Discrete port-controlled Hamiltonian dynamics and average passivation

The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity

Multiconsensus control of homogeneous LTI hybrid systems under time-driven jumps

In this paper, we consider a network of homogeneous LTI hybrid dynamics under time-driven aperiodic jumps and exchanging information over a fixed communication graph. Based on the notion of almost equitable partitions, we explicitly characterize the clusters induced by the network over the nodes and, consequently, the corresponding multi-consensus trajectories. Then, we design a decentralized control ensuring convergence of all agents to the corresponding multi-consensus trajectory. Simulations over an academic example illustrate the results

Design of a planar cable-driven parallel robot for non-contact tasks

Cable-driven parallel robots offer significant advantages in terms of workspace dimensions and payload capability. Their mechanical structure and transmission system consist of light and extendable cables that can withstand high tensile loads. Cables are wound and unwound by a set of motorized winches, so that the robot workspace dimensions mainly depend on the amount of cable that each drum can store. For this reason, these manipulators are attractive for many industrial tasks to be performed on a large scale, such as handling, pick-and-place, and manufacturing, without a substantial increase in costs and mechanical complexity with respect to a small-scale application. This paper presents the design of a planar overconstrained cable-driven parallel robot for quasi-static non-contact operations on planar vertical surfaces, such as laser engraving, inspection and thermal treatment. The overall mechanical structure of the robot is shown, by focusing on the actuation and guidance systems. A novel concept of the cable guidance system is outlined, which allows for a simple kinematic model to control the manipulator. As an application example, a laser diode is mounted onto the end-effector of a prototype to perform laser engraving on a paper sheet. Observations on the experiments are reported and discussed

Energy-Balance PBC of nonlinear dynamics under sampling and delays

The paper provides a new class of passivity-based controllers (PBCs) for stabilizing sampled-data input-delayed dynamics at a desired equilibrium via energy-balancing (EB) and reduction. Given a nonlinear dynamics under piecewise constant and retarded input, we first exhibit a new dynamics (the reduced dynamics) that is free of delays and equivalent to the original one. Accordingly, we design the digital controller assigning a suitable energetic behaviour to the reduced delay-free model with a stable target equilibrium. Then, it is proved that such a controller solves the EB-PBC problem on the original retarded system. The results are illustrated over a simple mechanical system

A new connection protocol for multi-consensus of discrete-time systems

In this paper, a new connection protocol for consensus of multi-agent discrete-time systems under a general communication graph is proposed. In particular, the coupling is realized based on the outputs making each agent passive in the u-average sense so guaranteeing convergence to the agreement steady-state, with no need of mitigating the coupling gain, as typically done in concerned literature. The proposed connection rule is shown to apply for network dynamics under aperiodic sampling when the sampling sequence is known to all agents

Virtual Holonomic Constraints for Euler-Lagrange systems under sampling

In this paper, we consider the problem of imposing Virtual Holonomic Constraints to mechanical systems in Euler-Lagrangian form under sampling. An exact solution based on multi-rate sampling of order two over each input channel is described. The results are applied to orbital stabilization of the pendubot with illustrative simulations

Stabilization of the Acrobot via sampled-data passivity-based control

The paper deals with the sampled-data asymptotic stabilization of the Acrobot at its upward equilibrium. The proposed controller results from the action of an Input-Hamiltonian-Matching (IHM) strategy that shapes the closed-loop energy combined with a Damping Injection (DI) feedback designed on the sampled-data equivalent model. Simulations show the effectiveness of the proposed controller

A new distributed protocol for consensus of discrete-time systems

In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols

A gradient descent algorithm built on approximate discrete gradients

We propose an optimization method obtained by the approximation of a novel discretization approach for gradient dynamics recently proposed by the authors. It is shown that the proposed algorithm ensures convergence for all amplitudes of the step size, contrarily to classical implementations

Discrete-time energy-balance passivity-based control

In this paper, new results for passivation and stabilization of discrete-time nonlinear systems via energy balancing are established. When specified on sampled-data systems, the approach is constructive for computing stabilizing digital controllers that assign, at all sampling instants, a target energy profile while stabilizing a target equilibrium. The class of mechanical systems is discussed as an example. Simulations are reported highlighting, for position regulation of a 2R robot, the effect of approximate solutions with respect to standard emulation