Monolithic Versus Distributed Structure/Control Optimization of Large Flexible Spacecraft
Authors:   Isae Supaero, Toulouse, France, Sanfedino Francesco , Alazard Daniel , Kiley Andy , Watt Mark , Simplicio Pedro , Ankersen Finn 
Published: January 2024

The widespread approach for Multi-Disciplinary Optimization (MDO) problems adopted in the Space industry generally follows a sequential logic by neglecting the interconnection among different disciplines. However, since the optimization objectives in the different fields are often conflicting, this methodology can fail to find global optimal solutions. By restricting the analysis to just structure and control fields, the common hierarchy is to preliminary define the structure by optimizing the physical design parameters and then leave the floor to the control optimization. This process can be iterated several times before a converging solution is found and control performance is met. Especially for large flexible structures, the minimization of the structural mass corresponds in fact to an increase in spacecraft flexibility, by bringing natural modes to lower frequencies where the interaction with the Attitude Control System (ACS) can be critical, especially in the presence of system uncertainties. Modern MDO techniques nowadays represents a tool to enhance the optimization task by integrating in a unique process all the objectives and constraints coming from each field.
Two kinds of architectures can be distinguished in the MDO framework: monolithic and distributed. In a monolithic approach, a single optimization problem is solved, while in a distributed architecture the same problem is partitioned into multiple sub-problems containing smaller subsets of the variables and constraints.
The development in the last decade of structured H∞ control synthesis opened the possibility of robust optimal co-design of structured controllers and tunable physical parameters. In fact, Linear Fractional Transform (LFT) formalism allows one to embed in the dynamic model tunable physical parameters treated as parametric uncertainties. In addition, thanks to these techniques, particular properties can be imposed on the controller, such as internal stability or performance respecting a frequency template, in the face of all the parametric uncertainties of the plant. This point is particularly important for aerospace applications where requirements are generally challenging and structural uncertainty, coming for example from an imperfect manufacturing or assembly, cannot be neglected. It has to be said that these techniques do not guarantee a global optimal solution of problem, so a good first guess can enhance the quality of the result.
Alazard et al. [1] demonstrated how this multi-model methodology implemented in H∞ framework can be enlarged to include integrated design between certain tunable parameters of the controlled system and the stabilizing structured controller.
There exist as well in literature a large class of problems where coupling between structure and control is considered unidirectional. This means that the objective function of the structural sub-problem depends only on the structural design parameters while the control criterion depends on both structural and control design parameters. A partition of the structure and controller design variables is desirable for practical implementation when the impact of the controller variables on the structural objective is relatively small. A strategy in this case is to solve the system-level problem as a nested optimization one, as in the BIOMASS test case [2].
For the present study both monolithic and distributed architectures are investigated on a real benchmark, the ENVISION spacecraft preliminary design.
In particular, the problem formulation in the multi-body Two-Input Two-Output Ports (TITOP) [3] modelling approach allows the author to easily define an MDO problem by including all possible system uncertainties from the very beginning of the spacecraft design. In this way not only a structure/control co-design is possible, but system performance is robustly guaranteed.
Where an analytical model of the structure is sufficient to describe the various spacecraft sub-components, a dependency from the design parameters can be captured in a minimal LFT model (built in SDTlib). In this approach the control/structure co-design problem is solved in a unique iteration by using the non-smooth techniques available in the Robust Control community. When the complexity of a structure cannot be handled with a simple analytical model (i.e. finer Finite Element Model (FEM) are necessary to ensure representativeness), a distributed architecture will be preferred. A nested optimization process is in fact necessary when a FEM software such as NASTRAN has to be interfaced with the control synthesis/analysis tools available within MATLAB/SIMULINK. In this case, the strategy is to iteratively optimize an inner H∞ control problem, which depends on both control and structural design variables, and the structural design themselves tare optimized by an outer global optimization routine.
The aim of this paper is finally to contribute to the evolution of industrial practice in control/structure co-design, by proposing a unified and generic approach based on a well-posed modelling problem that integrates both design parameters and parametric uncertainties in a unique representation. The advantage offered by this framework is dual: to shortcut the unnecessary iterations among different fields of expertise and to speed up the validation and verification process by directly producing a robust preliminary design.
References
[1] Alazard, D. et al. Avionics/Control co-design for large flexible space structures. (2013) In: AIAA Guidance, Navigation, and Control (GNC) Conference, 12 August 2013 – 22 August 2013 (Boston, United States).
[2] Falcoz, A., Watt, M., Yu, M., Kron, A., Menon, P. P., Bates, D., ... & Massotti, L. (2013). Integrated Control and Structure design framework for spacecraft applied to Biomass satellite. IFAC Proceedings Volumes, 46(19), 13-18.
[3] Alazard, D., Perez, J. A., Cumer, C., & Loquen, T. (2015). Two-input two-output port model for mechanical systems. In AIAA Guidance, Navigation, and Control Conference (p. 1778).