A fault-tolerant control method for the performance of a quadrotor UAV at a specified time

Abstract

The present invention provides a fault-tolerant control method for a quad-rotor unmanned aerial vehicle with a predetermined performance at a specified time. The method uses an adaptive method to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance, and unknown external disturbances. At the same time, a predetermined performance function at a specified time and a coordinate transformation are introduced to process tracking errors. In order to make the quad-rotor unmanned aerial vehicle meet higher transient and steady-state requirements, the present invention combines the predetermined performance function at a specified time, uses a new coordinate transformation function to act on the tracking error, simplifies the calculation process, ensures that the tracking error of the closed-loop system meets the predetermined transient and steady-state performance constraints, and can also flexibly adjust the convergence time and convergence speed.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and in particular to a fault-tolerant control method for a quad-rotor unmanned aerial vehicle with predetermined performance at a specified time. Background Art

[0002] A quadrotor unmanned aerial vehicle is a vertical take-off and landing unmanned aerial vehicle with a novel appearance and superior performance. It has the characteristics of simple structure, flexible operation, and strong carrying capacity, and has important military and civilian value. A quadrotor unmanned aerial vehicle, also known as Quadrotor, Four-rotor, 4rotors helicopter, X4-flyer, etc., is an aircraft with four propellers and the four propellers are in a cross-shaped cross structure. The relative four rotors have the same rotation direction and are divided into two groups, and the rotation directions of the two groups are different. Unlike traditional helicopters, quadrotors can only achieve various actions by changing the speed of the propellers. A quadrotor is a multi-rotor rotor aircraft. In terms of rotor layout, it belongs to a non-coaxial disc-shaped rotor aircraft, and the four rotors are symmetrically distributed in a cross shape. Compared with traditional single-rotor aircraft, quadcopters have many advantages. The four rotors of a quadcopter cancel each other's gyration effects, and there is no need for the tail rotor of a single-rotor aircraft, which is more energy-efficient and reduces the size of the aircraft. Quadcopters adjust the aircraft's attitude by adjusting the speed of the four rotors, and there is no need for the propeller angle adjustment device of a single-rotor helicopter, which is simpler in mechanical design: quadcopters have multiple rotors, so they have a larger load capacity, and the blades can also be made smaller, making them easy to miniaturize. It is precisely because quadcopters have so many advantages that they have broad application prospects and research value.

[0003] The quadrotor UAV system is a typical underactuated nonlinear coupling system. The quadrotor UAV has strong maneuverability and hovering ability. Due to its low production cost and convenient operation, it has been widely used in many fields and has broad development prospects. Nonlinear control systems are widely used in many fields. In addition to general engineering systems, it is also of great significance in the control of UAVs. At present, there are methods such as sliding mode control, back-step control, and adaptive control for the stability control of quadrotor UAVs. Quadrotors are easily subject to unknown external interference, and their actuators may be exposed to measurement noise. Under the combined influence of factors such as component loss, temperature, humidity changes, and external interference, the probability of actuator failure in actual systems is increasing.

[0004] Zhao Guanglei, Gao Rushuai, and Chen Jiannan published "Adaptive Predetermined Performance Control of Quadrotors with Actuator Failures", and Hu Zhongquan, Hua Changchun, and Zhang Liuliu published "Limited Time Predetermined Performance Control of Quadrotors with Time-Varying Disturbances". The existing technology requires accurate known system dynamics parameters, air resistance, external disturbances, and actuator failures, which brings great difficulties to the acquisition of control methods. At present, the study of fault-tolerant control of quadrotors with unknown time-varying loads, dynamic parameters, and external disturbances, and considering achieving the predetermined transient steady-state performance within a specified time, is still an unresolved problem. Summary of the invention

[0005] In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a fault-tolerant control method for a quadrotor UAV with a specified time predetermined performance for actuator failure and unknown system parameters, and an adaptive method is adopted to overcome the limitations of the need for precisely known system dynamic parameters, air resistance, external disturbances and actuator failures.

[0006] The technical solution adopted by the present invention is: an adaptive method is used to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance and unknown external disturbances, and a specified time predetermined performance function and coordinate transformation are introduced to handle tracking errors.

[0007] Furthermore, an evaluation model is constructed to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance, and unknown external disturbances using an adaptive method. The model is constructed by constructing a position subsystem and an attitude subsystem, as shown in Formula 2a and Formula 2b, respectively.

[0008]

[0009]

[0010]

[0011]

[0012]

[0013]

[0014] The following parameters are defined:

[0015] η mx =1 / m x ,η my =1 / m y ,η mz =1 / m z ,η mφ =1 / I xx,η mθ =1 / I yy ,η mψ =1 / I zz ,T mφ =(I yy -I zz ) / I xx , and control input

[0016] u φ =M φ ,u θ =M θ ,u ψ =M ψ ,u x =(cφsθcψ+sφsψ)F z ,u y =(cφsθsψ-sφcψ)F z ,u z =cφcθF z .

[0017] Furthermore, in order to meet the requirements of tracking error performance constraints, a positive decreasing smooth function F is used bi To meet the transient and steady-state performance, as shown in formula (4):

[0018]

[0019] in, And ι,n,ξ,∞,t e is a positive design parameter, ln(·) represents the natural logarithmic function, and tx is the initial time, which is generally set to 0.

[0020] Furthermore, in order to make the tracking error meet the specified performance constraints, the following coordinate transformation is performed on the tracking error to be used:

[0021]

[0022] where q i satisfy:

[0023]

[0024] Furthermore, the tracking error variable is defined as follows:

[0025]

[0026] Among them, x 1d ,x 3d ,x 5d is the reference signal, α i ,i=1,3,5 are virtual control inputs;

[0027] The boundary layer error is defined as:

[0028] y i =*α i-1 -α i-1 (i=2,4,6) (10);

[0029] Among them, α i ,i=1,3,5 are all ideal virtual control inputs;

[0030] Select the Lyapunov function:

[0031]

[0032] Among them, the design parameter r 1 >0,r 2 >0,r 3 >0,r 4 >0,r 5 >0.

[0033] Furthermore, for the position subsystem, verify whether the controller and adaptive law can maintain stability. The verification method is:

[0034]

[0035] in,

[0036]

[0037]

[0038] Design the translation position controller:

[0039]

[0040]

[0041] Among them, the design parameter c 2 >0, Yes D x The estimate, It's G x The estimate, yes The estimate of x =1 / τ x , They are the estimation errors of the fault coefficient and additive fault in actuator faults.

[0042] Controller y and u z Designed for:

[0043]

[0044]

[0045]

[0046]

[0047] Among them, the design parameter c 3 >0,c 5 >0.

[0048] Ideal virtual control input and Designed for:

[0049]

[0050]

[0051] Among them, the design parameter c 3 >0,c 5 >0;

[0052] The adaptive law is designed as:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] Among them, the design parameter δ 1 >0,δ 2 >0,δ 3 >0,δ 5 >0.

[0059] Furthermore, the position subsystem and the attitude subsystem are connected to each other through the attitude extraction algorithm; the reference input of the inner loop attitude angle is:

[0060]

[0061]

[0062] Furthermore, for the attitude subsystem, verify whether the controller and adaptive law can maintain stability. The verification method is:

[0063]

[0064] in:

[0065]

[0066] The ideal virtual control input for the roll angle attitude is:

[0067]

[0068] Among them, the design parameter c 7 >0;

[0069] Design the controller of the roll angle of the attitude subsystem as:

[0070]

[0071]

[0072] Among them, the design parameters ε7>0, c8>0;

[0073] Controller θ and u ψ Can be designed as:

[0074]

[0075]

[0076]

[0077] Ideal virtual control input and Can be designed as:

[0078]

[0079]

[0080] Among them, the design parameter c 9 >0,c 11 >0;

[0081] The adaptive law is designed as:

[0082]

[0083]

[0084]

[0085]

[0086] Among them, the design parameter δ 1 >0,δ 2>0,δ 3 >0,δ 5 >0.

[0087] The beneficial effects of the present invention are:

[0088] 1. In order to make the quad-rotor drone with actuator failure asymptotically stable under the interference of unknown disturbances, unknown air resistance and unknown dynamic parameters, the present invention adopts an adaptive method to overcome the limitations of accurately known system dynamic parameters, air resistance, external disturbances and actuator failures. In order to make the quad-rotor drone meet higher transient and steady-state requirements, the present invention combines the predetermined performance function at a specified time, uses a new coordinate transformation function to act on the tracking error, simplifies the calculation process, ensures that the tracking error of the closed-loop system meets the predetermined transient and steady-state performance constraints, and can also flexibly adjust the convergence time and convergence speed.

[0089] 2. In order to make the quadrotor drone with actuator failure asymptotically stable under the disturbance of unknown air flow, unknown air resistance and unknown dynamic parameters, an adaptive method is used to overcome the limitation of needing to know the system dynamic parameters, air resistance, external disturbance and actuator failure.

[0090] 3. In order to make the quadcopter meet higher transient and steady-state requirements, a new coordinate transformation function is used to act on the tracking error in combination with the predetermined performance function at a specified time to ensure that the tracking error of the closed-loop system meets the specified transient and steady-state performance constraints. In addition, the convergence time and convergence speed can be flexibly adjusted.

[0091] 4. Avoids the complex inverse calculation process under existing predetermined performance conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 It is the three-dimensional tracking trajectory in the data simulation of the present invention;

[0093] Figure 2 is a tracking error curve of the position loop error in the data simulation of the present invention;

[0094] Figure 3 is a tracking error curve of the attitude loop error in the data simulation of the present invention;

[0095] Figure 4 Schematic diagram of the control method of the present invention. DETAILED DESCRIPTION

[0096] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation mode, structure, characteristics and effects of the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments.

[0097] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0098] First, it should be noted that the discussion of any embodiment of the present invention is only exemplary and is not intended to imply that the scope of the present disclosure (including the claims) is limited to these examples; there are many other variations of the different aspects of the present invention described above, which are not provided in detail for the sake of brevity. Therefore, other embodiments are also within the scope of protection of the corresponding claims.

[0099] In addition, the drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In addition, these embodiments are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0100] Example

[0101] The present invention studies an adaptive specified time predetermined performance fault-tolerant control method for a quadrotor unmanned aerial vehicle system with parameter uncertainty and external interference. For the position subsystem and attitude subsystem, an adaptive method is used to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance and unknown external disturbances. At the same time, a new specified time predetermined performance function and coordinate transformation are introduced to deal with tracking errors. Based on the Lyapunov stability theory, an adaptive dynamic surface control method is proposed to ensure that the tracking position and attitude errors of the closed-loop system can converge within the specified time, as well as the transient and steady-state performance specified in the predetermined performance. In addition, the convergence speed and convergence time of the specified time predetermined performance function can be flexibly set.

[0102] This paper studies the stability control problem of a quad-rotor UAV under actuator failure and proposes a controller design that satisfies the predetermined performance conditions within a specified time. Figure 4 To understand the technical solution of the present invention, the specific method of the present invention is as follows:

[0103] In the case of small disturbances, it is assumed that the change law of the fuselage's attitude angle and the rotational angular velocity are approximately equal. Considering the influence of unknown time-varying loads, external disturbances and air resistance on the system, the dynamic equation of the quadrotor drone is:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] Where m x =m y =m z =m is the mass of the quadrotor drone, [x, y, z,] and [φ, θ, ψ] are the position and attitude angle of the quadrotor drone, g is the acceleration due to gravity, k i , i=1,2,3,4,5,6 are the aerodynamic damping coefficients of the system, represents the external disturbance, where and are respectively and, and Respectively and Matrix I xx ,I yy ,I zz represents the moment of inertia around the x, y, and z axes, F z is the control input, V = [V x ,V y ,V z ] T Indicates the linear velocity in the x, y, and z directions, M φ ,M θ ,M ψ They are rolling moment, pitching moment and yaw moment respectively. Define the vector

[0111] Then, the mathematical model of the quadrotor drone described by equations (1a) and (1b) can be expressed as the following position subsystem (2a) and attitude subsystem (2b):

[0112]

[0113]

[0114] The overall model components of the present invention are shown in 2a and 2b.

[0115] The following parameters are defined:

[0116] η mx =1 / m x ,η my =1 / m y ,η mz =1 / m z ,η mφ =1 / I xx ,η mθ =1 / I yy ,η mψ =1 / I zz ,T mφ =(I yy -I zz ) / I xx ,T mθ =(I zz -I xx ) / I yy ,T mψ =(I xx -I yy ) / I zz .

[0117] and control input

[0118] u φ =M φ ,u θ =M θ ,u ψ =M ψ ,u x =(cφsθcψ+sφsψ)F z ,u y =(cφsθsψ-sφcψ)F z ,u z =cφcθF z .

[0119] Assumption 1: Assume that parameter η mx ,η my ,η mz ,η mφ ,η mθ and η mψ are unknown, and their lower bounds are and is also unknown and greater than zero; the aerodynamic drag coefficient ki , i=1,2,3,4,5,6 are unknown and all greater than zero.

[0120] Assumption 2: Assume the following conditions hold:

[0121] The upper bound parameter and are all unknown; at the same time, assume that the following inequality holds:

[0122] |η mx d x |≤D x ,|η my d y |≤D y ,|η mz d z |≤D z ,|η mx k 1 |≤G x ,|η my k 2 |≤G y ,|η mz k 3 |≤G z , The upper bound parameter D x ,D y ,D z ,G x ,G y ,G z , and is unknown.

[0123] Note 1: In practical applications, it is assumed that the quadrotor drone has time-varying unknown loads and time-varying unknown dynamic parameters. At the same time, the load mass of the quadrotor drone changes with the mission execution and the dynamic parameters I x ,I y ,I z changes, the aerodynamic damping coefficient k i However, external airflow disturbance is not easy to obtain, so the information of these parameters cannot be used for controller design. The controller design based on assumptions 1 and 2 is reasonable and more suitable for the actual situation. Considering the unknown load and unknown disturbance, the adaptive method is used to estimate the bounds of these unknown parameters, including the inertia moment I of the unknown dynamic parameters of the system. x ,I y ,I z , eliminating the limitations of kinetic parameters in existing studies.

[0124] u i =τ i u ia +u if ,i=(x,y,z,φ,θ,ψ) (3), where u i represents the actual output of the actuator, uia Indicates a faulty actuator input. 0≤τ i ≤1 indicates actuator fault index, u if Indicates unknown additive fault. i and u if For different values ​​of , actuator faults can be divided into different types of faults. i =1 and u if =0, it is a fault-free type; if 0≤τ i ≤1 and u if =0, it is a partial failure fault type; if τ i =0 means a complete failure type.

[0125] Assumption 3: Assume that these inequalities still hold: |η mx u xf |≤u xF ,|η my u yf |≤u yF ,|η mz u zf |≤u zF ,|η mφ u φf |≤u φF ,|η mθ u θf |≤u θF ,|η mψ u ψf |≤u ψF , where the upper bound parameter u xF ,u yF ,u zF ,u φF ,u θF ,u ψF is unknown.

[0126] Note 2: The failure of the actuator often endangers the control strategy of the entire system, so when considering the actuator failure index τ i In the case of actuator failure, it effectively solves the trajectory tracking problem of the quadrotor drone and the unknown additive fault u if ,In this paper, an adaptive method is used to estimate the bounds of these unknown parameters.

[0127] In order to meet the requirements of tracking error performance constraints, a new positive decreasing smooth function F is designed. bi To meet the transient and steady-state performance, as described below:

[0128]

[0129] in And ι,n,ξ ∞,t e is a positive design parameter, ln(·) represents the natural logarithmic function, t 0 is the initial time, which is usually set to 0. As can be seen from the performance function specified above, the function F bi is positively decreasing and satisfies F bi (0) = lne ι +ξ ∞ >1,F bi (t e )=ξ ∞ > 0, the initial state can be determined by the parameters ι,ξ ∞ The steady-state value can also be adjusted by adjusting the parameter ξ ∞ To make adjustments. Tracking error e i The definition of is shown in the following equations (9) and (47), and the error e is defined as i , i=1,3,5,7,9,11 satisfies

[0130] -d 2 F bi <e i <d 1 F bi ,i=1,3,5,7,9,11 (5)

[0131] Among them, the adjustable parameter d of the specified performance requirement 1 and d 2 is a positive constant. 1 F bi and -d 2 F bi are the upper and lower bounds of the predetermined performance that the tracking error needs to meet. In summary, by choosing appropriate parameters ι, n, ξ ∞ ,t e and adjustable parameter d 1 and d 2 , so that the selected performance function (4) gives the performance characteristics of the tracking error.

[0132] In order to make the tracking error meet the specified performance constraints, the following coordinate transformation is performed on the tracking error to be used:

[0133]

[0134] Among them, q i satisfy:

[0135]

[0136] From formula (6), we can see that when e i (0)∈(-d 2 F bi ,d 1F bi ), as long as z i →0, then e i →0, and e i ∈(-d 2 F bi ,d 1 F b i), therefore, as long as the controller is designed to ensure that z i →0, the tracking error e i Asymptotically stable, satisfying constraint (5);

[0137] From equation (6), we can further deduce that z i The derivative of :

[0138] z i =F bi A Fi e i -F bi A Fi e i (8)

[0139] in:

[0140] First, define the tracking error variable as follows:

[0141]

[0142] Among them, x 1d ,x 3d ,x 5d is the reference signal, α i ,i=1,3,5 are virtual control inputs.

[0143] The boundary layer error is defined as:

[0144]

[0145] in, All are ideal virtual control inputs.

[0146] Select the Lyapunov function by choosing the form:

[0147]

[0148] The two system models are established.

[0149] The ideal virtual control input can be designed as:

[0150]

[0151] Among them, the design parameter c 1 >0.

[0152] The ideal virtual control input Substituting into formula (11) we get:

[0153]

[0154] Next, the Lyapunov function V 2 You can choose:

[0155]

[0156] Design the translation position controller:

[0157]

[0158]

[0159]

[0160] Among them, the design parameter c 2 >0, Yes D x The estimate, It's G x The estimate, yes The estimate of x =1 / τ x , They are the estimated errors of the fault coefficient and additive fault in the actuator fault. According to the designed controller (14), equation (13) can be rewritten as:

[0161]

[0162] in

[0163] Select the Lyapunov function V x for:

[0164]

[0165] Among them, the design parameter r 1 >0,r 2 >0,r 3 >0,r 4 >0,r 5 >0.

[0166] The adaptive law is designed as:

[0167]

[0168]

[0169]

[0170]

[0171]

[0172] Among them, the design parameter δ 1 >0,δ 2 >0,δ 3 >0,δ 5 >0.

[0173] V x The derivative of can be further obtained as:

[0174]

[0175] For the position subsystem, verify whether the controller and adaptive law can maintain stability.

[0176] in,

[0177]

[0178]

[0179] Similarly, the controller u y and u z Designed for:

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186] Among them, the design parameter c 4 ,c 6 >0, Yes D y The estimate, It's G y The estimate, yes The estimate, is u yF The estimate, Yes D z The estimate, It's G z The estimate, yes The estimate, is u zF Estimates.

[0187] Ideal virtual control input and Designed for:

[0188]

[0189]

[0190] Among them, the design parameter c 3 >0,c 5 >0.

[0191] In addition, the adaptive law is designed as:

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202] Among them, the design parameter r i >0,δ i >0,i=6,7,8,9,10,11,12,13,14,15.

[0203] Next, we will design the inner loop attitude subsystem controller. First, we connect these two subsystems to each other through the attitude extraction algorithm. The relevant relationship is as follows:

[0204] u x =(cφsθcψ+sφsψ)F z ,u y =(cφsθsψ-sφcψ)F z

[0205] u z =cφcθF z

[0206] The reference input of the inner ring attitude angle can be obtained:

[0207]

[0208]

[0209] Linking the two systems, the position subsystem (2a) and the attitude subsystem (2b),

[0210] The tracking error of the attitude system is defined as:

[0211]

[0212] where α 7 ,α 9 ,α 11 is the virtual control input, x 7d ,x 9d ,x 11d is the reference signal. The boundary layer error is defined as follows:

[0213]

[0214] in is the virtual control input.

[0215] Lyapunov function V φ The choices are as follows:

[0216] V φ =V φ1 +V φ2 +V φ3 (41)

[0217] in Among them, the design parameter r 16 >0,r 17 >0,r 18 >0,r 19 >0,r 20 >0, yes The estimate, yes The estimate, yes The estimate of φ =1 / τ φ , They are the estimated errors of the fault coefficient and additive fault in the actuator fault. The ideal virtual control input is designed as:

[0218]

[0219] Among them, the design parameter c 7 >0.

[0220] Design the attitude subsystem controller as:

[0221]

[0222]

[0223]

[0224] Among them, the design parameter ε 7 >0,c 8 >0.

[0225] According to the designed controller (42), equation (41) can be written as:

[0226]

[0227] The adaptive law is designed as:

[0228]

[0229]

[0230]

[0231]

[0232]

[0233] Among them, the design parameter r i >0,δ i >0,i=16,17,18,19,20.

[0234] In summary, we can further get V φ The derivative of is:

[0235]

[0236] Verify another system attitude subsystem to verify whether the controller and adaptive law can maintain stability, where:

[0237]

[0238]

[0239] Similarly, the controller u θ and u ψ Can be designed as:

[0240]

[0241]

[0242]

[0243]

[0244]

[0245]

[0246] Among them, the design parameter ε 9 ,ε 11 >0,c 10 ,c 12 >0, yes The estimate, yes The estimate, yes The estimate, is u θF The estimate, yes The estimate, yes The estimate, yes The estimate, is u ψ Estimate of F.

[0247] Ideal virtual control input and Can be designed as:

[0248]

[0249]

[0250] Among them, the design parameter c 9 >0,c 11 >0.

[0251] In addition, the adaptive law is designed as:

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259]

[0260]

[0261]

[0262] Among them, the design parameter r i >0,δ i >0,i=21,22,23,24,25,26,27,28,29,30.

[0263] In order to verify the effectiveness of the proposed adaptive specified time scheduled performance fault-tolerant control method, numerical simulations are then carried out. Figure 1 A three-dimensional tracking trajectory is given. The curve with the five-pointed star as the starting point is the expected trajectory, and the curve with the asterisk as the starting point is the actual trajectory of the quadrotor drone. It can be seen from the figure that the quadrotor drone quickly reaches the expected trajectory and keeps tracking. Figure 2 and Figure 3 The tracking error curves of the position loop and attitude loop errors are given respectively. At the same time, in order to more clearly show that the tracking error meets the predetermined transient and steady-state performance constraints, the predetermined performance function curves at the specified time are drawn in both figures. It can be seen from the figures that the tracking errors of the position loop and the attitude loop are ultimately bounded and stable, and do not exceed the upper and lower bounds of the predetermined performance function curves at the specified time during the entire dynamic process.

[0264] The main contributions of the present invention are mainly reflected in three aspects. First, for the uncertain quadrotor UAV system with unknown dynamic parameters, load changes and actuator failures, a new robust adaptive specified time predetermined performance fault-tolerant dynamic surface control scheme is proposed, which ensures that the tracking error of the closed-loop system is ultimately uniformly bounded and stable, and meets the steady-state and transient performance requirements of the specified time predetermined performance; in addition, the influence of external unknown interference and unknown air resistance on the system performance is overcome, the limitation of existing research requiring accurate understanding of the system load or dynamic parameters of the quadrotor UAV is eliminated, the limitation of fixed time initial conditions is avoided, and the steady-state performance requirements of the quadrotor UAV with actuator failure are guaranteed; in addition, a new combination of coordinate transformation and dynamic surface technology is introduced to simplify the design of the controller.

[0265] At present, the technical solution of the present invention has been put into pilot production, that is, a small-scale experiment before the large-scale mass production of the product. After the pilot production was completed, a user survey was conducted on a small scale, and the survey results showed that user satisfaction was high. Now, preparations have been started for the formal production and industrialization of the product (including intellectual property risk warning survey).

[0266] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technical personnel in this field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A fault-tolerant control method for a quad-rotor drone with predetermined performance at a specified time, characterized in that: Adaptive methods are used to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance and unknown external disturbances. At the same time, a specified time predetermined performance function and coordinate transformation are introduced to deal with tracking errors. The evaluation model is constructed to estimate the boundaries of unknown dynamic parameters, unknown time-varying loads, unknown air resistance, and unknown external disturbances using an adaptive method. The model is constructed by constructing a position subsystem and a posture subsystem, as shown in Formula 2a and Formula 2b, respectively. The following parameters are defined: m x =m y =m z =m is the mass of the quadrotor drone, matrix I xx , I yy , I zz is the moment of inertia about the x, y, and z axes, η mx =1 / m x , η my =1 / m y , η mz =1 / m z , η mφ =1 / I xx , η mθ =1 / I yy , η mψ =1 / I zz , T mφ =(I yy -I zz ) / I xx , T mθ =(I zz -I xx ) / I yy , T mψ =(I xx -I yy ) / I zz and control input u φ =M φ ,u θ =M θ ,u ψ =M ψ ,u x =(cosφsinθcosψ+sinφsinψ)F z ,u y =(cosφsinθcosψ-sinφcosψ)F z ,u z =cosφcosθF z , M φ is the rolling moment, M θ is the pitching moment, M ψ is the yaw moment, F z is the control input, J p =diag(I xx ,I yy ,I zz ),Ω r is the vector sum of the rotor speeds of the quadrotor drone; k i , i=1,2,3,4,5,6 are the aerodynamic damping coefficients of the system, [x,y,z] is the position of the quadrotor drone, d i ,i=x,y,z,φ,θ,ψ are external disturbances; In order to meet the requirements of tracking error performance constraints, a positive decreasing smooth function F is used. bi To meet the transient and steady-state performance, as shown in formula (4): in, And l, n, ξ ∞ , t e is a positive design parameter, In(·) represents the natural logarithmic function, t is the time, t0 is the initial time, which is set to 0; In order to make the tracking error meet the specified performance constraints, the following coordinate transformation is performed on the tracking error to be used: where q i satisfy: d1, d2 are adjustable parameters, e i is the tracking error; Define the tracking error variable as follows: e1=x1-x 1d ,e2=x2-α1,e3=x3-x 3d ,e4=x4-α3,e5=x5-x 5d ,e6=x6-α5 (9) Among them, x 1d , x 3d , x 5d is the reference signal, α i ,i=1,3,5 are virtual control inputs; The boundary layer error is defined as: in, is the virtual control input; Select the Lyapunov function: Among them, the design parameters are r1>0, r2>0, r3>0, r4>0, r5>0, V2 is the Lyapunov function, is η mx The lower bound parameter of for The estimate, D x is η mx d x The upper bound parameter of D x The estimate, G x is η mx The upper bound parameter of k1, G x The estimate, χ x =1 / τ x , is x The estimate, u xF is η mx u xf The upper bound parameter, u xf is an unknown additive fault, for u xF The estimate of τ x is the actuator fault index; For the position subsystem, verify whether the controller and adaptive law can maintain stability. The verification method is: in, γ2 is the time constant, D x is η mx d x The upper bound parameter, G x is η mx The upper bound parameter of k1, λ2, c1, and ε1 are design parameters; Design the translation position controller: Among them, the design parameter c2>0, Yes D x The estimate, It's G x The estimate, yes The estimate of x =1 / τ x , They are the estimated errors of the fault coefficient and additive fault in the actuator fault, z1 is the predetermined performance function, F bi , i=1,3,5 are positive decreasing smooth functions, is α i The derivative of Controller y and u z Designed for: Among them, ε1, ε3, ε4, c4, c6 are design parameters, c4>0, c6>0, χ y =1 / τ y , is y The estimated value of z =1 / τ z , is z The estimated value of , z3 and z5 are the predetermined performance functions; Ideal virtual control input and Designed for: Among them, the design parameters c3>0, c5>0; The adaptive rate is designed as: Among them, the design parameters are δ1>0, δ2>0, δ3>0, δ5>0.

2. The fault-tolerant control method for the predetermined performance at a specified time of a quad-rotor UAV according to claim 1 is characterized in that: The position subsystem and attitude subsystem are connected to each other through the attitude extraction algorithm; the reference input of the inner loop attitude angle is: φ d is the reference input value of the roll angle, θ d is the reference input value of the pitch angle, ψ d Reference input value for the yaw angle.

3. The fault-tolerant control method for the predetermined performance at a specified time of a quad-rotor UAV according to claim 2 is characterized in that: For the attitude subsystem, verify whether the controller and adaptive law can maintain stability. The verification method is: in: In the formula, the design parameter r 16 >0,r 17 >0,r 18 >0,r 19 >0,r 20 >0, for The estimate, yes The estimate, yes The estimate of φ =1 / τ φ , and is the upper bound parameter, T mφ =(I yy -I zz ) / I xx ; δ 16 r 16 ,δ 18 r 18 ,r 18 ,r 19 ,r 20 ,μ8,γ8 are design parameters, λ8 is the time constant, τ φ Actuator efficiency factor, is η mφ The lower bound parameter, u φF is η mφ u φf The upper bound parameter of The ideal virtual control input for the roll angle attitude is: Among them, the design parameter c7>0, z7 is the predetermined performance function; Design the controller of the roll angle of the attitude subsystem as: Among them, the design parameters ε7>0, c8>0; Controller θ and u ψ Designed for: Ideal virtual control input and Designed for: Among them, the design parameters c9>0, c 11 >0; The adaptive law is designed as: Among them, the design parameter r i >0,δ i >0, i=21,22,23,24,25,26,27,28,29,30, yes The estimate, yes The estimate, yes The estimate, yes The estimate, yes The estimate of i is the tracking error.

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