Four-rotor aircraft anti-interference backstepping control method based on feedback reference model

Abstract

The invention discloses a four-rotor aircraft anti-interference backstepping control method based on a feedback reference model. The four-rotor aircraft anti-interference backstepping control method comprises the following steps: constructing a four-rotor aircraft dynamics model; a flight control system of the four-rotor aircraft is decomposed into a horizontal position control subsystem and a height and attitude control subsystem; basic backstepping controllers are designed for the two subsystems, feedback reference models corresponding to the two subsystems are obtained, actual state variables are input into the two subsystems and the feedback reference models corresponding to the two subsystems, and generalized state errors corresponding to the two subsystems are obtained; based on the two generalized state errors and a backstepping control mode, anti-interference backstepping controllers based on feedback reference models and corresponding to the two subsystems are designed through the Lyapunov stability theory, anti-interference control over the four-rotor aircraft is achieved, and stable flight is ensured. The controller designed by the method is simple in structure and few in variable; the external airflow interference can be effectively suppressed, and the method has good robustness for load uncertainty.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft control, and more specifically to an anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model. Background Art

[0002] In recent years, many universities and research institutions around the world have been researching unmanned aerial vehicles (UAVs). Compared with fixed-wing UAVs, rotary-wing UAVs have the advantages of vertical take-off and landing and hovering. This allows rotary-wing UAVs to break free from the constraints of the site when taking off and landing. The hovering feature also gives rotary-wing UAVs an advantage that fixed-wing UAVs cannot replace in the fields of surveying and mapping, aerial photography, etc.

[0003] The rotor is further divided into tilt rotor and fixed rotor. Tilt rotor has become a new development direction and is widely used in the field of fault-tolerant control. The present invention does not study tilt rotors and will not be introduced here. All quadrotors mentioned below are fixed quadrotors. The structure of the quadrotor is symmetrical and the angle of attack of the propeller is fixed. By changing the speed of the four propellers to change the lift and torque, the attitude and position of the quadrotor are changed, and various flight states such as fixed-point hovering, vertical lifting and lowering, and pitch deflection are achieved.

[0004] Although quadrotors have many advantages, there are also inevitable problems. The nonlinearity and complexity of quadrotor systems make control design more difficult. A quadrotor has 6 degrees of freedom, but only 4 independent control source inputs. It is a typical underactuated system. In addition, in actual flight, it is susceptible to internal model parameter uncertainties and external airflow (such as ground proximity effect, blade fluctuations, gusts, etc.). Due to the strong coupling, underactuation and susceptibility to interference of quadrotors, the design of the controller is more complicated. Therefore, designing an anti-interference controller to ensure the stable flight of a quadrotor has become a hot issue and a key issue in the study of quadrotor control systems.

[0005] Many scholars at home and abroad have conducted extensive research on the control of quadrotors. The deviation-based PID controller is the most classic control method that can achieve the control of quadrotors. However, its ability to suppress interference is weak and its robustness is not strong. In the related art, the control system of the quadrotor is decomposed into a horizontal position control subsystem and an altitude and attitude control subsystem. MRAC is added to the horizontal position control subsystem to solve the problem that the horizontal position cannot be stabilized when disturbed. However, the altitude and attitude control subsystem still cannot guarantee strong anti-interference ability.

[0006] Existing literature has designed an attitude adaptive controller based on PID, and the height subsystem controller is designed separately, which increases the complexity of the control system. There is also a sliding mode controller based on disturbance observer, and the simulation results verify the effectiveness of the control algorithm. There is also a literature that designs a trajectory tracking method using the backstepping control method, which enables the quadcopter to accurately track the set trajectory. However, the above literature does not analyze the impact of interference on the quadcopter, which needs further research.

[0007] In summary, existing quadrotor control methods mainly include PID control, adaptive control and sliding mode control, etc. These control methods have the above-mentioned defects in practical applications, and those skilled in the art are in urgent need of solving them. Summary of the invention

[0008] In view of this, the present invention provides a method for anti-interference backstepping control of a quadrotor aircraft based on a feedback reference model. First, the flight control system of the quadrotor aircraft is decomposed into a horizontal position control subsystem and an altitude and attitude control subsystem. Since the attitude angle change of the quadrotor aircraft directly affects its position and speed, on the basis of designing the backstepping controllers of the inner and outer loop control subsystems, feedback reference models are added to the subsystems respectively. This not only eliminates the influence of the attitude angle on the horizontal position, but also realizes the suppression of the horizontal position interference. This structure also solves the problem of needing to design the altitude subsystem controller separately.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model provided by the present invention comprises the following steps:

[0011] S1. Construct a dynamic model of a quadrotor aircraft; decompose the flight control system of the quadrotor aircraft into a horizontal position control subsystem and an altitude and attitude control subsystem;

[0012] S2. Design basic backstepping controllers for the horizontal position control subsystem and the height and attitude control subsystem respectively, and obtain the feedback reference models corresponding to the two subsystems;

[0013] S3, inputting the actual state variables into the two subsystems and their corresponding feedback reference models respectively, and obtaining the generalized state errors corresponding to the two subsystems; the generalized state error is the difference between the feedback reference model output and the actual system output;

[0014] S4. Based on two generalized state errors and backstepping control methods, Lyapunov stability theory is used to design anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems respectively. Based on the anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems, anti-interference control of the quadrotor is realized to ensure stable flight.

[0015] It can be seen from the above technical solution that compared with the prior art, the present invention has the following advantages:

[0016] 1. Improve anti-interference ability:

[0017] The present invention introduces a feedback reference model, which can effectively suppress the influence of external airflow disturbance and internal parameter uncertainty on the aircraft. By inputting the actual state variables of the system into the feedback reference model and using the error between the two to design the controller, the system is made more robust to disturbance.

[0018] 2. Simple structure and few variables:

[0019] Compared with other anti-interference control methods, this scheme has a simple structure and involves fewer variables in the controller design process, which helps to reduce the computational complexity of the controller and improve the real-time performance of the controller.

[0020] 3. Double guarantee of position stability:

[0021] The horizontal position control subsystem indirectly controls the attitude angle and ensures the stability of the horizontal position by continuously adjusting the attitude angle. The height and attitude control subsystem directly controls the height and attitude, providing double protection for position stability. This enables the quadrotor to track the command signal more stably.

[0022] 4. Strong robustness:

[0023] The present invention has good robustness to internal parameter uncertainties such as load changes. Simulation results show that when the load changes, the technical solution of the present invention can still ensure the stable flight of the aircraft.

[0024] 5. Excellent control effect:

[0025] The simulation results show that compared with the backstepping control and the backstepping controller based on the independent reference model, the control effect of the technical solution of the present invention is better. The aircraft can reach the target position faster and maintain a stable flight state.

[0026] In summary, the present invention effectively improves the stability and anti-interference ability of the quadrotor in an interference environment by introducing a feedback reference model, and has the advantages of simple structure, few variables, and strong robustness, providing a new idea and method for the control of the quadrotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0028] Figure 1 A flow chart of the anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model provided by the present invention.

[0029] Figure 2 Schematic diagram of dynamic analysis of the quadrotor aircraft provided by the present invention.

[0030] Figure 3 This is a principle block diagram of the position control of the quadrotor aircraft provided by the present invention.

[0031] Figure 4 This is a block diagram of the X-axis backstepping control principle based on the feedback reference model provided by the present invention.

[0032] Figure 5 This is a schematic diagram of the structure of the quadrotor aircraft provided by the present invention.

[0033] Figure 6a This is a left-right fixed-point flight position response diagram of the quadrotor aircraft provided by the present invention.

[0034] Figure 6b This is a fixed-point flight position response diagram of the quadrotor aircraft moving forward and backward provided by the present invention.

[0035] Figure 6c This is a fixed-point flight position response diagram of the quadrotor aircraft provided by the present invention.

[0036] Figure 7a The present invention provides a quadrotor aircraft pitch motion fixed-point flight attitude angle response diagram.

[0037] Figure 7b The present invention provides a quadrotor aircraft rolling motion fixed-point flight attitude angle response diagram.

[0038] Figure 7c The present invention provides a quadrotor aircraft yaw motion fixed-point flight attitude angle response diagram.

[0039] Figure 8a This is a control input response diagram of the quadcopter U1 provided by the present invention.

[0040] Figure 8b This is the control input response diagram of the quadcopter U2 provided by the present invention.

[0041] Figure 8c This is a control input response diagram of the quadcopter U3 provided by the present invention.

[0042] Figure 8d This is a control input response diagram of the quadcopter U4 provided by the present invention.

[0043] Figure 9a An IAE schematic diagram of the left-right movement of the quadrotor aircraft provided by the present invention.

[0044] Figure 9b An IAE schematic diagram of the forward and backward motion of the quadrotor provided by the present invention.

[0045] Fig.9c An IAE schematic diagram of the up and down movement of the quadrotor aircraft provided by the present invention.

[0046] Figure 9d An IAE schematic diagram of the yaw motion of the quadrotor aircraft provided by the present invention.

[0047] Fig.10 The height response diagram of the quadrotor aircraft when the load changes provided by the present invention.

[0048] Fig.11 A control input U1 response diagram of the quadrotor aircraft when the load changes provided by the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] The embodiment of the present invention discloses a quadrotor aircraft anti-interference backstepping control method based on a feedback reference model, referring to Figure 1 As shown, the following steps are included:

[0051] S1. Construct a dynamic model of a quadrotor aircraft; decompose the flight control system of the quadrotor aircraft into a horizontal position control subsystem and an altitude and attitude control subsystem;

[0052] S2. Design basic backstepping controllers for the horizontal position control subsystem and the height and attitude control subsystem respectively, and obtain the feedback reference models corresponding to the two subsystems;

[0053] S3, inputting the actual state variables into the two subsystems and their corresponding feedback reference models respectively, and obtaining the generalized state errors corresponding to the two subsystems; the generalized state error is the difference between the feedback reference model output and the actual system output;

[0054] S4. Based on two generalized state errors and backstepping control methods, Lyapunov stability theory is used to design anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems respectively. Based on the anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems, anti-interference control of the quadrotor is realized to ensure stable flight.

[0055] Firstly, the dynamic model of the quadrotor is constructed, and the flight control system of the quadrotor is decomposed into the horizontal position control subsystem and the height and attitude control subsystem. The basic backstepping controllers of the two subsystems are designed respectively, and the feedback reference models corresponding to the two subsystems are obtained. The actual state variables are input into the feedback reference model. When the subsystem is disturbed, the change of the feedback reference model output is opposite to the actual output. This error is the key link in generating control variables. The difference between the feedback reference model output and the actual output of the system is defined as the generalized state error. Then, based on the generalized state error and the backstepping control method, the controller is designed using the Lyapunov stability theory. Finally, the backstepping anti-interference controller based on the feedback reference model is obtained. Compared with other anti-interference control methods, this control method has the advantages of simple structure and few variables. Due to the combined effect of improving the anti-interference performance in each subsystem, the position stability of the quadrotor is achieved.

[0056] The technical solution of the present invention is described in detail below:

[0057] 1. Quadrotor dynamics model

[0058] 1.1 Control Principle

[0059] A quadcopter is equipped with four rotors (see Figure 2 The lift force F of each rotor is i With its speed ω i is proportional to the square of, that is,

[0060]

[0061] Where b is the lift coefficient, ω i is the rotor speed, i is the index value of the rotor, i∈[1,4]. When the rotor rotates, the fuselage will be subjected to the reverse torque generated by the rotor. The magnitude of the reverse torque is:

[0062]

[0063] Where d is the counter torque coefficient.

[0064] In order to avoid the overturning moment, F1 = F3, F2 = F4 must be satisfied. In order to offset the reverse torque generated by each rotor, M must exist. D1 +M D3 =M D2 +M D4 When adjusting the speed of the four rotors, the quadrotor will undergo vertical motion, pitch motion, roll motion, and yaw motion.

[0065] 1.2 Coordinate system definition and direction cosine matrix

[0066] The body coordinate system B and the ground inertial coordinate system Z are defined, and the position and attitude of the quadrotor in space are determined.

[0067] The transformation relationship from the body coordinate system to the ground inertial coordinate system is expressed by the Euler angle:

[0068]

[0069] Among them, γ is the roll angle, θ is the pitch angle, is the yaw angle, C is the abbreviation of cos, S is the abbreviation of sin; the same applies to the following.

[0070] 1.3 Kinetic equation

[0071] Since a quadrotor is a complex dynamic system, it needs to be simplified.

[0072] 1). Consider the quadrotor as a uniform and symmetrical rigid body;

[0073] 2). The mass center coincides with the origin of the body coordinate system;

[0074] 3). The ground coordinate system is an inertial coordinate system that regards the surface of the earth as a plane;

[0075] 4). Ignore the gyroscopic effect caused by the rotation of the rotor.

[0076] Determine the control volume of the quadrotor:

[0077]

[0078] Among them, U1 is the up and down motion control amount, U2 is the front and back motion control amount, U3 is the left and right motion control amount, and U4 is the yaw motion control amount.

[0079] The dynamic model of the quadrotor in the ground coordinate system Z is:

[0080]

[0081] in, and is the acceleration of the quadrotor along the X-axis, Y-axis and Z-axis; and is the acceleration of the quadrotor’s pitch, roll, and yaw angles; and are the angular velocities of pitch, roll and yaw respectively; m is the mass of the quadrotor; g is the gravitational acceleration; j x ,j y and j z is the moment of inertia of the quadrotor along the X-axis, Y-axis and Z-axis; l is the length of the rotation axis.

[0082] 2. Design of anti-interference backstepping control system for quadrotor aircraft based on feedback reference model

[0083] The flight control system of the quadrotor aircraft is decomposed into inner and outer control subsystems (see Figure 3 As shown in Figure 1.1, the inner loop is the altitude and attitude control subsystem, and the outer loop is the horizontal position control subsystem. Backstepping controllers based on feedback reference models are designed for the two subsystems respectively. The horizontal motion of the quadrotor is achieved by changing its pitch angle θ and roll angle γ. The pitch angle θ and roll angle γ become intermediate variables for controlling the horizontal position. In this way, four independent control inputs ensure the stability of the four degrees of freedom of the quadrotor, namely the X-axis, Y-axis, Z-axis and yaw angle. Figure 3 The "expected trajectory" in is the expected 3D position and yaw angle.

[0084] 2.1 Design of backstepping controller for the horizontal position subsystem of quadrotor aircraft based on feedback reference model

[0085] The dynamic equation of the horizontal position subsystem of the quadrotor aircraft is:

[0086]

[0087] Let the two virtual inputs be:

[0088]

[0089] Among them, U x is the virtual control value of X axis, U y It is the virtual control value of Y axis;

[0090] Substituting equation (5) into equation (4) simplifies it to:

[0091]

[0092] Formula (6) is the dynamic equation for redefining the horizontal position control subsystem.

[0093] The following takes the X-axis as an example to derive the backstepping controller based on the feedback reference model as follows.

[0094] 2.1.1 Feedback reference model of X axis

[0095] The first step is to define the error variable for the X-axis:

[0096] e1=x d -x (7)

[0097] x d is the expected horizontal position, x is the actual horizontal position, and e1 represents the horizontal position error;

[0098] Take the derivative of e1:

[0099]

[0100] In the formula, is the virtual error variable, a1 is the virtual control variable;

[0101] Construct the Lyapunov function:

[0102]

[0103] Deriving it:

[0104]

[0105] Only when When the X axis converges stably, the virtual control amount will appear:

[0106] a1=-c1e1 (11)

[0107] Where c1 is the positive control gain; c i (i=1,2…16)>0 is the control gain;

[0108]

[0109] The second step is to extract the virtual error variable e2

[0110]

[0111] Construct the Lyapunov function:

[0112]

[0113] Take its derivative:

[0114]

[0115] To ensure the stable convergence of the designed X-axis, that is: The following relationship is satisfied:

[0116]

[0117] The corrected control rules are obtained as follows:

[0118]

[0119] Among them, U xb is the corrected control quantity of the X-axis; to obtain the feedback reference model.

[0120] The feedback reference model of the X-axis is derived from the backstepping controller and the mathematical model of the X-axis. In other words, the designed controller U xb Substitute into the mathematical model of the X-axis. The feedback reference model of the system is:

[0121]

[0122] in, is the acceleration of the quadrotor along the X-axis.

[0123] Note that the actual state variables of the system are input into the reference model, rather than the state variables of the reference model. When the X-axis is disturbed, the change in the feedback reference model output is opposite to the actual output. This error is the key link in generating the control variable.

[0124] 2.1.2 Design of the backstepping controller based on the feedback reference model of the X-axis

[0125] The block diagram of X-axis backstepping control based on feedback reference model is as follows Figure 4 shown. Figure 3 The control principle of the X-axis and Y-axis in the horizontal position backstepping controller based on the feedback reference model is as follows: Figure 4 As shown. Similarly, Figure 3 The control principle of the Z axis, pitch direction, roll direction and yaw direction in the height and attitude backstepping controller based on the feedback reference model is also as follows Figure 4 shown.

[0126] The first step is to define the generalized state error of the X-axis

[0127] e m1 =xx m (20)

[0128] Among them, x m is the position of the feedback reference model in the X-axis; x is the actual horizontal position.

[0129] Take e m1 Derivatives:

[0130]

[0131] in, is the dummy error variable; a m2 is the virtual control quantity;

[0132] Construct the Lyapunov function:

[0133]

[0134] Deriving it:

[0135]

[0136] Only when When the x channel converges stably, the virtual control amount will appear:

[0137] a m2 =-c3e m1 (twenty four)

[0138]

[0139] The second step is to use the virtual error variable e m2 Derivatives:

[0140]

[0141] Substitute the feedback reference model of the horizontal position control subsystem:

[0142]

[0143] Construct the Lyapunov function:

[0144]

[0145] Deriving it:

[0146]

[0147] In order to ensure the stable convergence of the designed X-axis, that is: The following relationship is satisfied:

[0148]

[0149] Backstepping anti-disturbance controller based on feedback reference model xp The controller of the X-axis is as follows:

[0150]

[0151] Among them, u xp is the backstepping anti-interference control rule of the feedback reference model in the X-axis direction; m To feedback the position of the reference model in the X-axis; is the speed of the feedback reference model in the X-axis; c1, c2, c3, c4 are control gains;

[0152] 2.1.3 Stability analysis of X axis

[0153] By combining equations (6), (19), and (32), we obtain:

[0154]

[0155] By simultaneously calculating equations (14), (26), (31), (32), and (33), we obtain:

[0156]

[0157] By combining equations (8), (11), (21), (24), and (31), we can obtain:

[0158]

[0159] The state space form of the state error equation is written as

[0160]

[0161] Choose appropriate controller parameters so that the system matrix

[0162]

[0163] For any x∈R 4 is Hurwitz, that is, all eigenvalues ​​are in the left half-open plane of the imaginary axis. According to the Hurwitz stability criterion, the X-channel anti-disturbance backstepping control system based on the feedback reference model is asymptotically stable.

[0164] same

[0165]

[0166] is the acceleration of the quadrotor in the Y-axis direction; (y d -y) is the position error in the Y-axis direction, that is, the expected position y d The difference between the actual position y and is the velocity error in the Y-axis direction, i.e. the expected velocity With actual speed The difference between is the desired acceleration in the Y-axis direction, which is determined by the acceleration of the desired trajectory.

[0167]

[0168] Among them, u yp is the backstepping anti-disturbance control rule based on the feedback reference model of the Y axis; m To feedback the position of the reference model in the Y axis; It is the velocity of the feedback reference model in the Y axis.

[0169] Finally, the expected values ​​of the pitch angle θ and the roll angle γ can be obtained through equation (5):

[0170]

[0171] 2.2 Design of backstepping controller for altitude and attitude subsystem of quadrotor aircraft based on feedback reference model:

[0172] Since the algorithm derivation is similar to that of the X-axis, only the derivation conclusions of the quadrotor height and attitude subsystem are given here.

[0173] 2.2.1 Feedback reference model of quadrotor altitude and attitude subsystem

[0174]

[0175] In the formula, are the accelerations of the Z axis, pitch angle, roll angle, and yaw angle respectively; d ,θ d , γ d , are the expected values ​​of the Z axis, pitch angle, roll angle, and yaw angle respectively; z, θ, γ, They are the actual values ​​of the Z axis, pitch angle, roll angle, and yaw angle respectively; are the desired velocities for the Z axis, pitch angle, roll angle, and yaw angle, respectively; They are the actual speeds of the Z axis, pitch angle, roll angle, and yaw angle respectively; are the expected accelerations of the Z axis, pitch angle, roll angle, and yaw angle respectively; c5~c 10 To control the gain.

[0176] 2.2.2 Backstepping controller of quadrotor altitude and attitude subsystem based on feedback reference model:

[0177]

[0178] Among them, U 1p , I 2p , U 3p , U4p are the control inputs in the Z-axis, pitch angle, roll angle and yaw angle directions respectively; (z d -z) is the position error in the Y-axis direction, i.e. the expected position z d The difference between the actual position z and is the expected speed error in the Y-axis direction, that is, the expected speed With actual speed The difference between is the desired acceleration in the Y direction; z m To feedback the position of the reference model in the Y axis; To feedback the speed of the reference model in the Y axis;

[0179] θ m is the pitch angle of the feedback reference model; is the expected angular velocity in the pitch direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the pitch angle;

[0180] γ m is the roll angle of the feedback reference model; is the expected angular velocity in the rolling direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the roll angle;

[0181] is the yaw angle of the feedback reference model; is the expected angular velocity in the yaw direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the yaw angle; c 11 ~c 16 To control the gain

[0182] 3. Simulation and analysis

[0183] In order to verify the effectiveness of the proposed method when applied to a quadrotor aircraft, the present invention simulated Figure 5 The specific parameters of the quadrotor aircraft in MATLAB / Simulink simulation were established, and the specific parameters are shown in Table 1.

[0184] Table 1 Specific parameters of the quadrotor

[0185] parameter Numeric unit m 2.2450 kg l <![CDATA[3.8750×10 -1 ]]> m <![CDATA[j x ]]> <![CDATA[5.5887×10 -2 ]]> <![CDATA[N / m 2 ]]> <![CDATA[j y ]]> <![CDATA[5.5887×10 -2 ]]> <![CDATA[N / m 2 ]]> <![CDATA[j z ]]> <![CDATA[1.3151×10 -1 ]]> <![CDATA[N / m 2 ]]> g 9.8 <![CDATA[m / s 2 ]]>

[0186] The initial position of the quadrotor is set to [0 0 0]m, the initial velocity is set to [0.5 0.5 0]m / s, the initial attitude angle is set to [0.15 0.15 0.15]rad, the initial angular velocity is set to [0 0 0]rad / s, the target position is set to [1 1 1]m, and the target yaw angle is set to 0rad. The adjustable gain parameters of the backstepping controller are set to c1=c2=2, c3=c4=4, c5=c6=c9=c 10 =6, c7=c8=c 11 =c 12 =c 15 =c 16 =24, c 13 =c 14 =48.

[0187] 3.1 Control effect of quadrotor under external airflow interference

[0188] The simulated quadrotor is subject to uncertain external airflow disturbances, and the external disturbances are set as:

[0189]

[0190] The simulation results are as follows Figure 6a , Figure 6b , Figure 6c and Figure 7a , Figure 7b , Figure 7cAs shown, it can be seen that under the same disturbance, when the quadrotor is controlled by a backstepping controller, its position and attitude are greatly affected by the disturbance and cannot track the command signal progressively. When the quadrotor is controlled by an independent reference model-based backstepping controller, its position and attitude have better robustness to disturbance. When the quadrotor is controlled by a feedback reference model-based backstepping controller, the controller has the best performance. It has a good suppression effect on uncertain disturbances. The quadrotor reaches the target position in the second second after the start of the simulation, and its position basically reaches a steady state. In the horizontal position X-axis and Y-axis, compared with the backstepping controller and the backstepping controller based on the independent reference model, the backstepping controller based on the feedback reference model can effectively suppress the influence of the disturbance on the horizontal position of the quadrotor. In the height Z axis, when the quadrotor is controlled by the backstepping controller, the height z produces an amplitude oscillation of about 0.1m. When the quadrotor is controlled by a backstepping controller based on a feedback reference model, the height z is basically asymptotically stabilized at the specified height of 1m. In the direction of pitch angle θ and roll angle γ, the backstepping controller has a good interference suppression effect. When the quadrotor is controlled by a backstepping controller based on a feedback reference model, the response angles of pitch angle θ and roll angle γ to the command are better than those of the backstepping controller and the backstepping controller based on an independent reference model. The system responds very quickly and stabilizes the horizontal position by adjusting the pitch angle θ and roll angle γ. At the yaw angle In terms of direction, the control effect of the backstepping controller based on the feedback reference model is greatly improved compared with the backstepping controller and the backstepping controller based on the independent reference model. The simulation results show that since the feedback reference model is added to the height and attitude subsystem, the backstepping controller based on the feedback reference model can ensure the stability of the height and attitude. On this basis, the anti-interference performance of the horizontal position subsystem can be greatly improved by applying the feedback reference model. Therefore, all six channels of the quadrotor have good anti-interference ability, which verifies the effectiveness of the proposed method.

[0191] from Figure 8a , Figure 8b , Figure 8c and Figure 8d It can be seen that the four independent control inputs all add control compensation to suppress disturbances.

[0192] A quadrotor has only four independent control inputs. When all six degrees of freedom are disturbed, only four degrees of freedom can be guaranteed to be stable. Therefore, the three-dimensional position and yaw angle of the quadrotor are selected as the stable control objects. Figure 9a , Figure 9b , Fig.9c and Figure 9d It can be seen that the system can be asymptotically stable only when the quadrotor is controlled by a backstepping controller based on a feedback reference model.

[0193] 3.2 Control effect of quadrotor when load changes

[0194] When the quadrotor is flying in fixed position for 5 seconds, the load is reduced by 30%, and the altitude response of the quadrotor is as follows: Fig.10 shown.

[0195] from Fig.10 It can be seen that when the load of the quadrotor is reduced by 30% at 5 seconds, the mass of the quadrotor suddenly decreases. When the quadrotor is controlled by the backstepping controller, its height deviates from the height command and rises by about 0.1m. When the quadrotor is controlled by the backstepping controller based on the feedback reference model and the backstepping controller based on the independent reference model, the height does not change and always stabilizes at the command height. The simulation results show that the backstepping controller based on the feedback reference model can effectively eliminate the influence of internal parameters such as the mass of the quadrotor on stable flight, and verify the effectiveness of the proposed method.

[0196] from Fig.11 It can be seen that the control quantity based on the feedback reference model backstepping control responds fastest. The new control method performs best.

[0197] from Fig.11 It can be seen that when the quadrotor is controlled by the feedback reference model backstepping controller, the quadrotor can stably track the command signal and fly to the target position with the best trajectory. It is stable whether it is flying or hovering at the target point. The simulation results show that the quadrotor can fly stably in an interference environment.

[0198] In order to make the quadcopter have higher flight performance, the present invention designs a backstepping controller based on the feedback reference model by analyzing the dynamic equations of the quadcopter. The horizontal position is indirectly controlled by the attitude angle, so the stability of the horizontal position is achieved by continuously adjusting the attitude angle. Therefore, on the basis of designing the backstepping controller of the inner and outer loop control subsystems, not only the feedback reference model of the subsystem is derived, but also the backstepping controller based on the feedback reference model is obtained. Finally, the position stability of the quadcopter is doubly protected, ensuring that the quadcopter can stably and smoothly track the command signal. The simulation results show that compared with the backstepping control and the backstepping controller based on the independent reference model, the backstepping controller based on the feedback reference model can effectively improve the stability and anti-interference performance of the system, and has certain theoretical research and practical application value.

[0199] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0200] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for anti-interference backstepping control of a quadrotor aircraft based on a feedback reference model, characterized in that: The following steps are involved: S1. Construct a dynamic model of a quadrotor aircraft; decompose the flight control system of the quadrotor aircraft into a horizontal position control subsystem and an altitude and attitude control subsystem; S2. Design basic backstepping controllers for the horizontal position control subsystem and the height and attitude control subsystem respectively, and obtain the feedback reference models corresponding to the two subsystems; S3, inputting the actual state variables into the two subsystems and their corresponding feedback reference models respectively, and obtaining the generalized state errors corresponding to the two subsystems; the generalized state error is the difference between the feedback reference model output and the actual system output; S4. Based on two generalized state errors and backstepping control methods, Lyapunov stability theory is used to design anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems respectively. Based on the anti-interference backstepping controllers based on feedback reference models corresponding to the two subsystems, anti-interference control of the quadrotor is realized to ensure stable flight.

2. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 1, characterized in that: In step S2, a basic backstepping controller is designed for the horizontal position control subsystem to obtain a corresponding feedback reference model, including: 1) Determine the dynamic equation of the horizontal position control subsystem, describe the acceleration of the quadrotor in the X-axis and Y-axis directions, and the up and down motion control quantity U1 and the virtual control quantity U x and U y Related: The dynamic equation is preliminarily defined as: Let the two virtual inputs be: Among them, U x is the virtual control value of X axis, U y It is the virtual control amount of Y axis; Substituting equation (5) into equation (4) simplifies it to: Formula (6) is the dynamic equation for redefining the horizontal position control subsystem; 2) According to the definition of X-axis virtual control quantity U x And the Y-axis virtual control amount U y , corresponding to the virtual control input of the X-axis and Y-axis respectively; 3) Based on the backstepping control method, design the control rules of the X-axis and Y-axis respectively to obtain the feedback reference model and in, is the acceleration of the quadrotor in the X-axis direction; (1+c1c2) is a coefficient determined by the virtual control gains c1 and c2 and used to adjust the tracking performance; (x d -x) is the position error in the X-axis direction, that is, the expected position x d The difference between the actual position x and the actual position x; (c1+c2) is also a coefficient, which is determined by the virtual control gains c1 and c2 and is used to adjust the tracking speed; is the speed error in the X-axis direction, that is, the expected speed With actual speed The difference between is the desired acceleration in the X-axis direction, which is determined by the acceleration of the desired trajectory; is the acceleration of the quadrotor in the Y-axis direction; (y d -y) is the position error in the Y-axis direction, that is, the expected position y d The difference between the actual position y and is the velocity error in the Y-axis direction, i.e. the expected velocity With actual speed The difference between is the desired acceleration in the Y-axis direction, which is determined by the acceleration of the desired trajectory.

3. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 2 is characterized in that: In step S3, the actual state variable is input into the horizontal position control subsystem and the corresponding feedback reference model to obtain the corresponding generalized state error, including: According to the feedback reference model and actual state variables of the horizontal position control subsystem, the generalized state errors in the X-axis and Y-axis directions are designed respectively; The output variable of the feedback reference model is subtracted from the actual state variable, and the difference is taken as the corresponding generalized state error.

4. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 3 is characterized in that: In step S4, based on the generalized state error and backstepping control mode of the horizontal position control subsystem, the Lyapunov stability theory is used to design an anti-interference backstepping controller based on a feedback reference model of the horizontal position control subsystem, including: 1) Design of X-axis direction: Take e m1 Derivatives: in, is the dummy error variable; a m2 is the virtual control quantity; Construct the lyapunov function: Deriving it: Only when When the X-axis direction converges stably, the virtual control amount will appear: a m2 =-c3e m1 (24) The virtual error variable e m2 Derivatives: Substitute the feedback reference model of the horizontal position control subsystem: Construct the Lyapunov function: Deriving it: In order to ensure stable convergence in the designed X-axis direction, that is: The following relationship is satisfied: Backstepping Anti-disturbance Controller U Based on Feedback Reference Model xp The control rules in the X-axis direction are as follows: Among them, u xp is the backstepping anti-interference control rule based on the feedback reference model in the X-axis direction; m To feedback the position of the reference model in the X-axis; is the speed of the feedback reference model in the X-axis; c1, c2, c3, c4 are control gains; 2) Design of Y-axis direction: Among them, u yp is the backstepping anti-disturbance control rule based on the feedback reference model of the Y axis; m To feedback the position of the reference model in the Y axis; It is the velocity of the feedback reference model in the Y axis.

5. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 2, characterized in that: In step S2, the feedback reference model of the altitude and attitude control subsystem is as follows: In the formula, are the accelerations of the Z axis, pitch angle, roll angle, and yaw angle respectively; d ,θ d , γ d , are the expected values ​​of the Z axis, pitch angle, roll angle, and yaw angle respectively; z, θ, γ, They are the actual values ​​of the Z axis, pitch angle, roll angle, and yaw angle respectively; are the desired velocities for the Z axis, pitch angle, roll angle, and yaw angle, respectively; They are the actual speeds of the Z axis, pitch angle, roll angle, and yaw angle respectively; are the expected accelerations of the Z axis, pitch angle, roll angle, and yaw angle respectively; c5~c 10 To control the gain.

6. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 5, characterized in that: In step S3, the actual state variable is input into the altitude and attitude control subsystem and the corresponding feedback reference model to obtain the corresponding generalized state error, including: According to the feedback reference model and actual state variables of the altitude and attitude control subsystem, the generalized state errors in the Z-axis, pitch angle, roll angle and yaw angle directions are designed respectively; The output variable of the feedback reference model is subtracted from the actual state variable, and the difference is taken as the corresponding generalized state error.

7. The anti-interference backstepping control method for a quadrotor aircraft based on a feedback reference model according to claim 6, characterized in that: In step S4, based on the generalized state error and backstepping control mode of the altitude and attitude control subsystem, the Lyapunov stability theory is used to design an anti-interference backstepping controller based on a feedback reference model for the altitude and attitude control subsystem, as follows: Among them, U 1p , U 2p , U 3p , U 4p are the control inputs in the Z-axis, pitch angle, roll angle and yaw angle directions respectively; (z d -z) is the position error in the Y-axis direction, i.e. the expected position z d The difference between the actual position z and is the expected speed error in the Y-axis direction, that is, the expected speed With actual speed The difference between is the desired acceleration in the Y direction; z m To feedback the position of the reference model in the Y axis; To feedback the speed of the reference model in the Y axis; θ m is the pitch angle of the feedback reference model; is the expected angular velocity in the pitch direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the pitch angle; γ m is the roll angle of the feedback reference model; is the expected angular velocity in the rolling direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the roll angle; is the yaw angle of the feedback reference model; is the expected angular velocity in the yaw direction of the feedback reference model; is the anti-torque compensation term, which is used to offset the effect of the anti-torque generated by the propeller rotation on the yaw angle; c 11 ~c 16 To control the gain.

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