4 research outputs found
Transverse Feedback Linearization with Partial Information for Single-Input Systems
“First Published in SIAM Journal on Control and Optimization in 2014, published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”')This paper is motivated by the problem of asymptotically stabilizing invariant sets
in the state space of control systems by means of output feedback. The sets considered are smooth
embedded in submanifolds and the class of system is nonlinear, finite-dimensional, autonomous,
deterministic, single-input and control-affine. Given an invariant set and a control system with fixed
output, necessary and sufficient conditions are presented for feedback equivalence to a normal form
that facilities the design of output feedback controllers that stabilize the set using existing design
techniques.This work was supported by supported by the National Science and Engineering Research Council
(NSERC) of Canad
Transverse Feedback Linearization with Partial Information for Single-Input Systems
This paper is motivated by the problem of asymptotically stabilizing
invariant sets in the state space of control systems by means of output
feedback. The sets considered are smooth embedded in submanifolds and the class
of system is nonlinear, finite-dimensional, autonomous, deterministic,
single-input and control-affine. Given an invariant set and a control system
with fixed output, necessary and sufficient conditions are presented for
feedback equivalence to a normal form that facilities the design of output
feedback controllers that stabilize the set using existing design techniques
Stabilization of Polytopes for Fully Actuated Euler-Lagrange Systems
Given an Euler-Lagrange system and a convex polytope in its output space, we design
a switched feedback controller that drives the output to the polytope. On the polytope,
the system output tracks assigned trajectories or follows assigned paths. The study of
this problem is motivated by industrial applications such as robotic painting, welding and
three dimensional printing. Many engineering systems, such as robotic manipulators, can
be modelled with Euler-Lagrange equations, and many engineered surfaces, designed using software, are naturally modelled as convex polytopes. We use feedback linearization to decompose the design problem into two subproblems; stabilizing the polytope surface, and controlling its motion along the surface.
The first subproblem, known as the design of the transversal controller, leverages the
fact that a polytope can be represented as a finite union of facets. The controller determines the closest facet to the system output and stabilizes that facet by stabilizing its
corresponding hyperplane via feedback linearization. The transversal dynamics can be
stabilized using linear controllers. At the boundary of a facet, we propose a switching law
that ensures weak invariance of the polytope for the closed-loop system.
The second subproblem, known as the design of the tangential controller, enforces
desired dynamics while the system output is restricted to the polytope. We investigate
control specifications such as following a predefined path on the surface and tracking a
trajectory that moves along the surface. The separation of the transversal and tangential
control design phases is possible because feedback linearization decouples the transversal and tangential dynamic subsystems.
This approach to control design is demonstrated experimentally on a four degree-of freedom robotic manipulator. The experimental implementation is made robust to modelling uncertainty via Lyapunov re-design methods