Energy-based tracking control methods for classes of port-Hamiltonian systems

Controller design for mechanical systems without velocity measurement is an interesting task from an application viewpoint. In this regard, the idea of using a dynamic extension in PH systems is applied in some papers. In one of those, the stabilization problem of a class of the mechanical PH is investigated by IDA-PBC control with only position measurements. The authors use the application of dynamic extension in order to inject damping and eliminate the velocity measurements. The same idea is investigated for the trajectory tracking of the fully-actuated PH mechanical systems in other work. In the mentioned work, the tracking problem is solved by interconnecting the error system with the virtual system and stabilizing the extended system by the canonical transformation. Accordingly, investigating the Timed IDA-PBC tracking method without velocity measurement applying the dynamic extension concept is an open problem. Since the mentioned tracking approach straightforwardly employs IDA-PBC for a class of contractive PH systems, researching the tracking control aim of an underactuated class of systems seems also traceable. Another research line is how we can use dynamical extensions (like the integral action) to increase the robustness of the controller with respect to constant disturbances while a reference signal is tracking without velocity measurements. The proposed method can be studied to develop a formation/distributed controller without velocity measurements in a network system.
In the case of multi-domain elements such as electrical and mechanical parts, energy-based modeling and control methods such as the port-Hamiltonian (pH) framework are investigated in the related literature. In the pH framework, the coupling between mechanical and electrical subsystems is defined via the interconnection matrix and/or the energy function. However, in some cases is energy shaping control methods cannot affect the coupling between the electrical and mechanical systems. Indeed, the desired energy function cannot be chosen such that the PH structure is preserved, simultaneously.
Investigating a dynamical model of the Timed IDA-PBC tracking method without velocity measurements while keeping the above issue into account, is another open problem that will be studied in this project.

Supervisors: Prof. Jacquelien Scherpen and Prof Mohammad Javad Yazdanpanah
PhD: Najmeh Javanmardi