D04.05 - Feasibility mock-ups of feedback schedulers

Control and computation co-design deals with the interaction between feedback control laws design and their implementation on a real execution resource. Control design is often carried out in the framework of continuous time, or under the assumption of ideal sampling with equidistant intervals and known delays. Implementation on a real-time execution platform introduces many timing uncertainties and distortions to the ideal timing scheme, e.g. due to variable computation durations, complex preemption patterns between concurrent activities, uncertain network induced communication delays or occasional data loss. Analyzing, prototyping, simulating and guaranteeing the safety of complex control systems are very challenging topics. Models are needed for the mechatronic continuous system, for the discrete controllers and diagnosers, and for network behavior. Real-time properties (task response times) and the network Quality of Service (QoS) influence the controlled system properties (Quality of Control, QoC). To reach effective and safe systems it is not enough to provide theoretic control laws and leave programmers and real-time systems engineers just do their best to implement the controllers. This report first describes, through the detailed design of a quadrotor drone controller, the main features of {\sc Orccad}, an integrated development environment aimed to bridge the gap between advanced control design and real-time implementation. Besides control design and implementation, a real-time (hardware-in-the-loop) simulation has been designed to assess the control design with a simulated target rather than with the real plant. Using this HIL structure, several experiments using flexible real-time control features are reported, namely Kalman filters subject to data loss, control under (m,k)-firm constraints, control with varying sampling rates and feedback scheduling using the MPC approach

Modeling and analysis of a flexible spinning Euler-Bernoulli beam with centrifugal stiffening and softening: A Linear Fractional Representation approach with application to spinning spacecraft

The derivation of a linear fractional representation (LFR) model for a flexible, spinning and uniform Euler-Bernoulli beam is accomplished using the {Lagrange} technique, fully capturing the centrifugal force generated by the spinning motion and accounting for its dependence on the angular velocity. This six degrees of freedom (DOF) model accounts for the behavior of deflection in the moving body frame, encompassing the bending, traction and torsion dynamics. The model is also designed to be compliant with the Two-Input-Two-Output Port (TITOP) approach, which offers the possibility to model complex multibody mechanical systems, while keeping the uncertain nature of the plant and condensing all the possible mechanical configurations in a single LFR. To evaluate the effectiveness of the model, various scenarios are considered and their results are tabulated. These scenarios include uniform beams with fixed root boundary conditions for different values of tip mass, root offset and angular velocity. The results from the analysis of the uniform cantilever beam are compared with solutions found in the literature and obtained from a commercial finite element software. Ultimately, this paper presents a multibody model for a spinning spacecraft mission scenario. A comprehensive analysis of the system dynamics is conducted, providing insights into the behavior of the spacecraft under spinning conditions