CN108107726A - A kind of limited backstepping control method of quadrotor output based on symmetrical time-varying obstacle liapunov function - Google Patents
A kind of limited backstepping control method of quadrotor output based on symmetrical time-varying obstacle liapunov function Download PDFInfo
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Abstract
一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，针对四旋翼飞行器的动力学系统，选择一种对称时变障碍李雅普诺夫函数，设计一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法。对称时变障碍李雅普诺夫函数的设计是为了保证系统的输出能够限制在一定的范围内，避免过大的超调，同时还能减少到达时间。从而改善四旋翼飞行器系统的动态响应性能。本发明提供一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，使系统具有较好的动态响应过程。
A four-rotor aircraft output-limited backstepping control method based on symmetrical time-varying obstacle Lyapunov function. Aiming at the dynamic system of quadrotor aircraft, a symmetrical time-varying obstacle Lyapunov function is selected, and a method based on symmetrical time-varying obstacle is designed. Output-limited backstepping control method for quadrotor aircraft with variable obstacle Lyapunov function. The design of the symmetric time-varying barrier Lyapunov function is to ensure that the output of the system can be limited within a certain range, avoid excessive overshoot, and reduce the arrival time at the same time. Thereby improving the dynamic response performance of the quadrotor aircraft system. The invention provides a four-rotor aircraft output-limited backstepping control method based on a symmetrical time-varying obstacle Lyapunov function, so that the system has a better dynamic response process.
Description
技术领域technical field
本发明涉及一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，使四旋翼飞行器系统有较好的动态响应过程。The invention relates to a four-rotor aircraft output-limited backstepping control method based on a symmetrical time-varying obstacle Lyapunov function, so that the four-rotor aircraft system has a better dynamic response process.
背景技术Background technique
四旋翼飞行器作为旋翼式飞行器的一种,以其体积小、机动性能好、设计简单、制造成本低廉等优点,吸引了国内外大学、研究机构、公司的广泛关注。然而，由于四旋翼飞行器体积小且重量轻，飞行中易受到外部干扰，如何实现对四旋翼飞行器的高性能运动控制已经成为一个热点问题。针对四旋翼飞行器的控制问题，存在很多控制方法，例如PID控制、自抗扰控制、滑模控制、反步控制等。As a kind of rotorcraft, quadrotor aircraft has attracted wide attention from domestic and foreign universities, research institutions and companies due to its small size, good maneuverability, simple design, and low manufacturing cost. However, due to the small size and light weight of quadrotor aircraft, it is vulnerable to external disturbances during flight, how to achieve high-performance motion control of quadrotor aircraft has become a hot issue. For the control problem of quadrotor aircraft, there are many control methods, such as PID control, active disturbance rejection control, sliding mode control, backstepping control, etc.
其中反步控制已经广泛应用于非线性系统，其优点包括响应速度快、实施方便、对系统不确定和外部干扰的鲁棒性等。传统的反步控制，只是考虑了四旋翼飞行器的稳态性能，并没有过多地关注其瞬态响应性能。因此，传统的反步控制方法使得四旋翼飞行器系统在实际情况中的应用有很大阻碍。为解决这一问题，基于障碍李雅普诺夫函数的反步控制方法被提出，这种方法在实际情况中能够有效地改善四旋翼飞行器系统的瞬态性能。Among them, backstepping control has been widely used in nonlinear systems, and its advantages include fast response speed, convenient implementation, robustness to system uncertainty and external disturbance, etc. The traditional backstep control only considers the steady-state performance of the quadrotor aircraft, and does not pay too much attention to its transient response performance. Therefore, the traditional backstepping control method greatly hinders the application of the quadrotor aircraft system in practical situations. To solve this problem, a backstepping control method based on obstacle Lyapunov function is proposed, which can effectively improve the transient performance of quadrotor aircraft system in practice.
发明内容Contents of the invention
为了改善四旋翼飞行器系统瞬态性能，本发明提供了一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限步控制方法，减少了超调量和超调时间，使四旋翼飞行器系统具有一个良好的动态响应性能。In order to improve the transient performance of the four-rotor aircraft system, the invention provides a four-rotor aircraft output limited step control method based on the symmetrical time-varying obstacle Lyapunov function, which reduces the overshoot and overshoot time, and makes the four-rotor aircraft The system has a good dynamic response performance.
为了解决上述技术问题提出的技术方案如下：The technical scheme proposed in order to solve the above technical problems is as follows:
一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，包括以下步骤：A quadrotor output-limited backstepping control method based on a symmetrical time-varying obstacle Lyapunov function, comprising the following steps:
步骤1，建立四旋翼飞行器系统的动态模型，设定系统的初始值、采样时间以及相关控制参数，过程如下：Step 1, establish the dynamic model of the quadrotor aircraft system, set the initial value, sampling time and related control parameters of the system, the process is as follows:
1.1确定从基于四旋翼飞行器系统的机体坐标系到基于地球的惯性坐标的转移矩阵T：1.1 Determine the transfer matrix T from the body coordinate system based on the quadrotor aircraft system to the inertial coordinate system based on the earth:
其中φ,θ,ψ分别是四旋翼飞行器的翻滚角、俯仰角、偏航角，表示无人机依次绕惯性坐标系的各坐标轴旋转的角度；Among them, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the quadrotor aircraft, respectively, indicating the angles at which the UAV rotates around each coordinate axis of the inertial coordinate system in turn;
1.2四旋翼飞行器平动过程中的动态模型如下：1.2 The dynamic model of the four-rotor aircraft during translation is as follows:
其中x,y,z分别表示四旋翼飞行器在惯性坐标系下的三个位置，Uf表示四旋翼飞行器的输入力矩，m为四旋翼飞行器的质量，g表示重力加速度，Among them, x, y, and z represent the three positions of the quadrotor aircraft in the inertial coordinate system, U f represents the input torque of the quadrotor aircraft, m is the mass of the quadrotor aircraft, g represents the acceleration of gravity,
将式(1)代入式(2)得：Substitute formula (1) into formula (2):
1.3四旋翼飞行器转动过程中的动态模型为：1.3 The dynamic model during the rotation of the quadrotor aircraft is:
其中τx,τy,τz分别代表机体坐标系上各个轴的力矩分量，Ixx,Iyy,Izz分别表示机体坐标系下的各个轴的转动惯量的分量，×表示叉乘，ωp表示翻滚角速度，ωq表示俯仰角速度，ωr表示偏航角速度，表示翻滚角加速度，表示俯仰角加速度，表示偏航角加速度；Among them, τ x , τ y , τ z respectively represent the moment components of each axis in the body coordinate system, I xx , I yy , I zz respectively represent the components of the moment of inertia of each axis in the body coordinate system, × represents the cross product, ω p represents roll angular velocity, ω q represents pitch angular velocity, ω r represents yaw angular velocity, is the roll angular acceleration, represents the pitch angular acceleration, Indicates the yaw angular acceleration;
考虑到无人机一般处于低速飞行或者悬停状态，姿态角变化较小，认为因此式(4)改写为：Considering that the UAV is generally in a low-speed flight or hovering state, and the attitude angle changes little, it is considered that So formula (4) is rewritten as:
联立式(3)和式(5)，得到四旋翼飞行器的动力学模型为：Combining formula (3) and formula (5), the dynamic model of the quadrotor aircraft is obtained as:
其中ux＝cosφsinθcosψ+sinφsinψ,uy＝cosφsinθsinψ-sinφcosψ； where u x =cosφsinθcosψ+sinφsinψ, u y =cosφsinθsinψ-sinφcosψ;
1.4根据式(6)，定义φ,θ的期望值为：1.4 According to formula (6), define the expected value of φ, θ as:
其中φd为φ的期望信号值，θd为θ期望信号值，arcsin为反正弦函数；Where φ d is the expected signal value of φ, θ d is the expected signal value of θ, and arcsin is the arcsine function;
步骤2，在每一个采样时刻，计算位置跟踪误差及其一阶导数；计算姿态角跟踪误差及其一阶导数；设计位置和姿态角控制器，过程如下：Step 2, at each sampling moment, calculate the position tracking error and its first-order derivative; calculate the attitude angle tracking error and its first-order derivative; design the position and attitude angle controller, the process is as follows:
2.1定义z跟踪误差及其一阶导数：2.1 Define the z tracking error and its first derivative:
其中zd表示z的期望信号；where z d represents the desired signal of z;
2.2设计障碍李雅普诺夫函数并求解其一阶导数：2.2 Design barrier Lyapunov function and solve for its first derivative:
其中Kb1为时变参数，满足为虚拟控制量，其表达式为:where K b1 is a time-varying parameter, satisfying is a virtual control quantity, and its expression is:
其中k11为正常数；Where k 11 is a normal number;
将式(10)代入式(9)，得：Substituting formula (10) into formula (9), we get:
2.3设计李雅普诺夫函数V12为：2.3 Design Lyapunov function V 12 as:
求解式(12)的一阶导数，得：Solving the first order derivative of formula (12), we get:
其中in
将式(14)和式(6)代入式(13)，得：Substituting formula (14) and formula (6) into formula (13), we get:
2.4设计Uf：2.4 Design U f :
其中k12为正常数；Where k 12 is a normal number;
2.5定义x,y跟踪误差分别为e2,e3,则有：2.5 Define x and y tracking errors as e 2 and e 3 respectively, then:
其中xd,yd分别表示x,y的期望信号；Where x d , y d represent the expected signals of x and y respectively;
2.6设计障碍李雅普诺夫函数分别求解其一阶导数，得：2.6 Design barrier Lyapunov function Solving the first order derivatives respectively, we get:
其中Kb2为时变参数，满足Kb2>|e2|；Kb3为时变参数，满足Kb3>|e3|；α2,α3为虚拟控制量，其表达式为:Where K b2 is a time-varying parameter, satisfying K b2 >|e 2 |; K b3 is a time-varying parameter, satisfying K b3 >|e 3 |; α 2 , α 3 are virtual control quantities, and their expressions are:
其中k21,k31为正常数；Among them, k 21 and k 31 are normal numbers;
将式(19)代入式(18)，得:Substituting formula (19) into formula (18), we get:
2.7设计李雅普诺夫函数V22,V32 2.7 Design Lyapunov functions V 22 , V 32
求解式(21)的一阶导数，得：Solving the first order derivative of formula (21), we get:
其中in
将式(23)，(6)代入式(22)，分别得：Substituting equations (23) and (6) into equation (22), we get:
2.8通过式(24)，(25)分别设计ux,uy：2.8 Design u x , u y respectively through equations (24) and (25):
其中k22,k32为正常数；Among them, k 22 and k 32 are normal numbers;
2.9定义姿态角跟踪误差及其一阶导数：2.9 Define attitude angle tracking error and its first derivative:
其中j＝4,5,6，x4＝φ,x5＝θ,x6＝ψ，x4d表示φ的期望值，x5d表示θ的期望值，x6d表示ψ的期望值，e4表示φ的跟踪误差，e5表示θ的跟踪误差，e6表示ψ的跟踪误差；Where j=4,5,6, x 4 =φ, x 5 =θ, x 6 =ψ, x 4d represents the expected value of φ, x 5d represents the expected value of θ, x 6d represents the expected value of ψ, e 4 represents the expected value of φ Tracking error, e 5 represents the tracking error of θ, and e 6 represents the tracking error of ψ;
2.10设计障碍李雅普诺夫函数并求解其一阶导数：2.10 Design barrier Lyapunov function and solve for its first derivative:
其中kj为时变参数，满足为姿态角的虚拟控制量，其表达式为:where k j is a time-varying parameter, satisfying is the virtual control quantity of the attitude angle, and its expression is:
其中kj1为正常数；Where k j1 is a normal number;
将式(29)代入式(28)，得：Substituting formula (29) into formula (28), we get:
2.11设计障碍李雅普诺夫函数：2.11 Design barrier Lyapunov function:
求解式(31)的一阶导数，得：Solving the first order derivative of formula (31), we get:
其中 in
将式(33)和式(6)代入式(32)，分别得：Substituting formula (33) and formula (6) into formula (32), we get:
2.12通过式(34)，(35)，(36)分别设计τx,τy,τz：2.12 Design τ x , τ y , τ z through equations (34), (35), and (36):
其中k42,k52,k62为正常数。Among them, k 42 , k 52 , and k 62 are normal numbers.
进一步，所述方法还包括以下步骤：Further, the method also includes the following steps:
步骤3，验证四旋翼飞行器系统的稳定性；Step 3, verify the stability of the quadrotor aircraft system;
3.1将式(16)代入式(15)，得：3.1 Substituting formula (16) into formula (15), we get:
3.2将式(26)代入式(24)、(25)，得：3.2 Substituting formula (26) into formulas (24) and (25), we get:
3.3把式(37)代入式(34)、(35)、(36)，得：3.3 Substituting formula (37) into formulas (34), (35), and (36), we get:
3.4通过(38)，(39)，(40)可知四旋翼飞行器系统是稳定的。3.4 Through (38), (39), (40), it can be known that the quadrotor aircraft system is stable.
本发明基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，改善了系统的瞬态性能，减少了超调量和到达时间。The invention is based on the output-limited backstepping control method of the four-rotor aircraft based on the symmetrical time-varying obstacle Lyapunov function, improves the transient performance of the system, and reduces the overshoot and arrival time.
本发明的技术构思为：针对四旋翼飞行器的动力学系统，设计一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法。对称时变障碍李雅普诺夫函数的设计是为了保证系统的输出能够限制在一定的范围内，避免过大的超调，同时还能减少到达时间。从而改善四旋翼飞行器系统的动态响应性能。The technical idea of the present invention is: aiming at the dynamic system of the quadrotor aircraft, a backstepping control method with limited output of the quadrotor aircraft based on the symmetrical time-varying obstacle Lyapunov function is designed. The design of the symmetric time-varying barrier Lyapunov function is to ensure that the output of the system can be limited within a certain range, avoid excessive overshoot, and reduce the arrival time at the same time. Thereby improving the dynamic response performance of the quadrotor aircraft system.
本发明优点为：降低超调量，减少到达时间，改善瞬态性能。The invention has the advantages of reducing the overshoot, reducing the arrival time and improving the transient performance.
附图说明Description of drawings
图1为本发明的位置跟踪效果示意图。FIG. 1 is a schematic diagram of the position tracking effect of the present invention.
图2为本发明的姿态角跟踪效果示意图。Fig. 2 is a schematic diagram of the attitude angle tracking effect of the present invention.
图3为本发明的位置控制器输入示意图。Fig. 3 is a schematic diagram of the input of the position controller of the present invention.
图4为本发明的姿态角控制器输入示意图。Fig. 4 is a schematic diagram of the input of the attitude angle controller of the present invention.
图5为本发明的控制流程示意图。Fig. 5 is a schematic diagram of the control flow of the present invention.
具体实施方式Detailed ways
下面结合附图对本发明做进一步说明。The present invention will be further described below in conjunction with the accompanying drawings.
参照图1-图5，一种基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法，包括以下步骤：Referring to Fig. 1-Fig. 5, a kind of quadrotor aircraft output limited backstepping control method based on symmetrical time-varying obstacle Lyapunov function, comprises the following steps:
步骤1，建立四旋翼飞行器系统的动态模型，设定系统的初始值、采样时间以及相关控制参数，过程如下：Step 1, establish the dynamic model of the quadrotor aircraft system, set the initial value, sampling time and related control parameters of the system, the process is as follows:
1.1确定从基于四旋翼飞行器系统的机体坐标系到基于地球的惯性坐标的转移矩阵T：1.1 Determine the transfer matrix T from the body coordinate system based on the quadrotor aircraft system to the inertial coordinate system based on the earth:
其中φ,θ,ψ分别是四旋翼飞行器的翻滚角、俯仰角、偏航角，表示无人机依次绕惯性坐标系的各坐标轴旋转的角度；Among them, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the quadrotor aircraft, respectively, indicating the angles at which the UAV rotates around each coordinate axis of the inertial coordinate system in turn;
1.2四旋翼飞行器平动过程中的动态模型如下：1.2 The dynamic model of the four-rotor aircraft during translation is as follows:
其中x,y,z分别表示四旋翼飞行器在惯性坐标系下的三个位置，Uf表示四旋翼飞行器的输入力矩，m为四旋翼飞行器的质量，g表示重力加速度，Among them, x, y, and z represent the three positions of the quadrotor aircraft in the inertial coordinate system, U f represents the input torque of the quadrotor aircraft, m is the mass of the quadrotor aircraft, g represents the acceleration of gravity,
将式(1)代入式(2)得：Substitute formula (1) into formula (2):
1.3四旋翼飞行器转动过程中的动态模型为：1.3 The dynamic model during the rotation of the quadrotor aircraft is:
其中τx,τy,τz分别代表机体坐标系上各个轴的力矩分量，Ixx,Iyy,Izz分别表示机体坐标系下的各个轴的转动惯量的分量，×表示叉乘，ωp表示翻滚角速度，ωq表示俯仰角速度，ωr表示偏航角速度，表示翻滚角加速度，表示俯仰角加速度，表示偏航角加速度；Among them, τ x , τ y , τ z respectively represent the moment components of each axis in the body coordinate system, I xx , I yy , I zz respectively represent the components of the moment of inertia of each axis in the body coordinate system, × represents the cross product, ω p represents roll angular velocity, ω q represents pitch angular velocity, ω r represents yaw angular velocity, is the roll angular acceleration, represents the pitch angular acceleration, Indicates the yaw angular acceleration;
考虑到无人机一般处于低速飞行或者悬停状态，姿态角变化较小，认为因此式(4)改写为：Considering that the UAV is generally in a low-speed flight or hovering state, and the attitude angle changes little, it is considered that So formula (4) is rewritten as:
联立式(3)和式(5)，得到四旋翼飞行器的动力学模型为：Combining formula (3) and formula (5), the dynamic model of the quadrotor aircraft is obtained as:
其中ux＝cosφsinθcosψ+sinφsinψ,uy＝cosφsinθsinψ-sinφcosψ； where u x =cosφsinθcosψ+sinφsinψ, u y =cosφsinθsinψ-sinφcosψ;
1.4根据式(6)，定义φ,θ的期望值为：1.4 According to formula (6), define the expected value of φ, θ as:
其中φd为φ的期望信号值，θd为θ期望信号值，arcsin为反正弦函数；Where φ d is the expected signal value of φ, θ d is the expected signal value of θ, and arcsin is the arcsine function;
步骤2，在每一个采样时刻，计算位置跟踪误差及其一阶导数；计算姿态角跟踪误差及其一阶导数；设计位置和姿态角控制器，过程如下：Step 2, at each sampling moment, calculate the position tracking error and its first-order derivative; calculate the attitude angle tracking error and its first-order derivative; design the position and attitude angle controller, the process is as follows:
2.1定义z跟踪误差及其一阶导数：2.1 Define the z tracking error and its first derivative:
其中zd表示z的期望信号；where z d represents the desired signal of z;
2.2设计障碍李雅普诺夫函数并求解其一阶导数：2.2 Design barrier Lyapunov function and solve for its first derivative:
其中Kb1为时变参数，满足为虚拟控制量，其表达式为:where K b1 is a time-varying parameter, satisfying is a virtual control quantity, and its expression is:
其中k11为正常数；Where k 11 is a normal number;
将式(10)代入式(9)，得：Substituting formula (10) into formula (9), we get:
2.3设计李雅普诺夫函数V12为：2.3 Design Lyapunov function V 12 as:
求解式(12)的一阶导数，得：Solving the first order derivative of formula (12), we get:
其中in
将式(14)和式(6)代入式(13)，得：Substituting formula (14) and formula (6) into formula (13), we get:
2.4设计Uf：2.4 Design U f :
其中k12为正常数；Where k 12 is a normal number;
2.5定义x,y跟踪误差分别为e2,e3,则有：2.5 Define x and y tracking errors as e 2 and e 3 respectively, then:
其中xd,yd分别表示x,y的期望信号；Where x d , y d represent the expected signals of x and y respectively;
2.6设计障碍李雅普诺夫函数分别求解其一阶导数，得：2.6 Design barrier Lyapunov function Solving their first derivatives respectively, we get:
其中Kb2为时变参数，满足Kb2>|e2|；Kb3为时变参数，满足Kb3>|e3|；α2,α3为虚拟控制量，其表达式为:Where K b2 is a time-varying parameter, satisfying K b2 >|e 2 |; K b3 is a time-varying parameter, satisfying K b3 >|e 3 |; α 2 , α 3 are virtual control quantities, and their expressions are:
其中k21,k31为正常数；Among them, k 21 and k 31 are normal numbers;
将式(19)代入式(18)，得:Substituting formula (19) into formula (18), we get:
2.7设计李雅普诺夫函数V22,V32 2.7 Design Lyapunov functions V 22 , V 32
求解式(21)的一阶导数，得：Solving the first order derivative of formula (21), we get:
其中in
将式(23)，(6)代入式(22)，分别得：Substituting equations (23) and (6) into equation (22), we get:
2.8通过式(24)，(25)分别设计ux,uy：2.8 Design u x , u y respectively through equations (24) and (25):
其中k22,k32为正常数；Among them, k 22 and k 32 are normal numbers;
2.9定义姿态角跟踪误差及其一阶导数：2.9 Define attitude angle tracking error and its first derivative:
其中j＝4,5,6，x4＝φ,x5＝θ,x6＝ψ，x4d表示φ的期望值，x5d表示θ的期望值，x6d表示ψ的期望值，e4表示φ的跟踪误差，e5表示θ的跟踪误差，e6表示ψ的跟踪误差；Where j=4,5,6, x 4 =φ, x 5 =θ, x 6 =ψ, x 4d represents the expected value of φ, x 5d represents the expected value of θ, x 6d represents the expected value of ψ, e 4 represents the expected value of φ Tracking error, e 5 represents the tracking error of θ, and e 6 represents the tracking error of ψ;
2.10设计障碍李雅普诺夫函数并求解其一阶导数：2.10 Design barrier Lyapunov function and solve for its first derivative:
其中kj为时变参数，满足Kbj>|ej|；αj为姿态角的虚拟控制量，其表达式为:Where k j is a time-varying parameter, satisfying K bj >|e j |; α j is the virtual control quantity of the attitude angle, and its expression is:
其中kj1为正常数；Where k j1 is a normal number;
将式(29)代入式(28)，得：Substituting formula (29) into formula (28), we get:
2.11设计障碍李雅普诺夫函数：2.11 Design barrier Lyapunov function:
求解式(31)的一阶导数，得：Solving the first order derivative of formula (31), we get:
其中 in
将式(33)和式(6)代入式(32)，分别得：Substituting formula (33) and formula (6) into formula (32), we get:
2.12通过式(34)，(35)，(36)分别设计τx,τy,τz：2.12 Design τ x , τ y , τ z through equations (34), (35), and (36):
其中k42,k52,k62为正常数；Among them, k 42 , k 52 , and k 62 are normal numbers;
步骤3，验证四旋翼飞行器系统的稳定性；Step 3, verify the stability of the quadrotor aircraft system;
3.1将式(16)代入式(15)，得：3.1 Substituting formula (16) into formula (15), we get:
3.2将式(26)代入式(24)、(25)，得：3.2 Substituting formula (26) into formulas (24) and (25), we get:
3.3把式(37)代入式(34)、(35)、(36)，得：3.3 Substituting formula (37) into formulas (34), (35), and (36), we get:
3.4通过(38)，(39)，(40)可知四旋翼飞行器系统是稳定的。3.4 Through (38), (39), (40), it can be known that the quadrotor aircraft system is stable.
为了验证所提方法的可行性，本发明给出了该控制方法在MATLAB平台上的仿真结果：In order to verify the feasibility of the proposed method, the present invention provides the simulation results of the control method on the MATLAB platform:
参数给定如下：式(2)中m＝1.1kg，g＝9.81N/kg；式(4)中，Ixx＝1.22kg·m2，Iyy＝1.22kg·m2，Izz＝2.2kg·m2；式(8),式(17)和式(27)中zd＝0.5，xd＝0.5，yd＝0.5，ψd＝0.5；式(10),式(19)和式(29)中k11＝1，k21＝1，k31＝1，k41＝1，k51＝1，k61＝1；式(16)，式(26)和式(37)中k12＝1，k22＝1，k32＝1，k42＝1，k52＝1，k62＝1；式(9)，式(18)和式(28)kb1＝3+0.9sint，kb2＝3+0.9sint，kb3＝3+0.9sint，kb4＝0.5+0.1cost，kb5＝0.8+0.1sint，kb6＝2+0.1cost。The parameters are given as follows: in formula (2), m=1.1kg, g=9.81N/kg; in formula (4), I xx =1.22kg·m 2 , I yy =1.22kg·m 2 , I zz =2.2 kg·m 2 ; z d = 0.5, x d = 0.5, y d = 0.5, ψ d = 0.5 in formula (8), formula (17) and formula (27); formula (10), formula (19) and In formula (29), k 11 =1, k 21 =1, k 31 =1, k 41 =1, k 51 =1, k 61 =1; in formula (16), formula (26) and formula (37) k 12 =1, k 22 =1, k 32 =1, k 42 =1, k 52 =1, k 62 =1; formula (9), formula (18) and formula (28) k b1 =3+0.9 sint, k b2 =3+0.9 sint, k b3 =3+0.9 sint, k b4 =0.5+0.1 cost, k b5 =0.8+0.1 sint, k b6 =2+0.1 cost.
从图1和2可知，系统具有良好的瞬态特性，到达时间为8.15秒，超调量为0。It can be seen from Figures 1 and 2 that the system has good transient characteristics, the arrival time is 8.15 seconds, and the overshoot is 0.
综上所述，基于对称时变障碍李雅普诺夫函数的四旋翼飞行器输出受限反步控制方法能有效地改善四旋翼飞行器系统的瞬态性能。In summary, the quadrotor output-limited backstepping control method based on symmetric time-varying obstacle Lyapunov function can effectively improve the transient performance of the quadrotor system.
以上阐述的是本发明给出的一个实施例表现出的优良优化效果，显然本发明不只是限于上述实施例，在不偏离本发明基本精神及不超出本发明实质内容所涉及范围的前提下对其可作种种变形加以实施。The above set forth is the excellent optimization effect shown by an embodiment of the present invention. Obviously, the present invention is not limited to the above-mentioned embodiment. It can be implemented in various modifications.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111679684A (en) * | 2020-06-16 | 2020-09-18 | 江苏师范大学 | Backstep control method of quadrotor UAV with input time delay |
| CN112327897A (en) * | 2020-11-04 | 2021-02-05 | 江苏师范大学 | Four-rotor unmanned aerial vehicle attitude control method with input dead zone |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106094855A (en) * | 2016-07-27 | 2016-11-09 | 浙江工业大学 | Terminal cooperative control method for quad-rotor unmanned aerial vehicle |
| CN107368088A (en) * | 2017-07-11 | 2017-11-21 | 浙江工业大学 | Four-rotor aircraft nonlinear sliding mode pose control method based on error exponential function |
| CN107368089A (en) * | 2017-07-11 | 2017-11-21 | 浙江工业大学 | Nonlinear sliding mode pose control method of quadrotor aircraft based on double exponential function |
-
2017
- 2017-12-06 CN CN201711274132.3A patent/CN108107726B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106094855A (en) * | 2016-07-27 | 2016-11-09 | 浙江工业大学 | Terminal cooperative control method for quad-rotor unmanned aerial vehicle |
| CN107368088A (en) * | 2017-07-11 | 2017-11-21 | 浙江工业大学 | Four-rotor aircraft nonlinear sliding mode pose control method based on error exponential function |
| CN107368089A (en) * | 2017-07-11 | 2017-11-21 | 浙江工业大学 | Nonlinear sliding mode pose control method of quadrotor aircraft based on double exponential function |
Non-Patent Citations (4)
| Title |
|---|
| 吴琛等: "四旋翼飞行器的轨迹跟踪抗干扰控制", 《控制理论与应用》 * |
| 薛晨琛: "高超声速飞行器分数阶滑模姿态控制方法研究", 《中国优秀硕士学位论文全文数据库工程科技II辑》 * |
| 陈强等: "四旋翼飞行器的轨迹跟踪抗干扰控制", 《2016（第六届）中国国际无人驾驶航空器系统大会论文集》 * |
| 陈强等: "基于全阶滑模的四旋翼无人机有限时间控制", 《探索 创新 交流（第7集）-第七届中国航空学会青年科学论坛文集》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111679684A (en) * | 2020-06-16 | 2020-09-18 | 江苏师范大学 | Backstep control method of quadrotor UAV with input time delay |
| CN112327897A (en) * | 2020-11-04 | 2021-02-05 | 江苏师范大学 | Four-rotor unmanned aerial vehicle attitude control method with input dead zone |
| CN112327897B (en) * | 2020-11-04 | 2022-07-29 | 江苏师范大学 | A quadrotor UAV attitude control method with input dead zone |
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