Longitudinal Dynamics and Navigation Performance ... - (NACA) Reports

Longitudinal Dynamics and Navigation Performance Analysis for an Unmanned Space Vehicle U. Tancredia, D. Accardob, M. Grassib and F. Curreric a Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università di Napoli, Aversa (CE) b Dipartimento di Scienza e Ingegneria dello Spazio, Università di Napoli “Federico II”, Napoli c Centro Italiano Ricerche Aerospaziali (CIRA) , Space Programs Office Products and Systems, Capua (CE)

Abstract In this paper the preliminary results of the phase-A study of the guidance, navigation and control subsystem for a reduced-scale demonstrator of CIRA Suborbital Re-entry Test (SRT) mission is presented. A baseline guidance law is defined, in order to satisfy SRT mission objectives and constraints, on two candidate system configurations. A supplementary, higher performance, higher risk guidance solution is identified, providing qualitative insight on vehicle and system constraints impact on the overall attainable mission objectives. Evaluation of the performance of a commercial-off-the-shelf GPS-aided, miniature inertial navigation system over the baseline trajectories is also conducted.

Introduction Recent years have seen an increasing interest by the scientific community toward the study and development of unmanned automatic vehicles, also in the Reusable Launch Vehicle (RLV) frame. Current R&D, because of the extremely high funding required by the development of a cost-effective completely reusable vehicle, is focusing on the technology challenges of a sub-orbital autonomous, fully reusable space vehicle, eventually to be coupled with an expendable stage. In this framework, the Unmanned Space Vehicle (USV) Program is being performed by the Italian Aerospace Research Centre (CIRA). The USV Program main focus is on the development and in-flight testing of critical technologies of autonomous, fully re-usable, winged-body launch vehicles. To this end, five flight tests (missions) are foreseen. Concerning the third mission, named Sub-Orbital Re-entry Test (SRT), CIRA has funded a feasibility study for a reduced-scale technology demonstrator of SRT, named mini-SRT. This paper presents some results of mini-SRT preliminary mission design, from the guidance, navigation and control system point of view. Main objectives are to provide the maximum attainable performance of the mission objectives, complying mission and system constraints. Following the practice recommended by [5], an open-loop baseline guidance solution has been computed, for which a navigation

performance analysis is conducted in order to provide preliminary attainable accuracies and navigation system structure adequateness. Given the markedly technology demonstration characteristics of the mini-SRT mission, mission objectives requirements conflict with vehicle and operational constraints. Hence, a supplementary guidance solution is identified, in which the more pressing system constraint is relaxed with regard to the baseline trajectory, resulting in higher mission performances, and, as a consequence, providing qualitative insight on vehicle and system constraints impact on the overall attainable mission objectives.

Mission and vehicle outline Mini-SRT is a reduced-scale (1:5) technology demonstrator aiming at validating some scientific and technological issues of the SRT mission whose main features are summarized in Table 1 and extensively described in [8]. Starting conditions

Ascent with balloon to 35 km. Balloon separation and motor ignition (41-sec burning time). Ballistic ascent to sub-orbital altitudes (120 km)

Specific mechanical energy at Re-entry

4.2 ( MJ/kg )

Final conditions Primary mission objective

Parachute aperture at an altitude of about 10 km and Mach within 0.6÷0.9 Experiencing stagnation point thermal fluxes > 650 kW/m2 for a time interval at least of 15 s

Table 1: CIRA SRT mission main features (CIRA permission) The vehicle is a two-stage system made of an expendable off-the-shelf solid propellant motor and a glider, whose aerodynamic shape basically is a reducedscale version of CIRA’s USV [8]. The Mini - SRT system analysis has identified two candidate configurations, one designed for high performance, the other for less system complexity and, mainly, cost. The two options, which we will refer to as MiniFTB and MiniFTB\A, differ mainly in the performances of the selected motor, as briefly described in Table 2. Configuration Motor Mean Thrust [N] Burntime [sec] Estimated 1st Stage Mass [kg] Estimated 2nd Stage Mass [kg]

MiniFTB ATK Thiokol Star 17 10834 17.6 84 52

MiniFTB\A ATK Thiokol Star 17\A 16810 19.0 131 58

Table 2: Mini – SRT Candidate Configurations.

Guidance analysis Since the Mini - SRT is a reduced scale mission, the emphasis in the guidance analysis is on assessing and quantifying the capability of the small scale vehicle to reproduce the full scale SRT mission objectives. The features that distinguish the Mini – SRT from the full scale system impact on the performances, in terms of mission objectives attainment, by means of new, and in general tighter, constraints on the guidance solution. Specifically, besides initial and final state constraints that are similar to SRT, tighter constraints are imposed on maximum axial and lateral load factors nx , nz , maximum dynamic pressure q and maximum thermal flux Q’s , as follows: Q& (t ) ≤ 730 kW m 2 , n ≤ 10 g , n ≤ 10 g , q ≤ 130 kPa (1) S

x

z

The guidance problem has been stated as a conventional Calculus of Variation (C.o.V.) problem, solved with a direct method [4] employing a custom developed numerical code on the two degree of freedom center of mass longitudinal dynamics [8]. Since different mission requirements and external force magnitudes characterize ascent and reentry, the guidance study has been conducted separately for the two phases.

Ascent phase In order to implement the mission requirements, with particular concern to the replication of flight conditions typical of orbital reentry, the specific mechanical energy at the required ceiling altitude (>120 km) has been selected as the merit function. The guidance strategy [8] foresees a constant pitch angle trajectory in the boosted phase, and a subsequent Angle of Attack (A.o.A.) guidance. Simulation results have shown that the specific mechanical energy at maximum altitude weakly depends (~ 5%) on drag and steering losses. This leads to a small sensitivity of the merit function w.r.t. the non propelled A.o.A. profile, and, hence, the optimal boosted phase pitch angle is driven essentially by the maximum altitude value imposed. However, even if small, drag and steering losses define a maximum energy value, that occurs at a ~70 km ceiling altitude. Thus, if the selected ceiling altitude is > 120 km, maximum energy will take place at the lowest allowed ceiling altitude, that is 120 km. The energy values and the boosted phase pitch angle resulted from the simulations for the two mini–SRT configurations are collected in Table 3. Two values are reported for the MiniFTB configuration because of the different ascent phase trajectory chosen per each case, as will be clarified in the following. Configuration MiniFTB MiniFTB\A

Specific Mechanical Energy @ Maximum Altitude [ MJ/kg ] 2.22 – 2.27 3.78 Table 3: Ascent Phase Baseline Results

Boosted Phase Pitch Angle [ ° ] 42.4 29.8

Reentry phase The solution of the reentry guidance problem, using as inputs both A.o.A. and bank angle, without enforcing crossrange requirements, is in general non-unique. Since the merit function and the path constraints collide, using both the two input variables to shape trajectory can significantly augment the vehicle overall performances, in terms of both mission objectives and system constraints. The applied solution technique is to determine an A.o.A. nominal profile, to be subsequently used as input to the C.oV. problem solved in bank angle. Because of the specific mission objectives, the merit function is the time spent experiencing thermal fluxes at the stagnation point higher than a prefixed threshold QTH, whose value depends on the configuration examined. Specifically, given SRT mission requirements on TPS materials testing, the thermal flux threshold QTH value has been adjusted to obtain “hot” time interval extension adequate to perform test (~15 s). Thus, the QTH value is obtained by imposing minimum extension to the velocity interval in which thermal fluxes higher than QTH are possible. Thermal flux and dynamic pressure behavior depend only on altitude and velocity, whereas the other path constraints can be varied, and, thus, accomplished, by A.o.A. modulation. As a consequence the profile of the A.o.A. independent constraints in the (h,V) plane drives considerations on the capability of the vehicle to attain high thermal fluxes. Figure 1 shows thermal flux and dynamic pressure constraints profiles for the two vehicle configurations.

Figure 1: QTH and α independent constraints in the (h,V) plane From Figure 1 it emerges that there is a minimum velocity, defined by the dynamic pressure constraint and the thermal flux merit threshold intersection, above which it is possible to experience “high” thermal fluxes. Since the starting reentry velocity is determined by the maximum energy values attained, the qMAX, Q’MAX and QTH values define a maximum velocity interval in which Q’> QTH are achievable, defined as ∆VHOT. The time interval in whom the vehicle can remain in ∆VHOT, that is the reentry merit function, depends thus only on the drag profile flown in this zone. Assuming constant drag, from an estimate of the plausible drag coefficients in that flight

regime, the requirement of 15 sec. on the time interval corresponds to a ~ 500 m/sec ∆VHOT extension. From inspection of Figure 1, QTH values that satisfy this requirement are 300 and 550 kW/m2 for the MiniFTB and MiniFTB\A respectively. The A.o.A. nominal profile determination is conducted maximizing the vehicle capability of reaching high thermal fluxes, while preserving the ability to safely perform the reentry. The latter issue is twofold; from one side vehicle capability to attain level flight before lowest allowed h(V) is maintained [approximate analytic solutions valid for reentry are inapplicable for the pull out maneuver], from the other it’s assured trajectory is flyable, providing that elevon control moment is sufficient to trim trajectory, with adequate margin for longitudinal control and roll actuation and control, defined as in [8]. From open literature and NASA’s X-15 flight experience a sufficient residual elevon moment margin for this application should be comprised between 30% and 20% [1],[6],[9]. The above arguments have contrasting impacts on the A.o.A. reentry nominal profile selection process. The TPS requirement forces the A.o.A. to be selected such that the load factors constraints, that also limit the lower flyable altitude, are not active constraints for these velocity values, thus preserving the extent of the (h,V) zone (∆VHOT) in which the vehicle can exceed the thermal flux merit threshold. Since the lateral load factor is the more pressing of the two structural constraints, and its value increases with α, this means that the A.o.A. maximum value has to be limited. On the other side, Lift increases with α in the considered A.o.A. range, thus the path constraint avoiding limits the lower flyable A.o.A. Moreover, since the merit set velocity interval extension doesn’t change if load factors are inactive constraints, to maximize the time spent in the merit set, low drag, and thus low A.o.A., is required. The last issue to be addressed concerns the moment margin. Figure 2 shows moment margin isolines in the (α,V) plane, evaluated neglecting sound speed dependency on altitude.

Figure 2: Moment Margin isolines [%] in the (AoA,V) plane Figure 2 shows that a 20%-30% moment margin requires high AoA values for high Mach numbers, as in the ∆VHOT. Since for the MiniFTB configuration ∆VHOT

comprises lower velocities than MiniFTB\A, the former has less stringent margin requirements on A.o.A. For medium Mach numbers there is a high moment margin, that progressively reduces as the transonic region is approached. In this flight conditions low A.o.A. values are required. The nominal α profiles resulting from the above considerations are plotted in Figure 3 as a function of velocity. Figure 3 collects also the alternative, “hot” trajectories α profiles, whose determination is conducted as follows.

Figure 3: Nominal A.o.A. Profiles for Baseline and Alternative Trajectories. In the ∆VHOT for the MiniFTB\A configuration the lowest allowable α(V) is limited by 30 % Moment Margin requirement, whereas, mainly due to the lower energy values, constraint avoiding at pull out maneuver is the active α lower border for MiniFTB. Focusing on the latter, pull out maneuver occurs because the specific mechanical energy is too low compared to sub-orbital conditions (~ 10%) to allow a Shuttle or X-33 type gliding entry. Indeed, the miniSRT trajectories are characterized by a constant energy ballistic phase, that lasts until aerodynamics forces equal gravity and energy starts decreasing. The low MiniFTB energy places the end of the ballistic phase at a relatively low altitude (h ~ 40 km). At this altitude the flight path angle value is directly connected to the apogee altitude (ceiling height). The lower the ceiling height, the shallowest the path angle at atmospheric entry, and, hence, the required impulse to execute pull out is smaller. Thus, in order to relax the constraint avoiding requirement in ∆VHOT, the MiniFTB alternative trajectory is developed reducing the ceiling altitude to 70 km, emerged as a maximum for mechanical energy in the trajectory ascent analysis. Instead, for the MiniFTB\A baseline trajectory, in ∆VHOT the lowest allowable α(V) is limited by 30 % Moment Margin requirement. The alternative trajectory is thus obtained flying on the path constraints avoiding α(V) limit. Hence, two open-loop guidance solutions have been identified per each configuration (MiniFTB; MiniFTB\A), with different performances, in terms of mission objectives attainment and system constraints compliance. Table 4 collects the main features of the determined trajectories, compared to full scale SRT

baseline mission. Results show that the MiniFTB\A, thanks to the more powerful Star 17\A motor, replicates SRT principal characteristic with limited differences. Despite a 1:5 geometric scale factor, a 10 % reduction in specific mechanical energy at the ceiling altitude is obtained, and the thermal test flux threshold has to be lowered from 650 to 550 kW/m2. Comparison between the baseline and alternative trajectories shows that the 15 seconds hot time extension requirement can be accomplished accepting a residual elevon torquing capability between 20% and 30 % of the deliverable moment. Instead the MiniFTB configuration can attain half the energy level of the full scale mission, and, as a consequence, significantly lower thermal fluxes. Indeed the baseline trajectory can exceed the 300 kW/m2 thermal flux threshold for a time around 13 sec. , slightly lesser than the 15 sec. requirement. As indicated by the alternative trajectory results, a reduction in the ceiling altitude to 70 km can lead to higher thermal fluxes, and to a corresponding 19 sec time interval in which the TPS testing can be performed. Feature Specific Mechanical Energy @ [Maximum Altitude MJ/kg] Ceiling Altitude [km] Time Above Thermal Flux [sec] Thermal Flux Threshold [kW/m2] Maximum Thermal Flux [kW/m2] Minimum Moment Margin [%]

MiniFTB MiniFTB\A Baseline Alternative Baseline Alternative

SRT

2.22

2.27

3.78

3.78

4.20

120

70

120

120

120

13.4

18.7

13.2

16.8

15

300

300

550

550

650

340

390

625

670

TBD

30

25

30

20

TBD

Table 4: Mini SRT and SRT trajectories comparison ( TBD = To Be Determined ).

Navigation performance analysis Navigation performance analysis for the baseline trajectories considered for the two vehicle configurations has been carried out by numerical simulation. The navigation system architecture is based on the integration of low-cost sensors with advanced capabilities [8]. Since the miniSRT mission lasts only about 10 min and the considered inertial-navigation unit has good performances in terms of bias stability and random walk [8], stand-alone inertial navigation is an interesting and reliable option to be investigated at a first stage of the study. To this end, numerical simulations have been carried out by a numerical code developed in MATLAB environment. The vehicle is assumed to fly its nominal trajectory over a great circle

from Trapani Birgi (latitude 37° 40', longitude 12° 50') to Capo Teulada (latitude 38° 04', longitude 8°43'), as planned for the SRT mission. At this stage of the study, simulations have been conducted by assuming the inertial unit placed at the vehicle C.o.M. and with its axes aligned along the body-fixed axes. As a consequence, lever arm and misalignment effects have not been modelled. Sensor output has been simulated considering biases, random walk, and scale factor effects. For the navigation analysis a flat non-rotating Earth has been assumed and the gravity, g, has been computed as in [10]. To evaluate navigation performances, the algorithm reported by Savage in [7] has been implemented assuming for the inertial sensors a measurement update rate of 10Hz. A series of simulations have been run to estimate the statistics of errors in the inertial navigation and evaluate adequacy of navigation sensors in measuring the vehicle state in terms of maximum error. Table 5 shows results of Montecarlo simulations of standalone inertial navigation. It can be observed that the maximum error in altitude is 5 km. Indeed the vertical channel suffers from the documented instability due to the non-perfect compensation of gravity [7].

Position E,N Altitude Attitude Velocity AoA

Unit m m ° m/s °

INS Systron DQI RMS err Max 1000 5000 2000 5000 0.1 0.5 1.5 3 0.8 2

Table 5: Summary of standalone INS Montecarlo simulation In order to improve A.o.A. and altitude accuracy a preliminary numerical test of GPS/INS performance has been performed. The scope of this test has been to show the effectiveness of the Kalman sensor fusion strategy in order to increase measurement accuracy. A typical form of the filter has been implemented [7]. In the simulation, INS measurement have been output by the DQI unit at 10 Hz. GPS measurements have been generated using a set of four satellites in view with best Geometric Dilution of Precision (GDOP) [2]. Results show that A.o.A. and altitude are the channels that have received the greatest benefits from sensor fusion. Indeed, estimated A.o.A. maximum error at the end of Montecarlo simulations has been in the order of 0.4° whereas the one resulting from standalone INS was 2.0°. Regarding the altitude, its error covariance has been in the order of 1 km instead of 5 km of standalone INS. Figure 4 compares the altitude as measured by the standalone INS and GPS/INS with the reference trajectory for STAR17A configuration. It can be observed that reference trajectory and GPS/INS output are almost superimposed.

Figure 4: Nominal vs. Measured Altitude Profile on MiniFTB\A Baseline Trajectory

Conclusions Mini SRT mission feasibility has been assessed from a GN&C point of view. The potentials of reproducing essential features of the full scale SRT mission have been quantified on two candidate system configurations differing mainly in the motor total thrust. Mission objectives have been scaled to values attainable by the reduced scale system. For each configuration a baseline guidance law has been defined, complying with the new system constraints, generally tighter than the SRT ones. A supplementary guidance solution is identified, in which the more pressing system constraint is relaxed with regard to the baseline trajectory, resulting in higher mission performances, and, as a consequence, providing qualitative insight on vehicle and system constraints impact on the overall attainable mission objectives. Results have shown that the lower thrust configuration reproduces the TPS requirement, the SRT main mission objective, with a consistent reduction in the attained thermal flux. The baseline trajectory suffers also of a limited TPS testing time interval, that is significantly increased (about 30%) lowering the trajectory ceiling altitude from 120 to 70 km, as in the alternative trajectory. The high thrust configuration instead reproduces, with acceptable differences, the whole full scale mission objectives. Comparison between the baseline and alternative trajectories show that higher thermal fluxes and/or TPS testing time can be obtained at the expense of an higher elevon torque spent to longitudinally trim the vehicle, and, thus, less residual maneuvering capability. The evaluation of the performance of a commercial-off-the-shelf GPS-aided, miniature inertial navigation system over the baseline trajectories has demonstrated satisfactory accuracies attainable by the navigation system, where altitude and A.o.A. determination substantially benefit from GPS aiding.

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