Abstract of the Thesis:
"Ein Beitrag zur adaptiven Regelung technischer Systeme nach biologischem
Vorbild"
by Dipl.-Math. Carsten Behn
This thesis deals with the control of mechanical systems, which are inspired by
biological ideas. The applications considered here include a worm-like
locomotion system, a sensor due to a tactile hair or a sensillum, and motion
studies of a pendulum with drive of muscles. All of these systems are described
by mathematical models that fall into the category of linear and nonlinearly
perturbed, multi-input, multi-output systems.In general, one cannot expect to
have complete information about a sophisticated mechanical or biological system,
but instead only structural properties (e.g. minimum phase condition, relative
degree) are known. Therefore, the method of adaptive control is chosen in this
thesis. The aim is to design a universal adaptive controller, which learns from
the behaviour of the system, so automatically adjusts its parameters and
achieves a prespecified control objective. Possible objectives are stabilization
of the system or lambda-tracking.
Since this thesis deals with nonlinearly perturbed multi-input, multi-output
systems, which are not necessary autonomous, particular attention is paid to the
lambda-tracking control objective. This means, that the output of the system
should stay close to (track) a given reference signal, where a prespecified
small tracking error of size lambda is tolerated. The goal is achieved by the
so-called lambda-tracker. This controller is simple in its design, relies only
on structural properties of the system (and not on the system's parameters) and
does not invoke any estimation or identification mechanism. It only consists of
a feedback strategy and a simple parameter adaptation law, and, moreover, does
not have to depend on the derivative of the output of the system. It is proved
that using this controller lambda-tracking and stabilization can be achieved for
the considered nonlinear perturbed mechanical systems with unknown parameters.
The feedback strategy reduces in dimension (the number of used variables
calculated by internal differential equations) if we restrict the class of
systems to single-input, single-output systems with zero-centre in the open
left-half complex plane. An example for this is given by a spring-mass-damper-
system with one degree of freedom, which is forced by an unknown ground
excitation at the case.
Numerical simulations of the mechanical systems mentioned above demonstrate and
illustrate that the adaptive controllers (stabilizers and lambda-trackers)
designed in this thesis work successfully and effectively.