Wednesday May 25 at 11.00. Lindstedtsvägen 25, room 3721

France

Abstract:
As vividly illustrated by the quintessential Watt's governor a
natural procedure to modify the behavior of
a dynamical system is to interconnect it with another dynamical system.
Examples of this approach abound
in modern high-performance practical applications and are
proven to be very robust and reliable.
These
include, among many others, mechanical suspension and flapper systems,
flotation devices, damping windings
and impedance matching filters in electrical systems,
(it may be even argued that drug infusion and vaccine
injection techniques are best studied invoking interconnection principles instead of simplistic cause-effect preconceptions.)
Adopting the interconnection perspective allows us to formulate the control problem in terms of the physical
properties of the systems like energy-shaping and damping injection, it furthermore underscores the role of
interconnection to achieve these objectives. This should be contrasted with the classical actuator-plant-sensor
paradigm that leads to a signal-processing view of control in which the systems physical properties are difficult
to incorporate.
In our previous works we have proposed a mathematical framework to design controllers using the afore-mentioned systems interconnection perspective that we called Control by Interconnection (CbI). Towards this
end we restricted ourselves to systems described by Port-Hamiltonian (PH) models, which suitably describe
the dynamics of many physical processes, and where the importance of the energy function, the interconnec-
tion pattern and the dissipation of the system is highlighted. In CbI the controller is another PH system
connected to the plant (through a power-preserving interconnection) to add up their energy functions. In
spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the
current version of CbI imposes a severe restriction on the plant dissipation structure that stymies its practical
application.
The purpose of this talk is to propose some extensions to the CbI method to make it more widely
applicable -- in particular, to overcome the dissipation obstacle [1]. Furthermore, we establish the connections
between CbI and Standard PassivityBased Control (PBC). Standard PBC, where energy shaping is achieved
via static state feedback, is one of the most successful controller design techniques. However, the control law
is usually derived from an uninspiring and non-intuitive "passive output generation" viewpoint.
We prove in
this talk that Standard PBC is obtained restricting CbI to a suitable subset of the state space -- providing a
nice geometric interpretation to Standard PBC.

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