Notch filters for port-Hamiltonian systems

Network modeling of lumped-parameter physical systems
naturally leads to a geometrically defined class of systems,
i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling
framework describes a large class of (nonlinear) systems
including passive mechanical systems, electrical systems,
electromechanical systems, mechanical systems with
nonholonomic constraints, thermal systems and distributed
parameter systems with boundary control. The popularity
of PH systems can be largely accredited to its application
for analysis and control design of multi-input multi-output
(MIMO) physical systems
Nonlinear modeling and control methods, including the PH
framework, have the great disadvantage of not including
any frequency information in the modeling and control design.
In practice the frequency-based control methods are
preferred because of the importance of the system behavior
in the frequency domain. In the frequency domain transfer
functions, Bode plots, PID controllers, lag-lead compensators
and filters are some examples of powerful tools for
analysis and control [1]. However, such methods are only
theoretically justified for linear systems. Many physical systems
are actually nonlinear, for which linearization is then
first required. However, the results only hold locally, (very)
close to the linearization point. On the other hand, nonlinear
control often offers methods to steer a nonlinear system to a
desired state for any initial condition. When global convergence
cannot be proven, techniques exist to define a region
of attraction [3]. Some results on including frequency