Energy and power based perspective of memristive controllers

The use of Casimir functions towards control of physical systems is well known, both in the context of Energy shaping as well as Power shaping techniques. In this paper we show that by use of a Memristive element in the controller design enables us to generate additional Casimir functions relating the state of the memristor to the plant state. This additional conserved quantity manifests itself in the control law in form of a state-modulated gain. We present our results with examples in the context of control by Casimir generation in the port-Hamiltonian framework, which essentially deals with shaping the energy of the system. We also present the applicability of the results towards control by power shaping of electrical circuits in the Brayton-Moser framework for modeling of electrical networks.

[1]  Dimitri Jeltsema,et al.  Memristive port-Hamiltonian Systems , 2010 .

[2]  E. Garcia-Canseco,et al.  A new passivity property of linear RLC circuits with application to power shaping stabilization , 2004, Proceedings of the 2004 American Control Conference.

[3]  Stefano Stramigioli,et al.  Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach , 2014 .

[4]  J.M.A. Scherpen,et al.  Multidomain modeling of nonlinear networks and systems , 2009, IEEE Control Systems.

[5]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[6]  Arjan van der Schaft,et al.  Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems , 2004, Eur. J. Control.

[7]  Dimitri Jeltsema,et al.  Port-Hamiltonian Formulation of Systems With Memory , 2012, Proceedings of the IEEE.

[8]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[9]  Arjan van der Schaft,et al.  Achievable Casimirs and its implications on control of port-Hamiltonian systems , 2007, Int. J. Control.

[10]  Guido Blankenstein,et al.  Power balancing for a new class of non-linear systems and stabilization of RLC circuits , 2005 .

[11]  Ramkrishna Pasumarthy,et al.  Achievable Casimirs and its implications on control , 2007 .

[12]  L. Chua.  Memristor-The missing circuit element , 1971 .

[13]  A. Delgado.  The memristor as controller , 2010, 2010 IEEE Nanotechnology Materials and Devices Conference.

[14]  Arjan van der Schaft,et al.  On control by interconnection of port Hamiltonian systems , 2005 .

[15]  Jacquelien M. A. Scherpen,et al.  Power shaping: a new paradigm for stabilization of nonlinear RLC circuits , 2003, IEEE Trans. Autom. Control..

[16]  Laurens van der Heijden,et al.  Memristive Port-Hamiltonian Control: Path-Dependent Damping Injection in Control of Mechanical Systems , 2012 .

[17]  J. K. Moser,et al.  A theory of nonlinear networks. I , 1964 .