Transition dynamics between the multiple steady states in natural ventilation systems : from theories to applications in optimal controls

In this study, we investigated the multiple steady state behavior, an important observation in numerical and experimental studies in natural ventilation systems. The-oretical models are developed and their applications in numerical simulations and ventilation controls are presented. In a system with multiple steady states, how the system reaches different steady states is determined by the initial values of the systems and the dynamical system characteristics of the system. Mathematical models are developed to model the dynamical system behavior of a series of ventilation systems, ranging from simple single-zone systems to complex systems with thermal mass. More importantly, we found that the system can transform from one steady state to another under sufficient perturbations (disturbances) when multiple steady states exist. A successful transition is determined by both the magnitudes and durations of the perturbations. The transition dynamics are found to be important in theoretical, computational, and control applications. For example, the actual stability of a mathematically (or locally) stable steady state is highly correlated to the minimum perturbation requirements for a state transition. If two indicative parameters-the minimum perturbation time and the minimum perturbation magnitude-are small for the system to transit from one steady state to another, a mathematically stable steady state can be unstable in actual conditions, where stochastic disturbances exist as "strong perturbations". Further, building thermal mass is also found to have significant impacts on the state transitions between the multiple steady states. With thermal mass, the state transition becomes more difficult to occur. The state transition dynamics can also be applied to numerical simulations.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Architecture.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Yuan, Jinchao

Advisor dc:contributor.advisor

• Leon R. Glicksman.

• Architecture.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/41717

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/41717