CN104199303A

CN104199303A - Stratospheric satellite planar path tracking control method based on vector field guidance

Info

Publication number: CN104199303A
Application number: CN201410476759.7A
Authority: CN
Inventors: 郑泽伟; 陈天; 闫柯瑜; 余帅先; 刘丽莎
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2014-09-18
Filing date: 2014-09-18
Publication date: 2014-12-10
Anticipated expiration: 2034-09-18
Also published as: CN104199303B

Abstract

A stratospheric satellite plane path tracking control method based on vector field guidance, the steps are as follows: 1. given expected tracking value: given expected plane path; given expected speed; calculated resistance resultant force F _f received under the expected speed; 2. Navigation calculation: Calculate the desired yaw angle ψ ^d required to eliminate the error between the desired position and the actual position; 3. Path tracking yaw angle error calculation: Calculate the error between the expected yaw angle and the actual yaw angle 4. Sliding mode controller calculation: Calculate the control quantity u required to eliminate the error between the desired yaw angle and the actual yaw angle. 5. Calculation of the control signal of each actuator: calculate the control quantity T, γ of the actuator required to realize the sliding mode control quantity u. The control flow is shown in the accompanying drawing.

Description

A Stratospheric Satellite Plane Path Tracking Control Method Based on Vector Field Guidance

技术领域 technical field

本发明提供一种基于矢量场制导的平流层卫星平面路径跟踪控制方法，它为平流层卫星提供一种跟踪参数化平面路径的新控制方法，属于自动控制技术领域。 The invention provides a method for tracking and controlling the plane path of stratospheric satellites based on vector field guidance, which provides a new control method for tracking parameterized plane paths for stratospheric satellites, and belongs to the technical field of automatic control. the

背景技术 Background technique

平流层卫星是一种新型低成本、低能耗的平流层飞行器。本方法控制对象为采用串列式矢量推进装置的平流层卫星，如图1所示。采用矢量推进的平流层卫星是一类非线性力学系统，其典型飞行状态包括起飞、巡航飞行、变轨、降落等。对于平流层卫星的巡航飞行，目前大多移植自低空飞艇控制方法，未能有针对平流层卫星自身模型、所处物理环境与巡航要求的成熟方法。平流层卫星巡航高度在20km以上，所处空间没有竖直方向对流，因此相比其他飞行器而言，平流层卫星的平面路径跟踪控制更具有工程应用价值。 The stratospheric satellite is a new type of low-cost, low-energy-consumption stratospheric vehicle. The control object of this method is a stratospheric satellite using a tandem vector propulsion device, as shown in Fig. 1 . Stratospheric satellites using vector propulsion are a type of nonlinear mechanical system, and their typical flight states include takeoff, cruise flight, orbit change, and landing. For the cruise flight of stratospheric satellites, most of them are transplanted from low-altitude airship control methods at present, and there is no mature method for the model of the stratospheric satellite itself, the physical environment and cruise requirements. The cruising altitude of stratospheric satellites is above 20km, and there is no vertical convection in the space. Therefore, compared with other aircraft, the planar path tracking control of stratospheric satellites has more engineering application value. the

目前主流路径跟踪算法多采用跟踪期望路径上虚拟点的方法进行导航解算。本方法中采用矢量场制导方法，与传统路径跟踪制导方法不同。采用在跟踪路径周围建立矢量场的方法解算期望姿态，而不是跟踪期望路径上虚拟点。矢量场制导方法的控制对象为卫星姿态，不涉及速度项。因而可以将控制器中时间与空间解耦，为后续其他控制目的(如协同飞行)的实现留下可能。 At present, mainstream path tracking algorithms mostly use the method of tracking virtual points on the desired path for navigation calculation. The vector field guidance method is adopted in this method, which is different from the traditional path-following guidance method. Instead of tracking virtual points on the desired path, the desired pose is solved by establishing a vector field around the tracked path. The control object of the vector field guidance method is the attitude of the satellite, which does not involve the velocity item. Therefore, the time and space in the controller can be decoupled, leaving the possibility for the realization of other subsequent control purposes (such as cooperative flight). the

本发明“一种基于矢量场制导的平流层卫星平面路径跟踪控制方法”，提出了基于动力学非线性模型的平面路径跟踪控制方法。该方法结合了基于矢量场的路径跟踪算法和滑模控制理论。由该方法控制的闭环系统是有界稳定的，且具有良好的收敛效果，这就为平流层卫星的巡航飞行工程的实现提供了有效的设计手段。 The invention "a vector field guidance-based plane path tracking control method for stratospheric satellites" proposes a plane path tracking control method based on a dynamic nonlinear model. The method combines vector field-based path-following algorithm and sliding mode control theory. The closed-loop system controlled by this method is bounded and stable, and has a good convergence effect, which provides an effective design method for the realization of the cruise flight engineering of stratospheric satellites. the

发明内容 Contents of the invention

(1)目的：本发明的目的在于提供一种基于矢量场制导的平流层卫星平面路径跟踪控制方法，控制工程师可以按照该方法并结合实际参数实现平流层卫星的巡航飞行。 (1) purpose: the purpose of the present invention is to provide a kind of stratospheric satellite plane path tracking control method based on vector field guidance, control engineer can realize the cruising flight of stratospheric satellite according to this method and in conjunction with actual parameter. the

(2)技术方案：本发明“一种基于矢量场制导的平流层卫星平面路径控制方法”，其主要内容及程序是： (2) Technical scheme: the present invention " a kind of stratospheric satellite plane path control method based on vector field guidance ", its main content and program are:

平流层卫星的巡航轨道通常为直线或者圆弧，其变轨路径也可近似分解为参数化的直线和圆弧。先利用矢量场理论在给定期望路径(包括直线和圆弧路径)所在平面建立导航矢量场，生成期望角度；然后利用滑模控制理论设计路径跟踪控制器，使其跟踪误差在有限时间内趋近于零。实际应用中，平流层卫星的位置、姿态、速度等状态量由组合惯导等机载传感器测量得到，将由该方法计算得到的控制量传输至矢量控制和推进螺旋桨等执行装置即可实现平流层卫星的平面路径跟踪功能。 The cruising orbit of a stratospheric satellite is usually a straight line or an arc, and its orbit change path can also be approximately decomposed into parameterized straight lines and arcs. First use the vector field theory to establish a navigation vector field on the plane where the desired path (including straight line and arc path) is located, and generate the desired angle; then use the sliding mode control theory to design the path tracking controller, so that the tracking error tends to close to zero. In practical applications, the position, attitude, speed and other state quantities of the stratospheric satellite are measured by airborne sensors such as integrated inertial navigation, and the control quantities calculated by this method are transmitted to vector control and propulsion propellers and other actuators to realize stratospheric Planar path tracking capabilities for satellites. the

本发明“一种基于矢量场制导的平流层卫星平面路径跟踪控制方法”，其具体步骤如下： The present invention " a kind of vector field guidance based on stratospheric satellite plane path tracking control method ", its specific steps are as follows:

步骤一给定期望跟踪值：给定期望平面路径；给定期望速度；计算该期望速度下受到的阻力合力F_f。 Step 1. Given the expected tracking value: given the expected plane path; given the expected speed; calculating the resultant force F _f of the resistance at the expected speed.

步骤二导航计算：计算消除期望位置与实际位置之间的误差所需的期望偏航角ψ^d。 Step 2 Navigation calculation: Calculate the expected yaw angle ψ ^d required to eliminate the error between the expected position and the actual position.

步骤三路径跟踪偏航角误差计算：计算期望偏航角与实际偏航角之间的误差 Step 3 path tracking yaw angle error calculation: calculate the error between the expected yaw angle and the actual yaw angle

步骤四滑模控制器计算：计算消除期望偏航角与实际偏航角之间误差所需的控制量u。 Step 4 Calculation of the sliding mode controller: Calculate the control quantity u required to eliminate the error between the desired yaw angle and the actual yaw angle. the

步骤五各执行部件控制信号计算：计算实现滑模控制量u所需的执行部件控制量T,γ。 Step 5 Calculation of the control signals of each execution unit: calculate the control quantities T, γ of the execution units required to realize the sliding mode control quantity u. the

其中，在步骤一中所述的给定期望平面路径分为直线和圆弧两种，直线路径由直线与北向夹角ξ确定，记作p_l(ξ)；圆路径由圆心位置与半径确定记作p_o(c_x,c_y,r)。所述的给定期望速度为υ_c＝[u_c,v_c,w_c]^T＝[C,0,0]^T，C＞0为常数，u_c,v_c,w_c为期望速度沿艇体坐标系的分解量。 Among them, the given expected plane path described in step 1 is divided into two types: straight line and circular arc. The straight line path is determined by the angle ξ between the straight line and the north direction, denoted as p _l (ξ); the circular path is determined by the center position and radius Denote it as p _o (c _x ,c _y ,r). The given desired speed is υ _c =[u _c ,v _c ,w _c ] ^T =[C,0,0] ^T , C>0 is a constant, _uc ,v _c ,w _c are the desired speed along the The decomposition amount of the hull coordinate system.

其中，在步骤二中所述的计算消除期望位置与实际位置之间的误差所需的期望偏航角ψ^d，其计算方法如下： Wherein, the desired yaw angle ψ ^d required to eliminate the error between the desired position and the actual position is calculated in step 2, and its calculation method is as follows:

直线：其中ψ^∞为设定的初始偏航角，y为机体与直线路径之间的位置误差，可由规划路径起始点坐标P_A＝[x_A y_A]^T机体位置坐标P_o＝[x_o y_o]^T与直线路径由直线与北向夹角ξ求得；ψ为平流层卫星偏航角，可由机体轴与北向夹角ζ与直线位置角ξ求得，即ψ＝ζ-ξ，k＞0为决定矢量场中矢量方向转换速度的参数； straight line: Where ψ ^∞ is the set initial yaw angle, y is the position error between the body and the straight path, which can be obtained from the coordinates of the starting point of the planned path P _A =[x _A y _A ] ^T body position coordinates P _o =[x _o y _o ] ^T and the straight-line path are obtained from the angle ξ between the straight line and the north direction; ψ is the yaw angle of the stratospheric satellite, which can be obtained from the angle ζ between the body axis and the north direction and the position angle ξ of the straight line, that is, ψ=ζ-ξ, k> 0 is the parameter that determines the vector direction conversion speed in the vector field;

圆弧：其中θ为机体位置与期望路径圆心连线与北向夹角，可由机体位置P_o＝[x_o y_o]与期望路径圆心位置P_c＝[x_c y_c]求得，d为机体位置与期望位置之间的距离，k＞0为决定矢量场中矢量方向转换速度的参数。 Arc: Where θ is the angle between the body position and the center of the expected path circle and the north direction, which can be obtained from the position of the body P _o = [x _o y _o ] and the position of the center of the expected path P _c = [x _c y _c ], d is the position of the body and The distance between desired positions, k>0 is a parameter that determines the vector direction conversion speed in the vector field.

其中，在步骤三中所述的路径跟踪偏航角误差其计算方法如下： Among them, the path tracking yaw angle error described in step three Its calculation method is as follows:

直线： $\tilde{ψ} = ψ - ψ^{d} (y)$ straight line: $\tilde{ψ} = ψ - ψ^{d} (the y)$

圆弧： $\tilde{ψ} = ψ - ψ^{d} (d)$ Arc: $\tilde{ψ} = ψ - ψ^{d} (d)$

其中，在步骤四中所述的消除期望偏航角与实际偏航角之间的误差所需的控制量u，其计算方法如下： Among them, the control quantity u required to eliminate the error between the expected yaw angle and the actual yaw angle described in step 4 is calculated as follows:

直线： $u_{l} = - β_{1} - β_{l} (x) sat (\frac{s}{ϵ}),$ 其中ε＞0 straight line: $u_{l} = - β_{1} - β_{l} (x) sat (\frac{the s}{ϵ}),$ Where ε>0

其中， in,

${β β}_{11} = = {ψ ψ}^{\infty \infty} \frac{22}{π π} ((\frac{{k k}^{33} y the y {V V}_{g g}^{22} {sin sin}^{22} ψ ψ}{{((11 + + {((ky ky))}^{22}))}^{22}} + + \frac{{kV kV}_{g g} \overset{. .}{ψ ψ} cos cos ψ ψ}{11 + + {((ky ky))}^{22}})) + + a a \overset{. .}{\overset{~ ~}{ψ ψ}},, k k > > 00,, a a > > 00$

${β β}_{l l} ((x x)) = = {k k}^{33} | | y the y | | {V V}_{g g}^{22} {ψ ψ}^{22} + + {β β}_{00},, {β β}_{00} > > 00$

圆弧： $u_{o} = - β_{2} - β_{o} (x) sat (\frac{s}{ϵ}),$ 其中ε＞0 Arc: $u_{o} = - β_{2} - β_{o} (x) sat (\frac{the s}{ϵ}),$ Where ε>0

其中， in,

${β β}_{22} = = tan the tan ((ψ ψ - - θ θ)) - - \frac{{V V}_{g g} \overset{. .}{ψ ψ} cos cos ((ψ ψ - - θ θ))}{d d} + + \frac{{22 k k}^{22} {V V}_{g g}^{22} \overset{~ ~}{d d} {cos cos}^{22} ((ψ ψ - - θ θ))}{{((11 + + {((k k \overset{~ ~}{d d}))}^{22}))}^{22}} + + \frac{{kV kV}_{g g} \overset{. .}{ψ ψ} sin sin ((ψ ψ - - θ θ))}{11 + + {((k k \overset{~ ~}{d d}))}^{22}} + + b b \overset{. .}{\overset{~ ~}{ψ ψ}},, k k > > 00,, b b > > 00$

${β β}_{o o} ((x x)) = = \frac{{V V}_{g g} ((22 d d + + 11))}{{22 d d}^{22}} + + {β β}_{00},, {β β}_{00} > > 00$

上述各式中ε为可调节正数，定义了围绕滑动面边界区的宽度。 In the above formulas, ε is an adjustable positive number, which defines the width of the boundary area around the sliding surface. the

其中，在步骤五中所述的实现滑模控制量u所需的执行部件控制量T,γ，其计算方法如下： Among them, the calculation method of the execution component control quantity T,γ required to realize the sliding mode control quantity u required in step five is as follows:

直线： straight line:

$\{\begin{matrix} γ γ = = {tan the tan}^{- - 11} ((\frac{- - 22 \overset{~ ~}{J J} (({β β}_{11} + + {β β}_{l l} ((x x)) sat sat ((\frac{s the s}{ϵ ϵ}))))}{{F f}_{f f} l l})) \\ T T = = \frac{{F f}_{f f}}{22 cos cos γ γ} \end{matrix}$

各参数要求为 Each parameter requires

a＞0,β₀＞0,ε＞0 a＞0, _β0 ＞0,ε＞0

圆弧： Arc:

$\{\begin{matrix} γ γ = = {tan the tan}^{- - 11} ((\frac{- - 22 \overset{~ ~}{J J} (({β β}_{22} + + {β β}_{o o} ((x x)) sat sat ((\frac{s the s}{ϵ ϵ}))))}{{F f}_{f f} l l})) \\ T T = = \frac{{F f}_{f f}}{22 cos cos γ γ} \end{matrix}$

各参数要求为 Each parameter requires

b＞0,β₀＞0,ε＞0 b＞0, _β0 ＞0,ε＞0

(3)优点及效果： (3) Advantages and effects:

本发明“一种基于矢量场制导的平流层卫星平面路径跟踪控制方法”，与现有技术比，其优点是： Compared with the prior art, the present invention "a method for tracking and controlling the plane path of stratospheric satellites based on vector field guidance" has the following advantages:

1)该方法直接利用路径周围矢量场而不是跟踪路径上虚拟点进行路径跟踪，将时间与空间解耦，可实现其他与时间相关的控制目的，如在时间约束下的协同飞行。 1) This method directly uses the vector field around the path instead of virtual points on the path to track the path, decouples time and space, and can achieve other time-related control purposes, such as cooperative flight under time constraints. the

2)该方法能够保证闭环系统的渐近稳定性能，且收敛速度及滑动流形边界层厚度可根据实际要求进行调节； 2) This method can guarantee the asymptotically stable performance of the closed-loop system, and the convergence rate and the thickness of the sliding manifold boundary layer can be adjusted according to actual requirements;

3)该方法采用滑模控制方法，能够克服系统的不确定性，对干扰和未建模动态具有很强的鲁棒性，尤其是对非线性系统的控制具有良好的控制效果。 3) This method adopts the sliding mode control method, which can overcome the uncertainty of the system, has strong robustness to disturbance and unmodeled dynamics, and has a good control effect especially on the control of nonlinear systems. the

4)该方法采用变结构控制算法，结构简单，响应速度快，易于工程实现。 4) This method adopts variable structure control algorithm, which has simple structure, fast response speed and easy engineering implementation. the

控制工程师在应用过程中可以根据实际平流层卫星给定任意期望巡航路径，并将由该方法计算得到的控制量直接传输至执行机构实现路径跟踪功能。 During the application process, the control engineer can give any desired cruise path according to the actual stratospheric satellite, and directly transmit the control quantity calculated by this method to the actuator to realize the path tracking function. the

附图说明 Description of drawings

图1为本发明所述控制方法流程框图； Fig. 1 is a flow diagram of the control method of the present invention;

图2为本发明平流层卫星示意图； Fig. 2 is the schematic diagram of stratospheric satellite of the present invention;

图3为本发明矢量场直线路径导航计算几何关系图； Fig. 3 is the vector field straight line path navigation calculation geometric relationship diagram of the present invention;

图4为本发明矢量场圆弧路径导航计算几何关系图； Fig. 4 is vector field circular arc path navigation calculation geometry relationship figure of the present invention;

符号说明如下： The symbols are explained as follows:

P_A P_A＝[x_A y_A]^T为直线期望路径规划起始点位置； P _A P _A ＝[x _A y _A ] ^T is the position of the starting point of the straight line expected path planning;

P_o P_o＝[x_o y_o]^T为飞艇在惯性坐标系下的当前位置； P _o P _o =[x _o y _o ] ^T is the current position of the airship in the inertial coordinate system;

ξ 期望直线路径与北向夹角； ξ The angle between the expected straight line path and the north direction;

ψ 平流层卫星偏航角； ψ Stratospheric satellite yaw angle;

ψ^d 平流层卫星期望偏航角； ψ ^d Stratospheric satellite expected yaw angle;

平流层卫星偏航角误差； Stratospheric satellite yaw angle error;

平流层卫星偏航角速度； Stratospheric satellite yaw rate;

ψ 平流层卫星偏航角； ψ Stratospheric satellite yaw angle;

T 单个螺旋桨产生推力； T A single propeller produces thrust;

γ 矢量装置的矢量偏角； γ the vector deflection angle of the vector device;

V_g 惯性系中平流层卫星速度； V _g is the velocity of the stratospheric satellite in the inertial frame;

[u v w] 平流层卫星机体坐标系下线速度； [u v w] Stratospheric satellite body coordinate system off-line speed;

[p q r] 平流层卫星机体坐标系下角速度； [p q r] Angular velocity in the coordinate system of the stratospheric satellite body;

ζ 机体轴与北向夹角； ζ The angle between the body axis and the north direction;

ψ^∞ 无穷远处偏航角，矢量场参数，为可调节正数； ψ ^∞ yaw angle at infinity, a vector field parameter, is an adjustable positive number;

(x_C,y_C) 圆弧路径圆心位置坐标； (x _C ,y _C ) The position coordinates of the center of the arc path;

R 圆弧路径半径； R arc path radius;

θ 机体位置和圆心位置连线与北向夹角 θ The angle between the line connecting the position of the body and the center of the circle and the north direction

d 机体距离圆心距离； d The distance between the body and the center of the circle;

具体实施方式 Detailed ways

下面结合附图，对本发明中的各部分设计方法作进一步的说明： Below in conjunction with accompanying drawing, each part design method in the present invention is further described:

本发明“一种基于矢量场制导的平流层卫星平面路径跟踪控制方法”，见图1所示，其具体步骤如下：步骤一：给定期望跟踪值 The present invention "a kind of stratospheric satellite plane path tracking control method based on vector field guidance" is shown in Fig. 1, and its specific steps are as follows: Step 1: given expected tracking value

1)如图2所示，以平流层卫星浮心为原点建立艇体坐标系Oxyz；以地面上任一点为原点建立惯性坐标系O_gx_gy_gz_g，其中原点O_g为地面任意一点，O_gx_g指向北，O_gy_g指向东，O_gz_g指向地心。 1) As shown in Figure 2, the hull coordinate system Oxyz is established with the buoyancy center of the stratospheric satellite as the origin; the inertial coordinate system O _g x _g y _g z _g is established with any point on the ground as the origin, where the origin O _g is any point on the ground , O _g x _g points to the north, O _g y _g points to the east, and O _g z _g points to the center of the earth.

2)给定期望平面路径，包括直线和圆弧。其中，如图3所示，直线路径由直线与北向坐标轴O_gx_g夹角ξ确定；如图4所示，圆弧路径由圆心位置P_c＝[x_c,y_c]^T与半径R确定记作p_o(x_c,y_c,R)。 2) Given the expected plane path, including straight lines and arcs. Among them, as shown in Figure 3, the linear path is determined by the angle ξ between the straight line and the northward coordinate axis O _g x _g ; as shown in Figure 4, the arc path is determined by the center position P _c =[x _c ,y _c ] ^T and the radius R is definitely recorded as p _o (x _c , y _c , R).

3)给定期望速度υ_c＝[u_c,v_c,w_c]^T＝[C,0,0]^T，C＞0为常数，u_c,v_c,w_c为期望速度沿机体坐标系的分解量。在平流层卫星工作环境中，无垂直方向风速，水平风速较小，可将其影响忽略。本方法中控制平流层卫星前向速度为定值，因而对于水平面内路径跟踪，可认为卫星前向速度与地速相等，即V_g＝u_c＝C。 3) Given the desired velocity υ _c =[ _uc ,v _c ,w _c ] ^T =[C,0,0] ^T , C>0 is a constant, uc _, v _c ,w _c are the coordinates of the desired velocity along the body The decomposition of the system. In the working environment of stratospheric satellites, there is no vertical wind speed, and the horizontal wind speed is small, so its influence can be ignored. In this method, the forward velocity of the stratospheric satellite is controlled to be a constant value, so for path tracking in the horizontal plane, the forward velocity of the satellite can be considered to be equal to the ground velocity, that is, V _g =u _c =C.

步骤二：计算期望偏航角 Step 2: Calculate the expected yaw angle

1)直线路径期望偏航角计算： 1) Calculate the expected yaw angle of the straight path:

首先，计算机体距离直线的位置误差y，如图3所示y＝(x_o-x_A)cosξ-(y_o-y_A)sinξ； First, calculate the position error y between the body and the straight line, as shown in Figure 3 y=(x _o -x _A )cosξ-(y _o -y _A )sinξ;

然后，给定无穷远处偏航角ψ^∞，..； Then, given the yaw angle ψ ^∞ at infinity, ..;

最后，计算直线路径期望偏航角ψ^d(y)， Finally, calculate the desired yaw angle ψ ^d (y) for the straight-line path,

2)圆弧路径期望偏航角计算： 2) Calculate the expected yaw angle of the arc path:

首先，计算机体距离圆心的位置误差d，如图4所示， First, calculate the position error d of the body from the center of the circle, as shown in Figure 4,

然后，计算机体位置与圆心位置连线与北向坐标轴O_gx_g夹角θ，如图4所示， Then, calculate the angle θ between the line connecting the position of the body and the center of the circle and the north coordinate axis O _g x _g , as shown in Figure 4,

最后，计算圆弧路径期望偏航角ψ^d(d)， Finally, calculate the desired yaw angle ψ ^d (d) of the arc path,

步骤三：计算路径跟踪偏航角误差 Step 3: Calculate path tracking yaw angle error

1)对于直线路径，偏航角为机体轴Ox相对于直线的偏转角度，可由机体轴Ox与北向坐标轴O_gx_g夹角ζ与直线位置角ξ求得，即ψ＝ζ-ξ； 1) For a straight line path, the yaw angle is the deflection angle of the body axis Ox relative to the straight line, which can be obtained from the angle ζ between the body axis Ox and the north coordinate axis O _g x _g and the straight line position angle ξ, that is, ψ=ζ-ξ;

2)对于圆弧路径，偏航角为机体轴Ox与北向坐标轴O_gx_g夹角，可直接测得； 2) For a circular path, the yaw angle is the angle between the body axis Ox and the north coordinate axis O _g x _g , which can be directly measured;

3)分别求直线与圆弧路径的偏航角误差 3) Calculate the yaw angle error of straight line and arc path respectively

圆弧： $\tilde{ψ} = ψ - ψ^{d} (d) .$ Arc: $\tilde{ψ} = ψ - ψ^{d} (d) .$

步骤四：设计滑模控制路径跟踪控制器 Step 4: Design the sliding mode control path tracking controller

1)对于前后串列式矢量推进平流层卫星，其水平面内动力学模型可表示如下 $\{\begin{matrix} m {\dot{V}}_{g} = T + F_{f} \\ J \overset{. .}{ψ} = N_{T} + N_{add} \end{matrix}$ 其中T为推力项，F_f为阻力项，包括空气阻力与附加惯性力；为推力引起的力矩项，为附加惯性力矩项。动力学模型方程中各项的具体值随不同飞艇结构和参数而不同，在实际应用中根据实际情况确定。 1) For the forward and backward tandem vector propulsion stratospheric satellites, the dynamic model in the horizontal plane can be expressed as follows $\{\begin{matrix} m {\dot{V}}_{g} = T + f_{f} \\ J \overset{. .}{ψ} = N_{T} + N_{add} \end{matrix}$ Where T is the thrust item, F _f is the drag item, including air resistance and additional inertial force; is the moment term caused by thrust, is the additional moment of inertia term. The specific values of the items in the dynamic model equations vary with different airship structures and parameters, and are determined according to actual conditions in practical applications.

故对于机体轴方向，由定速可得因而对于绕Oz坐标轴，有 $(J + J^{'}) \overset{. .}{ψ} = Tl \sin γ .$ Therefore, for the direction of the body axis, from the constant velocity, we can get thus For around the Oz coordinate axis, we have $(J + J^{'}) \overset{. .}{ψ} = Tl \sin γ .$

2)对于直线路径，采用一个滑动模型来保证系统路径在有限时间内收敛到期望路径： 2) For straight-line paths, a sliding model is used to ensure that the system path converges to the desired path within a finite time:

$s the s = = \overset{. .}{\overset{~ ~}{ψ ψ}} + + a a \overset{~ ~}{ψ ψ} = = 00,, a a > > 00$

则有 then there

$\overset{. .}{s the s} = = \overset{. . . .}{\overset{~ ~}{ψ ψ}} + + a a \overset{. .}{\overset{~ ~}{ψ ψ}} = = \frac{Tl Tl}{\overset{~ ~}{J J}} sin sin γ γ + + {ψ ψ}^{\infty \infty} \frac{22}{π π} ((\frac{{22 k k}^{33} y the y {V V}_{g g}^{22} {sin sin}^{22} ψ ψ}{{((11 + + {((ky ky))}^{22}))}^{22}} + + \frac{k k {\overset{. .}{V V}}_{g g} sin sin ψ ψ + + {kV kV}_{g g} \overset{. .}{ψ ψ} cos cos ψ ψ}{11 + + {((ky ky))}^{22}})) + + a a \overset{. .}{\overset{~ ~}{ψ ψ}}$

其中， $\dot{\tilde{ψ}} = \dot{ψ} + ψ^{\infty} \frac{2}{π} \frac{k}{1 + {(ky)}^{2}} V_{g} \sin ψ .$ in, $\dot{\tilde{ψ}} = \dot{ψ} + ψ^{\infty} \frac{2}{π} \frac{k}{1 + {(ky)}^{2}} V_{g} \sin ψ .$

①取控制项为 ① Take the control item as

${μ μ}_{l l} = = \frac{Tl Tl}{\overset{~ ~}{J J}} sin sin γ γ,, \overset{~ ~}{J J} = = J J + + {J J}^{' '}$

②计算状态反馈控制器 ②Calculation state feedback controller

${β β}_{11} = = {ψ ψ}^{\infty \infty} \frac{22}{π π} ((\frac{{k k}^{33} y the y {V V}_{g g}^{22} {sin sin}^{22} ψ ψ}{{((11 + + {((ky ky))}^{22}))}^{22}} + + \frac{{kV kV}_{g g} \overset{. .}{ψ ψ} cos cos ψ ψ}{11 + + {((ky ky))}^{22}})) + + a a \overset{. .}{\overset{~ ~}{ψ ψ}}$

③计算滑模切换器边界层厚度 ③ Calculate the boundary layer thickness of the sliding mode switcher

$β_{l} (x) = k^{3} | y | V_{g}^{2} ψ^{2} + β_{0},$ 其中β₀＞0，为可调参数。 $β_{l} (x) = k^{3} | the y | V_{g}^{2} ψ^{2} + β_{0},$ Among them, β ₀ >0 is an adjustable parameter.

④计算直线路径跟踪滑模控制器 ④ Calculate the linear path tracking sliding mode controller

$μ_{l} = - β_{1} - β_{l} (x) sat (\frac{s}{ϵ}),$ 其中ε＞0 $μ_{l} = - β_{1} - β_{l} (x) sat (\frac{the s}{ϵ}),$ Where ε>0

3)对于圆弧路径，采用一个滑动模型来保证系统路径在有限时间内收敛到期望路径： 3) For the arc path, a sliding model is used to ensure that the system path converges to the desired path within a finite time:

则有 then there

$\begin{matrix} \overset{. .}{s the s} = = \overset{. . . .}{\overset{~ ~}{ψ ψ}} + + b b \overset{. .}{\overset{~ ~}{ψ ψ}} \\ = = \frac{Tl Tl}{\overset{~ ~}{J J}} sin sin γ γ + + tan the tan ((ψ ψ - - θ θ)) - - \frac{{V V}_{g g} \overset{. .}{ψ ψ} cos cos ((ψ ψ - - θ θ))}{d d} + + \frac{{V V}_{g g}}{{d d}^{22}} sin sin ((ψ ψ - - θ θ)) cos cos ((ψ ψ - - θ θ)) \\ + + \frac{{22 k k}^{22} {V V}_{g g}^{22} \overset{~ ~}{d d} {cos cos}^{22} ((ψ ψ - - θ θ))}{{((11 + + {((k k \overset{~ ~}{d d}))}^{22}))}^{22}} + + \frac{{kV kV}_{g g} \overset{. .}{ψ ψ} sin sin ((ψ ψ - - θ θ))}{11 + + {((k k \overset{~ ~}{d d}))}^{22}} + + \frac{{V V}_{g g} {sin sin}^{22} ((ψ ψ - - θ θ))}{d d ((11 + + {((k k \overset{~ ~}{d d}))}^{22}))} + + b b \overset{. .}{\overset{~ ~}{ψ ψ}} \end{matrix}$

其中 $\dot{\tilde{ψ}} = \dot{ψ} - \frac{V_{g}}{d} \sin (ψ - θ) + \frac{k}{1 + {(k \tilde{d})}^{2}} \cos (ψ - θ), \tilde{d} = d - r .$ in $\dot{\tilde{ψ}} = \dot{ψ} - \frac{V_{g}}{d} \sin (ψ - θ) + \frac{k}{1 + {(k \tilde{d})}^{2}} \cos (ψ - θ), \tilde{d} = d - r .$

①取控制项为 ① Take the control item as

$μ μ = = \frac{Tl Tl}{\overset{~ ~}{J J}} sin sin γ γ,, \overset{~ ~}{J J} = = J J + + {J J}^{' '}$

②计算状态反馈控制器 ②Calculation state feedback controller

${β β}_{22} = = tan the tan ((ψ ψ - - θ θ)) - - \frac{{V V}_{g g} \overset{. .}{ψ ψ} cos cos ((ψ ψ - - θ θ))}{d d} + + \frac{{22 k k}^{22} {V V}_{g g}^{22} \overset{~ ~}{d d} {cos cos}^{22} ((ψ ψ - - θ θ))}{{((11 + + {((k k \overset{~ ~}{d d}))}^{22}))}^{22}} + + \frac{{kV kV}_{g g} \overset{. .}{ψ ψ} sin sin ((ψ ψ - - θ θ))}{11 + + {((k k \overset{~ ~}{d d}))}^{22}} + + b b \overset{. .}{\overset{~ ~}{ψ ψ}}$

$β_{o} (x) = \frac{V_{g} (2 d + 1)}{{2 d}^{2}} + β_{0},,$ 其中β₀＞0，为可调参数。 $β_{o} (x) = \frac{V_{g} (2 d + 1)}{{2 d}^{2}} + β_{0},,$ Among them, β ₀ >0 is an adjustable parameter.

$μ_{o} = - β_{2} - β_{o} (x) sat (\frac{s}{ϵ}),$ 其中ε＞0 $μ_{o} = - β_{2} - β_{o} (x) sat (\frac{the s}{ϵ}),$ Where ε>0

步骤五：计算各执行部件控制信号 Step 5: Calculate the control signals of each execution component

1)计算直线路径所需各执行部件控制信号 1) Calculate the control signals of each executive component required for the straight line path

各参数要求为a＞0,β₀＞0,ε＞0 The parameters are required to be a>0, β ₀ >0, ε>0

2)计算圆弧路径所需各执行部件控制信号 2) Calculate the control signals of the execution components required for the arc path

各参数要求为b＞0,β₀＞0,ε＞0 。 Each parameter is required to be b>0, β ₀ >0, ε>0.

Claims

1. A stratosphere satellite plane path tracking control method based on vector field guidance is characterized by comprising the following steps: the method comprises the following specific steps:

step one given the desired tracking value: given a desired planar path; giving a desired speed; calculating the resultant force F of the resistance force received at the expected speed_f。

Step two, navigation calculation: calculating a desired yaw angle psi required to eliminate an error between the desired position and the actual position^d。

Calculating the yaw angle error of the path tracking: calculating an expectationError between yaw angle and actual yaw angle

Step four, calculating by a sliding mode controller: a control amount u required to eliminate an error between the desired yaw angle and the actual yaw angle is calculated.

Step five, calculating control signals of each execution part: an execution-member control amount T, γ required to realize the sliding-mode control amount u is calculated.

2. The stratosphere satellite plane path tracking control method based on vector field guidance according to claim 1, characterized in that:

the given expected plane path in the step one is divided into a straight line and a circular arc, wherein the straight line path is determined by an included angle xi between the straight line and the north direction and is marked as p_l(ξ); the circle path is determined by the position of the center of the circle and the radius and is recorded as p_o(c_x,c_yR). Said given desired velocity is υ_c＝[u_c,v_c,w_c]^T＝[C,0,0]^TC > 0 is a constant, u_c,v_c,w_cThe decomposition of the desired speed along the hull coordinate system.

3. The stratosphere satellite plane path tracking control method based on vector field guidance according to claim 1, characterized in that:

the calculation described in step two of the desired yaw angle psi required to eliminate the error between the desired position and the actual position^dThe calculation method is as follows:

straight line:wherein psi^∞For the set initial yaw angle, y is the position error between the machine body and the straight path, and the coordinate P of the starting point of the planned path can be used_A＝[x_A y_A]^TBody position coordinate P_o＝[x_o y_o]^TSolving the angle xi between the straight line and the north direction of the straight line path; psi is the yaw angle of the stratosphere satellite, and can be obtained by the included angle zeta between the axis of the body and the north direction and the position angle xi of the straight line, namely psi is zeta-xi, and k is more than 0 and is a parameter for determining the vector direction conversion speed in the vector field;

arc:wherein theta is the included angle between the north direction and the line connecting the machine body position and the center of the expected path, and can be determined from the machine body position P_o＝[x_o y_o]To the desired path center position P_c＝[x_c y_c]And d is the distance between the position of the machine body and the expected position, and k is more than 0 and is a parameter for determining the vector direction conversion speed in the vector field.

4. The stratosphere satellite plane path tracking control method based on vector field guidance according to claim 1, characterized in that:

path tracking yaw angle error as described in step threeThe calculation method is as follows:

straight line:

arc:。

5. the stratosphere satellite plane path tracking control method based on vector field guidance according to claim 1, characterized in that:

the control quantity u required to eliminate the error between the desired yaw angle and the actual yaw angle, which is described in step four, is calculated as follows:

straight line:wherein epsilon is more than 0

Wherein,

arc:wherein epsilon is more than 0

Wherein,

in each of the above formulas, ε is an adjustable positive number defining the width of the boundary region around the sliding surface.

6. The stratosphere satellite plane path tracking control method based on vector field guidance according to claim 1, characterized in that:

the execution-member control amount T, γ required to realize the sliding-mode control amount u described in step five is calculated as follows:

straight line:

each parameter is required to be

a＞0,β₀＞0,ε＞0

Arc:

each parameter is required to be

b＞0,β₀＞0,ε＞0 。