飛行器再入走廊設(shè)計與分析,飛行器,再入,走廊,設(shè)計,分析 英 文 翻 譯 系 別 自動化 專 業(yè) 自動化 班 級 191001 學生姓名 王應(yīng)超 學 號 103566 指導教師 石國祥 A Reentry Corridor Calculation Methodfor Reusable Launch Vehicles Based on SkiPPing Trajectory in this paper, according to lift vehicle dynamics, this paper proposes a border as a benchmark in aircraft under the reentry corridor corridor by track jumping fast calculation method of boundary. Combining the kinematics equation and the simulation experiment of concrete analysis of the reliability of the method and the optimality. The experimental results showed that the traditional condition of quasi-equilibrium glide into the corridor again has some conservative estimates, in this paper, the method to calculate the reentry corridor can reflect more aircraft mobility. And, compared with general corridor was calculated by the method to solve the problem of optimization of the direct method and indirect method, the proposed approach with a small amount of calculation, the calculation time is short, the advantages of strong convergence, which have stronger practicability. 1 the introduction A reusable spacecraft "'" (ReusableLaunchVehicle, RLV) is the height of the crystallization of aviation, space technology, will be the future development trend in the field of aerospace technology, it implements the cheap and reliable space transportation. Reentry guidance control of the process of "2" technology is the study of the key technologies of reusable spacecraft. Spacecraft reentry corridor "3" surround describes the reentry process craft can achieve high range, is in the process of the reentry trajectory planning, guidance and control scheme of the important basis. Reentry corridor generally lower boundary by reusable spacecraft reentry process constraints (dynamic pressure constraint, overload constraint, the heating rate constraint) sure, go up into the corridor of the boundary condition of quasi-equilibrium glide available a [6] [7] (Quasi E Ming ilibriumGlideCondition, QEGC) approximation. Quasi-equilibrium glide is refers to the aircraft in the process of reentry is ever approximate to zero, the flight trajectory smooth state of decline. Quasi-equilibrium glide into the corridor again estimate the condition of boundary enjoys wide application in engineering, but with the constant improvement of the guidance and control requirements, in the face of large deviation, pneumatic controller of fault and special maneuver flight mission, quasi equilibrium glide into the corridor again estimate the condition of boundary often is too conservative, cannot reflect the aircraft's largest mobility. Especially in the presence of a fault and maneuvering flight change after the spacecraft trajectory to refactor, guidance system, control system of "8" [9 j, fast calculation of reentry corridor is particularly important. Calculation precision of reentry corridor boundary essence is to calculate a series of continuous optimal control problem, the search for a series of the optimal trajectory can achieve the largest craft flying height. At present, the accurate calculation of reentry corridor on the boundary of the main methods including indirect method based on classical variational method and direct method based on nonlinear programming theory. The indirect method is to use the pound in the gold plan algorithm for maximum principle. Both indirect and direct method are requires a lot of time iteration to calculate the optimal control and optimal trajectory, and the iterative initial control sequence or initial trajectory is very sensitive, can guarantee absolute convergence. 2. lift reentry vehicle model According to the description of the document [10], lift aircraft six degrees of freedom motion equation in the process of reentry as shown in type (l). (1) Type of the variable r said vehicle centroid radial distance from the center of the earth; is the location of aircraft's geographic longitude; said the geographic latitude; V says the speed of the aircraft; said track Angle, is the velocity vector and the Angle between the local level. Said course Angle, is the local longitude line and the velocity vector in the horizontal plane of projection, the Angle between the clockwise along the north when its value is positive; M for the quality of the aircraft, as the earth rotation angular velocity, Angle of attack the default as the function of speed, L and D respectively lifting acceleration and acceleration resistance. At the same time, the vehicle reentry to meet in the process of heating rate, dynamic pressure and overload constraints, such as type (2) a (4) (2) (3) (4) Practice,, which respectively is allowed maximum heating rate, dynamic pressure and maximum overload,C， is related with the thermal model of gas constant. 2.1 motion equation and calculation problem of the corridor With a high speed section describes spacecraft reentry corridor, to simplify the equation of motion of type (l) : the earth's rotation is affected, a negligible; Corridor computation involves only aircraft longitudinal motion, only consider type (l) 1, four, five of the equation can be obtained: (5) Speed as independent variables, the equation (5) can be transferred to: (6) Set into the starting point again and again into the end points of unit mass of mechanical energy, respectively, and, because of lack of dynamic gliding reentry period of aircraft do, energy drab, so ridge. Set the speed of flight corridor point respectively, the corresponding boundary as the lower boundary, as on the radius vector, k = 1, 2, 3,... , N. N is the number of discrete points of the corridor. Continuous calculation problem was converted into discrete upper and lower bounds of the corridor corridor various points of the upper bound optimization problem, namely to find the optimal control sequence for: (7) 3 flight corridor calculation based on the skip trajectory 3.1 flight corridor lower calculation Flight corridors lower generally determined by the reentry process constraints, atmospheric model can be represented as: (8) Among them, for the sea level atmospheric density, as the radius of the earth, for the normalization constant atmospheric density, here. And acceleration to lift, drag acceleration can be represented as: (9) Among them, the aircraft is effective pneumatic area is determined by aircraft model, and is made by Angle of attack and Mach number Ma interpolation. At the same time, combining with the type (2) a (4) the reentry process constraints can be obtained: (10) For lower corridor, corridor of the lower bound for the heating rate, dynamic pressure constraint, to determine the lower bound of the maximum overload constraint, the speed in a high profile is a piecewise continuous curve is determined. 3.2 quasi-equilibrium glide conditions to determine the upper bound of the corridor Spacecraft reentry process, precise equilibrium glide, the resultant force basic for the O, trajectory smooth down without oscillation, at this time have a dead reckoning Angle, and, under the cover type: (11) Using Newton iterative method calculated under the each speed v meet on type r, get the equilibrium glide explicit relationship between the height of a speed, forming a quasi equilibrium glide upper bound constraint corridor. 3.3 based on the upper bound of skip trajectory flight corridor is calculated Corridor boundary is essentially calculation type (7) is shown in continuous optimization problems, can be used based on the classical variational method to solve the problem of the indirect method and direct method based on nonlinear programming, but both face complicated process constraints, difficult to guess the initial value, the convergence of algorithm and computation problem. This article proposed a method of fast calculation of the hallway boundary is determined by the movement characteristics of the aircraft itself, because the lift aircraft again into the main force of gravity and the power, in the process of the aerodynamic force Accept to the influence of altitude, the lower the height of the air density, the greater the, in turn, the greater the aerodynamic force, will flight trajectory to lift; And the higher the height, the smaller the air density, the smaller the aerodynamic force, and gravity will aircraft track down. To lift aircraft, to achieve higher trajectory from lower store up energy. In the condition of known flight corridor lower bound, can think that there is a feasible path can achieve lower corridor, so there is no need to consider from the reentry corridor of the starting point to the lower point of actual trajectory. At the same time, considering the nature of the craft, the height from the lower position to fly to the top of the position, the need for aircraft provides maximum lift, so, to determine the amount of control, ensure the aircraft is on the rise in the process has the maximum lift. According to the above described, based on the boundary of skip trajectory the hallway to calculate the specific steps are as follows: L) discretization speed in a high profile corridor and lower bounds of the constraints determined by the process, and k corridor and lower bounds of the discrete points (,); 2) set up under the reentry trajectory and reentry corridor boundary tangent at point (,) (at this point, the track is the most close to the border, and not lower boundary), the trajectory of tangent to the lower boundary condition is: (12) By (zha, rc, and from among them), the boundary tangential fire/dv hallway underneath for speed derivative, namely by type (12) can get the state of the tangent point of: ; ; (13) Type (13) by the state as the initial values, the value of the control volume = 0 (at this point, the vehicle lift in vertical plane, the largest aircraft to maximize the ability to rise) (6) the trajectory equation of integral type, until/symbol is negative, the trajectory began to decline, at this point the point (,) is at the boundary points in the reentry corridor; Calculate according to the step 2), 3) under a reentry corridor under boundary point (,) corresponding to the reentry corridor boundary point (,), until you got all the discrete boundary point matching Reentry corridor boundary point; 4) will be at the boundary points in the reentry corridor between progressive linear interpolation and curve fitting, can be relatively smooth boundary curve into the hallway again. According to the practical engineering requirements can use linear interpolation cubic spline interpolation, the curve fitting can use five or six order polynomial fitting. 4 summarizes According to lift vehicle dynamics, this paper proposes a lift spacecraft reentry corridor based on skip trajectory calculation method. , in the process of the reentry flight track jumping with similar characteristics of the spring, the closer the corridor lower trajectory tend to jump to a higher level, the upper and lower bounds of the corridor and calculation method to calculate the corridor upper bound and upper bound condition of quasi-equilibrium glide calculate corridor, and based on the functional analysis of the traditional direct method to calculate the corridor of the upper bound were compared, the results show that the presented calculation compared with the upper and lower bounds of the corridor than the traditional method has the following advantages: does not need to be iterative calculation, and easy to implement without a lot of time optimal trajectory calculation, greatly saves the computation; Don't need to compute the whole path, just calculate trajectory of the last paragraph, short calculation time. Algorithm based on boundary under reentry corridor, process constraints (boundary conditions) under strictly meet, do not need special treatment; Don't need to guess the initial control sequence and the initial trajectory, without iterative process, the algorithm convergence; The reentry corridor and into the corridor again under the boundary Organic union, make the reentry corridor form a complete system. 一種基于跳躍軌跡的可重復使用飛行器再入走廊預測方法 本文依據(jù)升力式飛行器的動力學特性，提出了一種以飛行器再入走廊下邊界為基準，通過軌跡跳躍快速計算走廊上邊界的方法。文章結(jié)合具體的運動學方程和仿真實驗分析了該方法的可靠性和最優(yōu)性。實驗結(jié)果還表明，傳統(tǒng)的準平衡滑翔條件估計的再入走廊具有一定保守性，本文的方法計算的再入走廊更能反映飛行器的機動能力。而且，比起一般的用解決最優(yōu)化問題的方法計算走廊的直接法和間接法，本文提出的方法具有計算量小，計算時間短，收斂性強等優(yōu)點，從而有更強的工程實用性。 1引言 可重復使用飛行器「‘」(ReusableLaunchVehicle，RLV)是航空、航天技術(shù)的高度結(jié)晶，是未來航空航天技術(shù)領(lǐng)域的發(fā)展趨勢，它實現(xiàn)了廉價、可靠的航天運輸。再入過程的制導控制「2」技術(shù)是研究可重復使用飛行器的關(guān)鍵技術(shù)。飛行器再入走廊「3」一圍描述了再入過程飛行器所能達到的高度范圍，是再入過程中軌跡規(guī)劃、制導與控制方案制定的重要依據(jù)。再入走廊的下邊界一般由可重復使用飛行器的再入過程約束(動壓約束，過載約束，加熱率約束)確定，再入走廊的上邊界可用準平衡滑翔條件〔6〕一〔7〕(Quasi一E明ilibriumGlideCondition，QEGC)近似確定。準平衡滑翔是指飛行器再入過程中所受的合外力近似為零，飛行軌跡平穩(wěn)下降的狀態(tài)。準平衡滑翔條件估計的再入走廊上邊界在工程上應(yīng)用較廣，但是隨著制導與控制要求的不斷提高，面對大的氣動偏差、控制器故障以及特殊的機動飛行任務(wù)時，準平衡滑翔條件估計的再入走廊上邊界往往太過保守，不能反映飛行器最大的機動能力。特別是在存在故障以及機動飛行任務(wù)改變后的飛行器軌跡重構(gòu)、制導系統(tǒng)、控制系統(tǒng)重構(gòu)「8」一[9j時，準確快速的計算再入走廊顯得尤為重要。 計算精確的再入走廊上邊界實質(zhì)是計算一系列的連續(xù)最優(yōu)控制問題，即尋找一系列的最優(yōu)軌跡使得飛行器軌跡能達到最大的飛行高度。目前，精確的計算再入走廊上邊界的主要方法包括基于經(jīng)典變分法的間接法和基于非線性規(guī)劃理論的直接法。間接法是利用龐德里亞金極大值原理規(guī)劃算法進行求解。無論是間接法還是直接法均需要耗費大量的時間迭代求取最優(yōu)的控制量和最優(yōu)軌跡，且對迭代初始控制序列或初始軌跡極為敏感，不能保證絕對收斂。 2.升力式再入飛行器建模 根據(jù)文獻[10]的描述，升力式飛行器再入過程中六自由度運動方程如式(l)所示。 (1) 式中，變量r表示飛行器質(zhì)心距地心的徑向距離;表示飛行器位置所處的地理經(jīng)度;表示地理緯度;v表示飛行器的速度;表示航跡傾角，是速度矢量與當?shù)厮矫嬷g的夾角;表示航向角，是當?shù)亟?jīng)度線與速度矢量在水平面上的投影之間的夾角，沿正北順時針旋轉(zhuǎn)時其值為正;m為飛行器的質(zhì)量，為地球自轉(zhuǎn)角速度，攻角預設(shè)為速度的函數(shù)，L和D分別為升力加速度和阻力加速度。 同時，飛行器再入過程中要滿足加熱率、動壓和過載約束，如式(2)一(4)所示 (2) (3) (4) 其中練,,分別是允許的最大加熱率·最大動壓和最大過載，C，氣是與熱模型有關(guān)的常數(shù)。 2.1運動方程處理及走廊計算問題轉(zhuǎn)化 用速度一高度剖面描述飛行器再入走廊，對式(l)的運動方程進行簡化:地球自轉(zhuǎn)影響較小，可忽略不計;走廊計算只涉及飛行器縱向運動，只考慮式(l)中的第1，4，5個方程可以得到: (5) 以速度為自變量，可將方程(5)轉(zhuǎn)化為: (6) 設(shè)再入開始點和再入結(jié)束點的單位質(zhì)量具有的機械能分別為:，，由于再入段飛行器做無動力滑翔，能量單調(diào)下降，所以嶺。設(shè)飛行走廊的速度點分別為，對應(yīng)的矢徑上邊界為·下邊界為，k=1，2，3，…，N。N為走廊離散點的個數(shù)。連續(xù)的走廊上界計算問題就被轉(zhuǎn)化為離散的走廊上界各個點的優(yōu)化問題，即尋找最優(yōu)的控制序列使得: (7) 3基于跳躍軌跡的飛行走廊計算 3.1飛行走廊下界計算 飛行走廊下界一般由再入過程約束確定，大氣模型可表示為: (8) 其中，為海平面的大氣密度，為地球半徑，為大氣密度歸一化常數(shù)，這里。 又升力加速度，阻力加速度可表示為: (9) 其中，是飛行器有效的氣動面積由飛行器模型確定，,是由攻角和馬赫數(shù)Ma插值得到。 同時，結(jié)合式(2)一(4)的再入過程約束可得到: (10) 記為走廊下界，即走廊下界為加熱率約束，動壓約束，過載約束確定的下界的最大值，在速度一高度剖面內(nèi)是一段分段確定連續(xù)曲線。 3.2準平衡滑翔條件確定的走廊上界 飛行器再入過程中，作準平衡滑翔時，受合力基本為O，軌跡平滑下降無振蕩，此時有航跡傾角，且，即滿足下式: (11) 利用牛頓迭代法在每個速度v下計算滿足上式的r，得到在平衡滑翔段的高度一速度的顯式關(guān)系，從而形成準平衡滑翔約束走廊上界。 4.基于跳躍軌跡的飛行走廊上界計算 計算走廊上邊界實質(zhì)上是計算式(7)所示的連續(xù)優(yōu)化問題，解決此問題可以用基于經(jīng)典變分法的間接法和基于非線性規(guī)劃的直接法，但二者都要面對復雜的過程約束，難以猜測的初值，算法的收斂性和計算量的問題。 本文所提出的快速計算走廊上邊界的方法是飛行器本身的運動特性所決定的，由于升力式飛行器再入過程中主要受力為重力和氣動力，其中，氣動力間 接受到飛行高度的影響，高度越低則空氣密度越大，進而氣動力越大，會將飛行器軌跡往上抬;而高度越高，則空氣密度越小，氣動力越小，因而重力會將飛行器軌跡往下拉。對于升力式飛行器，要想達到更高軌跡就要從更低處積攢能量。 在飛行走廊下界已知的情況下，可以認為存在一條可行的軌跡可以達到走廊下界，因此不需要考慮從再入起始點到走廊下界點的實際軌跡。同時，考慮飛行器自身的特性，從高度較低的位置飛到最高的位置，需要給飛行器提供最大升力，這樣，確定了控制量，保證飛行器在上升過程中具有最大升力。 根據(jù)以上描述，基于跳躍軌跡的走廊上邊界計算的具體步驟如下: l)離散化速度一高度剖面內(nèi)由過程約束確定的走廊下界，及第k個離散的走廊下界點為(，); 2)設(shè)再入軌跡與再入走廊下邊界在點(，)處相切(此時，軌跡最接近下邊界，且不會過下邊界)，軌跡與下邊界相切的條件為: (12) 其中從由(咋，rc，、)確定，下邊界切線火/dv即走廊下邊對速度導數(shù)，由式(12)可以得到切點的狀態(tài)量為: ; ; (13) 式(13)得到的狀態(tài)量的值作為初始值，令控制量=0(此時，飛行器在縱向平面內(nèi)升力最大，飛行器以最大能力上升)積分式(6)的軌跡方程，直至/符號變負，軌跡開始下降，此時得到的點(，)即為再入走廊上邊界的點; 3)按照步驟2)，計算下一個再入走廊下邊界點(，)對應(yīng)的再入走廊上邊界點(，)，直至得到全部離散的下邊界點對應(yīng)的 再入走廊上邊界點; 4) 將再入走廊上邊界的點之間順次進行線性插值或曲線擬合，即可得到比較光滑的再入走廊上邊界曲線。按照工程實際需求線性插值可采用三次樣條插值，曲線擬合可采用五階或六階的多項式擬合。 4總結(jié) 本文依據(jù)升力式飛行器的動力學特性，提出了一種基于跳躍軌跡的升力式飛行器再入走廊計算方法。飛行其再入過程中，軌跡跳躍具有類似彈簧的特性，越接近走廊下界的軌跡往往能跳躍到更高的高度，并以此計算走廊上界將該方法計算的走廊上界與準平衡滑翔條件計算的走廊上界，以及傳統(tǒng)基于泛函分析的直接法計算的走廊上界進行了比較，結(jié)果顯示本文所提出的計算走廊上界相比傳統(tǒng)的方法相比具有如下優(yōu)勢:實現(xiàn)簡單，不需要迭代計算，不用計算大量次優(yōu)軌跡，大大節(jié)省了計算量;不需要計算整條軌跡，只需計算軌跡的最后一段，計算時間短;算法基于再入走廊下邊界，過程約束(下邊界條件)嚴格滿足，不需特別處理;不需要猜測初始控制序列和初始軌跡，無迭代過程，算法收斂;將再入走廊下邊界與再入走廊上邊界有機的結(jié)合起來，使再入走廊形成一個完整的系統(tǒng)。 13