18,978 research outputs found
Stabilization of Physical Systems via Saturated Controllers With Partial State Measurements
This article provides a constructive passivity-based control (PBC) approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering bounded inputs. As customary in PBC, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other PBC techniques: 1) the energy shaping is carried out without solving partial differential equations and 2) the damping injection is performed without measuring the passive output. As a result, the proposed methodology is suitable to control a broad range of physical systems, e.g., mechanical, electrical, and electromechanical systems, with saturated control signals. We illustrate the applicability of the technique by designing controllers for systems in different physical domains, where we validate the analytical results via simulations and experiments
On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems
Interconnection and damping assignment passivity-based control (IDA-PBC) is
an excellent method to stabilize mechanical systems in the Hamiltonian
formalism. In this paper, several improvements are made on the IDA-PBC method.
The skew-symmetric interconnection submatrix in the conventional form of
IDA-PBC is shown to have some redundancy for systems with the number of degrees
of freedom greater than two, containing unnecessary components that do not
contribute to the dynamics. To completely remove this redundancy, the use of
quadratic gyroscopic forces is proposed in place of the skew-symmetric
interconnection submatrix. Reduction of the number of matching partial
differential equations in IDA-PBC and simplification of the structure of the
matching partial differential equations are achieved by eliminating the
gyroscopic force from the matching partial differential equations. In addition,
easily verifiable criteria are provided for Lyapunov/exponential
stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with
arbitrary degrees of underactuation and for all nonlinear controlled
Hamiltonian systems with one degree of underactuation. A general design
procedure for IDA-PBC is given and illustrated with examples. The duality of
the new IDA-PBC method to the method of controlled Lagrangians is discussed.
This paper renders the IDA-PBC method as powerful as the controlled Lagrangian
method
Matching in the method of controlled Lagrangians and IDA-passivity based control
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u
Energy Shaping Control of an Inverted Flexible Pendulum Fixed to a Cart
Control of compliant mechanical systems is increasingly being researched for
several applications including flexible link robots and ultra-precision
positioning systems. The control problem in these systems is challenging,
especially with gravity coupling and large deformations, because of inherent
underactuation and the combination of lumped and distributed parameters of a
nonlinear system. In this paper we consider an ultra-flexible inverted pendulum
on a cart and propose a new nonlinear energy shaping controller to keep the
pendulum at the upward position with the cart stopped at a desired location.
The design is based on a model, obtained via the constrained Lagrange
formulation, which previously has been validated experimentally. The controller
design consists of a partial feedback linearization step followed by a standard
PID controller acting on two passive outputs. Boundedness of all signals and
(local) asymptotic stability of the desired equilibrium is theoretically
established. Simulations and experimental evidence assess the performance of
the proposed controller.Comment: 11 pages, 7 figures, extended version of the NOLCOS 2016 pape
Solution to IDA-PBC PDEs by Pfaffian Differential Equations
Finding the general solution of partial differential equations (PDEs) is
essential for controller design in some methods. Interconnection and damping
assignment passivity based control (IDA-PBC) is one of such methods in which
the solution to corresponding PDEs is needed to apply it in practice. In this
paper, such PDEs are transformed to corresponding Pfaffian differential
equations. Furthermore, it is shown that upon satisfaction of the integrability
condition, the solution to the corresponding third order Pfaffian differential
equation may be obtained quite easily. The method is applied to the PDEs of
IDA-PBC in some benchmark problems such as Magnetic levitation system, Pendubot
and underactuated cable driven robot to verify its applicability
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