114 research outputs found
Repetitive Control Meets Continuous Zero Phase Error Tracking Controller for Precise Tracking of B-spline Trajectories
In this paper, a novel repetitive control scheme is presented and discussed, based on the so-called B-spline filters. These dynamic filters are able to generate a B-spline trajectory if they are fed with the sequence of control points defining the curve. Therefore, they are ideal tools for generating online reference signals with the prescribed level of smoothness for driving dynamic systems, possibly together with a feedforward compensator. In particular, a Continuous Zero Phase Error Tracking Controller (ZPETC) can be used for tracking control of non-minimum phase systems but because of its open-loop nature it cannot guarantee the robustness with respect to modeling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in non-ideal conditions, provided that the desired reference trajectory and the disturbances are periodic. Asymptotic stability of the overall control scheme is proved mathematically and experimental validation based on a non-minimum phase system is performed. Different models of the same physical system have been identified and used in the implementation of this model-based control scheme, allowing a real evaluation of the relationship between control system performance and model accuracy
Repetitive Control Systems: Stability and Periodic Tracking beyond the Linear Case
Periodic output regulation studies the problem of steering the output of a dynamical system along a periodic reference. This is a fundamental control problem which has a great interest from a practical point of view, since most industrial activities oriented to production are based on tasks with a cyclic nature.
Nevertheless this interest extends rapidly to a theoretical framework once the problem is formalized. Mathematical tools coming from different fields can be used to provide an insight to the output regulation problem in different ways.
An important control technique that is classically used to achieve periodic out- put regulation si called Repetitive Control (RC) and this thesis focuses on (but is not limited to) the development and the analysis with novel tools of RC schemes.
Periodic output regulation for nonlinear dynamical systems is a challenging topic. This thesis, besides of providing consistent and practically useful results in the linear case, introduces promising tools dealing with the nonlinear periodic output regulation problem, whose solution is presented for particular classes of systems.
The contribution of this research is mainly theoretical and relies on the use of mathematical tools like infinite-dimensional port-Hamiltonian systems and autonomous discrete-time systems to study stability and tracking properties in RC schemes and periodic regulation in general. Differently from the classical continuous-time formulation of RC, internal model arguments are not directly used is this work to study asymptotic tracking. In this way the linear case can be reinterpreted under a new light and novel strategies to consistently attack the nonlinear case are presented.
Furthermore an application-oriented chapter with experimental results is present which describes the possibility of implementing a discrete-time RC scheme involving trajectory generation and non-minimum phase systems
Passivizing learned policies and learning passive policies with virtual energy tanks in robotics
Within a robotic context, we merge the techniques of passivity-based control
(PBC) and reinforcement learning (RL) with the goal of eliminating some of
their reciprocal weaknesses, as well as inducing novel promising features in
the resulting framework. We frame our contribution in a scenario where PBC is
implemented by means of virtual energy tanks, a control technique developed to
achieve closed-loop passivity for any arbitrary control input. Albeit the
latter result is heavily used, we discuss why its practical application at its
current stage remains rather limited, which makes contact with the highly
debated claim that passivity-based techniques are associated with a loss of
performance. The use of RL allows us to learn a control policy that can be
passivized using the energy tank architecture, combining the versatility of
learning approaches and the system theoretic properties which can be inferred
due to the energy tanks. Simulations show the validity of the approach, as well
as novel interesting research directions in energy-aware robotics.Comment: 8 pages, 5 figure
Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models
We present a framework for safety-critical optimal control of physical
systems based on denoising diffusion probabilistic models (DDPMs). The
technology of control barrier functions (CBFs), encoding desired safety
constraints, is used in combination with DDPMs to plan actions by iteratively
denoising trajectories through a CBF-based guided sampling procedure. At the
same time, the generated trajectories are also guided to maximize a future
cumulative reward representing a specific task to be optimally executed. The
proposed scheme can be seen as an offline and model-based reinforcement
learning algorithm resembling in its functionalities a model-predictive control
optimization scheme with receding horizon in which the selected actions lead to
optimal and safe trajectories
Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and Incompressible Flow
Part I of this paper presented a systematic derivation of the Stokes Dirac
structure underlying the port-Hamiltonian model of ideal fluid flow on
Riemannian manifolds. Starting from the group of diffeomorphisms as a
configuration space for the fluid, the Stokes Dirac structure is derived by
Poisson reduction and then augmented by boundary ports and distributed ports.
The additional boundary ports have been shown to appear naturally as surface
terms in the pairings of dual maps, always neglected in standard Hamiltonian
theory. The port-Hamiltonian model presented in Part I corresponded only to the
kinetic energy of the fluid and how its energy variables evolve such that the
energy is conserved.
In Part II, we utilize the distributed port of the kinetic energy
port-Hamiltonian system for representing a number of fluid-dynamical systems.
By adding internal energy we model compressible flow, both adiabatic and
isentropic, and by adding constraint forces we model incompressible flow. The
key tools used are the interconnection maps relating the dynamics of fluid
motion to the dynamics of advected quantities.Comment: This is a prevprint submitted to the journal of Geometry and Physics.
Please DO NOT CITE this version, but only the published manuscrip
Energetic decomposition of Distributed Systems with Moving Material Domains:the port-Hamiltonian model of Fluid-Structure Interaction
We introduce the geometric structure underlying the port-Hamiltonian models
for distributed parameter systems exhibiting moving material domains
Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach
A port-Hamiltonian model for compressible Newtonian fluid dynamics is
presented in entirely coordinate-independent geometric fashion. This is
achieved by use of tensor-valued differential forms that allow to describe
describe the interconnection of the power preserving structure which underlies
the motion of perfect fluids to a dissipative port which encodes Newtonian
constitutive relations of shear and bulk stresses. The relevant diffusion and
the boundary terms characterizing the Navier-Stokes equations on a general
Riemannian manifold arise naturally from the proposed construction.Comment: This is a preprint submitted to the journal of Physics of Fluids.
Please do not CITE this version, but only the published manuscrip
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