CN111324138A - Four-rotor attitude designated time performance-guaranteeing output feedback control method - Google Patents

Abstract

The invention discloses a feedback control method for performance guarantee output of a quadrotor attitude designated time, which relates to the field of automatic control of aircrafts, and comprises the following steps of firstly, establishing a quadrotor unmanned aerial vehicle attitude power/kinematics model based on Euler angle description; secondly, constructing an Extended State Observer (ESO) to carry out online observation and compensation on lumped interference including parameter uncertainty and external interference; and then designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and finally constructing an attitude loop virtual control law and an angular velocity loop actual control law so as to realize prior adjustment of attitude response transient and steady-state performance. The invention has the following advantages: (1) the method can ensure that the four-rotor attitude maneuver control meets the requirement of a preset performance index, and the convergence speed can be randomly specified through the time constant of a performance profile; (2) and by introducing the extended state observer technology, the interference accurate estimation and compensation in the output feedback sense can be realized.

Description

A time-guaranteed performance-preserving output feedback control method for quadrotor attitude

technical field

The invention relates to the field of automatic control of aircraft, in particular to a quadrotor attitude-specified time-guaranteed output feedback control method, which is applied to the finite-time-guaranteed control of the quadrotor attitude from an arbitrary initial value to a target value under the condition of independent angular rate measurement .

Background technique

In recent years, with the rapid development of MEMS sensing technology, information network technology, and control technology, the design, development and practice of quadrotor UAVs have received unprecedented attention. Compared with fixed-wing UAVs, quadrotors show the following performance advantages: simple structure, low manufacturing cost, easy maintenance, light fuselage, easy manipulation, and maneuverability, environmental durability, hovering, vertical lift. It has remarkable performances such as degradability, and has significant dual-use value for both military and civilian use. The quadrotor is a highly nonlinear, underactuated coupled system with multiple-input multiple-output (MIMO). At the same time, the quadrotor dynamics contain various sources of uncertain disturbances, including parameter changes, model mismatches, and environmental disturbances. In addition, due to limited load or simple configuration requirements, some states (such as angular rate) are often unmeasurable or the measurement accuracy cannot meet the requirements of closed-loop feedback control. Therefore, how to solve the quadrotor trajectory/attitude control problem under the condition of unmeasurable speed is more practical.

The existing quadrotor attitude control methods usually rely on tracking differentiators or state observers, most of which can only achieve the final consistent and bounded attitude tracking error in the sense of output feedback, and pay less attention to the attitude control guarantee performance in the presence of unknown interference. question. Although the current preset performance control can realize a priori adjustment of the controlled object performance, because it adopts a function profile in the form of exponential decay, it can only ensure that the system state converges to the preset target in infinite time, and it is difficult to meet the requirement of rapid convergence in practical engineering. demanding requirements. However, the disclosed control method (such as finite or fixed time control) that can realize any specified convergence time, its convergence time strictly depends on the initial value of the system state and the controller parameters, and the estimation of the upper bound of the convergence time is highly conservative, which seriously affects the Limit its engineering applications. Furthermore, the above-mentioned control strategies cannot achieve a priori regulation of the steady-state behavior of the system. Based on the analysis of the existing results, it is very necessary to study the finite-time guaranteed performance control method of the quadrotor attitude from any initial value to the target value under the condition of independent angular rate measurement.

SUMMARY OF THE INVENTION

In order to solve the limited time-guaranteed control of the quadrotor attitude from any initial value to the target value under the condition of independent angular rate measurement, the present invention provides a quadrotor attitude specified time-guaranteed output feedback control method.

The present invention is achieved through the following technical solutions: a method for output feedback control of quadrotor attitude designation time-guaranteed performance, comprising the following steps:

(1) Establish a quadrotor UAV attitude dynamics/kinematics model based on Euler angle description:

Among them, Θ=[φ, θ, ψ] ^T represents the Euler angle in the body coordinate system, and φ, θ, ψ respectively represent the roll angle, pitch angle and yaw angle in the attitude of the quadrotor UAV; Ω= [Ω _φ ,Ω _θ ,Ω _ψ ] ^T is the angular velocity vector, Ω _φ ,Ω _θ ,Ω _ψ are the roll angular velocity, pitch angular velocity and yaw angular velocity respectively; J=diag(J _φ ,J _θ ,J _ψ ) means Positive definite inertia matrix; Π=diag(k _φ , k _θ , k _ψ ) represents the uncertain damping matrix in the attitude loop, _ki (i=φ, θ, ψ) represents the damping coefficient; K=diag(l,l, c) Represents a symmetric constant matrix, l represents the distance from each motor to the center of mass of the quadrotor, c represents the torque coefficient; U=[u _φ , u _θ , u _ψ ] ^T represents the rotational torque input by the attitude angle of the quadrotor UAV ; d=[d _φ , d _θ , d _ψ ] ^T represents the unknown bounded external disturbance imposed on the attitude kinematics;

To facilitate controller design, the following symbolic variables are introduced:

K₂＝J^-1K，d_Θ＝-J^-1ΠΩ+J^-1d表示四旋翼无人机姿态回路中集总干扰，包括系统中的参数不确定性和未知的有界外部干扰；通过这些变换，将四旋翼无人机姿态动力学模型写成如下的紧凑形式：X ₁ =Θ,

K ₂ =J ^-1 K, d _Θ = -J ^-1 ΠΩ+J ^-1 d represents the aggregate disturbance in the attitude loop of the quadrotor UAV, including parameter uncertainty in the system and unknown bounded external disturbance; Through these transformations, the quadrotor UAV attitude dynamics model is written in the following compact form:

(2) According to the uncertain attitude model of the quadrotor given in step (1), an extended state observer ESO is constructed to perform online observation and compensation of the lumped interference:

Construct the following quadrotor attitude expansion state observer:

w₀表示扩张状态观测器的带宽，满足w₀＞0，而且w₀是扩张状态观测器中唯一需要调节的参数；

分别为四旋翼角速率和集总干扰的估计值；in,

w ₀ represents the bandwidth of the extended state observer, satisfying w ₀ > 0, and w ₀ is the only parameter that needs to be adjusted in the extended state observer;

are the estimated values of the quadrotor angular rate and the aggregate interference, respectively;

(3) Design the boundary performance function whose attitude adjustment time can be specified arbitrarily, and construct the virtual control law of the attitude loop and the actual control law of the angular velocity loop in combination with the interference estimation given in step (2), so as to realize the transient and steady-state performance of attitude response. The prior adjustment of :

Define X _id , (i=φ, θ, ψ) as a given enough smooth attitude command, the actual attitude angle is X ₁ =[X _φ1 , X _θ1 , X _ψ1 ] ^T , then the quadrotor UAV attitude tracking The error is e _i1 =X _i1 -X _id , in order to ensure that the attitude tracking error satisfies the following performance constraints:

a_i(t)为收敛时间可任意指定的性能函数：in,

a _i (t) is an arbitrarily specified performance function for the convergence time:

Among them, ri ∈(0,1), a _i0 , a _i∞ , T _i are the adjustment parameters of the specified time performance profile _, and the performance function a _i (t ₎ can be converged at the specified time by adjusting the value of time Ti;

Next, the constrained pose tracking error can be transformed into an unconstrained tracking error by using the error transfer function S _i ( ):

是归一化误差；where _zi (t) is the transformed tracking error,

is the normalization error;

Based on the converted tracking error, the virtual control law of the attitude subsystem is constructed as:

Among them, k _i1 is the control gain of the attitude loop;

考虑速度状态和集总干扰是不可测的，设计角速度子系统的实际控制器为：definition

Considering that the velocity state and the aggregate disturbance are unmeasurable, the actual controller for designing the angular velocity subsystem is:

Among them, k ₂ is the control gain matrix of the angular velocity loop.

The main process of the feedback control method provided by the present invention is as follows: firstly, establishing a quadrotor UAV attitude dynamics/kinematics model based on Euler angle description; secondly, constructing an extended state observer (ESO) pair including parameter uncertainty On-line observation and compensation of aggregate disturbances including external disturbances; then, a boundary performance function whose attitude adjustment time can be specified arbitrarily is designed; finally, a virtual control law of attitude loop and an actual control law of angular velocity loop are constructed to realize attitude response transient A priori conditioning with steady-state performance.

Compared with the prior art, the present invention has the following beneficial effects: a four-rotor attitude specification time-guaranteed performance output feedback control method provided by the present invention proposes a performance profile that can arbitrarily specify a convergence time, which can not only ensure the attitude The error guarantees performance constraints, and it can also control the quadrotor from any initial state to reach the steady state according to the specified convergence time, that is, it can ensure that the quadrotor attitude maneuver control meets the preset performance index requirements, and the convergence speed can pass the time constant of the performance profile. Arbitrary designation; further, the combination of preset performance control and extended state observer technology realizes the performance-preserving tracking of quadrotor attitude at any time under the framework of output feedback, and the introduction of extended state observer technology can achieve accurate interference estimation in the sense of output feedback with compensation.

Description of drawings

FIG. 1 is a flow chart of a method of the present invention for a quadrotor attitude-specified time-guaranteed output feedback control method.

Detailed ways

The present invention will be further described below in conjunction with specific embodiments.

A quadrotor attitude specification time-guaranteed output feedback control method, the process is shown in Figure 1, including the following steps:

(1) Establish a quadrotor UAV attitude dynamics/kinematics model based on Euler angle description:

表示正定惯性矩阵；Π＝diag(0.0024,0.0024,0.0024)Nms²表示姿态回路中的不确定阻尼矩阵，k_i(i＝φ,θ,ψ)表示阻尼系数；K＝diag(l,l,c)表示对称的常数矩阵，l＝0.4m表示每一个电机到四旋翼质心的距离，c＝0.05表示力矩系数；U＝[u_φ,u_θ,u_ψ]^T表示四旋翼无人机姿态角输入的转动扭矩；d＝[d_φ,d_θ,d_ψ]^T＝[0.2(sin(t)+sin(0.5t)),0.2(cos(0.5t)-cos(0.8t)),0.2(sin(t)sin(0.5t))]^T表示施加于姿态运动学中的未知有界外部干扰；Among them, Θ=[φ, θ, ψ] ^T represents the Euler angle in the body coordinate system, and φ, θ, ψ represent the roll angle, pitch angle and yaw angle in the attitude of the quadrotor UAV; Ω= [Ω _φ ,Ω _θ ,Ω _ψ ] ^T is the angular velocity vector, Ω _φ ,Ω _θ ,Ω _ψ are the roll angular velocity, pitch angular velocity and yaw angular velocity respectively;

Represents the positive definite inertia matrix; Π=diag(0.0024,0.0024,0.0024)Nms ² represents the uncertain damping matrix in the attitude loop, ki ( _i =φ,θ,ψ) represents the damping coefficient; K=diag(l,l, c) Represents a symmetric constant matrix, l=0.4m represents the distance from each motor to the center of mass of the quadrotor, c=0.05 represents the torque coefficient; U=[u _φ , u _θ , u _ψ ] ^T represents the attitude of the quadrotor UAV Rotational torque of angular input; d=[d _φ , d _θ , d _ψ ] ^T = [0.2(sin(t)+sin(0.5t)), 0.2(cos(0.5t)-cos(0.8t)), 0.2(sin(t)sin(0.5t))] ^T represents the unknown bounded external disturbance imposed on the attitude kinematics;

To facilitate controller design, the following symbolic variables are introduced:

K₂＝J^-1K，d_Θ＝-J^-1ΠΩ+J^-1d表示四旋翼无人机姿态回路中集总干扰，包括系统中的参数不确定性和未知的有界外部干扰；通过这些变换，将四旋翼无人机姿态动力学模型写成如下的紧凑形式：X ₁ =Θ,

K ₂ =J ^-1 K, d _Θ = -J ^-1 ΠΩ+J ^-1 d represents the aggregate disturbance in the attitude loop of the quadrotor UAV, including parameter uncertainty in the system and unknown bounded external disturbance; Through these transformations, the quadrotor UAV attitude dynamics model is written in the following compact form:

(2) According to the uncertain attitude model of the quadrotor given in step (1), an extended state observer ESO is constructed to perform online observation and compensation of the lumped interference:

Construct the following quadrotor attitude expansion state observer:

w₀＝20表示扩张状态观测器的带宽，满足w₀＞0，而且w₀是扩张状态观测器中唯一需要调节的参数；

分别为四旋翼角速率和集总干扰的估计值；in,

w ₀ =20 represents the bandwidth of the extended state observer, satisfying w ₀ >0, and w ₀ is the only parameter that needs to be adjusted in the extended state observer;

are the estimated values of the quadrotor angular rate and the aggregate interference, respectively;

(3) Design the boundary performance function whose attitude adjustment time can be specified arbitrarily, and construct the virtual control law of the attitude loop and the actual control law of the angular velocity loop in combination with the interference estimation given in step (2), so as to realize the transient and steady-state performance of attitude response. The prior adjustment of :

Define X _id =[20sin(3t),30sin(t),sin(2t)] as a given sufficiently smooth gesture command. The actual attitude angle response is X ₁ =[X _φ1 , X _θ1 , X _ψ1 ] ^T , then the attitude tracking error of the quadrotor UAV is e _i1 =X _i1 -X _id ;

The initial state of the system is set as X ₁ (0)=[4,2,2] ^T , X ₂ (0)=[0,0,0] ^T ;

To ensure that the attitude tracking error satisfies the following performance constraints:

a_i(t)为收敛时间可任意指定的性能函数：in,

a _i (t) is an arbitrarily specified performance function for the convergence time:

Among them, ri = 0.6, a _i0 =6, a _i∞ =0.1, T _i =5 are the adjustment parameters of the specified time performance profile, and the performance function a _i (t) can be made to _converge at the specified time by adjusting the value of time T _i ;

Next, the constrained pose tracking error can be transformed into an unconstrained tracking error by using the error transfer function S _i ( ):

是归一化误差；where _zi (t) is the transformed tracking error,

is the normalization error;

Based on the converted tracking error, the virtual control law of the attitude subsystem is constructed as:

Wherein, k _i1 =4 is the control gain of the attitude loop;

考虑速度状态和集总干扰是不可测的，设计角速度子系统的实际控制器为：definition

Considering that the velocity state and the aggregate disturbance are unmeasurable, the actual controller for designing the angular velocity subsystem is:

Wherein, k ₂ =diag(8,8,8) is the control gain matrix of the angular velocity loop.

The scope of protection of the present invention is not limited to the above specific embodiments, and for those skilled in the art, the present invention may have various modifications and changes, any modifications, improvements and equivalents made within the concept and principle of the present invention All replacements should be included within the protection scope of the present invention.

Claims (1)

1. A four-rotor attitude designated time performance-guaranteeing output feedback control method is characterized by comprising the following steps: the method comprises the following steps:

(1) establishing a quadrotor unmanned aerial vehicle attitude dynamic/kinematic model based on Euler angle description:

wherein, theta is [ phi, theta, psi ═ phi]^TExpressing Euler angles in a body coordinate system, and respectively expressing a rolling angle, a pitching angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle by phi, theta and psi; omega-omega_φ,Ω_θ,Ω_ψ]^TDenotes the angular velocity vector, Ω_φ,Ω_θ,Ω_ψRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity; j ═ diag (J)_φ,J_θ,J_ψ) Representing a positive definite inertia matrix; ii ═ diag (k)_φ,k_θ,k_ψ) Representing an uncertain damping matrix, k, in an attitude loop_i(i ═ Φ, θ, ψ) represents a damping coefficient; k ═ diag (l, l, c) denotes a symmetric constant matrix, l denotes the distance of each motor to the four rotor centroids, c denotes the moment coefficient; u ═ U_φ,u_θ,u_ψ]^TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; d ═ d_φ,d_θ,d_ψ]^TRepresentation applied in gesture kinematicsUnknown bounded external interference;

for convenience of controller design, the following symbolic variables are introduced:

X₁＝Θ，

K₂＝J^-1K，d_Θ＝-J^-1ΠΩ+J^-1d represents lumped interference in the quad-rotor drone attitude loop, including parametric uncertainty in the system and unknown bounded external interference; through these transformations, the quad-rotor drone attitude dynamics model is written in a compact form as follows:

(2) aiming at the uncertain attitude model of the four rotors given in the step (1), an Extended State Observer (ESO) is constructed to carry out online observation and compensation on lumped interference:

the following four-rotor attitude extended state observer is constructed:

wherein,

w₀represents the bandwidth of the extended state observer, satisfies w₀> 0, and w₀Is the only parameter to be adjusted in the extended state observer;

estimated values of the angular rate and the aggregate interference of the quadrotors respectively;

(3) designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and respectively constructing an attitude loop virtual control law and an angular velocity loop actual control law by combining the interference estimation given in the step (2) so as to realize the prior adjustment of attitude response transient and steady-state performance:

definition of X_id(i ═ phi, theta, psi) is given a sufficiently smooth attitude command, the actual attitude angle being X₁＝[X_φ1,X_θ1,X_ψ1]^TAnd then the attitude tracking error of the quad-rotor unmanned aerial vehicle is e_i1＝X_i1-X_idTo ensure that the attitude tracking error meets the following performance constraints:

wherein,σ∈(0,1),

a_i(t) is a performance function whose convergence time can be arbitrarily specified:

wherein r is_i∈(0,1),a_i0,a_i∞,T_iFor specifying the adjustment parameters of the temporal performance profile by adjusting the time T_iMay be such that the performance function a_i(t) specifying time convergence;

next, an error transfer function S is used_i(. h) can convert constrained attitude tracking errors into unconstrained tracking errors:

wherein z is_i(t) is the converted tracking error,

is the normalized error;

based on the converted tracking error, constructing a virtual control law of the attitude subsystem as follows:

wherein k is_i1Is the control gain of the attitude loop;

definition of

Considering that the speed state and the collective disturbance are not measurable, the actual controller of the angular velocity subsystem is designed as follows:

wherein k is₂Is a control gain matrix of the angular velocity loop.

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