Simulation tool for generic launcher flight dynamics ...

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

Simulation tool for generic launcher flight dynamics-control interaction analysis Gianluigi BALDESI1, Donato SCIACOVELLI 2, Anthony THIRKETTLE3 1 2

AOES BV [email protected]

ESTEC/ESA [email protected]

3

AOES BV [email protected]

Structures Section, Thermal and Structures Division - ESTEC Keplerlaan 1, 2201 AG Noordwijk ZH, The Netherlands

Abstract – In order to study the performance of any dynamic systems it is essential to use appropriate software, which allows the user to model the particular problem in the « best » way. In particularly, for a flight simulator the task can be quite cumbersome since it requires modelling of the environment, the complex GNC and the inner dynamics of a vehicle. At the state of art, there are quite few software, which are able of accomplishing this and often the detriment of the computer time. The latter can be an important main issue, especially, for the sensitive analysis, which are necessary to establish and confirm the choice of the algorithm solutions proposed by the designer, studying new concepts and redundancy algorithms, and by tuning each module to achieve the performance required. To verify the adaptability of the flight mission data in response of the mission characteristics, several Monte Carlo analyses should be performed especially for off nominal flight. These campaigns, which repeatly generate random values for uncertain variables, require a powerful tool primarily in terms of computation time. Interesting results are obtained using the DCAP (Dynamic and Control Analysis Package), which uses a symbolic approach based on the formulation of Order(n) for the dynamics of multi-rigid or flexible-body system, possibly subjected to time varying structural characteristics and space environment loads. In order to have a crosscheck of them, the same software can use a numerical approach based on Lagrange method. The paper presents the results of the comparison between the symbolic and numerical approach for an example of a 3D flight trajectory of the first stage for a launch vehicle with flexible time varying structural properties modelled with a combination of DCAP (for the dynamics) and Simulink/Matlab (for the control), combining ease of implementation with computational efficiency.

1. – Introduction In order to study the performance of generic controlled dynamic systems, it is essential to have a dedicated tool, which allows the user to model, in a short time, the complex behaviour of the dynamic systems and their interactions with the control. In fact, some systems require a model with more than one body in order to take into account their different characteristics and their mutual interactions. This task is pretty complex and requires one to dedicate quite some time to understand the code and to validate the dynamic behaviour of the system. A lot of research has gone into the development and improvement of multibody software, with the aim of reducing the time of modelling a system and the computation time required to run an analysis. Multibody software involve the derivation of the equations of motion for multibody systems, which are systems characterized by several bodies connected by hinges that permit relative motion across them. Robots, launchers and spacecraft including articulated appendages such as solar arrays are typical examples for such systems. In particular, for a flight simulator the task is quite cumbersome since it requires to model the environment of the planet and the complex guidance, navigation and control system as well. In the framework of the VEGA launcher support, an activity has been initiated at Estec to perform verification tasks relative to the thrust vector control (TVC) system and of the VEGA LV dynamics performance. In order to model the launcher dynamics, it was decided to use the multibody dynamic simulation software DCAP (Dynamic and Control Analysis Package) [1] [3]. DCAP provides the user with an outstanding capability to model, simulate and analyse a complex multi-body system made up of coupled rigid and flexible structures with time-varying mass characteristics including the control systems. The software interface directly with several other software such as Nastran, Simulink/Matlab and OpenGL.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

2. – Multibody approach Early approaches to the dynamics formulation for multibody systems lead to the equations of motion, for openloop tree topologies, of the form: (1) where, M is an (n x n) mass matrix, q = [q1 q2 … qn]T is an (n x 1) column matrix representing the generalised coordinates and F is the column matrix containing the contributions from centrifugal, Coriolis and external forces. For a numerical simulation of such a system, the mass matrix must be inverted. Since the inversion of an (n x n) matrix involves operations proportional to the cubic power of n, this is called an Order(n3) approach. As the number of degrees of freedom increases, this matrix inversion for every integration step, becomes computationally expensive. Thus, researchers have sought methodologies to circumvent the mass matrix inversion and to improve computational efficiency. The research into improvements in formulations that increase computational speed resulted in - what are today called - Order(n) algorithms. The reason for this nomenclature is that the computational burden in these schemes increases only linearly with n. More details have already been presented in [2] and [5]. DCAP, which has currently been used in the Structures Section at ESTEC (ESA), has the possibility to simulate the same problem performing the analysis based on Order(n3) approach, derived by Lagrange method, and on Order(n) one using Kane's method of generalized speeds [7] [8]. For the latter a dedicated symbolic manipulation pre-processor, used in the coding optimisation, has been coded in order to compute the minimum set of equations of motion for each particular problem.

2.1. – Environment model The environmental disturbances consist mainly of aerodynamic loads, gravity gradient, magnetic field interaction and solar pressure. These produce forces and moments, which need to be accounted for in the generalised forces and moments on the right hand side of the equations of motion. DCAP already includes all of these types of disturbances, which the user can easily apply and tune for his other particular application. It is quite important to underline that DCAP takes into account whether of not the analysis involves flexible bodies applying the loads in an appropriate manner. Since the paper presents the results for atmospheric flight of launcher, the magnetic field and the solar pressure disturbances are not presented.

2.1.1. Gravity loads The gravity force is a distributed force that acts on each elementary mass particle, dm, of each body in a multibody system. The effect of this force can be divided into a major part and a minor part. The major part can be thought of as acting on the mass centre of body and is the force that determines the spacecraft orbit. The minor part of the gravity force is called “Gravity Gradient”. Since it is using an Inertial Reference Frame, the force and torque due to gravity gradient are defined as follows: (2)

(3)

Using the following nomenclature:

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

2.1.2. Aerodynamic loads The aerodynamic model is based on forces/moments arising from the interaction with the atmosphere and opposing the system motion along the relative body velocity direction and implies the computation of the following terms: n

F j = ∑ F ai i =1

n

M j = ∑ r cpi × F ai + M ai

(4)

i =1

where:

Fj

=

Aerodynamic force on body j

F ai

=

Aerodynamic force on ith surface

M

=

Aerodynamic moment on body j

M ai

=

Aerodynamic moment on ith surface

n r cpi

=

Number of Surfaces belonging to body j

=

Vector locating the ith surface

j

In fact, each body of the multibody system experiences an aerodynamic loads that depends on body “shape” and on the relative wind velocity (difference between the launcher velocity and the atmosphere velocity, which is due to the air, assumed fixed with the earth, wind and gust). The shape is composed of a number of “surfaces” and for its modelling there are available simple one (Cylinder, Plate and Sphere), which produce only drag force mainly used for the low-orbit satellite, or a lifting surface used for axial-symmetric body. Each lifting surface is characterized by shape dimensions (Aref, Lref), aerodynamic coefficients (CL, CD and CM) function of angle of attack (α) and Mach (M) and its location and orientation. The aerodynamics loads applied to the lifting body are:

F ai where: Drag force: Lift force: Momemt:

⎧− Di ⎫ ⎪ ⎪ = ⎨0 ⎬ ⎪− L ⎪ ⎩ i ⎭ AP

M

ai

⎧0 ⎫ ⎪ ⎪ = ⎨ M AERO i ⎬ ⎪ ⎪ ⎩0 ⎭ AP

(5)

Di = ½ · ρ · Vrel2 · Aref · CDi(αi,Mi) Li = ½ · ρ · Vrel2 · Aref · CL i(αi,Mi) MAERO i= ½ · ρ · Vrel2 · Aref · Lref · CM i(αi,Mi)

The aerodynamic forces are derived using the standard Air-Path reference frame (AP) as described inTable 1 and Fig. 1.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

Table 1 Air-Path reference frame {AP} definition

Origin x-axis z-axis y-axis

LV origin Coincident with the air speed vector result of the cross product body orientation axis and relative air vector Completes a right-handed frame

The aerodynamic force computation requires the atmospheric density and sound speed with respect to the altitude in order to compute the Mach number of the launcher during flight. These are physical inputs derived from the standard launch site atmospheric data. In additional there are some atmospheric disturbances such as a wind and gust, which can be applied. The wind represents an additional velocity of the air, with respect the assumption of air-fixed with the Earth, generally for the whole atmospheric flight. On the other hand, the gust represents a locally strong, abrupt rush of wind, acting at a particular altitude (H0_G). In view of the fact that the unknown disturbances can act in different directions, DCAP allows the user to choose where the particular wind profile should be applied. FIG. 1 : Surface orientation and Air-Path reference frame

2.2. – Control models

The control system represents a crucial component of a launcher, since it always requires autonomous operation during flight. Indeed, by means of the control system the vehicle can be steered along the desired flight path and it can autonomously counteract the disturbances of an internally unstable system. Existing multibody software, chosen for describing the intricate dynamic part, have some troubles to model the control system. Some of them allow the user to code it in some common computer language such as Fortran or C. Especially complex algorithms can require quite some time to program. With the aim of reducing this phase, DCAP has the capability to avoid this step. Based on the fact that nowadays a significant number of control designers use Simulink/Matlab environment, it was decided to import the DCAP dynamics into Simulink environment as a block. To this end, it is possible to automatically create a dedicated Simulink S-function, which describes both the dynamics and the DCAP environment model. This s-function, as any other Simulink block, can be linked directly to the control model (see FIG. 2). It makes the modelling of the control systems much easier and efficient. More information can be found in [2] and [6].

FIG. 2 : VEGA-DCAP Simulink model

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

3. – Launchers Flight dynamics application During the atmospheric flight, the launcher is subjected to all of the previously described environments. In addition, since the vehicle is usually an unstable system, the interactions between the control and the dynamics become quite important especially if flexible structural elements are modelled. These interactions can introduce some critical effects in different domain such as system stability, aeroelasticity effects, pistons crosscoupling, etc. Therefore it is compulsory to have an appropriate simulator, which allows quantifying these elastic effects and can be easily adapted to other similar application. In the Structures section at Estec it was decided to use DCAP to develop a Launcher flight simulator, which can allow to model different configuration of launch vehicle with minimal workload. An example is reported in Fig. 3, which represents one example configuration of a future launcher study. The first stage consists of 4 boosters and a main motor is controlled by 5 nozzles, which can be tilted independently. Using the multibody software, it proved relatively straightforward to model, despite being a rather complex problem to model. Thus more time was available to investigate the best philosophy to command the individual nozzles to accomplish the requirements placed on the control part. In the next section, the Vega-DCAP simulator, already presented in [1], is briefly described in order to demonstrate the simulators capabilities and emphasise the available options.

FIG. 3 : Heavy Liftoff Launcher Vehicle study

3.1. VEGA launcher The VEGA launcher model is based on a flexible LV with time varying characteristics directly imported from Nastran models in different flight condition. The nozzle, which has been modelled as a separate rigid body, is attached to the main LV at the pivot point including the structural stiffness and damping properties of this joint. Two pistons (electro-mechanic actuators) are used to point the nozzle in the desired orientation (FIG. 4). Again the small loop for the Thrust Vector Control (TVC) was linked as a Simulink block. Fortran was used, because this was a benchmark case for DCAP interface to Matlab, but otherwise the 4 week Fortran programming effort would have reduced to just days or even hours using Simulink block (Fig. 2). FIG. 4 : VEGA nozzle and pistons The preliminary Guidance, Navigation and Control part is model as well as model it is shown in Fig. 5. Since a completed description has been presented in detail [1], the attention is focused on the modelling only in the aerodynamic disturbances, which has been updated, and on the analysis in some different DCAP capability.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

FO RCE o n p is t o n 1

tra je c to ry d a ta FO RCE o n p is t o n 2

I M U

CURREN T L V c o n f ig u r a t io n

N AVIGA TIO N

CURRENT L V c o n f ig u r a t io n

CURRENT P is t o n s c o n f ig u r a t io n

D ES IRED L V c o n f ig u r a t io n

O PTIM A L L V c o n f ig u r a t io n

a c t u a l p is t o n 1 d ip la c e m e n t

TVC a c t u a l p is t o n 2 d ip la c e m e n t

GU IDA N CE (O P E N L O O P )

D ESIRED p is t o n s d ip la c e m e n t

BIG LO O P TVC

TVC CO N TROL

FIG. 5 : LV GNC description

3.1.1. Aerodynamic model Using the distributed aerodynamic coefficients of the launcher (FIG. 6), the vehicle has been divided in smaller slices. Each slice has a reference area for the aerodynamics. These reference areas modelled by DCAP surface are characterised by their own particularly aerodynamic coefficients based on a consistent discretisation of the aerodynamic data (FIG. 7). Using the surface elements, DCAP can compute a local angle of attack for each section (FIG. 14) and the correspondent aerodynamic loads. Although there is no information on the sensibility of the aerodynamic coefficients with respect to LV shape, this quasi-static approach, is a first reasonable approximation to take into account aeroelasticity effects. CD at alpha =0 deg and Mach =0.95 0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

FIG. 6 : Distributed aerodynamic coefficients for CD

0

5

10

15 20 Length [m]

25

30

35

FIG. 7 : Example of the discretitation in 30 slides

3.2. Results capabilities overview The VEGA-DCAP simulator can provide several results. These allow the user to gradually build up a simulator adding small increments of complexity, maintaining transparency of the results and validating the model for each level of complexity. In the end there is a full model to validate the control, small loop and big loop, for time varying mass, flexible launch vehicle and all other option for the environment disturbances.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

¾ Linear analysis The linear analysis is implemented in DCAP by means of numerical linearisation of the non–linear dynamic equations around a particular equilibrium state. For a lift-off condition, FIG. 8 shows examples of frequency response from demanded piston 1 displacement to actual nozzle yaw angle, while FIG. 9 shows the corresponding cross-coupling from demanded piston 1 displacement to actual piston 2 force. These results are achieved having the control system in open loop and the thrust vector control in closed loop. DCAP can also provide information about the [A], [B], [C] and [D] matrixes, which describe the LVnozzle linear system, which can then be used by other software for linear analysis. Frequency Response I/0 : INPUT: demanded piston 1 displacement OUTPUT: actual piston 2 force

100

0

0

-50

GAIN

GAIN

Frequency Response I/0 : INPUT: Demanded piston 1 displacement OUTPUT: actual nozzle yaw angle

-100 -200 -2 10

-1

10

0

1

10 10 Frequency [Hz]

2

10

-150 -2 10

3

10

-1

10

0

1

0

1

10 10 Frequency [Hz]

2

10

3

10

200 PHASE

PHASE

200

0

-200 -2 10

-1

10

0

1

10 10 Frequency [Hz]

2

10

FIG. 8 : Frequency response from demanded piston 1 displacement to actual nozzle yaw angle

¾

-100

3

10

0

-200 -2 10

-1

10

10 10 Frequency [Hz]

2

10

3

10

FIG. 9 : Frequency response from demanded piston 1 displacement to actual piston 2 force

Nonlinear time simulation Typical non-linear time simulation results for 1st stage 3D non-linear trajectory simulation in offnominal condition are reported in FIG. 10 to FIG. 15. As is shown in Fig. 10 the actual LV yaw angle closely follows the desired one due to the actions of the piston, which deflect the nozzle and therefore the thrust. For this particular case a wind profile was added in same direction as the air velocity and an additional gust of 9 m/s hits the launcher at an altitude of 3500 m. The latter has a considerable impact on the angle of attack around 26 s (see Fig. 12). An interesting feature of DCAP is that the constraint forces and torques on the nozzle joint can be plotted (see Fig. 13, Fig. 14 and Fig. 15). We are also interested in the maximum actuator loads.

FIG. 10 : Actual vs desired yaw angle [deg]

FIG. 11 : Desired vs Actual Piston 1 Position [mm]

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

FIG. 12 : Local angle of attacks for some surfaces along the LV

FIG. 13 : Constarint forces around X-axis and Y-axis for the hinge nozzle-LV [T m]

FIG. 14 : Constarint torque around X-axis for the hinge nozzle-LV [N m]

FIG. 15 : Zoom in of FIG. 14 [T m]

The results were performed using the two different DCAP dynamic algorithms, one based on Order(n) and the other one on Order(n3). Although no significant differences were identified for the set of possible output and for the precision of the results, there was a remarkable difference in computer time. Indeed the Order(n) performs the simulation in less than 7% of the total computational time used by the Order(n3). This result is perfectly in line with previous validation and testing campaigns. Previous studies were done by an independent team, Fokker Space, which was not involved in the DCAP software development. More information about the benchmarking on the performance verification of DCAP with respect to other dynamics analysis packages (MECANO, ADAMS, DADS and SMX-Hera) is available in [10].

¾ Sensitivity analysis A useful capability has been added to DCAP to perform sensitivity runs (ie MonteCarlo analysis), which allows to change any parameters of the simulation, in either the dynamic and control part, by substitution of them by means of randomly generated data in accordance with a user defined standard probability distribution, such as a linear, uniform or Gaussian one. To demonstrate this capabilities a sensitivity analysis on the misalignment of thrust force (Fig. 16) with respect the LV longitudinal axis is presented.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

x

z

Thrust y

FIG. 16 : Thrust misalignment for two axis (Y-Z)

In the FIG. 17 and FIG. 18 the analyzed misalignment configuration are plotted in circle among those the unstable one are pointed out with a star. The results highlight that a big misalignment measured in a negative yaw deflection does not cause a critical problem for the launcher since the residual angle of attack (FIG. 12) produces a lift, which force the control to deflect the nozzle in a negative yaw direction. The FIG. 19 and FIG. 20 plot the motion of the launch vehicle with respect to the nozzle. So, if there is a misalignment (in negative yaw) the nozzle has to deflect less (FIG. 20) since a part of the thrust already is creating a reacting moment to the lift force. Thrust Misalignment

Zyaw axis

yaw Z axis

Thrust Misalignment

Y axis

pitch

FIG. 17 : Thrust misalliment for two axis (Y-Z)

FIG. 19 : Launcher deflection angles wrt the nozzle in nominal condition

Y axis

pitch

FIG. 18 : Zoom of Fig. 17

FIG. 20 : Launcher deflection angles wrt the nozzle with thrust misalignment around minus yaw

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

¾ Data Recovery Procedure As it is illustrated in FIG. 20, a data recovery procedure has been implemented in DCAP and validated using ATV finite element model [4]. This procedure allows to post-process the DCAP results in Nastran to compute the internal loads. From the modal coordinates information (FIG. 22), output of DCAP, can be used to recover the deformation of the flexible structure and enforce the motion. Then the forces and stresses can be computed in Nastran (FIG. 23). The following figures represent the typical results of the VEGA launcher using a beam model. Some results, not presented, are available for the 3D VEGA FEM model as well.

Modal Analysis (Nastran)

Analysis with enforced Motion (Nastran)

Non Linear Time simulation (DCAP) DRP Pre-processor: Deformation in physical coordinates (Matlab)

FIG 21 : Flow chart for the Data Recoveryi pre-processor

T = 3.4 s

T = 16 s

Variable

T = 16 s

Modal coordinate 1, body 2

Forces

Modal coordinate 2, body 2

[N]

T = 3.4 s

Moments [Nm]

FIG. 22 : 1st and 2nd Modal coordination behaviour and VEGA deformation for two different flight conditions

FIG. 23 : DRP Forces and moments results for two different flight time

4. – Conclusions In order to model the launcher flight dynamics a flight simulator was developed using DCAP. A very capable simulator was created with minimal manpower considering the numerous capabilities. As quick recap the DCAP and VEGA-DCAP simulator combines all of the following: – flexible structural characteristics directly importing Nastran Finite Element Models – environment and disturbances for flexible bodies – flexible or rigid bodies both with time varying mass and inertia – complex nonlinear dynamics in Simulink format – multiple bodies to model separation and nozzles – Monte Carlo capabilities – Internal loads computation Among the different dynamics formulation a comparison between the Order-n and Lagrange approach was presented. The Order-n is able to perform the same simulations with the same results in less than 7% of the total computational time with respect the Lagrange one, at least for these examples. Finally, quite a detailed overview of the analysis capabilities, performed by DCAP for VEGA LV application, has been presented.

6th Int. Symp. on “Launcher Technologies: Flight Environment Control for Future and Operational Launchers”, 8-11 Nov 2006, Munich, Germany

Now following the simulator’s successful development, the focus will be on specific support tasks such as multi stage modelling, in particularly stage separation as dynamically triggered events from fixed to six degrees of freedom for the connecting hinge. The capabilities for the analysis of stage separation have already been implemented. For the purpose of the latter simulator, the geometry of the interstages structures are modelled in Wavefront format, and taking advantage of PCM Polygon Contact Modelling algorithm for contact dynamics [9].

5. - References [1] D. Sciacovelli, S. Kiryenko, G. Baldesi, A. Thirkettle, R. Redondo & P. D. Resta,“Vega Prototype 3D Simulation Software with Time Varying structural characteristics”, 5th Inter. Conference “Space Launchers: Missions, Control and Avionics”, Madrid, Spain, November 25-27, 2003 [2] Portigliotti, S., Dumontel, M., Baldesi, G., & Sciacovelli, D., DCAP: an effective tool for modeling and simulating of coupled controlled rigid flexible structure in space environment, 6th International Conference on Dynamics and Control of Systems and Structures [3] R. Franco,M, L. Dumontel, S. Portigliotti & R. Venugopal : “The Dynamics and Control Analysis Package (DCAP) A versatile tool for satellite control”, ESA Bulletin Nr. 87 August 1996 (http://esapub.esrin.esa.it/bulletin/bullet87/franco87.htm) [4] A. Oliveira, G. Baldesi & D. Sciacovelli: “A space application of a data recovery procedure based on direct enforced motion using a multi-body dynamcis software (DCAP)”, European Conference on Spacecraft Structures, Materials and Mechanical Testing, 10-12 May 2005 at ESTEC [5] M. L. Dumontel, S. Portigliotti, R.Venugopal : “DCAP: A Tool for Analysis and Simulation of Multi-Body Systems”, 45th IAF Conference, Oslo, October 1995 [6] G. Baldesi : “Modelling Launch Vehicle Nozzle and TVC loop with DCAP & Importing the Non-Linear Dynamics in Simulink/Matlab Environment”, report in Fulfillment of Master in Satellites and Orbiting Platforms, University “La Sapienza”, Rome, Italy 19-11-2003 [7] Kane, T.R., and Levinson, D.A.: “ Dynamics, Theory and Applications”, 1985, Mc Graw-Hill, New York [8] Kane, T.R., Likins, P.W., and Levinson, D.A. “Spacecraft Dynamics”, 1983, Mc Graw-Hill, New York. [9] Hippmann, G.: “An Algorithm for compliant contact between complexly shaped surfaces in multi-body dynamics”, Proceedings of the International Conference on Advances in Computational Multibody Dynamics, Lisbon, Portugal, July 1-4, 2003 [10] “Selection of NRT Multibody Dynamics SW Package for Hera Simulation Facility”, Fokker Report, H-M-3M22000683-FSS, Iss. 3, Rev. 2, September 1993