position constraints, characterized in that: Includes the following modules: The model building module is used to establish a composite model of the UAV that takes into account time-varying position constraints, model uncertainty, and external wind disturbances. The composite model is mapped using nonlinear mapping relationships to convert it into an unconstrained model. The tracking error of the unconstrained system is limited using a preset performance function, and the tracking error is processed using an error transformation function. This is then used to design a preset performance controller for the UAV. The controller design module is used to estimate model uncertainty based on an unconstrained system using an adaptive fuzzy system, estimate and compensate for external wind disturbances and actuator failures using a disturbance observer, and design a preset performance controller for the UAV using the preset performance method and backstepping method; And the actuator fault control module is used to use the UAV preset controller to realize trajectory tracking control of the unconstrained system obtained after nonlinear mapping, and according to the nonlinear mapping relationship, the expected signal of the original constrained system can be obtained to stably follow without violating the constraint conditions.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the method for controlling the preset performance of a drone considering time-varying position constraints are implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by the processor, the steps of the method for controlling the preset performance of a drone considering time-varying position constraints as described in any one of claims 1 to 7 are implemented.

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