Port Hamiltonian systems are usually passive with respect to port variables that are power conjugate (eg: voltage and current, force and velocity) and this lead to energy shaping control methods. But systems with 'dissipation obstacle' cannot be controlled using these port variables and therefore we need to search for alternative passive maps. One option is within the Brayton Moser framework, where passivity is obtained by differentiating one of the port variables. This has led to power shaping methods for control, but the solutions (if exists) obtained impose constraints on the physical parameters of the system. In this paper, starting from the Brayton Moser framework we present a new passivity property with differentiation at both the port variables. Further using this new passive map, a PI like controller is proposed and presented using parallel RLC circuit and transmission line system with non zero boundary conditions as examples. © 2017 IEEE.

Ramkrishna Pasumarthy

Department of Electrical Engineering

Resonant circuits

ENERGY SHAPING CONTROL

PASSIVITY PROPERTIES

Physical parameters

PI-LIKE CONTROLLER

Port-hamiltonian systems

RLC CIRCUIT

SHAPING METHOD

TRANSMISSION LINE SYSTEMS

Hamiltonians

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IIT Madras

Control using new passivity property with differentiation at both ports

2017 Indian Control Conference, ICC 2017 - Proceedings

In this paper we derive new passive maps akin to incremental passive maps, for a class of nonlinear systems using dynamic feedback and Krasovskii's method. Further using the passive maps we present a control methodology for stabilization to a desired operating point. This work is illustrated by designing a controller for a nonlinear building heating ventilating and air conditioning (HVAC) subsystem. © 2018 AACC.

Fulltext

Proceedings of the American Control Conference

Differential passivity like properties for a class of nonlinear systems

In this letter, we present passivity-based convergence analysis of continuous time primal-dual gradient method for convex optimization problems. We first show that a convex optimization problem with only affine equality constraints admits a Brayton Moser formulation. This observation leads to a new passivity property derived from a Krasovskii-type storage function. Second, the inequality constraints are modeled as a state dependent switching system. Using tools from hybrid systems theory, it is shown that each switching mode is passive and the passivity of the system is preserved under arbitrary switching. Finally, the two systems: 1) one derived from the Brayton Moser formulation and 2) the state dependent switching system, are interconnected in a power conserving way. The resulting trajectories of the overall system are shown to converge asymptotically, to the optimal solution of the convex optimization problem. The proposed methodology is applied to an energy management problem in buildings and simulations are provided for corroboration. © 2017 IEEE.

IEEE Control Systems Letters

Stability analysis of constrained optimization dynamics via passivity techniques

This paper aims at developing a Brayton-Moser analogue of an infinite-dimensional system in the port-Hamiltonian framework, defined with respect to a Stokes-Dirac structure. It is shown that such a formulation leads to defining alternative passive maps, which differ from those in the port-Hamiltonian framework via a "power-like" function called the mixed-potential function. This mixed-potential function can also be used for stability analysis. We present our results for a general port-Hamiltonian system, with Maxwell's equations and the transmission line, with nonzero boundary conditions, as examples. © 2015, IFAC.

IFAC-PapersOnLine

Alternative passive maps for infinite-Dimensional systems using mixed-Potential functions

In this chapter we aim to extend the Brayton Moser (BM) framework for modeling infinite-dimensional systems. Starting with an infinite-dimensional port- Hamiltonian system we derive a BM equivalent which can be defined with respect to a non-canonical Dirac structure. Based on this model we derive stability and new passivity properties for the system. The state variables in this case are the “effort” variables and the storage function is a “power-like” function called the mixed potential. The new property is derived by “differentiating” one of the port variables. We present our results with the Maxwell’s equations, and the transmission line with non-zero boundary conditions as examples. © Springer International Publishing Switzerland 2015.

Lecture Notes in Control and Information Sciences

Power-based methods for infinite-dimensional systems

52nd IEEE Conference on Decision and Control

On differential passivity of physical systems

Automatica

Power-based control of physical systems

European Journal of Control

Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs

Journal	Data powered by Typeset2017 Indian Control Conference, ICC 2017 - Proceedings
Publisher	Data powered by TypesetInstitute of Electrical and Electronics Engineers Inc.
Open Access	No