In the methodology contributed, both the kinematic and dynamic equations were considered, avoiding cascaded control that leads to inadmissible torque levels. The continuous-time models were transformed into normal forms. In order to consider the effect of sampling from the beginning in the design process, the approach followed was based on an equivalent nonlinear discrete-time model of the normal forms, the Exact Sampled Representation (ESR). The ESRs obtained, from a computation point of view, have the appealing characteristic of finite computability, a property that permits to design discrete-time controllers without approximations. Multi-rate sampled-data techniques were implemented on the ESR models, where the control variables are adequately kept piecewise constant over fractions of the sampling period. The multiple changes of the control variables in the inter-sampling interval produce the increased number of degrees of freedom required to achieve one step dead beat control, invert the input-state map and achieve robust stabilization via an adequate feedback control strategy.
The performance of the novel algorithms was validated with extensive Model-In the-Loop simulations on the MATLAB/Simulink environment and, in more realistic conditions, by developing a more sophisticated design tool that includes an orbit propagator, the complete spacecraft equations, an Unscented Kalman Filter for attitude determination, the dynamics of the reaction wheels including PWM signals and saturation effects and environmental disturbances. This flexible tool gives the potentiality to design and test sampled-data based algorithms also for the fully actuated spacecraft. Various on-orbit attitude control operations, during all phases of the mission, like detumbling, desaturation, nadir pointing and ground station tracking have been simulated.
The applicability of the methodology was confirmed by the means of a hardware prototype built, based on a spherical air-bearing that offers friction-free motion on three rotational axes, equipped with an embedded STM32F4 microprocessor, an MPU-9250 9-axis MEMS sensor and three Maxon EC 45 flat 70W brushless DC motors with press-fitted aluminum flywheels and driven by ESCON 36/3 EC servo controllers.
The software tool designed, if further developed, could be marketed, targeting at the CubeSat market. The control methodology conceived can be implemented as a fail-safe mode on the OBC of a microsatellite. This twofold exploitation potentiality and the resulting IPR handling are currently under investigation in collaboration with G.A.U.S.S. Srl, a spin-off of the Sapienza University, with launch services, design and manufacturing of microsatellites activities.
The project outcomes will be disseminated through open access publications. They were presented at the ‘Open DIAG’ events held at the host institution, where projects and activities conducted are presented to students and will be presented in the framework of the Sapienza Aerospace Research Centre and of the ‘Master in Satelliti e Piattaforme Orbitanti’. The prototype platform will be used to motivate pupils of all levels towards science, research and innovation, promote EU investment in research and science and highlight control principles in space, in the framework of a digital festival held in 18 cities all over Greece, under the aegis of the Ministry of Education.
