An unmanned aerial vehicle anti-disturbance control method under a finite time state observer

Abstract

The application provides an unmanned aerial vehicle anti-disturbance control method based on a finite time state observer, a finite time state observer is designed in a double closed-loop control framework based on a self-disturbance control, errors and disturbances are estimated and eliminated in a finite time, and the anti-disturbance capacity of the system is increased. Meanwhile, a robust control rate is added in the outer loop, the transient performance of the system is improved, the system is prevented from appearing in a large overshoot and an actuator saturation, and the control performance of the system is comprehensively improved.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) technology, specifically relating to a UAV anti-disturbance control method under a finite-time state observer. Background Technology

[0002] Unmanned aerial vehicles (UAVs) were initially designed for military and intelligence reconnaissance missions. With technological advancements and cost reductions, they have been steadily applied in civilian fields such as logistics, transportation, traffic safety, photography, and environmental testing. Quadcopter UAVs are susceptible to interference, including gusts, unmodeled dynamics, parameter uncertainties, and time delays, as they are typical underactuated unstable systems. Therefore, ensuring strong robustness and high performance of attitude control remains an important research problem.

[0003] For quadrotor UAVs, there are many control techniques, including PID control, robust and adaptive control, post-control, sliding mode control, and MPC control. However, these methods rely too heavily on the accuracy of the model and are ineffective in controlling disturbances introduced by unknown models. In the late 1990s, Han Jinqing proposed the Extended State Observer (ESO) to simultaneously estimate the system's state and disturbances, and developed the Active Disturbance Suppression Control (ADRC) method, which improved the control performance of quadrotor UAVs while handling external disturbances and parameter uncertainties. However, these methods still struggle to guarantee settling time and cannot meet the needs of some systems requiring rapid response and stable control. Summary of the Invention

[0004] In view of this, the present invention provides a UAV anti-disturbance control method based on a finite-time state observer, which can increase the system's anti-disturbance capability and improve the system's transient performance.

[0005] A disturbance rejection control method for unmanned aerial vehicles (UAVs) based on a finite-time state observer includes:

[0006] Step 1: Represent the inertial reference coordinate system as E O = [x,y,z], represented in body coordinate system as E B =[x B ,y B ,z B Let Ξ = [φ, θ, ψ] represent the directions of the quadcopter UAV's body coordinate system relative to the inertial reference coordinate system, which are the roll angle, pitch angle, and yaw angle, respectively; the forces and moments acting on the UAV are as follows:

[0007]

[0008]

[0009] Where, ω=[ω x ,ωy ,ω z ] · It is the angular velocity of the UAV body on the three axes of the inertial reference coordinate system, I = diag{I xx ,I yy ,I zz τ is the moment of inertia of the body along the three axes of the inertial reference coordinate system; d =[τ dx ,τ dy ,τ dz ] · It is the sum of the unmodeled part and external disturbances such as wind disturbance; matrix W Ξ Defined as:

[0010]

[0011] The control matrix τ represents the torque produced by the motor, and is expressed as:

[0012]

[0013] Where, k t It is the thrust coefficient of the motor, k d Ω is the resistance coefficient of the motor. i It is the angular velocity of the i-th motor, where i = 1, 2, 3, 4; l x and l y These represent the rotor to x B and y B Distance between axes;

[0014] Step 2: Design a dual-loop control framework. In the inner loop, a finite-time extended state observer is used to estimate the system's disturbances and state, and a composite controller in the inner loop is used to eliminate the disturbances, thus tracking the model's angular velocity. In the outer loop of the dual-loop control framework, a controller combining linear and nonlinear feedback is used to track the model's angle. The specific design is as follows:

[0015] The system (1.1) was rewritten, and the results are shown below:

[0016]

[0017]

[0018] Where x1(t) = ω, u1(t)=τ, and f(t)=I -1 (-ω×Iω+τ d ) represents the nonlinear part and perturbation of the model; y1(t)=Ξ, c=diag{c1,c2,c3}>0 indicates an adjustable coefficient matrix. Represents the nonlinear part of the model;

[0019] Step 3: Using the concept of an extended state observer, the nonlinear part of the model and the perturbation f(t) are set as an extended state x2(t) of the system, and its derivative is set to... Where h1(t), h2(t), and h3(t) represent the nonlinear components of the roll, pitch, and yaw channels of the system, and the derivatives of the disturbance, respectively; then, (1.2) is rewritten as follows:

[0020]

[0021]

[0022] Viewing the system as a decoupled system, we have:

[0023]

[0024]

[0025] Where, x i Represents a vector x∈R 3 The i-th element, i = p, q, r;

[0026] For (1.5), the following finite-time nonlinear disturbance observer (FTNDO) is designed to estimate the real-time angular velocity and unknown components of the system, and in step four, a composite controller is used to eliminate the disturbances caused by the unknown components:

[0027]

[0028]

[0029] in, The actual value of angular velocity x 1i and estimated value The error; r1=1+α, r2=1-α, α∈(-1 / 2,0), Representative | e 1i | n sign(e 1i ),

[0030] Then, let The actual value x represents the unknown part and the disturbance. 2i and estimated value The error, and its derivative, are as follows:

[0031]

[0032]

[0033] Step 4: Design a composite controller in the inner loop of the dual-loop control framework, including a linear feedback term, an estimation error compensation term, and a robust compensation term, to eliminate unknown disturbances in the system. Specifically:

[0034]

[0035] Among them, u 1i (t) represents the output of the composite controller; λ>0 is the adjustable feedback gain, e i (t)=x 1i (t)-x si (t) represents the error between the system's real-time angular velocity and the given angular velocity, where x is the reference input of the inner loop. si (t) equals the output v of the outer loop. 1i (t); It is the robust compensation term of the system, where σ>0 is an adjustable constant;

[0036]

[0037] Where, ω s It is a positive adjustable gain;

[0038] Step 5: Design a controller in the outer loop that incorporates both linear and nonlinear feedback, expressed as:

[0039]

[0040] The first and second terms represent linear feedback, λ0>0 is the gain coefficient of the linear feedback, and y si (t) is the reference input for the angle, which is the desired angle value generated by the given motor signal. The third term is the nonlinear feedback, where y 0i For y 1i The initial value of (t)(real-time signal measured by IMU), where β>0 is the gain coefficient of nonlinear feedback; The expression for the nonlinear feedback component is y. 1i (t) and y si The function of (t), and varies with the output feedback error e yi (t)=y 1i (t)-y si (t) and changes.

[0041] The present invention has the following beneficial effects:

[0042] This invention provides a disturbance rejection control method for unmanned aerial vehicles (UAVs) based on a finite-time state observer. A finite-time state observer is designed within a dual-closed-loop control framework based on active disturbance rejection control (ADRC) to estimate errors and disturbances and eliminate them within a finite time, thereby increasing the system's disturbance rejection capability. Simultaneously, a robust control law is added to the outer loop to improve the system's transient performance, preventing excessive overshoot and actuator saturation, thus comprehensively improving the system's control performance. Attached Figure Description

[0043] Figure 1 This is a control model for a quadcopter drone.

[0044] Figure 2 This is a block diagram of the control framework of the present invention;

[0045] Figure 3 This is to track performance in simulation experiments;

[0046] Figure 4 This represents the angle error in the simulation experiment. Detailed Implementation

[0047] This invention provides a method for anti-disturbance control of unmanned aerial vehicles (UAVs) based on a finite-time state observer, comprising:

[0048] Step 1: As Figure 1 Define an inertial reference coordinate system E O = [x,y,z] and a body coordinate system E B =[x B ,y B ,z B Let's briefly explain the quadcopter model. Ξ=[φ,θ,ψ] represents the orientation of the body coordinate system relative to the inertial frame. The forces and moments acting on the quadcopter are as follows:

[0049]

[0050]

[0051] Where, ω=[ω x ,ω y ,ω z ] · It is the angular velocity of the body on the three axes, I = diag{I xx ,I yy ,I zz} is the moment of inertia of the aircraft (assuming the mass distribution of the quadrotor is symmetrical), τ d =[τ dx ,τ dy ,τ dz ] ·It is the sum of the unmodeled parts (parts not considered in the model, such as assuming the UAV is a rigid body) and external disturbances such as wind disturbance. Matrix W Ξ Defined as:

[0052]

[0053] The control matrix τ represents the torque produced by the motor, and is expressed as:

[0054]

[0055] Where, k t It is the thrust coefficient of the motor, k d Ω is the resistance coefficient of the motor. i It is the angular velocity of the i-th motor (i = 1, 2, 3, 4), l x and l y These represent the rotor to x B and y B Distance between axes.

[0056] Step Two: Based on the above model, we design as follows Figure 2 A dual-closed-loop control framework is proposed. Since a standard quadrotor is equipped with an inertial measurement unit (IMU), we can simultaneously obtain the quadrotor's attitude Ξ and angular velocity ω. In the inner loop, we estimate the system's disturbances and state using a finite-time extended state observer, and eliminate the disturbances using a composite controller in the inner loop, thus achieving tracking of the model's angular velocity. In the outer loop, we use a controller combining linear and nonlinear feedback to achieve tracking of the model's angle. The specific design is as follows:

[0057] Now we rewrite system (1.1), and the result is as follows:

[0058]

[0059]

[0060] Where x1(t) = ω, u1(t)=τ, and f(t)=I -1 (-ω×Iω+τ d ) represents the nonlinear part and perturbation of the model. y1(t) = Ξ, c = diag{c1,c2,c3} > 0 indicates an adjustable coefficient matrix. This represents the nonlinear part of the model.

[0061] Step 3: Because quadcopter drones are difficult to model completely, and various disturbances such as gusts exist, it is difficult to accurately calculate the system's state and disturbances. To achieve better control, the idea of ​​an extended state observer is used. The nonlinear part of the model and the disturbance f(t) are set as an extended state x2(t) of the system, and its derivative is set... Then, we can rewrite (1.2) as follows:

[0062]

[0063]

[0064] If we now consider the system as a decoupled system, then we have:

[0065]

[0066]

[0067] Where x i Represents a vector x∈R 3 The i-th element, i = p, q, r, represents the three channels of the system respectively.

[0068] Regarding (1.5), we designed the following finite-time nonlinear disturbance observer (FTNDO) to estimate the real-time angular velocity and unknown components of the system, and then used a composite controller in step four to eliminate the disturbances caused by the unknown components:

[0069]

[0070]

[0071] in This represents the error between the actual and estimated values ​​of angular velocity. r1=1+α, r2=1-α, α∈(-1 / 2,0), Representative | e 1i | n sign(e 1i ),

[0072] Then, we make The error between the actual and estimated values ​​of the unknown part and the disturbance is represented by the following derivative:

[0073]

[0074]

[0075] Using the Lyapunov method, it can be proven that (1.7) can reach stability in a finite time. At this point, the estimated value tracks the real-time value of the system, thus obtaining a total estimate of the unknown disturbances and unmodeled disturbances of the system. This value is then eliminated using a controller to achieve stable control of the system.

[0076] Step Four: In Figure 2 The inner loop design incorporates a composite controller, including a linear feedback term, an estimation error compensation term, and a robust compensation term, to eliminate unknown disturbances in the system. Specifically:

[0077]

[0078] Where λ>0 is the adjustable feedback gain, e i (t)=x 1i (t)-x si (t) represents the error between the system's real-time angular velocity and the given angular velocity, where x is the reference input of the inner loop. si (t) equals the output v of the outer loop. 1i (t). It is the robust compensation term of the system, where σ>0 is an adjustable constant.

[0079] sgn(ω s e i (t) is a special nonlinear function.

[0080]

[0081] Where ω s It is a positive adjustable gain.

[0082] This controller eliminates the unknown disturbances in the system estimated by the finite-time extended state observer and uses a robust compensation term for dynamic compensation to prevent jitter at the critical point, thus achieving good tracking performance.

[0083] Step 5: A controller that incorporates both linear and nonlinear feedback was designed in the outer loop.

[0084]

[0085] The first and second terms represent linear feedback, λ0>0 is the gain coefficient of the linear feedback, and y si (t) is the reference input for the angle, and the third term is the nonlinear feedback, where y 0i For y 1i (t) is the initial value of the real-time signal measured by the IMU, and β>0 is the gain coefficient of the nonlinear feedback. The expression for the nonlinear feedback component is y. 1i (t) and y siThe function of (t), and varies with the output feedback error e yi (t)=y 1i (t)-y si (t) and changes.

[0086] When the inner loop system is stable, x 1i (t) and v 1i (t) is equivalent. This controller can eliminate the error between the real-time value and the given value of the angle to zero, and enhance the stability of the speed of this process by utilizing the nonlinear part.

[0087] The above describes how stable tracking of angle and angular velocity in attitude control of a quadcopter drone is achieved through inner and outer double rings.

[0088] Example:

[0089] The following simulation comparison between the traditional ADRC controller and the improved finite-time stable ADRC controller, along with accompanying drawings and embodiments, provides a detailed description of the invention.

[0090] Based on the above, we established a simulation model. The initial conditions are [φ0θ0ψ0]=[0° 0° 0°], [ω x0 ω y0 ω z0

[000] . All initial states of FNESO are set to zero. The reference signal is... ψ s (t) = 0.

[0091] In actual flight, measurement data always contains noise. Therefore, white noise with a mean covariance of 0.1° is added to both the angular feedback loop and the angular velocity feedback loop. Simulation results are as follows. Figure 3 and Figure 4 As shown, this method can quickly and stably track a given signal with minimal error under noisy conditions.

[0092] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1.A method for disturbance rejection control of unmanned aerial vehicle based on finite time state observer, characterized in that, Comprise: Step 1: Denote the inertial reference frame as E O = [x, y, z], the body frame as E B = [x B , y B , z B ]; let Ξ = [φ, θ, ψ] represent the orientation of the body frame of the quadrotor UAV relative to the inertial reference frame, respectively, the roll angle, the pitch angle, and the yaw angle; the forces and moments on the UAV are as follows: where ω = [ω x , ω y , ω z ] is the angular velocity of the UAV body in the three axes of the inertial reference frame, I = diag{I xx , I yy , I zz} is the moment of inertia of the body in the three axes of the inertial reference frame; τ d = [τ dx , τ dy , τ dz ] is the sum of the unmodeled parts and the external disturbances; the matrix W Ξ is defined as: The control matrix τ represents the torque brought by the motor, expressed as: wherein k t is the thrust coefficient of the electric motor, k d is the drag coefficient of the electric motor, Ω j is the angular velocity of the jth electric motor, j = 1, 2, 3, 4; l x and l y represent the distance of the rotor to the x B and y B axes, respectively; Step two: design a double closed-loop control framework; in the inner loop of the framework, estimate the disturbance and state of the system through the finite-time extended state observer, and eliminate the disturbance through the inner loop composite controller to realize the tracking of the model angular velocity; in the outer loop of the double closed-loop control framework, control through a controller combining linear feedback and nonlinear feedback to realize the tracking of the model angle, the specific design is as follows: Rewrite the system (1.1), the result is as follows: where x1(t) = ω, u1(t) = τ, and f(t) = I -1 (-ω x I ω + τ d ) is the nonlinear part of the model and the disturbance; y1(t) = Ξ, c = diag{c1, c2, c3} > 0 represents a tunable coefficient matrix, represents the nonlinear part of the model; Step three: Using the idea of extended state observer, the nonlinear part of the model and the disturbance f(t) are set as an extended state x2(t) of the system, and its derivative is where h1(t), h2(t), h3(t) represent the derivatives of the nonlinear part and the disturbance of the roll channel, the pitch channel and the yaw channel of the system, respectively; then, (1.2) is rewritten as follows: Regarding the system as a decoupled system, there are: where x i represents the i-th element of the vector x ∈ R 3 , i = p, q, r; For (1.5), design the following finite-time nonlinear disturbance observer FTNDO to estimate the real-time angular velocity and unknown part of the system, and use the composite controller in step four to eliminate the disturbance caused by the unknown part: wherein the actual value x of the angular velocity 1i and the estimated value the error; e 1i " n |e 1i | n sign(e 1i ), Then, let x 2i denote the actual value of the unknown part and the disturbance, and the error of the estimate, the derivative of the error is as follows: Step four: design a composite controller containing a linear feedback term, an estimated error compensation term and a robust compensation term in the inner loop of the double closed-loop control framework to eliminate the unknown disturbance of the system, specifically: where u 1i (t) is the output of the complex controller; λ > 0 is an adjustable feedback gain, e i (t) = x 1i (t) - x si (t) is the error between the real-time angular velocity of the system and the given angular velocity, the reference input x si (t) of the inner loop is equal to the output v 1i (t) of the outer loop; is the robust compensation term of the system, where σ > 0 is an adjustable constant; where ω s is a positive adjustable gain; Step five: design a controller containing both linear and nonlinear feedback in the outer loop, expressed as: The first and second terms are linear feedback, λ0>0 is the gain coefficient of the linear feedback, y si (t) is the reference input of the angle, is the desired angle value generated by the signal of the given motor, the third term is nonlinear feedback, where y 0i is the real-time signal measured by the IMU, y 1i (t) is the initial value of y 1i (t), and β>0 is the gain coefficient of the nonlinear feedback. is the expression of the nonlinear feedback component, which is a function of y si (t) and y yi (t), and changes with the output feedback error e 1i (t) = y si (t) - y (t).

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