In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.

This paper studies the tuning process of controllers for fully actuated manipulators. To this end, we propose a methodology to design the desired damping matrix—alternatively, the derivative gain of a PD controller—of the closed-loop system such that n second-order systems can approximate its behavior with a prescribed damping coefficient, where n denotes the degrees of freedom of the system. The proposed approach is based on the linearization of the closed-loop system around the desired configuration and is suitable for different control approaches, such as PD control plus gravity compensation, impedance control, and passivity-based control. Furthermore, we extensively analyze simulations and experimental results in a cobot.

This paper investigates a distributed formation tracking control law for large-scale networks of mechanical systems. In particular, the formation network is represented by a directed communication graph with leaders and followers, where each agent is described as a port-Hamiltonian system with a constant mass matrix. Moreover, we adopt a distributed parameter approach to prove the scalable asymptotic stability of the network formation, i.e., the scalability with respect to the network size and the specific formation preservation. A simulation case illustrates the effectiveness of the proposed control approach.

This paper proposes a passivity-based control approach that addresses the trajectory tracking problem for a class of mechanical systems that comprises a broad range of robotic arms. The resulting controllers can be naturally saturated and do not require velocity measurements. Moreover, the proposed methodology does not require the implementation of observers, and the structure of the closed-loop system permits the construction of a Lyapunov function, which eases the convergence analysis. To corroborate the effectiveness of the methodology, we perform experiments with the Philips Experimental Robot Arm.