改进的加速度再入制导律方案研究.doc

Simulation of Evolved Acceleration Reentry Guidance for Reusable Launch VehiclesAbstract：The transitional reentry guidance of space shuttles was the base line method that had poor adaptability. Hence Evolved Acceleration Guidance Logic for Entry ( EAGLE) is studied here. Basing on the estimated range-to-go, the reference drag acceleration profile is updated every period. In the lateral profile, basing on the generated reference drag profile, two reversal times are got successively through numerical predictive method. The technique of feedback linearization is used to track the reference drag acceleration profile. The algorithms of updating reference drag profile and searching reversal times are both the method of golden-section search, so the EAGLE method can be performed onboard. The simulation runs of a variety of reentry conditions show that the approach has good robustness and real-time ability.KeyWords: Reentry guidance; Range-to-go; Reference drag acceleration; Lateral guidance1. IntroductionThe reusable launching vehicle (RLV) will become the mainstream of the future space transportation for its advantage of high reliability and low risk. Furthermore, the guidance problem of RLV, especially in the reentry phase, poses a challenge to the safe return of RLV under the threat of high heat rate, high dynamic pressure and high normal load. Except the inequality constraints, RLVis supposed to fly from initial condition to a fixed end( terminal area energy management，TAEM) , which means that the end state of RLV is also constrained. Then the reentry guidance problem can be regarded as a two point boundary value problem ( TPBVP). The transitional reentry guidance for space shuttles is a nominal profile of drag acceleration vs. earth relative velocity tracking one, which is generated by the equipments on groud first and followed by changing the shuttles lift-to-drag ratio (L/D) in the shuttles reentry.Evolved Acceleration Guidance Logic for Entry ( EAGLE) is a direct extension of the longitudinal acceleration guidance used for the Shuttle. And its follower is a linear time-varying feed-back controller , but the input of nominal states (drag deceleration , lift to drag ratio , and attitude rate) will be regulated according to the range to the target and the predicted (or nominal ) one. Whats more , the error between them is another feedback item. The cross range is also controlled by the bank reversal logic.2. Reentry Guidance ProblemsNeglecting winds and centripetal acceleration from planet rotation, the 3DOF dynamics for the reentry are described by following dimensionless equations of motion. (1)where for better numerical conditioning, all the variables are normalized or nondimensional. The variable is the radial distance from the center of the Earth to the vehicle, normalized by the radius of the Earth （km）. The longitude and latitude in radian are and , respectively. The Earth-relative velocity is normalized by the circular velocity with = 9.81 . The terms and are the aerodynamic lift and drag accelerations in , respectively. Note that and are also functions of , the angle of attack, through the dependence of the drag and lift coefficients and on . The flight path angle of the Earth-relative velocity is and is the bank angle, positive to the right. The velocity azimuth angle is measured from the north in a clockwise direction. The differentiation is with respect to the dimensionless time =.The gravitational acceleration , Where is the gravitational constant, monotonically decreases along the trajectory.Since the time is not a critical parameter in entry flight, we will Introduce an energy-like variable E as the independent variable (2)Energy is an appropriate independent variable for the dynamics, and (3)To simple the model, the energy parameter E is normalized as follow (4)where is the energy of the vehicle at the initial poit of the reentry, and is the he energy at the end. With this definition = 0 at the start of the entry phase and reaches a value of 1 at the nominal TAEM condition. The reference trajectory variables are provided at a fixed number of points between 0 and 1; linear interpolation is used to obtain the reference variables at intermediate values of .3. Reentry Trajectory ConstraintsIn the entire reentry process, the motion of RLV is constrained by heat rate, dynamic pressure and normal acceleration which can be categorized into “hard constraint”, which means that these constraints must be satisfied to avoid disaster; meanwhile there are“soft”constraints called equilibrium glide condition with its purpose to maintain sufficient control authority over so that the vehicle wouldnt be out of control and descend too rapidly. All the trajectory constraints are given as follows: (5)where , and are maximum limits of heat rate, dynamic pressure and normal load, respectively; c is a constant that related to the geometry characteristic of the vehicle; is a specied bank angle used to acquire control margin, here = 510.The RLV is supposed to fly to TAEM ( terminal area energy management) to end its reentry phase. And the TAEM is defined by the vehicle s states, typ ically the height and velocity. Actually there is a tolerance range over these states: (6)where, is the vehicles parameters at the end of the reentry, and is the ideal paramerts at the start of the TAEM. are allowed tolerances.4. Guidance Law DescriptionThe EAGLE includes two algorithms, the trajectory planning algorithm and the tracking algorithm. The planning algorithm is to generate a reference drag acceleration profile and update it in every specified period. the tracking algorithm is a linear time-varying feed-back controller.4.1. Estimating Range-to-goThe flight path angle and the velocity azimuth angle can be ignored in the preliminary estimate ,so according Equ (3) we can get the predicted range to go is (7)Where is current time, is terminal time, is current energy, is terminal energy.Actually for the whole flight, this assumption is feasible. For the range-to-go and the reference profile is updated in every specified period in real-time, the RLV is more close to TAEM, the range-to-go is more like a straight line, the estimate is more accurate. 4.2. Generating Reference Drag Acceration ProfileAccording Eq. (7) we can get that changing the fuction of the darg acceleration vs energy can change the range-to-go. EAGLE chooses a drag profile using a 3-segment linear spline fit for a profile that fits within the drag versus velocity constraints and gives the correct value for downrange distance. These constraints can include thermal, dynamic pressure, normal acceleration, and equilibrium glide constraints. The lateral motion is determined through a bank reversal chosen to minimize the final crossrange.The reference darg acceleration vs energy profile is supposed as Figure 1, where is the darg acceleration at the start time of the reentry, is a constant darg acceleration, is the darg acceleration at the terminal time of the reentry. For and can be computed according the initial coditions and terminal coditions offline, so there is only one parameter required to be sought.Fig 1 supposed reference darg acceleration vs energy4.3 Bank Reversal ManagementEAGLE plans a fixed number of bank reversals. To meet the last crossrange error which can be predicted by a numeric integral strategy the bank reversal time is got through the golden-section search method. Because the reference darg acceleration profile shoud be updated until to TAEM , the last crossrange error would increased after the first bank reversal. If the range-to-go is long, the last crossrange error would be unacceptable. To avoid above error a second bank reversal is planned. Actually to get enough crossrange maneuverability to perform a second bank reverse the first bank reversal time is completed earlier than the time computed by the golden-section search method according the predicted range-to-go.4.4 Tacking the Reference Drag Acceleration ProfileRefered to reference 1 the trajectory tracking algorithm with feedback linearization is adopted, in which the bank angle is the main control variable and the angle of attack is scheduled. The profile tracking law is as followwhere is the lift-to-drag ratio, is the difference between the actual drag acceleration and desired one, is the difference between the actual change altitude rate and the reference one, and , are gains changed with the energy of the RLV.The reference lift-to-drag ratio and altitude rate of the reference drag acceleration porfile is like the formula of reference 1. The function between the drag acceleration and the energy of RLV is supposed to be linearly related, as belowwhere is a constant variable. And the reference lift-to-drag ratio is The reference altitude rate is Where is the index of the air density formulation assumed. 5. Simulations and AnalysisA 3-DOF simulation of the X-33 is used for the conceptual development of the EAGLE method. Limited by the article length, only a few typical simulation results are given here. To facilitate discussion the terminal conditions are simplified. We assume the target airport is located 0 degree latitude and 125 degrees east longitude. The reentry missions are as follow table.Table 1 Initial coditions of typical reentry missionsMission 1Mission 2Mission 3Mission 4Mission 5Altitudel (Km)120000120000120000120000120000Longitude ()70 E70 E70 E70 E70 ELatitude ()00000Velocity ()76207620762076207620Flight path angle ()-1.0-1.0-1.0-1.0-1.0Velocity azimuth angle ()00015-15Compared with mission 1, the difference of mission 2 and 3 is only the latitude which is located at each side of the equator. Mission 2 and 3 can be considered as missions having a large crossrange. Compared with mission 1, the difference of mission 4 and 5 is only the initial velocity azimuth angle which is 15 and -15 respectively.Fig 2 Latitude and longitude Histories of typical missionsFrom the simulation results we can get that the absolute value of the bank angles of mission 2 and 3 are the same, but has different sign. The situation of mission 4 and 5 is similar with mission 2 and 3. So we only give the simulation results of mission 1, 2 and 4 in Fig 3.Fig 3 Bank angle histories of typical missionsFrom simulation results we also get that the actual drag acceleration profile is not a 3-segment linear curve like Fig 1, but a irregular curve. This is because there are always errors in the process of estimating range-to-go and tracking the reference drag profile. So the value of the reference constant drag is different in every iterative circle. Fig 4 show the reference drag acceleration profile and tracking results of mission 1. Fig 4 also can show us the tracking method is efficient.Fig 4Actual and reference drag profiles6. ConclusionsAn entry guidance algorithm, called EAGLE (Evolved Acceleration Guidance Logic for Entry) was introduced. The algorithm based on the ranging technology , to regulate the nominal profile parameters for tracking controller. The results of these simulations show that EAGLE achieves the desired entry performance for almost all the cases and the allowable entry performance for all the cases. There should be some amelioration to do, such as regulating the angle-of-attack to enhance the ranging ability.References： 1 赵汉元. 飞行器再入动力学和制导M . 国防科技大学