Model and Controller Reduction Applied to Structural Control Using Passivity Theory
In this paper, model and controller reduction problems for the large-scale control of building models are analyzed. First, the model reduction problem is posed in a projection framework, and some techniques are shown, such as modal reduction, balanced truncation, and moment matching by Krylov subspace, to obtain reduced-order models. Based on those techniques, reduced-order controllers are obtained from the large-scale building models. However, there is the lack of closed-loop stability guarantees using the above methods. In order to overcome this issue, it is proposed to use the so-called passivity preserving model reduction, where one performs reduction based on the spectral zeros of the system and passive controller design. It is shown from the results of some simulations applied to the second generation of benchmark building control problem that the proposed algorithm indeed guarantees closed-loop stability and offers good performance.
Gildin, E.; Antoulas, A. C.; and Bishop, Robert H., "Model and Controller Reduction Applied to Structural Control Using Passivity Theory" (2009). Mechanical Engineering Faculty Research and Publications. 18.