Four-rotor aircraft attitude repeated learning control method based on fixed time disturbance observer

Abstract

The invention discloses a four-rotor aircraft attitude repeated learning control method based on a fixed time disturbance observer, and the method comprises the steps: building a kinetic model of a four-rotor aircraft system, and initializing the state and control parameters of the system; designing a fixed time disturbance observer; designing a fixed time sliding mode variable; designing a full-saturation repeated learning law; and designing a repetitive learning controller based on the fixed time disturbance observer, the fixed time sliding mode variable and the full-saturation repetitive learning law. According to the method, the influence of the system uncertainty on the control precision of the four-rotor aircraft can be effectively inhibited, the influence of the initial state on the system uncertainty estimation and compensation rapidity is reduced, and the accurate tracking of the four-rotor aircraft on the periodic expected attitude angle within the fixed time is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of attitude control of quadrotor aircraft. Aiming at the uncertainty existing in the quadrotor aircraft system and the system executing periodic characteristic tasks, a quadrotor aircraft attitude repeated learning control method based on a fixed time disturbance observer is proposed. Background Art

[0002] The rotors of the quadcopter are symmetrically distributed, and the four propellers are directly connected to the motor, which can freely hover and move in space, and has great flexibility. In addition, it has many advantages such as low cost, simple structure, and wide application range. It has been widely used to perform various tasks, such as aerial photography, search and rescue, military reconnaissance, environmental monitoring, etc.

[0003] Good attitude control of quadrotor aircraft is a prerequisite for the normal operation of the aircraft payload and the fundamental guarantee for the aircraft to accurately complete its mission. Therefore, it is very meaningful to conduct in-depth research on the attitude control method of quadrotor aircraft.

[0004] In actual work, quadcopters often encounter periodic motion. Traditional control methods such as PID control, inversion control, and sliding mode control usually ignore the periodic characteristics of the reference trajectory, making it difficult to achieve high-precision control goals. The repeated learning control method can use the data of the previous cycle to correct the control input of the current cycle, and achieve high-precision tracking of the bounded periodic desired attitude angle by the quadcopter.

[0005] Accurate, fast and reliable aircraft attitude control has always been one of the hot issues in space vehicle system research. Fixed-time stability, as an extension of finite-time stability, reduces the dependence of convergence time on the initial state. Unlike finite-time control, the fixed-time controller contains two fractional powers p and q, where p>1,q<1, which increases the convergence speed when the system state is close to the equilibrium point and far away from the equilibrium point, while improving the transient and steady-state performance of the aircraft.

[0006] In practical applications, aircraft are exposed to multiple external disturbances such as gusts and payload changes, as well as system uncertainties including parameter disturbances, unmodeled dynamics and coupling, which may cause large control deviations. In order to estimate and compensate for system uncertainties, disturbance observers or extended state observers are usually used to estimate and compensate for disturbances using the state information in the system, effectively enhancing the anti-disturbance capability of quadrotors. However, the convergence time of these disturbance observers depends on the initial state and tends to infinity as its norm increases, making the quadrotor control method based on these disturbance observers unable to meet the requirements of fast convergence. Fixed-time disturbance observers can not only further improve the rapidity of estimating and compensating system uncertainties, but also reduce the dependence of convergence time on the initial state.

[0007] Therefore, for quadrotor aircraft that perform periodic characteristic tasks and have system uncertainties, it is very meaningful to design a control method that can effectively estimate and compensate for system uncertainties, reduce the influence of the initial state on the rapidity of system uncertainty estimation and compensation, and achieve rapid convergence within a fixed time. Summary of the invention

[0008] In order to overcome the shortcomings of the prior art, in order to reduce the influence of system uncertainty on the control accuracy of the quadrotor, and at the same time enable the quadrotor to quickly reach a stable state and have good robustness, the present invention proposes a quadrotor attitude repetitive learning control method based on a fixed-time disturbance observer. The proposed method first divides the lumped uncertainty in the system into two parts: periodic uncertainty and non-periodic uncertainty. Secondly, the fixed-time disturbance observer method is used to quickly estimate the non-periodic uncertainty in the system, and the fully saturated repetitive learning law is designed to estimate the periodic uncertainty in the system. On this basis, a fully saturated repetitive learning controller is designed. This design can effectively suppress the influence of the system lumped uncertainty on the control accuracy of the quadrotor, and at the same time reduce the dependence of the convergence time on the initial state, ensuring that the system state converges to the specified limit within a fixed time.

[0009] The technical solutions proposed to solve the above technical problems are as follows:

[0010] A method for repeated attitude learning control of a quadrotor aircraft based on a fixed-time disturbance observer comprises the following steps:

[0011] Step 1: Establish the dynamic model of the quadrotor system and initialize the state and control parameters of the system. The process is as follows:

[0012] 1.1 The dynamics of a quadrotor is expressed as:

[0013]

[0014] Among them, τ x ,τ y ,τ z They represent the control torque acting on the roll axis, pitch axis and yaw axis of the quadrotor in the body coordinate system respectively; I xx ,I yy ,I zz Respectively represent the moment of inertia of each axis of the quadrotor in the body coordinate system; ω x ,ω y ,ω z They respectively represent the angular velocity of each axis of the quadrotor in the body coordinate system; They are ω x ,ω y ,ω z The first-order derivative of represents the angular acceleration of each axis of the quadrotor in the body coordinate system; × represents the cross product; · represents the dot product;

[0015] 1.2 Through formula (1), the expression of the attitude angular acceleration of each axis of the quadrotor aircraft during motion is obtained as follows:

[0016]

[0017] 1.3 Define the following state variables:

[0018]

[0019] Among them, φ, θ, ψ are the roll axis attitude angle, pitch axis attitude angle and yaw axis attitude angle of the quadrotor aircraft in the body coordinate system respectively; x1 represents the attitude angle state quantity, and x2 represents the attitude angular velocity state quantity;

[0020] 1.4 Further considering the external interference to the system in the actual environment, combining equations (2)-(3), the following state equation is constructed:

[0021]

[0022] in, Represent the first-order derivatives of x1 and x2 respectively; represents the control torque;

[0023]

[0024] Among them, d x ,d y ,d z They represent the external disturbances acting on the control channels of each axis of the quadrotor in the body coordinate system respectively;

[0025] Step 2: Design a fixed-time disturbance observer for the pitch axis of the quadrotor aircraft. The process is as follows:

[0026] 2.1 Combined with formula (4), the following quadrotor pitch axis attitude angle system model is obtained:

[0027]

[0028] Among them, x θ1 ,x θ2 They represent the pitch-axis attitude angle and pitch-axis attitude angular velocity of the quadrotor in the body coordinate system, x θ1 ,x θ2 The first derivative of ; They are respectively the pitch axis control torque gain, pitch axis control torque, pitch axis system term and external disturbance on the pitch axis control channel of the quadrotor in the body coordinate system;

[0029] 2.2 In the actual flight of the quadrotor, considering the error between the model parameters and the true values, the pitch axis system term f θ and the external disturbance d on the pitch axis control channel θ The sum of ′ is regarded as the lumped uncertainty Δ θ , that is, Δ θ =f θ +d θ ′, the lumped uncertainty Δ θ Divided into periodic uncertainty term f θr and the non-periodic uncertainty d θ , combined with formula (5), the system model is transformed into the following form:

[0030]

[0031] Among them, the non-periodic uncertainty term d θ =f θ -f θr +d θ ′;

[0032] 2.3 In actual flight, the pitch angle of a quadrotor is bounded, and the total uncertainty Δ θ and the lumped uncertain first-order derivative There is an upper bound, let D be Δ θ The upper limit value of L is The upper bound value of

[0033]

[0034] 2.4 The following observation error is defined:

[0035]

[0036] Among them, η1, η2 represent the observation error, z θ1 Represents state x θ2 The estimated value of z θ2 represents the non-periodic uncertainty term d θ An estimated value of

[0037] 2.5 For any constant scalar r and δ, define sig r The (δ) function is:

[0038] sig r (δ)=|δ r sign(δ) (8)

[0039] Among them, sign(·) represents the sign function;

[0040] 2.6 For the pitch axis attitude angle system model (6), the fixed time disturbance observer is designed as follows:

[0041]

[0042] in, are the estimated values ​​z θ1 ,z θ2 The first derivative of; k1>0, k2>0, 0.5<a<1, 1<b<1.5;

[0043] Step 3: Design the fixed time sliding mode variable. The process is as follows:

[0044] 3.1 Define the following attitude angle tracking error:

[0045] e1=x θ1 -x θr (10)

[0046] Among them, e1 represents the pitch axis attitude angle tracking error of the quadrotor aircraft, x θr Indicates the desired pitch-axis attitude angle of the quadrotor;

[0047] Derivation of formula (10) yields:

[0048]

[0049] in,

[0050] Represent e1,x respectively θr The first derivative of ;

[0051] 3.2 Design the following fixed time sliding mode variables:

[0052]

[0053] in,

[0054]

[0055] Where s represents the fixed time sliding mode variable, An odd number that is relatively prime to m2 and n2 respectively;

[0056] Step 4: Design a fully saturated repetitive learning law to compensate for the periodic term in the quadrotor system. The process is as follows:

[0057] Design a fully saturated repeated learning law as follows:

[0058]

[0059] in, f θr (t), The estimated value of Expressed as The value at time tT; μ0>0 is the repeated learning gain; the transition function φ(t) is expressed as:

[0060]

[0061] Saturation function and The expression is:

[0062]

[0063] in, for and The limit value of

[0064] Step 5: Design a fixed-time sliding mode repetitive learning controller.

[0065] Further, the process of step 5 is as follows:

[0066] 5.1 Taking the derivative of equation (12), we get:

[0067]

[0068] in,

[0069]

[0070] in, Respectively The derivative of

[0071] 5.2 Combining equations (9), (14) and (18), the fixed-time sliding mode controller is designed as:

[0072]

[0073] in, express The first-order derivative of , 0<b1<1,b2>1,β1,β2>0,k≥0.5;

[0074] 5.3 Choose the following Lyapunov function:

[0075]

[0076] Derivative of formula (21) yields:

[0077]

[0078] in, represents the first-order derivative of V1(t);

[0079] Substituting equation (18) and equation (20) into equation (22), we get That is, the system is judged to be stable.

[0080] The technical concept of the present invention is: for an uncertain quadrotor system, and the system performs periodic characteristic tasks, the present invention divides the lumped uncertainty in the system into two parts: periodic uncertainty and non-periodic uncertainty, designs a fixed-time disturbance observer, estimates the unknown state of the system and compensates for non-periodic uncertainty, thereby improving the system's anti-disturbance capability. In addition, a repetitive learning law is designed to estimate the system's periodic uncertainty and improve the system's control accuracy. The present invention proposes a method that can effectively suppress the influence of uncertainty on the attitude control accuracy of a quadrotor, while achieving the control of the quadrotor over the periodic desired attitude angle within a fixed time.

[0081] The effective effects of the present invention are as follows: realizing the control of the periodic desired attitude angle of the quadrotor aircraft within a fixed time, and improving the ability to quickly estimate and compensate for system uncertainty, making it less susceptible to the influence of the initial state. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a control flow chart of the present invention;

[0083] Figure 2 It is the pitch angle tracking effect;

[0084] Figure 3 is the pitch angle tracking error signal;

[0085] Figure 4 is the sliding mode variable signal;

[0086] Figure 5 is the control torque signal;

[0087] Figure 6 Estimating curves for repeated learning;

[0088] Figure 7 is the observation effect of the disturbance observer. DETAILED DESCRIPTION

[0089] The present invention will be further described below in conjunction with the accompanying drawings.

[0090] Reference Figure 1-Figure 7 A quadrotor attitude repetitive learning control method based on a fixed-time disturbance observer is proposed. While using the fully saturated repetitive learning law to solve the influence of periodic uncertainty on the tracking accuracy of the quadrotor, the proposed fixed-time disturbance observer can effectively estimate the non-periodic uncertainty in the system and make the convergence time less dependent on the initial state, thereby improving the system's anti-disturbance performance and the convergence speed of the system state, and realizing the precise control of the quadrotor to the periodic desired attitude angle within a fixed time.

[0091] The quadrotor aircraft attitude repeated learning control method comprises the following steps:

[0092] Step 1: Establish the dynamic model of the quadrotor system and initialize the state and control parameters of the system. The process is as follows:

[0093] 1.1 The dynamics of a quadrotor is expressed as:

[0094]

[0095] Among them, τ x ,τ y ,τ z They represent the control torque acting on the roll axis, pitch axis and yaw axis of the quadrotor in the body coordinate system respectively; I xx ,I yy ,I zz Respectively represent the moment of inertia of each axis of the quadrotor in the body coordinate system; ω x ,ω y ,ω z They respectively represent the angular velocity of each axis of the quadrotor in the body coordinate system; They are ω x ,ω y ,ω z The first-order derivative of represents the angular acceleration of each axis of the quadrotor in the body coordinate system; × represents the cross product; · represents the dot product;

[0096] 1.2 Through formula (1), the expression of the attitude angular acceleration of each axis of the quadrotor aircraft during motion is obtained as follows:

[0097]

[0098] 1.3 Define the following state variables:

[0099]

[0100] Among them, φ, θ, ψ are the roll axis attitude angle, pitch axis attitude angle and yaw axis attitude angle of the quadrotor aircraft in the body coordinate system respectively; x1 represents the attitude angle state quantity, and x2 represents the attitude angular velocity state quantity;

[0101] 1.4 Further considering the external interference to the system in the actual environment, combining equations (2)-(3), the following state equation is constructed:

[0102]

[0103] in,

[0104] Represent the first-order derivatives of x1 and x2 respectively; represents the control torque;

[0105]

[0106] Among them, d x ,d y ,d z They represent the external disturbances acting on the control channels of each axis of the quadrotor in the body coordinate system respectively;

[0107] Step 2: Design a fixed-time disturbance observer for the pitch axis of the quadrotor aircraft. The process is as follows:

[0108] 2.1 Combined with formula (4), the following quadrotor pitch axis attitude angle system model is obtained:

[0109]

[0110] Among them, x θ1 ,x θ2 They represent the pitch-axis attitude angle and pitch-axis attitude angular velocity of the quadrotor in the body coordinate system, x θ1 ,x θ2 The first derivative of ; They are respectively the pitch axis control torque gain, pitch axis control torque, pitch axis system term and external disturbance on the pitch axis control channel of the quadrotor in the body coordinate system;

[0111] 2.2 In the actual flight of the quadrotor, considering the error between the model parameters and the true values, the pitch axis system term f θand the external disturbance d on the pitch axis control channel θ The sum of ′ is regarded as the lumped uncertainty Δ θ , that is, Δ θ =f θ +d θ ′, the lumped uncertainty Δ θ Divided into periodic uncertainty term f θr and the non-periodic uncertainty d θ , combined with formula (5), the system model is transformed into the following form:

[0112]

[0113] Among them, the non-periodic uncertainty term d θ =f θ -f θr +d θ ′;

[0114] 2.3 In actual flight, the pitch angle of a quadrotor is bounded, and the total uncertainty Δ θ and the lumped uncertain first-order derivative There is an upper bound, let D be Δ θ The upper limit value of L is The upper bound value of

[0115]

[0116] 2.4 The following observation error is defined:

[0117]

[0118] Among them, η1, η2 represent the observation error, z θ1 Represents state x θ2 The estimated value of z θ2 represents the non-periodic uncertainty term d θ An estimated value of

[0119] 2.5 For any constant scalar r and δ, define sig r The (δ) function is:

[0120] sig r (δ)=|δ r sign(δ) (30)

[0121] Among them, sign(·) represents the sign function;

[0122] 2.6 For the pitch axis attitude angle system model (6), the fixed time disturbance observer is designed as follows:

[0123]

[0124] in, are the estimated values ​​z θ1 ,z θ2 The first derivative of; k1>0, k2>0, 0.5<a<1, 1<b<1.5;

[0125] Step 3: Design the fixed time sliding mode variable. The process is as follows:

[0126] 3.1 Define the following attitude angle tracking error:

[0127] e1=x θ1 -x θr (32)

[0128] Among them, e1 represents the pitch axis attitude angle tracking error of the quadrotor aircraft, x θr Indicates the desired pitch-axis attitude angle of the quadrotor;

[0129] Derivation of formula (10) yields:

[0130]

[0131] in, Represent e1,x respectively θr The first derivative of ;

[0132] 3.2 Design the following fixed time sliding mode variables:

[0133]

[0134] in,

[0135]

[0136] Where s represents the fixed time sliding mode variable, An odd number that is relatively prime to m2 and n2 respectively;

[0137] Step 4, design a fully saturated repetitive learning law to compensate for the periodic term in the quadrotor system, that is, design a fully saturated repetitive learning law, as follows:

[0138]

[0139] in, They are The estimated value of Expressed as The value at time tT; μ0>0 is the repeated learning gain; the transition function φ(t) is expressed as:

[0140]

[0141] Saturation function and The expression is:

[0142]

[0143] in, for and The limit value of

[0144] Step 5: Design a fixed-time sliding mode repetitive learning controller. The process is as follows:

[0145] 5.1 Taking the derivative of equation (12), we get:

[0146]

[0147] in,

[0148]

[0149] in, Respectively The derivative of

[0150] 5.2 Combining equations (9), (14) and (18), the fixed-time sliding mode controller is designed as:

[0151]

[0152] in, express The first-order derivative of , 0<b1<1,b2>1,β1,β2>0,k≥0.5;

[0153] 5.3 Choose the following Lyapunov function:

[0154]

[0155] Derivative of formula (21) yields:

[0156]

[0157] in, represents the first-order derivative of V1(t);

[0158] Substituting equation (18) and equation (20) into equation (22), we get That is, the system is judged to be stable.

[0159] To verify the effectiveness of the proposed method, the present invention conducts a simulation experiment on the control effect shown in formula (20). The initial conditions and control parameters in the experiment are set as follows: the sampling step is 0.001s; the system parameters are set as I xx=0.0552,I yy =0.0551,I zz =0.0555; the disturbance observer parameters are set to a=0.565, k1=30, k2=30, b=1.3; the controller parameters are set to λ1=11 / 13, λ2=7 / 9, c1=5, c2=1, z=0.5, ε=0.0001, b1=11 / 13, b2=9 / 7, β1=4, β2=4, k=1, μ0=10, The desired attitude angle is given as x φr =10sin(0.2πt),x θr =10sin(0.2πt),x ψr =10sin(0.2πt); the non-periodic uncertainty term of the system is set to d=0.01rand; the initial state of the disturbance observer is set to (z φ1 ,z θ1 ,z ψ1 ,z φ2 ,z θ2 ,z ψ2 )=(1,1,1,1,1,1); the initial state of the system is (x φ1 ,x θ1 ,x ψ1 ,x φ2 ,x θ2 ,x ψ2 )=(2,2,2,0,0,0).

[0160] Figure 2-Figure 7 This is a simulation result diagram of the proposed fixed-time disturbance observer-based quadrotor attitude repeated learning control on system (6). Figure 2 This is the pitch angle tracking effect diagram. It can be seen from the figure that the pitch angle tracks the expected signal in about 2s, and then maintains a good match with the expected pitch angle signal; Figure 3 is the pitch angle tracking error signal. It can be seen from the figure that the pitch angle tracking error converges to near 0 in about 2s, and the steady-state error converges to ±2×10 -3 rad within the bounds; Figure 4 It is the sliding mode variable signal. It can be seen from the figure that the sliding mode variable converges to near 0 in about 1s; Figure 5 It is the control torque signal. It can be seen from the figure that the control signal is periodic and relatively smooth. Figure 6 is the repeated learning estimation curve. It can be seen from the figure that the designed repeated learning law can achieve accurate estimation of the system periodic term; Figure 7It is the observation effect of the disturbance observer. It can be seen from the figure that the disturbance observer can estimate the disturbance and system state very well. In summary, the quadrotor attitude repeated learning control method based on the fixed-time disturbance observer can effectively realize the fixed-time tracking of the quadrotor attitude angle, suppress the influence of uncertainty on the quadrotor attitude control accuracy, and realize accurate estimation of the system state and accurate tracking of the periodic expected attitude angle.

[0161] The above description is that the simulation experiment given by the present invention shows the superiority of the designed method. Obviously, the present invention is not limited to the above examples. It can be implemented in various ways without departing from the basic spirit of the present invention and not exceeding the scope of the essential content of the present invention. The control method designed by the present invention has a good control effect on the tracking of the periodic desired attitude angle of the quadrotor with system uncertainty, can reduce the influence of the initial state on the rapidity of system uncertainty estimation and compensation, and effectively improve the control accuracy and rapidity of the quadrotor.

Claims

1. A method for repeated attitude learning control of a quadrotor aircraft based on a fixed-time disturbance observer, characterized in that the method comprises the following steps: Step 1: Establish the dynamic model of the quadrotor system and initialize the state and control parameters of the system. The process is as follows: 1.1 The dynamics of a quadrotor is expressed as: Among them, τ x ,τ y ,τ z They represent the control torque acting on the roll axis, pitch axis and yaw axis of the quadrotor in the body coordinate system respectively; I xx ,I yy ,I zz Respectively represent the moment of inertia of each axis of the quadrotor in the body coordinate system; ω x ,ω y ,ω z They respectively represent the angular velocity of each axis of the quadrotor in the body coordinate system; They are ω x ,ω y ,ω z The first-order derivative of represents the angular acceleration of each axis of the quadrotor in the body coordinate system; × represents the cross product; · represents the dot product; 1.2 Through formula (1), the expression of the attitude angular acceleration of each axis of the quadrotor aircraft during motion is obtained as follows: 1.3 Define the following state variables: in, φ, θ, ψ are the roll axis attitude angle, pitch axis attitude angle and yaw axis attitude angle of the quadrotor aircraft in the body coordinate system respectively; x1 represents the attitude angle state quantity, and x2 represents the attitude angular velocity state quantity; 1.4 Further considering the external interference to the system in the actual environment, combining equations (2)-(3), the following state equation is constructed: in, Represent the first-order derivatives of x1 and x2 respectively; represents the control torque; Among them, d x ,d y ,d z They represent the external disturbances acting on the control channels of each axis of the quadrotor in the body coordinate system respectively; Step 2: Design a fixed-time disturbance observer for the pitch axis of the quadrotor aircraft. The process is as follows: 2.1 Combined with formula (4), the following quadrotor pitch axis attitude angle system model is obtained: in, x θ1 ,x θ2 They represent the pitch-axis attitude angle and pitch-axis attitude angular velocity of the quadrotor in the body coordinate system, x θ1 ,x θ2 The first derivative of ; u θ =τ y , They are respectively the pitch axis control torque gain, pitch axis control torque, pitch axis system term and external disturbance on the pitch axis control channel of the quadrotor in the body coordinate system; 2.2 In the actual flight of the quadrotor, considering the error between the model parameters and the true values, the pitch axis system term f θ and the external disturbance d on the pitch axis control channel θ The sum of ′ is regarded as the lumped uncertainty Δ θ , that is, Δ θ =f θ +d θ ′, the lumped uncertainty Δ θ Divided into periodic uncertainty term f θr and the non-periodic uncertainty d θ , combined with formula (5), the system model is transformed into the following form: Among them, the non-periodic uncertainty term d θ =f θ -f θr +d θ ′; 2.3 In actual flight, the pitch angle of a quadrotor is bounded, and the total uncertainty Δ θ and the lumped uncertain first-order derivative There is an upper bound, let D be Δ θ The upper limit value of L is The upper bound value of 2.4 The following observation errors are defined: in, η1,η2 represent the observation error, z θ1 Represents state x θ2 The estimated value of z θ2 represents the non-periodic uncertainty term d θ An estimated value of 2.5 For any constant scalar r and δ, define sig r The (δ) function is: sig r (d)=|d r sign(δ)(8) Among them, sign(·) represents the sign function; 2.6 For the pitch axis attitude angle system model (6), the fixed time disturbance observer is designed as follows: in, are the estimated values ​​z θ1 ,z θ2 The first derivative of; k1>0, k2>0, 0.5<a<1, 1<b<1.5; Step 3: Design the fixed time sliding mode variable. The process is as follows: 3.1 Define the following attitude angle tracking error: e1=x θ1 -x θr (10) Among them, e1 represents the pitch axis attitude angle tracking error of the quadrotor aircraft, x θr Indicates the desired pitch-axis attitude angle of the quadrotor; Derivation of formula (10) yields: in, Represent e1,x respectively θr The first derivative of ; 3.2 Design the following fixed time sliding mode variables: in, Where s represents a fixed time sliding mode variable, c1, c2>0, ε>0, m1,n1 and m2,n2 are respectively coprime odd numbers; z>0; Step 4, design a fully saturated repetitive learning law to compensate for the periodic term in the quadrotor system, that is, design a fully saturated repetitive learning law, as follows: in, f θr (t), The estimated value of Expressed as The value at time tT; μ0>0 is the repeated learning gain; the transition function φ(t) is expressed as: Saturation function and The expression is: in, for and The limit value of Step 5: Design a fixed-time sliding mode repetitive learning controller.

2. The method for repeated attitude learning control of a quadrotor aircraft based on a fixed-time disturbance observer according to claim 1, characterized in that: The process of step 5 is as follows: 5.1 Taking the derivative of equation (12), we get: in, in, They represent α(e1), s, The derivative of 5.2 Combining equations (9), (14) and (18), the fixed-time sliding mode controller is designed as: in, express The first-order derivative of , 0<b1<1,b2>1,β1,β2>0,k≥0.5; 5.3 Choose the following Lyapunov function: Derivative of formula (21) yields: in, represents the first-order derivative of V1(t); Substituting equation (18) and equation (20) into equation (22), we get That is, the system is judged to be stable.

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