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.

Ramkrishna Pasumarthy

Department of Electrical Engineering

Maxwell equations

BRAYTON

DIRAC STRUCTURES

INFINITE DIMENSIONAL PORT HAMILTONIAN SYSTEMS

INFINITE-DIMENSIONAL SYSTEM

MIXED POTENTIAL

PASSIVITY PROPERTIES

State variables

Storage function

Hamiltonians

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IIT Madras

Power-Based Methods for Infinite-Dimensional Systems

Lecture Notes in Control and Information Sciences

Regulating indoor air environment is one of the core functions of building energy management system. Heating, ventilation, and air-conditioning (HVAC) control systems play an important role in adjusting the room temperature to provide occupants a desired level of comfort. Occupant comfort has a direct effect on the energy consumption and providing an optimal balance between comfort and energy consumption is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power-shaping paradigm that exploits the passivity property of a system. The system dynamics are expressed in the Brayton-Moser (BM) form which exhibits a gradient structure with the mixed-potential function, which has the units of power. The power-shaping technique is used to synthesize the controller by assigning a desired power function to the closed-loop dynamics so as to make the equilibrium point asymptotically stable. The proposed methodology is demonstrated on HVAC subsystems: RC network building zone model and a heat exchanger system. © 2017 by ASME.

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

A Passivity-Based Power-Shaping Control of Building HVAC Systems

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.

2017 Indian Control Conference, ICC 2017 - Proceedings

Control using new passivity property with differentiation at both ports

Heating, Ventilating and Air-conditioning (HVAC) control systems play an important role in regulating indoor air temperature to provide building occupants a comfortable environment. Design of HVAC control system to provide an optimal balance between comfort and energy usage is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power shaping paradigm that exploits passivity theory. The controller design uses Brayton-Moser formulation for the system dynamics wherein the mixed potential function is the power function and the power shaping technique is used to synthesize the controller by assigning a desired power function to the closed loop dynamics so as to make the equilibrium point asymptotically stable. The methodology is demonstrated using two example HVAC subsystems - a two-zone building system and a heat exchanger system. © 2016 American Automatic Control Council (AACC).

Proceedings of the American Control Conference

Building HVAC systems control using power shaping approach

Power-based methods for infinite-dimensional systems

Journal	Data powered by TypesetLecture Notes in Control and Information Sciences
Publisher	Data powered by TypesetSpringer Verlag
ISSN	01708643
Open Access	No