This article presents a summary of the development work that has been undertaken during the last ten years by Alenia Spazio under ESA contract, culminating in the production of DCAP the Dynamics and Control Analysis Package.

DCAP is a suite of fast, effective computer programs that provides the spacecraft analyst with a powerful tool for designing and verifying the dynamics and control performance of coupled rigid and flexible structural systems. The software modules that it contains can be grouped into four general categories (Fig. 1):

Figure 1. The DCAP software modules

- pre-processing
- processing (time and frequency domains)
- post-processing utilities.

Communication between the modules is achieved via the dedicated file structure shown in Figure 2, in which the logical hierarchy of the DCAP programs is also illustrated.

Figure 2. Modules and file interfaces

The package provides the user with an outstanding capability to model, simulate and analyse a complex multi-body system. The latter can be connected in open- and closed-loop topologies (Fig. 3), where relative motion is defined through 'hinges'. Each hinge allows from zero to six relative degrees of freedom, as it can be free, locked or constrained to pre-defined motion.

Figure 3a,b. Open-loop and closed-loop tree topologies

From a general viewpoint, the DCAP model is the combination of four components:

- 'structure' or 'plant': the multi- body topology itself
- 'sensors': the feature that allows the extraction of system motion information for performance monitoring
- 'actuators': the feature through which forces and torques are applied to the structure
- 'controller': the part of the system driving the multi-body structure in order to achieve the allocated objective.

**DCAP Capabilities**

- Rigid and Flexible Body Chains
- Open- and Closed- Loop Topology
- Six Degree-of-Freedom Hinges
- Large-Angle Rotations
- Linear and Non-linear Time Domain Simulations
- Order (N) Algorithm
- Symbolic Code Generation
- Orbital Environment
- Built-in Sensors and Actuators
- Non-linear
Devices (
*including Coulomb Dampers*) - Numerical Linearisation
- Continuous/Discrete/User Controllers
(
*Transfer Function, State Space, Block Diagram*) - File Interface to MATLAB and MATRIXx
- File Interface to NASTRAN and ASKA
- Frequency Response
- LQG and Model Order Reduction
- Interactive Pre- and Post-processing.

DCAP provides an interactive menu-driven environment (Fig. 4a), which assists the user in defining the model, preparing and executing the simulation run, and analysing the results. The model definition is supported by a user-friendly X/MOTIF-based graphical user interface that allows both for the interactive inputting of the data required by each building block (Fig. 4a) and for the geometrical three-dimensional (3D) modelling of the structure (Fig. 4b).

Figure 4a. Menu-driven environment

Figure 4b. 3D modelling and animation

Interfaces to popular finite-element software packages such as NASTRAN (MSC and COSMIC) and ASKA, are available and give a direct capability to define complex flexible structures. Similar interfaces are provided to control design packages like MATLAB and MATRIXx. The modelling capability is completed with the possibility of user-defined software integration, allowing for the use of specific features (sensor and actuator dynamics, user controller, etc.) not directly included in the package's library.

The results analysis is supported by a specific plotting package that can handle time-domain plots, harmonic analysis (direct and inverse FFT), and Bode, Nichols, Nyquist and Root locus charts. Performance can also be inspected via a powerful 3D animation tool, which helps the user to visualise the simulation results (Fig. 4b).

The core of the package consists of the computational modules, particularly oriented towards the simulation of the non-linear dynamics of multi-body systems. In addition, programs for numerical linearisation, matrix representation manipulation (state space) and system combination allow linear problems in both the time and frequency domains to be handled.

The current DCAP is running on VAX/VMS computers and on UNIX (Sun, Silicon Graphics) work stations, and the software package is complemented by a full set of manuals (User, Theory, Demonstration and Installation).

Considerable efforts have been made to achieve efficient formulation and solution of the dynamic equations of multi-body systems. The solution must be developed carefully to provide the requisite fidelity and accuracy, and at the same time minimise the computational costs associated with the time-history simulation. The formulation for the dynamics of multi-rigid/flexible-body systems, as defined in the DCAP software, is based on Kane's method and it exploits a dedicated symbolic manipulation preprocessor. The equations are first derived based on body pairs (Fig. 5), i.e. the basic dynamics solution is formulated for recursive operations: given a body j, its motion is completely known from the knowledge of inboard body (L(j)) motion, relative joint motion, and active forces due to control-system actuators or the environment surrounding the body. In particular, this approach implies three basic steps:

- a first 'forward sweep' from the 'core' body (body 1 in Fig. 3) to the 'leaf' bodies to compute the kinematics
- the implicit computation of the acceleration of each body in terms of the external forces and torques acting on it, and of the acceleration of the body directly inboard; this part of the solution process is identified as the 'frontal part', and it starts from the 'leaf bodies' and ends when the 'core' body is reached
- a second 'forward sweep' to explicitly compute the acceleration of each body via a back-substitution process.

This scheme allows one to avoid the explicit computation of a system mass matrix and its inversion, and it results in a minimum-dimension formulation exhibiting close to Order(n) behaviour, n being the number of system degrees of freedom.

Symbolic processing of the equations of motion can result in a substantially more efficient simulation. This increase in efficiency is achieved through simplifications that are possible because of special configuration characteristics, as well as arithmetic and algebraic simplifications.

A schematic of the symbolic processing and simulation modules, along with their relationship with the DCAP package, is shown in Figure 6. They receive their input from three sources:

- a configuration data file which describes the multi-body system being simulated, its topology and properties
- a flexible-body data set that contains data relating to the flexibility properties of each flexible body in the system
- an equation file containing the templates of the equations of motion of a generic multi-body system.

The output from the symbolic processor is a set of FORTRAN files containing the implementation of the specific set of equations of motion that are applicable to the multi-body configuration defined. This source code is then compiled and linked with the simulation library to generate the executable module.

The latest release of DCAP (Release 7) has been extensively tested through a dedicated testing campaign carried out by an independent team at Alenia Spazio. In addition, during the last phase of DCAP's development (1991 1994), the current implementation of the multi-body dynamics was compared extensively with similar packages like Treetops, SSIM (Space Station SIMulation), and against exact analytical solutions implemented in tools like MATLAB.

During 1993, DCAP's performance was assessed against those of other software products for the non-real-time simulation of robotic manipulators of the HERA (Hermes Robotic Arm) type. The testing and evaluation were carried out by Fokker Space Systems in the framework of the HERA Simulation Facility activities. The evaluation was based on multiple criteria, including: functional model and interface requirements coverage, run performance, accuracy, test case results, and cost. DCAP was the only software package that ran all of the test cases successfully, with perfect matching of energy and momentum balances. It also offered the best cost/benefits ratio.

Finally, as part of the final acceptance exercise, an executable DCAP tape was distributed by the Agency to a number of space industries and universities in order to collect expert feedback and comments.

DCAP software has been available to the European space community since the end of 1983 and has been used extensively within the Agency for satellite simulations (e.g. for Olympus, ERS-1), pilot studies, and checking of contractors' work. Since 1991, the dynamics formulation, as implemented in Release 7, has been successfully applied in technological studies as well as projects, in the field of spacecraft and robotic- system dynamic simulation, mechanism analysis, and control performance verification. Some of these applications are described below in a little more detail to demonstrate the package's flexibility in terms of modelling capability and simulation fidelity.

**Microgravity dynamic disturbance study**

The goals of this study were to assess the environmental
disturbances to microgravity experiments induced on flexible
large platforms and to define a methodology for their evaluation.
In this context, DCAP has been used to:

- compute frequency responses between source disturbance points and target microgravity locations
- verify acceleration levels with time- domain responses
- analyse the effects induced by antenna pointing mechanisms and control
- implement a six degree-of- freedom micro-gravity isolation mount model to reduce the acceleration spectra at specific payload locations below Space Staion/Columbus specifications.

The analysis was carried on a full flexible spacecraft, modelled as a five-body system (core body, two solar arrays, antenna mast and a payload platform). Direct interfacing to NASTRAN finite-element data was used for component-body characterisation:

- Model characteristics

532 grid- point core body

80 grid points for each solar panel

20 grid points antenna mast

rigid payload platform - Craig-
Bampton component-mode synthesis redundant constraint modes and
fixed-interface normal modes

91 flexible modes retained (25+27*2+12)

14 rigid degrees of freedom (6 d.o.f core body, azimuth and elevation antenna freedoms, 6 d.o.f isolation mount) - Perfect overlapping of DCAP frequency response w.r.t. NASTRAN up to the 30 Hz range
- Unique ability to include mechanisms in flexible-body chains (NASTRAN limitation with mechanisms and related control).

**Drag-free satellite control study**

This
study was aimed at addressing the drag-free-control approach for
mission scenarios like Aristoteles and STEP. The use of DCAP was
particularly oriented to the verification of the STEP satellite's
drag-free design performance by means of a simulation combining
the complete model of the satellite configuration and the control
laws as defined during the study's evolution. To this end, the
spacecraft was modelled as a three-body structure: a central
rigid body, one flexible solar array, and a third rigid body
connected by a spring-dashpot device to account for the helium
sloshing.

Special attention was paid to the definition of the sensor, actuator and control-law modelling to reflect the design and the approach adopted by Matra Marconi Space (MMS), responsible for this task within the study. In particular, the models of the actual sensors and actuators were accommodated in a 'User Continuous Controller'. The attitude-control laws were implemented in a 'User Discrete Controller' that incorporated the FORTRAN routines defined by MMS for the attitude estimation and control schemes and the thruster firing logic. Finally, the drag- free control laws for translation were introduced as a 'Discrete Matrix Controller'.

Based on this model, simulations spanning 20 orbits (about 105 seconds) were run with the discrete controllers sampled at 10 Hz and an integration step of 5x10-³ seconds to check the transient actuator dynamics between controller updates. The synthesis of the response power spectra was performed using the built-in harmonic analysis and Fast Fourier Transform (FFT) computation. In these runs, 1 second of CPU time on an SGI Indigo R4000 work station was required to solve 5 seconds of real system time.

**Atmospheric Re-entry Demonstrator (ARD)**

This application was related to the study of the dynamic behaviour of the ARD re-entry capsule under parachute loadings, the analyses being performed within the framework of the ARD/DRS Programme. The DCAP software was used to model and analyse:

- the back-cover extraction driven by the pilot parachute
- the drogue-parachute stabilisation phase
- the main parachute cluster descent.

To perform these analyses, both the built-in features of DCAP and its ability to incorporate user-defined software were extensively exploited. In particular, the handling of closed-loop topology and the non-linear hard-stop devices allowed multiple contacts between the back cover's corner and the capsule itself during the separation phase to be studied. A special set of user- defined subroutines was developed to support the simulation of the stabilisation and descent phases. This allowed extensive study of the system's behaviour, including:

- analysis of the 3D capsule aerodynamics at low altitudes with aerodynamic- coefficient interpolation with respect to the angle of attack and Mach number
- modelling of the flexible suspension lines, parachute bridles and riser, accounting for non-linear stiffness and loss of tension (slack condition)
- simulation of parachute reefing stages, with trapped air masses under canopies.

The analysis of the results benefitted substantially from the use of the DCAP graphical modelling and animation tools, particularly the contact determination during the separation phase. An accurate validation will be possible against the physical data expected from the ARD balloon-borne flight-test scheduled for July 1996.

**SAX satellite**

Figure 8. SAX and ROBOTICS examples

DCAP was used extensively during the design and development of the SAX X-ray astronomy satellite, developed by Alenia Spazio for the Italian Space Agency (ASI), for:

- analysis of deployment manoeuvres and shock loadings on the spacecraft's Advanced Rigid Arrays (ARAs)
- modelling and simulation of deployment springs, synchronisation cables and locking mechanisms
- external- disturbance evaluation and momentum-wheel management
- analysis of internal and external torques induced by the orbital environment, structural flexibility, fuel sloshing and locking mechanisms
- validation of the SAX real-time dynamic simulator.

The telemetry data collected during the first months of the SAX satellite's operation have shown very good agreement with the DCAP predictions for the solar-array deployment manoeuvres.

**Robotics**

The non-linear dynamics module
of DCAP was used for an Autonomous Robot Control Simulation
(ARCS-1) as part of an ESA study for the development of a
prototype of a robot simulator. It was integrated within the
overall architecture used to perform the simulation of various
robotics tasks, including the 'grasp' and 'release' of objects,
and to run in connection with the robot controller simulator.

DCAP was also used in the Automated Manipulation and Transportation System (AMTS) study for modelling the manipulator arm and for verifying the accelerations induced in the Attached Pressurised Module (APM) by the arm's manoeuvring.

The structure and the features of the DCAP package have been presented along with a number of selected applications. From this material it can be concluded that DCAP provides an outstanding and generic capability for modelling complex multibody systems and for analysis and simulation of their dynamic behaviour.