飞行控制翻译

1、A new nonlinear guidance logic, that has demonstrated superior performance in guiding unmanned air vehicles (UAVs) on curved trajectories, is presented. The logic approximates a proportional-derivative controller when following a straight line path, but the logic also contains an element of anticipa

2、tory control enabling tight tracking when following curved paths. The method uses inertial speed in the computation of commanded lateral acceleration and adds adaptive capability to the change of vehicle speed due to external disturbances, such as wind. Flight tests using two small UAVs showed that

3、each aircraft was controlled to within 1.6 meters RMS when following circular paths. The logic was ultimately used for air rendezvous of the two aircraft, bringing them in close proximity to within 12 meters of separation, with 1.4 meters RMS relative position errors一种新的非线性导航理论被提出了，它在无人飞行器在弯曲轨迹飞行的运用

4、中表现出了优良性能。当直线飞行时，这个理论接近于一个比例微分控制器，但是，这个理论包含了一个预期控制的元素，使飞行器紧紧跟随曲线路径。该方法把惯性速度运用于command横向加速度的计算（command lateral acceleration）并且增加了针对由于外部干扰（例如风）而引起飞行器的速度变化的自适应能力。使用两架小型无人飞行器的飞行试验表明：当以圆形轨迹飞行时，飞行器将被控制在1.6米以内时。该理论最终运用于飞行器的空中交会，使飞行器之间保持在接近12米的距离内，允许1.4米的相对误差Nomenclature 术语V Vehicle velocity 飞行速度 补偿速度 L1 A

5、line defined from vehicle position to a reference point on a desired trajectory在预定轨迹中，定义前飞行位置到参考点的的直线（距离？）Angle created from V to the line L1 (clockwise direction is positive)速度方向V与我们的L1直线的方向的夹角（顺时针方向为正）ascmd Acceleration command sideways i.e. perpendicular to vehicle velocity direction侧向加速度，垂直于飞行器的

6、速度方向d Cross-track error交叉航迹误差R Radius of circle or circular segment圆或则圆弧的半径L Lyapunov function李亚普诺夫函数I. Introduction 1介绍Two approaches can be considered for the problem of trajectory tracking. One method separates the vehicle guidance and control problems into an outer guidance loop and an inner con

7、trol loop. The inner loop controls the vehicle to follow acceleration commands which are generated by the outer loop. Simple strategies,based on geometric and kinematic properties, are typically used in the outer guidance loop. The alternative method uses an integrated approach wherein the inner and

8、 outer loops are designed simultaneously. In this case, a number of modern control design techniques can be applied, such as receding horizon 1, differentialfatness 2, 3 and neural network based adaptive controls我们有两套可以考虑的关于轨迹跟踪问题的方法，一种方法就是将飞行器引导和控制的问题分为外引导回路和内控制回路。内引导回路控制飞行器跟随由外控制回路产生的加速度。基于几何和运动特性

9、的简单策略通常被运用于外引导回路。另一种方法是应用集成手段将内外集成一体，其中内外控制回路是同时设计的。在这种情况下，一些现代的控制设计技术可以被应用，如：滚动优化，differential fatness，神经网络的自适应控制。In most actual flight applications the separate inner and outer loop approach is more commonly taken because it is usually simpler and well-established design methods are available for

10、inner loop vehicle control. Linear controllers are commonly used for the outer loop guidance of an aircraft. Typically, proportional and derivative (PD) controllers are used on the cross-track error, which is the lateral deviation from a desired flight path. If the desired trajectory path is similar

11、 to a straight line, then this simple strategy will provide reasonably good outer loop performance. However, when tasks require tight tracking of complex curved paths, linear feedback on the cross-track error may not provide satisfactory performance. The guidance logicpresented in this paper contain

12、s an anticipatory control element which overcomes the inherent limitation of feedback control in following curved paths.在大多数实际飞行应用中，单独的内或外控制回路方法是比较常用的，因为这样通常是比较简单的，而且对内回路的飞行器的控制是一个非常有效的设计方法。线性控制器通常用于飞机的外环制导控制。通常情况下，比例以及它的衍生（比例微分）控制器被用于交叉误差的跟踪，交叉误差就是偏离于期望飞行路径的横向偏差。如果期望的轨迹路径近似一条直线，那么这个简单的策略将提供非常好的外环控制

13、性能。然而当我们需要精确跟踪复杂弯曲的路径时，基于交叉轨迹跟踪的线性反馈不能提供令人满意的性能。在本文中提出的制导理论包含了一种预期控制的元素，它克服了在跟随弯曲路径的反馈控制的固有限制。There are several terminal phase guidance laws for short-range tactical missiles that can be used to do trajectory following by using an imaginary point moving along the desired flight path as a pseudo targ

14、et. Of these, proportional navigation generally provides the best performance, with less control effort, in constantvelocity intercepts, and it is widely accepted as the preferred method of guidance 57. The trajectory following guidance logic presented in this paper was motivated by this proportiona

15、l navigation method. An important element in the proportional navigation is the use of the change in the line-of-sight between a missile and a target. A similar feature is also found in the trajectory following guidance logic between a vehicle and a pseudo target on a desired path.An important di

16、74;erence between the two methods is that,unlike the proportional navigation, the speed of the pseudo target is not taken into account in the trajectory tracking guidance logic. A detailed discussion on the relationship of the trajectory following guidance logic to proportional navigation is provide

17、d in Section II-B.有几种末端引导规律的短程战术导弹，他被使用在轨迹跟踪中，具体方式是通过使用一个假想的沿着期望的飞行路径飞行的点作为伪目标。其中，比例引导一般提供了最好的性能，在等速拦截中需要的控制力度更小，这种比例引导方法被广泛地认可为制导的首选方法。本文提出的轨迹跟踪引导理论源于这个比例引导方法。在比例引导中一个关键元素就是导弹与目标之间瞄准线变化的使用。相似的特点也出现在飞行器与在期望路径上的假想目标之间的轨迹跟踪理论中。两种方法有一个非常大的不同之处，与比例引导不同的是，在轨迹追踪引导理论中伪目标的速度是不被考虑的。轨迹跟踪引导理论与比例引导理论的关系我们将在第二部分

18、的B篇进行详细的讨论。Section II introduces the guidance logic and describes related properties. While the guidance logic developed here is simple and easy to apply, it is shown to have a number of benefits over linear approaches for curved paths. First, it contains proportional and derivative controls on cros

19、s-track error. Second, it has an element of anticipation for the upcoming local desired flight path. This property enables tight tracking on curved flight trajectories. Third, it uses instantaneous vehicle speed in the algorithm. This kinematic factor adds an adaptive feature with respect to changes

20、 in vehicle inertial speed caused by external disturbances such as wind.第二部分介绍引导理论并叙述相关属性。然而发展到现在，制导理论已经可以简单容易的应用了，它被证明有很多优于对曲线路径的线性控制方法。首先，它包含了在交叉跟踪中的比例和微分控制。其次，它有一个预算的元素，预期将要来的本地期望飞行路径。这个属性可以使他紧紧跟随曲线飞行轨迹。最后，它在算法中采用了瞬时的飞行速度。这个运动因素增加了自适应功能，用于调节由于外部干扰（例如风）引起的飞行器固有速度的变化The algorithm is easily implemen

21、ted, and flight test results showing excellent tracking performance are given in Section III. The proposed guidance logic was implemented in two unmanned air vehicles (UAVs) in the Parent Child Unmanned Air Vehicle (PCUAV) Project 8, 9 at MIT, under the sponsorship of Draper Laboratory.该算法易于实现，飞行测试中

22、所表现出来的优良跟踪性能将在第三部分讲解。在麻省理工的赞助下，在Draper实验室中，该引导理论提案在两个无人飞行器中应用测试。II. The New Guidance LogicThe guidance logic presented in this paper selects a reference point on the desired trajectory, and generates a lateral acceleration command using the reference point.本文提出的引导理论在预期轨迹上选择一个参考点，并且用这个参考点产生一个横向加速度指令。

23、.The reference point is on the desired path at a distance (L1) forward of the Lateral Acceleration CommandThe lateral acceleration command is determined by （1）Two properties of the guidance equation are significant.1. The direction of the acceleration depends on the sign of the angle between the L1

24、line segment and the vehicle velocity vector. For example, if the selected reference point is to the right of the vehicle velocity vector, then the vehicle will be commanded to accelerate to the right, which is the case in Figure 1. In other words, the vehicle will tend to align its velocity directi

25、on with the direction of the L1 line segment加速度的方向取决于L1线段和飞行器速度矢量的夹角，例如，如果选定的参考点是在飞行器的速度矢量右边，这个飞行器将被控制向右加速，这就是图1所示情况，换句话说，飞行器将会调整其速度方向，使其速度方向与L1直线方向对齐。2. At each point in time a circular path can be defined by the position of the reference point, the vehicle position, and tangential to the vehicle v

26、elocity vector; as indicated by the dotted line in Figure 1. The acceleration command generated by Eq. (1) is equal to the centripetal acceleration required to follow this instantaneous circular segment. This is readily shown by noting that每个瞬时点的圆是由参考点和飞行器的位置以及飞行器速度矢量的切向确定和定义的；如图1虚线所示。由等式1所产生的加速度就是这

27、个瞬时圆的向心加速度。下面等式很容易证明，如下： （2）So Centripetal acceleration=sin =Hence the guidance logic will produce a lateral acceleration that is appropriate to follow a circle of any radius R.因此，引导理论将产生一个横向加速度，这个加速度指向一个圆的半径方向This section describes a discrete time simulation that was performed to gain further insig

28、hts about the performance of the nonlinear guidance law. First, consider Figure 2 showing the evolution of the guidance logic in one small time step increment. In this diagram, the reference point is to the right of the direction of the vehicle velocity. Therefore, at the next time step the velocity

29、 direction rotates clockwise due to the acceleration command.本节描述一个离散系统模拟，用于进一步获得的关于非线性引导定律在性能方面的表现。首先，图2显示了在一个很小的时间步长增量下由引导理论控制而产生的变化。在这个图中，参考点是在飞行器速度方向的右边。因此，在加速度作用下，下一步的速度方向将顺时针旋转。With this one time step increment in mind, Figure 3 shows the trajectory of the vehicle over several time steps, wher

30、e the vehicle initially starts from a location far away from the desired path, and eventually converges to the desired path. Given a certain length L1 as shown in Figure 3, it can be inferred that带着时间步长增量的概念，图3显示了一些时间步长后的飞行轨迹，其中飞行器最初从一个远离期望路径的位置开始，并最终收敛到期望路径。给定某一个长度L1如图3所示，那么可以推断： The direction of L

31、1 makes a large angle with the desired path, when the vehicle is far away from the desired path.当飞行器远离目标时，L1方向将会与期望路径之间有一个很大的夹角。 The direction of L1 makes a small angle with the desired path, when the vehicle is close to the desired path.当飞行器接近目标时，L1的方向将会与期望路径的夹角变小Therefore, if the vehicle is far aw

32、ay from the desired path, then the guidance logic tends to rotate the vehicle so that its velocity direction approaches the desired path at a large angle. On the other hand, if the vehicle is close to the desired path, then the guidance logic rotates the vehicle so its velocity direction approaches

33、the desired path at a small angle.因此，如果飞行器是远离期望路径，引导控制理论将旋转飞行器使其速度方向与期望路径的夹角是一个大角度。另一方面，如果飞行器接近期望路径，那么引导控制理论将旋转飞行器使其速度方向与期望路径的夹角是一个小的夹角。Consider the reference point as a target and the aircraft as a missile. Then, an interesting similarity is found in relation to proportional navigation missile guid

34、ance. The formula in Eq. (1) for the lateral acceleration command in the trajectory following guidance logic can be shown to be equivalent to the formula把参考点视作目标，飞行器视作导弹。有趣的是，我们发现导弹中使用的比例引导法。在轨迹追踪引导理论中的横向加速度的等式1的形式可以证明是与这个公式是等价的。for the acceleration command perpendicular to the line-of-sight in the

35、proportional navigation with a navigation constant of N0=2, under the assumption that the reference point is stationary in the computation of the line-of-sight rate and the closing velocity. This equivalence can be shown using Figure 4.对于垂直于在比例引导中的瞄准线的加速度的引导常数是2.，假设在瞄准线的rate和接近速度的计算中参考点是静止的，这个等式如图4所

36、示，首先注意到，在这个飞行器的横向加速度和这个垂直于LOS的加速度之间的不同Case 1: Following a Straight-line and Selection of L1Figure 5 defines the notation used in the linearization. L1 is the distance from the vehicle to the referencepoint, d is the cross-track error, and V is a vehicle nominal speed. Assuming is small in magnitude图

37、5定义了一个在线性化中的标记，L1是飞行器和参考点之间的距离，d是交叉跟踪误差，V是飞行器的理论速度，是一个很小的量Hence, linearization of the nonlinear guidance logic yields a PD (proportional and derivative) controller for the cross-track error. Also, the ratio of the vehicle speed V and the separation distance L1 is an important factor in determining t

38、he gains of the proportional and derivative controllers. For instance, a small value forL1 would lead to a high control gain and the ratio L1=V determines the time constant of the PD controller.The separation distance can be chosen by performing a stability analysis with the linear plant model and t

39、he derived linear controller. The plant model should include the vehicle dynamics with inner-loop bank angle controller (if bank angle is used to generate lateral acceleration for aircraft) and any sensor dynamics in the associated loop transmission function.因此，非线性引导理论的线性化然后做成一个PD控制方法来消除横向轨迹误差。在确定比例

40、和微分控制器的增益中，改飞行器的速度变化率和L1的距离是一个非常关键的因素。例如，一个很小的L1的值将会将会产生一个很高的控制增益，L1/V的变化率决定着PD控制器的时间常数我们可以通过线性控制模型和衍生线性控制器来进行稳定性分析，然后来选择间隔距离。装置模型应该包括动态飞行器的内环坡度控制（如果倾斜角用于给飞行器产生横线加速度）和相关环路传送功能的任何动力学传感。Eq. (4) indicates that an approximate linear model, for the case of following a straight line, is a simple second or

41、der system that always has a damping ratio of 0.707 and its natural frequency is determined by the ratio of the vehicle speed and the length for the reference point selection.等式4指示一个近似的追踪直线的线性模型，是一个简单的二阶系统，它的阻尼比是0.707，并且它的自然震荡频率是由飞行速度和参考点选择的长度的比率所决定。Case 2: Following a Perturbed Non-Straight Line追踪一

42、个扰动且非直线的路径The tracking capability on a curved path is demonstrated in this section by performing a linear analysis for a case with non-straight desired trajectory as shown in Figure 6. In this case the desired path is a perturbed curved line from a nominal straight line. In Figure 6, d is the latera

43、l position of the current vehicle location and indicates the position of the reference point. Assuming the magnitude of the angles, and are small本节中，我们将通过对非直线轨迹的线性分析来证明曲线追踪能力，如图6所示。期望路径是由一条绕着标称直线的扰动曲线。d是飞行器当前位置的横向位置，指示参考点的横向位置（相对于标称直线）。假设角度和都很小。Eq. (6) represents a second order low-pass linear syste

44、m with a unity steady state gain from the reference point input to the vehicle position. The damping ratio（） is 0.707 and the undamped natural frequency( ) is determined by . The input of the transfer function in Eq. (6) is the lateral position of the referencepoint, not the position of the desired

45、path at current vehicle location (i.e., d?ref:pt: not d?). The use of a reference point in front enables phase recovery around the bandwidth frequency . For example, consider a sinusoidal trajectory command written as where A is a small path amplitude, Lp is a length-scale of the sinusoid, and x is

46、distance along the path. Assuming x = V t then if Lp =, the commanded trajectory expressed by Eq. (7) will excite the system at the bandwidth frequency (recall ). For a well-damped second order system asin Eq. (6) the phase lag at this frequency is 90 degrees. But this phase loss is from position in

47、put of the reference point , not from d*, in Figure 6. Recalling that the reference point is at L1 = Lp=4:4 (about a quarter of period) distance away, there will be about 90 degrees of phase lead in over d*. Therefore,these two effects will cancel each other, and the phase difference between the veh

48、icle position and the desired path at current vehicle location (i.e. between d and d*) will be significantly reduced.等式6代表一个二阶低通线性系统，并且从参考点输入到飞行器位置的一个稳态增益。阻尼比是0.707,无阻尼自然震荡频率是由决定。等式6中传递函数的输入是参考点的横向位置（），特别注意不是当前飞行器位置所期望的参考点位置。前面一个参考点的使用会使得带宽频率周围的相位恢复。例如：式中，A是一个小的路径幅度，Lp is a length-scale of the sinus

49、oid(Lp是正弦上的一段尺寸)，x是沿着路径的距离，假设x=V*t 且Lp= 。由等式7所表示的方程将会刺激系统的带宽频率。对于一个阻尼较好的二阶系统（等式6）,。在这个频率上的相位滞后是90度。但是这个相位的损失是由于参考点（）的位置输入引起的（而不是）。Recalling这个参考点是在远处（大约1/4周期）。将会超前90度的相位。这两种效应将会相互抵消。飞行器的当前位置和飞行器应该所在预定轨迹上的位置之间的相位差将会减少(i.e. between d and d*) 。本系统的伯德图，以L1/Lp为横轴的函数，如图7所示，图清楚地展示了，由于期望所产生在系统带宽附近的相位改善（当L1/L

50、p1/4.4=0.23）。如果Lp是在期望路径最高频成分的波长，要想准确跟踪期望路径，那么L1的选择就必须少于Lp/4.4。例3，曲线路径追踪图8为例，展示了圆弧路径的追踪。以下分析，我们都假定和是一个很小的量，但并不是足够的小。可以注意到，的角是与圆弧段有关的。飞行器的当前位置由r=R+d和指定的。表示速度方向，是由速度方向和预定圆弧的切向所形成的夹角。D. Comparison of the New Guidance Logic with the Traditional Linear MethodD.新的引导理论与传统的线性方法比较In the previous section, it w

51、as shown that the nonlinear guidance logic approximates a linear PD controller,on cross-track error, in following a straight line. This section will compare, by simulations, the performance of the nonlinear guidance logic and the associated linear controller, for various cases of trajectories and wi

52、nd conditions.In the simulation analysis presented below, 25 m/s of nominal vehicle speed and the separation distance(L1)of 150 m were used for the associated linear controller given by Eq. (3).在上一节中，我们看到，非线性制导理论在对直线追踪中的轨道误差的控制近似为一个一个线性PD控制法。本节将通过仿真讨论在不同轨迹和风力条件下非线性控制理论和线性控制法的性能。在如下仿真分析中，飞行器的速度是25m/s

53、，相隔距离是150m(L1),使用相关的线性方法来进行控制。Comparison 1 - Straight Trajectory FollowingFirst, the two methods were applied for tracking a straight line. Figure 9 shows the simulation setup with an initial cross-track error of 10 meters and the associated results using the two methods. The simulation results indi

54、cate that the performances of the two methods are roughly the same in following a straight trajectory.比较1:直线路径追踪第一，两种方法都被运用于直线路径追踪。仿真设置起始轨迹误差为10米，两种控制方法的结果如图9所示，仿真结果表明，在直线追踪中两种控制方法是几乎一致的。Comparison 2 - Curved Trajectory FollowingNext, the two methods were applied to tracking a curved line. Figure 10

55、 shows the simulation setup, the desired curved flight trajectory, and the associated simulation results. The aircraft is initially at level flight heading due north. The trajectory plot (a) in Figure 10 is the case where the linear controller was used. ThePD controller resulted in a steady state er

56、ror of about 40 meters. The steady state error can be explained by noting that the system is type 2. There are two pure integrators in the associated loop transmission with a plant model and the PD controller. The two integrators are from the kinematics of the plant model - fromacceleration input to

57、 position output. The steady state error occurs because the position reference command for cross-track is imposed in a parabolic fashion, when the desired path is a circle.比较2:曲线路径追踪：接着，两种方法被应用于曲线追踪。图10仿真设置了期望的飞行曲线路径，显示了相关仿真结果。飞行器最初飞行方向是水平正北。图10中的路径图a是线性控制器的控制结果图。PD控制方法将会产生40米的稳态误差。这个系统是一个2型系统，我们可以使用2型系统来解释这个误差。在这个plant模型和PD控制器相关环路的传递函数有两个1/s。这两个纯积分plant模型的运动学中来自加速度输入和位置输出。当期望路径是一个圆的时候，稳态误差的产生是由于对于交叉误差的参考点是抛物线类型的。In order to eliminate the steady state error, an integrato