Abstract
In this thesis, the focus is on two control problems for nonsmooth systems.
Firstly, the disturbance attenuation problem for piecewise linear (PWL) and
piecewise affine (PWA) systems is studied. Here, we focus on applications in the
field of perturbed flexible mechanical systems with PWL restoring characteristics.
Secondly, the stabilization problem for Lur’e type systems with setvalued
nonlinearities is examined. In the latter context, the focus is on the application
area of mechanical systems with setvalued friction characteristics, where the
friction is noncollocated with the control action. In this thesis, in order to deal
with both the disturbance attenuation problem and the stabilization problem,
observerbased outputfeedback control strategies are proposed.
More specifically, the disturbance attenuation problem for perturbed PWL
and PWA mechanical systems is an important control problem. Namely, the
attenuation of the disturbances acting on these systems is important because it
avoids damages to the structures and allows for increased system performance.
Classical examples of mechanical systems with PWL and PWA restoring characteristics
are tower cranes, suspension bridges, snubbers on solar panels on
satellites, floating platforms for oil exploration, etc.
Therefore, a controller design strategy is proposed for a class of perturbed
PWL/PWA systems based on the notions of convergence and inputtostate
convergence. The control design aims at the performance of such control designs
in terms of disturbance attenuation for the specific class of periodic disturbances
and the more general class of bounded disturbances. Roughly speaking,
a system that is convergent, has, for each bounded disturbance, a unique globally
asymptotically stable steadystate solution that is bounded for all time.
A system is inputtostate convergent for a class of bounded disturbances if it
is convergent and ISS with respect to the system’s unique steadystate solution.
The inputtostate convergence property is instrumental in constructing
outputfeedback schemes. In the present work, we render a system convergent
by means of feedback.
To guarantee the practical applicability of the convergencebased controllers,
a saturation constraint is proposed that provides a guaranteed upper bound on
the control input, given an upper bound for the disturbances and a set of initial
conditions. Next, an ultimate bound for the system state given a bound on the
disturbances is proposed. Finally, performance measures based on computed
steadystate responses for a specific class of disturbances (in our case harmonic
disturbances) are presented. The motivation for the choice of harmonic disturbances
lies in the fact that in engineering practice many disturbances can be
approximated by a finite sum of harmonic signals (or are even harmonic as in
systems with massunbalance). The ultimate objective of this part of the thesis
is the implementation of the controller design strategy in an experimental environment,
which implies that only measurements of a limited number of state
variables will be available. Therefore, observers for PWL/PWA systems are
used and a result that combines the controller and the observer in an outputfeedback
strategy is provided. The convergentbased controller design strategy
is applied to an experimental piecewise linear system and its effectiveness is
shown in experiments.
The stabilization of mechanical systems with friction is another challenging
unsolved control problem because the presence of friction can induce unwanted
phenomena such as selfsustained vibrations, chatter and squeal. These
phenomena are unwanted in many engineering applications because they can
destabilize a system and/or limit the system performance. Classical examples
of mechanical systems with friction are industrial robots, drilling rigs, turbine
blade dampers, accurate mirror positioning systems on satellites, printers and
many more.
Therefore, a control design strategy is proposed for a class of discontinuous
systems; namely Lur’e systems with setvalued mappings. Here the focus
is on the application area of mechanical systems with discontinuous friction.
These systems exhibit unwanted (stickslip) limit cycling which we aim to avoid
entirely by the control design. In this work, we consider the problem of noncollocated
friction and actuation, which rules out the application of common
friction compensation techniques. The control design strategy proposed here
is based on the notion of passivity and the Popov criterion. In addition to
that, it is shown that the resulting closedloop system is robust with respect to
uncertainties in the discontinuous friction model under some mild constraints
for the model that describes the friction. Once again, the aim is to implement
this strategy on a mechanical experimental setup with limited measurements.
Therefore, an observer for Lur’e systems with multivalued mappings is used as
a state estimator and a result that combines the controller and the observer in
an outputfeedback strategy is provided. The passivitybased controller design
strategy is implemented on a dynamic rotor system with friction in one of its
components. The implemented outputfeedback controller is evaluated in both
simulations and experiments.
Generally speaking, to show the strengths, weaknesses and potential of
outputfeedback controllers beyond their theoretical importance, it is indispensable
to evaluate them in experimental and industrial setups. As such
the presented case studies can be considered as benchmarks for the proposed
observerbased controller designs for nonsmooth and discontinuous systems.
The value of nonsmooth and discontinuous models and observerbased controllers
is also evidenced by this work, as it demonstrates the effectiveness for
reallife applications.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  11 Sep 2007 
Place of Publication  Eindhoven 
Publisher  
Print ISBNs  9789038610658 
DOIs  
Publication status  Published  2007 