Francesco Ferrante

Francesco Ferrante, Frédéric Gouaisbaut, Ricardo G. Sanfelice et al.

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples.

Michele A. Mandolino, Francesco Ferrante, Gianluca Rizzello

In this paper, a hybrid model for single-crystal Shape Memory Alloy (SMA) wire actuators is presented. The result is based on a mathematical reformulation of the Müller-Achenbach-Seelecke (MAS) model, which provides an accurate and interconnection-oriented description of the SMA hysteretic response. The strong nonlinearity and high numerical stiffness of the MAS model, however, hinder its practical use for simulation and control of complex SMA-driven systems. The main idea behind the hybrid reformulation is based on dividing the mechanical hysteresis of the SMA into five operating modes, each one representing a different physical state of the material. By properly deriving the switching conditions among those modes in a physically-consistent way, the MAS model is effectively reformulated within a hybrid dynamical setting. The main advantage of the hybrid reformulation is the possibility of describing the material dynamics with a simplified set of state equations while maintaining all benefits of the physics-based description offered by the MAS model After describing the novel approach, simulation studies are conducted on a flexible robotic module actuated by protagonist-antagonist SMA wires. Through comparative numerical analysis, it is shown how the hybrid model provides the same accuracy as the MAS model while saving up to 80% of the simulation time. Moreover, the new modeling framework opens up the possibility of addressing SMA control from a hybrid systems perspective.